Scientific Output

Over 10.000 scientific papers have been published by members of the Materials Chain since the foundation of the University Alliance Ruhr in 2010. This tremendous output is proof of the excellent environment the Ruhr Area provides for research in the field of materials science and technology.

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  • 2020 • 179 Role of coherency loss on rafting behavior of Ni-based superalloys
    Ali, M.A. and Görler, J.V. and Steinbach, I.
    Computational Materials Science 171 (2020)
    The role of coherency loss on rafting of superalloys under high temperature low stress creep conditions is investigated by phase-field crystal plasticity simulations. It is demonstrated that coalescence, critically depending on the state of coherency between precipitate and matrix is crucial to understand the rafting behavior of superalloys. An explicit mechanisms is developed predicting coherency loss based on the plastic activity in the matrix. The simulations are verified using experimental creep test results. © 2019 Elsevier B.V.
    view abstractdoi: 10.1016/j.commatsci.2019.109279
  • 2020 • 178 Effect of γ′ precipitate size on hardness and creep properties of Ni-base single crystal superalloys: Experiment and simulation
    Ali, M.A. and López-Galilea, I. and Gao, S. and Ruttert, B. and Amin, W. and Shchyglo, O. and Hartmaier, A. and Theisen, W. and Steinbach, I.
    Materialia 12 (2020)
    The role and effect of γ′ precipitate size on the mechanical properties of Ni-base single crystal superalloy is investigated. The underlying mechanisms are analyzed on the one hand with the help of experiments including hardness and creep tests, and on the other hand with the help of two different simulation approaches by taking the typical γ/γ′ microstructure into account. Simulations, based on the crystal plasticity finite element method (CPFEM) are carried out for the hardness tests, whereas simulations, based on the crystal plasticity coupled phase-field method (CPPFM) are carried out for the creep tests. The hardness test simulation results show that the hardness of material varies inversely with the size of γ′ precipitates for a given γ′ phase volume fraction and it varies directly with the volume fraction of γ′ precipitates for a given precipitate size. These results are qualitatively consistent with the experimental observations. The creep simulation results show that the refinement of γ′ precipitates with a certain volume fraction of precipitates leads to an improvement of creep resistance by delaying the plastic activity in the material. © 2020 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.mtla.2020.100692
  • 2020 • 177 Towards deterministic computation of internal stresses in additively manufactured materials under fatigue loading: Part I
    Awd, M. and Labanie, M.F. and Moehring, K. and Fatemi, A. and Walther, F.
    Materials 13 (2020)
    The ongoing studies of the influence of internal defects on fatigue strength of additively manufactured metals adopted an internal crack or notch-like model at which the threshold stress intensity factor is the driving mechanism of fatigue failure. The current article highlights a shortcoming of this approach and offers an alternative based on X-ray microcomputed tomography and cyclic plasticity with a hybrid formulation of Chaboche and Armstrong-Frederick material laws. The presented tessellation and geometrical transformation scheme enabled a significantly more realistic morphological representation of internal defects that yielded a cyclic strain within 2% of the experimental values. This means that cyclic plasticity models have an accurate prediction of mechanical properties without repeating a full set of experiments for additively manufactured arbitrary microstructures. The coupling with a material law that is oriented towards the treatment of cyclic hardening and softening enabled more accurate computation of internal stresses under cyclic loading than ever before owing to the maturity of tessellation and numerical tools since then. The resulting stress-strain distributions were used as input to the Fatemi-Socie damage model, based on which a successful calculation of fatigue lifetime became possible. Furthermore, acting stresses on the internal pores were shown to be more than 450% concerning the applied remote stress amplitude. The results are a pretext to a scale bridging numerical solution that accounts for the short crack formation stage based on microstructural damage. © 2020 by the authors.
    view abstractdoi: 10.3390/ma13102318
  • 2020 • 176 Optimized reconstruction of the crystallographic orientation density function based on a reduced set of orientations Reconstruction of the orientation density function
    Biswas, A. and Vajragupta, N. and Hielscher, R. and Hartmaier, A.
    Journal of Applied Crystallography 53 178-187 (2020)
    Crystallographic textures, as they develop for example during cold forming, can have a significant influence on the mechanical properties of metals, such as plastic anisotropy. Textures are typically characterized by a non-uniform distribution of crystallographic orientations that can be measured by diffraction experiments like electron backscatter diffraction (EBSD). Such experimental data usually contain a large number of data points, which must be significantly reduced to be used for numerical modeling. However, the challenge in such data reduction is to preserve the important characteristics of the experimental data, while reducing the volume and preserving the computational efficiency of the numerical model. For example, in micromechanical modeling, representative volume elements (RVEs) of the real microstructure are generated and the mechanical properties of these RVEs are studied by the crystal plasticity finite element method. In this work, a new method is developed for extracting a reduced set of orientations from EBSD data containing a large number of orientations. This approach is based on the established integer approximation method and it minimizes its shortcomings. Furthermore, the L 1 norm is applied as an error function; this is commonly used in texture analysis for quantitative assessment of the degree of approximation and can be used to control the convergence behavior. The method is tested on four experimental data sets to demonstrate its capabilities. This new method for the purposeful reduction of a set of orientations into equally weighted orientations is not only suitable for numerical simulation but also shows improvement in results in comparison with other available methods. © 2020 Abhishek Biswas et al.
    view abstractdoi: 10.1107/S1600576719017138
  • 2020 • 175 The brittle-to-ductile transition in cold-rolled tungsten sheets: the rate-limiting mechanism of plasticity controlling the BDT in ultrafine-grained tungsten
    Bonnekoh, C. and Reiser, J. and Hartmaier, A. and Bonk, S. and Hoffmann, A. and Rieth, M.
    Journal of Materials Science 55 12314-12337 (2020)
    Conventionally produced tungsten (W) sheets are brittle at room temperature. In contrast to that, severe deformation by cold rolling transforms W into a material exhibiting room-temperature ductility with a brittle-to-ductile transition (BDT) temperature far below room temperature. For such ultrafine-grained (UFG) and dislocation-rich materials, the mechanism controlling the BDT is still the subject of ongoing debates. In order to identify the mechanism controlling the BDT in room-temperature ductile W sheets with UFG microstructure, we conducted campaigns of fracture toughness tests accompanied by a thermodynamic analysis deducing Arrhenius BDT activation energies. Here, we show that plastic deformation induced by rolling reduces the BDT temperature and also the BDT activation energy. A comparison of BDT activation energies with the trend of Gibbs energy of kink-pair formation revealed a strong correlation between both quantities. This demonstrates that out of the three basic processes, nucleation, glide, and annihilation, crack tip plasticity in UFG W is still controlled by the glide of dislocations. The glide is dictated by the mobility of the screw segments and therefore by the underlying process of kink-pair formation. Reflecting this result, a change of the rate-limiting mechanism for plasticity of UFG W seems unlikely, even at deformation temperatures well below room temperature. As a result, kink-pair formation controls the BDT in W over a wide range of microstructural length scales, from single crystals and coarse-grained specimens down to UFG microstructures. © 2020, The Author(s).
    view abstractdoi: 10.1007/s10853-020-04801-5
  • 2020 • 174 A fourth-order gauge-invariant gradient plasticity model for polycrystals based on Kröner’s incompatibility tensor
    Ebobisse, F. and Neff, P.
    Mathematics and Mechanics of Solids 25 129-159 (2020)
    In this paper we derive a novel fourth-order gauge-invariant phenomenological model of infinitesimal rate-independent gradient plasticity with isotropic hardening and Kröner’s incompatibility tensor inc(εp):=Curl[(Curl εp)T], where εp is the symmetric plastic strain tensor. Here, gauge-invariance denotes invariance under diffeomorphic reparametrizations of the reference configuration, suitably adapted to the geometrically linear setting. The model features a defect energy contribution that is quadratic in the tensor inc(εp) and it contains isotropic hardening based on the rate of the plastic strain tensor (Formula presented.). We motivate the new model by introducing a novel rotational invariance requirement in gradient plasticity, which we call micro-randomness, suitable for the description of polycrystalline aggregates on a mesoscopic scale and not coinciding with classical isotropy requirements. This new condition effectively reduces the increments of the non-symmetric plastic distortion (Formula presented.) to their symmetric counterpart (Formula presented.). In the polycrystalline case, this condition is a statement about insensitivity to arbitrary superposed grain rotations. We formulate a mathematical existence result for a suitably regularized non-gauge-invariant model. The regularized model is rather invariant under reparametrizations of the reference configuration including infinitesimal conformal mappings. © The Author(s) 2019.
    view abstractdoi: 10.1177/1081286519845026
  • 2020 • 173 Data-oriented constitutive modeling of plasticity in metals
    Hartmaier, A.
    Materials 13 (2020)
    Constitutive models for plastic deformation of metals are typically based on flow rules determining the transition from elastic to plastic response of a material as function of the applied mechanical load. These flow rules are commonly formulated as a yield function, based on the equivalent stress and the yield strength of the material, and its derivatives. In this work, a novel mathematical formulation is developed that allows the efficient use of machine learning algorithms describing the elastic-plastic deformation of a solid under arbitrary mechanical loads and that can replace the standard yield functions with more flexible algorithms. By exploiting basic physical principles of elastic-plastic deformation, the dimensionality of the problem is reduced without loss of generality. The data-oriented approach inherently offers a great flexibility to handle different kinds of material anisotropy without the need for explicitly calculating a large number of model parameters. The applicability of this formulation in finite element analysis is demonstrated, and the results are compared to formulations based on Hill-like anisotropic plasticity as reference model. In future applications, the machine learning algorithm can be trained by hybrid experimental and numerical data, as for example obtained from fundamental micromechanical simulations based on crystal plasticity models. In this way, data-oriented constitutive modeling will also provide a new way to homogenize numerical results in a scale-bridging approach. © 2020 by the authors.
    view abstractdoi: 10.3390/ma13071600
  • 2020 • 172 Crystal structure and composition dependence of mechanical properties of single-crystalline NbCo2 Laves phase
    Luo, W. and Kirchlechner, C. and Zavašnik, J. and Lu, W. and Dehm, G. and Stein, F.
    Acta Materialia 184 151-163 (2020)
    Extended diffusion layers of the cubic C15 and hexagonal C14 and C36 NbCo2 Laves phases with concentration gradients covering their entire homogeneity ranges were produced by the diffusion couple technique. Single-phase and single-crystalline micropillars of the cubic and hexagonal NbCo2 Laves phases were prepared in the diffusion layers by focused ion beam (FIB) milling. The influence of chemical composition, structure type, orientation and pillar size on the deformation behavior and the critical resolved shear stress (CRSS) was studied by micropillar compression tests. The pillar orientation influences the activated slip systems, but the deformation behavior and the CRSS are independent of orientation. The deformation of the smallest NbCo2 micropillars (0.8 µm in top diameter) appears to be dislocation nucleation controlled and the CRSS approaches the theoretical shear stress for dislocation nucleation. The CRSS of the 0.8 µm-sized NbCo2 micropillars is nearly constant from 26 to 34 at.% Nb where the C15 structure is stable. It decreases as the composition approaches the Co-rich and Nb-rich boundaries of the homogeneity range where the C15 structure transforms to the C36 and the C14 structure, respectively. The decrease in the CRSS at these compositions is related to the reduction of shear modulus and stacking fault energy. As the pillar size increases, stochastic deformation behavior and large scatter in the CRSS values occur and obscure the composition effect on the CRSS. © 2019
    view abstractdoi: 10.1016/j.actamat.2019.11.036
  • 2020 • 171 Robust optimization scheme for inverse method for crystal plasticity model parametrization
    Shahmardani, M. and Vajragupta, N. and Hartmaier, A.
    Materials 13 (2020)
    A bottom-up material modeling based on a nonlocal crystal plasticity model requires information of a large set of physical and phenomenological parameters. Because of the many material parameters, it is inherently difficult to determine the nonlocal crystal plasticity parameters. Therefore, a robust method is proposed to parameterize the nonlocal crystal plasticity model of a body-centered cubic (BCC) material by combining a nanoindentation test and inverse analysis. Nanoindentation tests returned the load-displacement curve and surface imprint of the considered sample. The inverse analysis is developed based on trust-region-reflective algorithm, which is the most robust optimization algorithm for the considered non-convex problem. The discrepancy function is defined to minimize both the load-displacement curves and the surface topologies of the considered material under applying varied indentation forces obtained from numerical models and experimental output. The numerical model results based on the identified material properties show good agreement with the experimental output. Finally, a sensitivity analysis performed changing the nonlocal crystal plasticity parameters in a predefined range emphasized that the geometrical factor has the most significant influence on the load-displacement curve and surface imprint parameters. © 2020 by the authors.
    view abstractdoi: 10.3390/ma13030735
  • 2020 • 170 Joint investigation of strain partitioning and chemical partitioning in ferrite-containing TRIP-assisted steels
    Tan, X. and Ponge, D. and Lu, W. and Xu, Y. and He, H. and Yan, J. and Wu, D. and Raabe, D.
    Acta Materialia 186 374-388 (2020)
    We applied two types of hot-rolling direct quenching and partitioning (HDQ&P) schemes to a low-C low-Si Al-added steel and obtained two ferrite-containing TRIP-assisted steels with different hard matrix structures, viz, martensite or bainite. Using quasi in-situ tensile tests combined with high-resolution electron back-scattered diffraction (EBSD) and microscopic digital image correlation (µ-DIC) analysis, we quantitatively investigated the TRIP effect and strain partitioning in the two steels and explored the influence of the strain partitioning between the soft and hard matrix structures on the TRIP effect. We also performed an atomic-scale analysis of the carbon partitioning among the different phases using atom probe tomography (APT). The results show that the strain mainly localizes in the ferrite in both types of materials. For the steel with a martensitic hard-matrix, a strong strain contrast exists between ferrite and martensite, with the local strain difference reaching up to about 75% at a global strain of 12.5%. Strain localization bands initiated in the ferrite rarely cross the ferrite/martensite interfaces. The low local strain (2%–10%) in the martensite regions leads to a slight TRIP effect with a transformation ratio of the retained austenite of about 7.5%. However, for the steel with bainitic matrix, the ferrite and bainite undergo more homogeneous strain partitioning, with an average local strain in ferrite and bainite of 15% and 8%, respectively, at a global strain of 12.5%. The strain localization bands originating in the ferrite can cross the ferrite/bainite (F/B) interfaces and increase the local strain in the bainite regions, resulting in an efficient TRIP effect. In that case the transformation ratio of the retained austenite is about 41%. The lower hardness difference between the ferrite and bainite of about 178 HV, compared with that between the ferrite and martensite of about 256 HV, leads to a lower strain contrast at the ferrite/bainite interfaces, thus retarding interfacial fracture. Further microstructure design for TRIP effect optimization should particularly focus on adjusting the strength contrast among the matrix structures and tuning strain partitioning to enhance the local strain partitioning into the retained austenite. © 2020 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2019.12.050
  • 2020 • 169 Comparison of cryogenic deformation of the concentrated solid solutions CoCrFeMnNi, CoCrNi and CoNi
    Tirunilai, A.S. and Hanemann, T. and Reinhart, C. and Tschan, V. and Weiss, K.-P. and Laplanche, G. and Freudenberger, J. and Heilmaier, M. and Kauffmann, A.
    Materials Science and Engineering A 783 (2020)
    The current work compares the deformation behavior of CoCrFeMnNi and CoCrNi in the temperature interval between 295 K and 8 K through a series of quasi-static tensile tests. Temperature-dependent yield stress variation was found to be similarly high in these two alloys. Previous investigations only extended down to 77 K and showed that a small amount of ε-martensite was formed in CoCrNi while this phase was not observed in CoCrFeMnNi. The present study extends these investigations down to 8 K where similar low levels of ε-martensite were presently detected. Based on this result, a rough assessment has been made estimating the importance of deformation twinning to the strength. The relative work hardening rates of CoCrFeMnNi and CoCrNi were comparable in value despite the differences in ε-martensite formation during deformation. CoCrFeMnNi deforms by dislocation slip and deformation twinning while deformation in CoCrNi is also accommodated by the formation of ε-martensite at cryogenic temperatures. Additionally, CoNi, a solid solution from the Co–Cr–Fe–Mn–Ni system with low strength, was used for comparison, showing contrasting deformation behavior at cryogenic temperatures. © 2020 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2020.139290
  • 2020 • 168 Towards an understanding of grain boundary step in diamond cutting of polycrystalline copper
    Wang, Z. and Zhang, J. and Zhang, J. and Li, G. and Zhang, H. and ul Hassan, H. and Hartmaier, A. and Yan, Y. and Sun, T.
    Journal of Materials Processing Technology 276 (2020)
    Microstructural deformation at the grain level has an inherent impact on the achievable ultimate machining accuracy of polycrystalline materials. In the present work, numerical simulations and experiments of diamond cutting of polycrystalline copper are carried out to investigate the formation of surface step at grain boundaries on machined surface. Single crystal diamond cutting tool with straight cutting edge is chosen for experiments to mimic the tool geometry utilized in 2D crystal plasticity finite element simulations. Moreover, the same crystallography configuration of bi-crystal Cu is employed between experiments and simulations. Formation mechanisms of surface steps at grain boundaries are revealed by finite element simulations and corresponding experimental validation, as well as cross-sectional transmission electron microscope characterization. Finally, finite element simulations of orthogonal cutting of bi-crystal Cu are carried out to examine effects of both extrinsic cutting edge radius of diamond cutting tool and intrinsic misorientation angle of grain boundary on the propensity of grain boundary surface step formation. The present work provides theoretical guidelines on the strategy of suppressing grain boundary surface step formation for achieving superior surface finish of polycrystalline materials by diamond cutting. © 2019 Elsevier B.V.
    view abstractdoi: 10.1016/j.jmatprotec.2019.116400
  • 2020 • 167 On the crystallographic anisotropy of plastic zone size in single crystalline copper under Berkovich nanoindentation
    Wang, Z. and Zhang, J. and Ma, A. and Hartmaier, A. and Yan, Y. and Sun, T.
    Materials Today Communications 25 (2020)
    Aiming at revealing plastic deformation mechanisms of nanoindentation tests, we investigate the crystallographic orientation-influenced indentation size effect in the Berkovich nanoindentation tests of single crystalline copper, by using the nonlocal crystal plasticity finite element approach and specifically designed experiments. In our simulation model of nanoindentation, a new geometrically necessary dislocation density-based crystal plasticity model is proposed, and the utilized model parameters are calibrated by fitting the measured load-displacement curves of indentation tests. Then the size of plastic zone of indentation tests is defined by the surface pile-up profile, i.e. the diameter of a circle consisting of material points with half of maximum pile-up height. It is found that the modified plastic zone model incorporated with the newly developed scaling factor provides good predication of the indentation depth-dependent hardness of single crystalline copper. © 2020 Elsevier Ltd
    view abstractdoi: 10.1016/j.mtcomm.2020.101314
  • 2020 • 166 Crystal anisotropy-dependent shear angle variation in orthogonal cutting of single crystalline copper
    Wang, Z. and Zhang, J. and Xu, Z. and Zhang, J. and Li, G. and Zhang, H. and Li, Z. and Hassan, H.U. and Fang, F. and Hartmaier, A. and Yan, Y. and Sun, T.
    Precision Engineering 63 41-48 (2020)
    Shear deformation that dominates elementary chip formation in metal cutting greatly relies on crystal anisotropy. In the present work we investigate the influence of crystallographic orientation on shear angle in ultra-precision orthogonal diamond cutting of single crystalline copper by joint crystal plasticity finite element simulations and in-situ experiments integrated in scanning electron microscope. In particular, the experimental cutting conditions including a straight cutting edge are the same with that used in the 2D finite element simulations. Both simulations and experiments demonstrate a well agreement in chip profile and shear angle, as well as their dependence on crystallography. A series of finite element simulations of orthogonal cutting along different cutting directions for a specific crystallographic orientation are further performed, and predicated values of shear angle are used to calibrate an extended analytical model of shear angle based on the Ernst–Merchant relationship. © 2020 Elsevier Inc.
    view abstractdoi: 10.1016/j.precisioneng.2020.01.006
  • 2019 • 165 Experimental and numerical study of mechanical properties of multi-phase medium-Mn TWIP-TRIP steel: Influences of strain rate and phase constituents
    Benzing, J.T. and Liu, Y. and Zhang, X. and Luecke, W.E. and Ponge, D. and Dutta, A. and Oskay, C. and Raabe, D. and Wittig, J.E.
    Acta Materialia 177 250-265 (2019)
    In the current work we investigate the room temperature tensile properties of a medium-Mn twinning- and transformation-induced plasticity (TWIP-TRIP) steel from quasi-static to low-dynamic strain rates (ε˙ = 10−4 s−1 to ε˙ = 102 s−1). The multi-phase microstructure consists of coarse-grained recovered α'-martensite (inherited from the cold-rolled microstructure), multiple morphologies of ultrafine-grained (UFG) austenite (equiaxed, rod-like and plate-like), and equiaxed UFG ferrite. The multi-phase material exhibits a positive strain-rate sensitivity for yield and ultimate tensile strengths. Thermal imaging and digital image correlation allow for in situ measurements of temperature and local strain in the gauge length during tensile testing, but Lüders bands and Portevin Le Chatelier bands are not observed. A finite-element model uses empirical evidence from electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM), plus constitutive equations to dissect the microstructural influences of grain size, dislocation density and TWIP-TRIP driving forces on tensile properties. Calibration of tensile properties not only captures the strain rate sensitivity of the multi-phase TWIP-TRIP steel, but also provides opportunity for a complete parametric analysis by changing one variable at a time (phase fraction, grain size, strain-induced twin fraction and strain-induced ε-martensite fraction). An equivalent set of high-rate mechanical properties can be matched by changing either the austenite phase fraction or the ratio of twinning vs. transformation to ε-martensite. This experimental-computational framework enables the prediction of mechanical properties in multi-phase steels beyond the experimental regime by tuning variables that are relevant to the alloy design process. © 2019 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2019.07.036
  • 2019 • 164 A canonical rate-independent model of geometrically linear isotropic gradient plasticity with isotropic hardening and plastic spin accounting for the Burgers vector
    Ebobisse, F. and Hackl, K. and Neff, P.
    Continuum Mechanics and Thermodynamics 31 1477-1502 (2019)
    In this paper, we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into non-symmetric elastic and plastic distortions, with a defect energy contribution taking account of the Burgers vector through a dependence only on the dislocation density tensor Curlp giving rise to a non-symmetric nonlocal backstress, and isotropic hardening response only depending on the accumulated equivalent plastic strain. The model is fully isotropic and satisfies linearized gauge invariance conditions, i.e., only true state variables appear. The model satisfies also the principle of maximum dissipation which allows to show existence for the weak formulation. For this result, a recently introduced Korn’s inequality for incompatible tensor fields is necessary. Uniqueness is shown in the class of strong solutions. For vanishing energetic length scale, the model reduces to classical elasto-plasticity with symmetric plastic strain εp and standard isotropic hardening. © 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
    view abstractdoi: 10.1007/s00161-019-00755-5
  • 2019 • 163 Micromechanical modelling of coupled crystal plasticity and hydrogen diffusion
    Hassan, H.U. and Govind, K. and Hartmaier, A.
    Philosophical Magazine 99 92-115 (2019)
    Hydrogen transport behaviour in metals is greatly influenced by the mechanical stress and the underlying microstructural features. In this work, a micromechanical model based on coupled crystal plasticity and hydrogen diffusion is developed and applied to model hydrogen diffusion and storage in a polycrystalline microstructure. Particular emphasis is laid on mechanical influences on hydrogen transport, invoked by internal stresses and by trapping of dislocations generated by plastic strains. First, a study of a precharged material is carried out where hydrogen is allowed to redistribute under the influence of mechanical loading. These simulations demonstrate to which extent hydrogen migrates from regions with compressive strains to those with tensile strains. In the next step, the influence of plastic prestraining on hydrogen diffusion is analysed. This prestraining produces internal residual stresses in the microstructure, that mimic residual stresses introduced into components during cold working. Lastly, a series of permeation simulations is performed to characterise the influence of hydrogen trapping on effective diffusivity. It is shown that the effective diffusivity decreases with stronger traps and the effect is more prominent at a larger predeformation, because the trapped hydrogen concentration increases considerably. The reduction of effective diffusivity with plastic deformation agrees very well with experimental findings and offers a way to validate and parameterise our model. With this work, it is demonstrated how micromechanical modelling can support the understanding of hydrogen transport on the microstructural level. © 2018, © 2018 Informa UK Limited, trading as Taylor & Francis Group.
    view abstractdoi: 10.1080/14786435.2018.1530466
  • 2019 • 162 Joint contribution of transformation and twinning to the high strength-ductility combination of a FeMnCoCr high entropy alloy at cryogenic temperatures
    He, Z.F. and Jia, N. and Ma, D. and Yan, H.L. and Li, Z.M. and Raabe, D.
    Materials Science and Engineering A 759 437-447 (2019)
    The microstructure-mechanical property relationships of a non-equiatomic FeMnCoCr high entropy alloy (HEA), which shows a single face-centered cubic (fcc) structure in the undeformed state, have been systematically investigated at room and cryogenic temperatures. Both strength and ductility increase significantly when reducing the probing temperature from 293 K to 77 K. During tensile deformation at 293 K, dislocation slip and mechanical twinning prevail. At 173 K deformation-driven athermal transformation from the fcc phase to the hexagonal close-packed (hcp) martensite is the dominant mechanism while mechanical twinning occurs in grains with high Schmid factors. At 77 K athermal martensitic transformation continues to prevail in addition to dislocation slip and twinning. The reduction in the mean free path for dislocation slip through the fine martensite bundles and deformation twins leads to the further increased strength. The joint activation of transformation and twinning under cryogenic conditions is attributed to the decreased stacking fault energy and the enhanced flow stress of the fcc matrix with decreasing temperature. These mechanisms lead to an elevated strain hardening capacity and an enhanced strength-ductility combination. The temperature-dependent synergy effects of martensite formation, twinning and dislocation plasticity originate from the metastability alloy design concept. This is realized by relaxing the equiatomic HEA constraints towards reduced Ni and increased Mn contents, enabling a non-equiatomic material with low stacking fault energy. These insights are important for designing strong and ductile Ni-saving alloys for cryogenic applications. © 2019 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2019.05.057
  • 2019 • 161 An incompatibility tensor-based gradient plasticity formulation—Theory and numerics
    Kaiser, T. and Menzel, A.
    Computer Methods in Applied Mechanics and Engineering 345 671-700 (2019)
    In this work we discuss a gradient plasticity formulation which relies on the introduction of higher-order gradient contributions as additional arguments of the free energy function. These gradients can be interpreted in terms of the local geometrically necessary dislocation density. This gives rise to physically well-motivated kinematic-type hardening models in contrast to purely phenomenological approaches. At the same time, the framework results into a regularisation of the formulation such that localised plastic deformation processes in softening materials, e.g.the formation of shear bands, can be simulated. The employed theory is based on an extended nonlocal form of the Clausius–Duhem inequality, motivated by a possible energy exchange between particles at the microstructural level. This gives rise to the balance equation of a nonlocal stress tensor that is found to be work-conjugated to the plastic velocity gradient. The solution of the governing system of partial differential equations is approached by means of a multi-field finite element formulation with the solution of the Karush–Kuhn–Tucker conditions being addressed on a global level by means of Fischer–Burmeister complementary functions. We discuss a specific quadratic energy contribution in terms of the incompatibility, respectively dislocation density tensor that results into well-interpretable contributions to the nonlocal stress field and study the formation of shear bands induced by geometric imperfections as well as the constitutive response at a material interface where the yield limit exhibits a jump discontinuity. © 2018 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2018.11.013
  • 2019 • 160 A dislocation density tensor-based crystal plasticity framework
    Kaiser, T. and Menzel, A.
    Journal of the Mechanics and Physics of Solids 131 276-302 (2019)
    The present contribution addresses a crystal plasticity formulation which incorporates hardening effects that are related to the presence of geometrically necessary dislocations. To this end, higher gradient contributions are introduced as additional arguments of the energy function based on microstructural considerations. Extending the derivations presented in Kaiser and Menzel (2019) for a purely phenomenological, associated type plasticity model to crystal plasticity, it is shown that the higher gradient contributions in terms of dislocation density tensors give rise to the balance equation of a generalised stress field together with non-ambiguous constitutive boundary conditions. This stress field can be shown to be energetically conjugated to the plastic flow and is additively composed of two parts: the classic stress field and a back-stress type stress field which is closely related to incompatibilities in the plastic deformation field and hence interpretable in terms of geometrically necessary dislocations. For a specific model which features twelve slip systems the constitutive response on material point level is studied in a first step before finite element based simulations, which are motivated by experimental findings on copper micro wires, are analysed in two- and three-dimensional settings. © 2019 Elsevier Ltd
    view abstractdoi: 10.1016/j.jmps.2019.05.019
  • 2019 • 159 A review of the intrinsic ductility and toughness of hard transition-metal nitride alloy thin films
    Kindlund, H. and Sangiovanni, D.G. and Petrov, I. and Greene, J.E. and Hultman, L.
    Thin Solid Films 688 (2019)
    Over the past decades, enormous effort has been dedicated to enhancing the hardness of refractory ceramic materials. Typically, however, an increase in hardness is accompanied by an increase in brittleness, which can result in intergranular decohesion when materials are exposed to high stresses. In order to avoid brittle failure, in addition to providing high strength, films should also be ductile, i.e., tough. However, fundamental progress in obtaining hard-yet-ductile ceramics has been slow since most toughening approaches are based on empirical trial-and-error methods focusing on increasing the strength and ductility extrinsically, with a limited focus on understanding thin-film toughness as an inherent physical property of the material. Thus, electronic structure investigations focusing on the origins of ductility vs. brittleness are essential in understanding the physics behind obtaining both high strength and high plastic strain in ceramics films. Here, we review recent progress in experimental validation of density functional theory predictions on toughness enhancement in hard ceramic films, by increasing the valence electron concentration, using examples from the V1-xWxN and V1-xMoxN alloy systems. © 2019 Elsevier B.V.
    view abstractdoi: 10.1016/j.tsf.2019.137479
  • 2019 • 158 On the interaction of precipitates and tensile twins in magnesium alloys
    Liu, C. and Shanthraj, P. and Robson, J.D. and Diehl, M. and Dong, S. and Dong, J. and Ding, W. and Raabe, D.
    Acta Materialia 178 146-162 (2019)
    Although magnesium alloys deform extensively through shear strains and crystallographic re-orientations associated with the growth of twins, little is known about the strengthening mechanisms associated with this deformation mode. A crystal plasticity based phase field model for twinning is employed in this work to study the strengthening mechanisms resulting from the interaction between twin growth and precipitates. The full-field simulations reveal in great detail the pinning and de-pinning of a twin boundary at individual precipitates, resulting in a maximum resistance to twin growth when the precipitate is partially embedded in the twin. Furthermore, statistically representative precipitate distributions are used to systematically investigate the influence of key microstructural parameters such as precipitate orientation, volume fraction, size, and aspect ratio on the resistance to twin growth. The results indicate that the effective critical resolved shear stress (CRSS) for twin growth increases linearly with precipitate volume fraction and aspect ratio. For a constant volume fraction of precipitates, reduction of the precipitate size below a critical level produces a strong increase in the CRSS due to the OROWAN-like strengthening mechanism between the twin interface and precipitates. Above this level the CRSS is size independent. The results are quantitatively and qualitatively comparable with experimental measurements and predictions of mean-field strengthening models. Based on the results, guidelines for the design of high strength magnesium alloys are discussed. © 2019 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2019.07.046
  • 2019 • 157 Modelling cyclic behaviour of martensitic steel with J2 plasticity and crystal plasticity
    Sajjad, H.M. and Hanke, S. and Güler, S. and ul Hassan, H. and Fischer, A. and Hartmaier, A.
    Materials 12 (2019)
    In order to capture the stress-strain response of metallic materials under cyclic loading, it is necessary to consider the cyclic hardening behaviour in the constitutive model. Among different cyclic hardening approaches available in the literature, the Chaboche model proves to be very efficient and convenient to model the kinematic hardening and ratcheting behaviour of materials observed during cyclic loading. The purpose of this study is to determine the material parameters of the Chaboche kinematic hardening material model by using isotropic J2 plasticity and micromechanical crystal plasticity (CP) models as constitutive rules in finite element modelling. As model material, we chose a martensitic steel with a very fine microstructure. Thus, it is possible to compare the quality of description between the simpler J2 plasticity and more complex micromechanical material models. The quality of the results is rated based on the quantitative comparison between experimental and numerical stress-strain hysteresis curves for a rather wide range of loading amplitudes. It is seen that the ratcheting effect is captured well by both approaches. Furthermore, the results show that concerning macroscopic properties, J2 plasticity and CP are equally suited to describe cyclic plasticity. However, J2 plasticity is computationally less expensive whereas CP finite element analysis provides insight into local stresses and plastic strains on the microstructural length scale. With this study, we show that a consistent material description on the microstructural and the macroscopic scale is possible, which will enable future scale-bridging applications, by combining both constitutive rules within one single finite element model. © 2019 by the authors.
    view abstractdoi: 10.3390/ma12111767
  • 2019 • 156 Magnetic properties of a 17.6 Mn-TRIP steel: Study of strain-induced martensite formation, austenite reversion, and athermal α′-formation
    Souza Filho, I.R. and Sandim, M.J.R. and Cohen, R. and Nagamine, L.C.C.M. and Sandim, H.R.Z. and Raabe, D.
    Journal of Magnetism and Magnetic Materials 473 109-118 (2019)
    Strain-induced martensite (SIM) formation was evaluated upon cold-rolling of a 17.6 wt.%Mn-TRIP steel by means of magnetic measurements, X-ray diffraction, and high-resolution electron backscatter diffraction (EBSD). α′-martensite formation was observed to be dependent on the presence of prior ε-martensite. Upon deformation, the coercivity of the ferromagnetic α′-martensite is characterized by strong magnetic shape anisotropy. Austenite (γ) reversion was evaluated by means of in situ magnetic measurements during continuous annealing. The experimental results were compared to thermodynamic simulations. It turned out that γ-reversion was not completed in the regime where a γ-single phase field is expected, which suggests the splitting of α′ → γ transformation into two stages. The Curie temperature of remaining α′-martensite was determined as being ∼620 °C. Magnetic properties presented an annealing time-dependence within the temperature range of 500–600 °C, suggesting long-range diffusional α′ → γ transformation. With the aid of electron channeling contrast image technique (ECCI), we noticed that the formation of γ-nanograins in the early stages of reversion is sufficient to induce strong magnetic shape anisotropy in this steel. After full austenitization at 800 °C, further in situ magnetic measurements were also used to track the magnetic response of the material upon controlled cooling. Athermal formation of α′-martensite within the prior athermal ε-phase was clearly observed for temperatures lower than 100 °C. Using thermodynamic modeling we also calculated the start temperature for ε-formation (Ms ε). Results showed that ε-martensite is indeed expected to form before α′ which was confirmed in all cases by means of EBSD. © 2018 Elsevier B.V.
    view abstractdoi: 10.1016/j.jmmm.2018.10.034
  • 2019 • 155 Hierarchical microstructure design to tune the mechanical behavior of an interstitial TRIP-TWIP high-entropy alloy
    Su, J. and Raabe, D. and Li, Z.
    Acta Materialia 163 40-54 (2019)
    We demonstrate a novel approach of utilizing a hierarchical microstructure design to improve the mechanical properties of an interstitial carbon doped high-entropy alloy (HEA) by cold rolling and subsequent tempering and annealing. Bimodal microstructures were produced in the tempered specimens consisting of nano-grains (∼50 nm) in the vicinity of shear bands and recovered parent grains (10–35 μm) with pre-existing nano-twins. Upon annealing, partial recrystallization led to trimodal microstructures characterized by small recrystallized grains (<1 μm) associated with shear bands, medium-sized grains (1–6 μm) recrystallized through subgrain rotation or coalescence of parent grains and retained large un-recrystallized grains. To reveal the influence of these hierarchical microstructures on the strength-ductility synergy, the underlying deformation mechanisms and the resultant strain hardening were investigated. A superior yield strength of 1.3 GPa was achieved in the bimodal microstructure, more than two times higher than that of the fully recrystallized microstructure, owing to the presence of nano-sized grains and nano-twins. The ductility was dramatically improved from 14% to 60% in the trimodal structure compared to the bimodal structure due to the appearance of a multi-stage work hardening behavior. This important strain hardening sequence was attributed to the sequential activation of transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP) effects as a result of the wide variation in phase stability promoted by the grain size hierarchy. These findings open a broader window for achieving a wide spectrum of mechanical properties for HEAs, making better use of not only compositional variations but also microstructure and phase stability tuning. © 2018 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2018.10.017
  • 2019 • 154 Crystal plasticity finite element modeling and simulation of diamond cutting of polycrystalline copper
    Wang, Z. and Zhang, J. and Xu, Z. and Zhang, J. and Hassan, H.U. and Li, G. and Zhang, H. and Hartmaier, A. and Fang, F. and Yan, Y. and Sun, T.
    Journal of Manufacturing Processes 38 187-195 (2019)
    Microstructural-related deformation behavior leads to anisotropic machining characteristics of polycrystalline materials. In the present work, we develop a crystal plasticity finite element model of ultra-precision diamond cutting of polycrystalline copper, aiming to evaluate the influence of grain boundaries on the correlation between microscopic deformation behavior of the material and macroscopic machining results. The crystal plasticity dealing with the anisotropy of polycrystalline copper is implemented in a user subroutine (UMAT), and an efficient element deletion technique based on the Johnson-Cook damage model is adopted to describe material removal and chip formation. The effectiveness of as-established crystal plasticity finite element model is verified by experiments of nanoindentation, nanoscratching and in-situ diamond microcutting. Subsequent crystal plasticity finite element simulation of diamond cutting across a high angle grain boundary demonstrates significant anisotropic machining characteristics in terms of machined surface quality, chip profile and cutting force, due to heterogeneous plastic deformation behavior in the grain level. © 2019
    view abstractdoi: 10.1016/j.jmapro.2019.01.007
  • 2019 • 153 Crystal plasticity finite element simulation and experiment investigation of nanoscratching of single crystalline copper
    Wang, Z. and Zhang, H. and Li, Z. and Li, G. and Zhang, J. and Zhang, J. and Hassan, H.U. and Yan, Y. and Hartmaier, A. and Sun, T.
    Wear 430-431 100-107 (2019)
    Mechanical properties of crystalline materials strongly correlate with deformation behaviour at the grain level. In the present work, we establish a 3D crystal plasticity finite element model of nanoscratching of single crystalline copper using a Berkovich probe, which is capable of addressing the crystallography influence. In particular, nanoindentation experiments and high resolution electron back-scatter diffraction characterization are jointly carried out to precisely calibrate parameters used in the crystal plasticity finite element model. Subsequent finite element simulations of nanoscratching are performed to reveal fundamental deformation behaviour of single crystalline copper in terms of mechanical response and surface pile-up topography, as well as their dependence on crystallographic orientation. Furthermore, nanoscratching experiments with the same parameters used in the finite element simulations are carried out, the results of which are further compared with predication results by the finite element simulations. Simulation data and experimental results jointly demonstrate the strong anisotropic characteristics of single crystalline copper under nanoscratching, due to the crystallographic orientation dependent coupled effects of intrinsic dislocation slip and extrinsic discrete stress distribution by probe geometry. © 2019 Elsevier B.V.
    view abstractdoi: 10.1016/j.wear.2019.04.024
  • 2019 • 152 On the mechanism of extraordinary strain hardening in an interstitial high-entropy alloy under cryogenic conditions
    Wang, Z. and Lu, W. and Raabe, D. and Li, Z.
    Journal of Alloys and Compounds 734-743 (2019)
    We investigate the cryogenic deformation response and underlying mechanisms of a carbon-doped interstitial high-entropy alloy (iHEA) with a nominal composition of Fe49.5Mn30Co10Cr10C0.5 (at. %). Extraordinary strain hardening of the iHEA at 77 K leads to a substantial increase in ultimate tensile strength (∼1300 MPa) with excellent ductility (∼50%) compared to that at room temperature. Prior to loading, iHEAs with coarse (∼100 μm) and fine (∼6 μm) grain sizes show nearly single face-centered cubic (FCC) structure, while the fraction of hexagonal close-packed (HCP) phase reaches up to ∼70% in the cryogenically tensile-fractured iHEAs. Such an unusually high fraction of deformation-induced phase transformation and the associated plasticity (TRIP effect) is caused by the strong driving force supported by the reduced stacking fault energy and increased flow stress at 77 K. The transformation mechanism from the FCC matrix to the HCP phase is revealed by transmission electron microscopy (TEM) observations. In addition to the deformation-induced phase transformation, stacking faults and dislocation slip contribute to the deformation of the FCC matrix phase at low strains and of the HCP phase at medium and large strains, suggesting dynamic strain partitioning among these two phases. The combination of TRIP and dynamic strain partitioning explain the striking strain hardening capability and resulting excellent combination of strength and ductility of iHEAs under cryogenic conditions. The current investigation thus offers guidance for the design of high-performance HEAs for cryogenic applications. © 2018 Elsevier B.V.
    view abstractdoi: 10.1016/j.jallcom.2018.12.061
  • 2019 • 151 Unraveling indentation-induced slip steps in austenitic stainless steel
    Xia, W. and Dehm, G. and Brinckmann, S.
    Materials and Design 183 (2019)
    Nanoindentation has been used intensively during the last decades to characterize experimentally the elastic and plastic material properties of phases at the microscale. Accompanying simulations have investigated the plastic mechanisms during nanoindentation. While experiments and simulations have led to a thorough understanding of most mechanisms during nanoindentation, the plasticity on positively and negatively inclined slip planes is still not completely clear. In this work, {1 0 0}-, {1 0 1}- and {1 1 1}-grains of an austenitic stainless steel are indented to better understand the dislocation mediated plasticity through slip step analysis. We observe that slip occurs on positively and negatively inclined slip planes during nanoindentation and we propose methods to differentiate between both types of planes. We find that slip steps on positively inclined slip planes form preferentially during the early stage as compared to the formation of slip steps on negative inclination, which occurs during the later deformation stage due to the change in surface topography. By calculating the resolved shear stress in the presence and absence of pile-ups, we reveal the origin of slip on positively and negatively inclined planes as well as the reason for the sequence of occurrences. We conclude that accounting for the surface topography evolution in experiments and simulations is essential in predicting the plastic slip activation during nanoindentation. © 2019 The Authors
    view abstractdoi: 10.1016/j.matdes.2019.108169
  • 2018 • 150 Effects of strain rate on mechanical properties and deformation behavior of an austenitic Fe-25Mn-3Al-3Si TWIP-TRIP steel
    Benzing, J.T. and Poling, W.A. and Pierce, D.T. and Bentley, J. and Findley, K.O. and Raabe, D. and Wittig, J.E.
    Materials Science and Engineering A 711 78-92 (2018)
    The effects of quasi-static and low-dynamic strain rate (ε̇ = 10−4 /s to ε̇ = 102 /s) on tensile properties and deformation mechanisms were studied in a Fe-25Mn-3Al-3Si (wt%) twinning and transformation-induced plasticity [TWIP-TRIP] steel. The fully austenitic microstructure deforms primarily by dislocation glide but due to the room temperature stacking fault energy [SFE] of 21 ± 3 mJ/m2 for this alloy, secondary deformation mechanisms such as mechanical twinning (TWIP) and epsilon martensite formation (TRIP) also play an important role in the deformation behavior. The mechanical twins and epsilon-martensite platelets act as planar obstacles to subsequent dislocation motion on non-coplanar glide planes and reduce the dislocation mean free path. A high-speed thermal camera was used to measure the increase in specimen temperature as a function of strain, which enabled the use of a thermodynamic model to predict the increase in SFE. The influence of strain rate and strain on microstructural parameters such as the thickness and spacing of mechanical twins and epsilon-martensite laths was quantified using dark field transmission electron microscopy, electron channeling contrast imaging, and electron backscattered diffraction. The effect of sheet thickness on mechanical properties was also investigated. Increasing the tensile specimen thickness increased the product of ultimate tensile strength and total elongation, but had no significant effect on uniform elongation or yield strength. The yield strength exhibited a significant increase with increasing strain rate, indicating that dislocation glide becomes more difficult with increasing strain rate due to thermally-activated short-range barriers. A modest increase in ultimate tensile strength and minimal decrease in uniform elongation were noted at higher strain rates, suggesting adiabatic heating, slight changes in strain-hardening rate and observed strain localizations as root causes, rather than a significant change in the underlying TWIP-TRIP mechanisms at low values of strain. © 2017 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2017.11.017
  • 2018 • 149 On the nature of twin boundary-associated strengthening in Fe-Mn-C steel
    Choi, W.S. and Sandlöbes, S. and Malyar, N.V. and Kirchlechner, C. and Korte-Kerzel, S. and Dehm, G. and Choi, P.-P. and Raabe, D.
    Scripta Materialia 156 27-31 (2018)
    We unravel the nature of twin boundary-associated strengthening in Fe-Mn-C twinning-induced plasticity steel (TWIPs) by micro-pillar compression tests. Dislocation interactions with a coherent twin boundary and their role on strain hardening were investigated. The results indicate that twin-matrix bundles dynamically introduced by deformation twinning and their interaction with dislocations are required for strengthening Fe-Mn-C TWIPs, while single coherent twin boundaries enable dislocation transmission. Correlative studies on orientation dependent deformation mechanisms, detailed dislocation-twin boundary interactions, and the resulting local stress-strain responses suggest that twin boundary-associated strengthening is primarily caused by the reduction of the mean free dislocation path in nano-twinned microstructures. © 2018
    view abstractdoi: 10.1016/j.scriptamat.2018.07.009
  • 2018 • 148 Existence result for a dislocation based model of single crystal gradient plasticity with isotropic or linear kinematic hardening
    Ebobisse, F. and Neff, P. and Aifantis, E.C.
    Quarterly Journal of Mechanics and Applied Mathematics 71 99-124 (2018)
    We consider a dislocation-based rate-independent model of single crystal gradient plasticity with isotropic or linear kinematic hardening. The model is weakly formulated through the so-called primal form of theflowrule as a variational inequality for which a result of existence and uniqueness is obtained using the functional analytical framework developed by Han-Reddy. © The Author, 2017.
    view abstractdoi: 10.1093/qjmam/hbx026
  • 2018 • 147 Precipitation hardening effects on extension twinning in magnesium alloys
    Fan, H. and Zhu, Y. and El-Awady, J.A. and Raabe, D.
    International Journal of Plasticity 106 186-202 (2018)
    Precipitation is an efficient method to strengthen metallic materials. While precipitation hardening effects on dislocation slip have been studied extensively in the past, the influence of precipitates on twinning mediated plasticity and the development of corresponding hardening models that account for twin-precipitate interactions have received less attention. Here, the interaction of {10-12} extension twin boundaries (TBs) in pure magnesium with precipitates of plate-, sphere- and rod-like shapes is studied using molecular dynamics (MD) simulations. We find that TBs that engulf precipitates are absorbed by the precipitate-matrix interfaces, and the precipitates are neither twinned nor sheared but deform elastically leading to their rotation. TBs can pass small precipitates (length? 20 nm) and remain intact. In contrast when TBs are interacting with large precipitates (length? 50 nm), basal dislocations or stacking faults nucleate from the interfaces, causing local plastic relaxation. The stress field around a plate-like precipitate as calculated in the MD simulations suggests that a strong back-stress is imposed on the TBs. We then coarse grain these mechanisms into an analytical mean field model of precipitation hardening on twinning in magnesium alloys, which is based on the energy conservation during the TB-precipitate interaction. The model is in good agreement with the current MD simulations and published experimental observations. The hardening model shows that spherical precipitates have the strongest hardening effect on twinning, basal and prismatic plate-like precipitates have a medium effect while rod-like precipitates exert the weakest influence. We also find that most types of precipitates show a stronger hardening effect on twinning mediated plasticity than on basal dislocation slip. Finally, prismatic plate-like precipitates are predicted to have reasonable hardening effects on both twinning and basal slip. These results can help guiding the development of magnesium alloys with enhanced strength and ductility. © 2018 Elsevier Ltd.
    view abstractdoi: 10.1016/j.ijplas.2018.03.008
  • 2018 • 146 Multiple slip dislocation patterning in a dislocation-based crystal plasticity finite element method
    Grilli, N. and Janssens, K.G.F. and Nellessen, J. and Sandlöbes, S. and Raabe, D.
    International Journal of Plasticity 100 104-121 (2018)
    Dislocation structures forming during cyclic loading of fcc metals are fatigue damage precursors. Their specific structures are caused by the motion and interactions of dislocations. Depending on the load conditions, the grain orientation, the stacking fault energy, a variety of different dislocation structures appear in the material such as labyrinths, cells, veins and persistent slip bands. We present a continuum dislocation-based model for cyclic fatigue and incorporate it into a crystal plasticity finite element solver. A method for the simulation of dislocation junction formation is introduced, which reproduces the behaviour of discrete objects, such as dislocations, in a continuum framework. The formation of dislocation walls after 50 and 100 deformation cycles at 0.95% and 0.65% strain amplitude starting from an initial random dislocation distribution is predicted for 〈001〉 and 〈11¯0〉 oriented crystals. Simulations and cyclic tension-compression experiments of polycrystalline 316L stainless steel are performed to compare our model with another model based on edge and screw dislocation densities. The simulated dislocation structures and experimental results, obtained with the electron channeling contrast imaging technique, are compared using a 2D orientation distribution function of the dislocation structures. The dominant orientation of dislocation walls is predicted by the new model; it turns out to be perpendicular to the intersection line between the two slip planes involved in their formation and at an angle of around 45o from the loading axis. This agrees well with the experimental observations and represents a step forward for understanding the formation mechanism of these dislocation structures. © 2017 Elsevier Ltd
    view abstractdoi: 10.1016/j.ijplas.2017.09.015
  • 2018 • 145 The influence of the nitrogen/nickel-ratio on the cyclic behavior of austenitic high strength steels with twinning-induced plasticity and transformation-induced plasticity effects [Einfluss des Stickstoff-/Nickel-Verhältnisses auf das zyklische Verhalten austenitischer hochfester Stähle mit durch Zwillingsbildung und Umwandlung induzierter Plastizität]
    Güler, S. and Schymura, M. and Fischer, A. and Droste, M. and Biermann, H.
    Materialwissenschaft und Werkstofftechnik 49 61-72 (2018)
    Austenitic high nitrogen (AHNS) and austenitic high interstitial steels (AHIS) are of interest for mechanical engineering applications because of their unique combination of mechanical (strength, ductility), chemical (corrosion resistance) and physical (non-ferromagnetic) properties. But despite their high strength values e. g. after cold deformation up to 2 GPa in combination with an elongation to fracture of 30 %, which is based on twinning-induced plasticity (TWIP) mechanisms and transformation-induced plasticity (TRIP) mechanisms, the fatigue limit remains relatively small. While for chromium-nickel steels the fatigue limit rises with about 0.5-times the elastic limit it does not at all for austenitic high-nitrogen steels or only to a much smaller extent for nickel-free austenitic high-interstitial steels. The reasons are still not fully understood but this behavior can roughly be related to the tendency for planar or wavy slip. Now the latter is hindered by nitrogen and promoted by nickel. This contribution shows the fatigue behavior of chromium-manganese-carbon-nitrogen (CrMnCn) steels with carbon+nitrogen-contents up to 1.07 wt.%. Beside the governing influence of these interstitials on fatigue this study displays, how the nitrogen/nickel-ratio might be another important parameter for the fatigue behavior of such steels. © 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim
    view abstractdoi: 10.1002/mawe.201700107
  • 2018 • 144 Computationally-efficient modeling of inelastic single crystal responses via anisotropic yield surfaces: Applications to shape memory alloys
    Hartl, D.J. and Kiefer, B. and Schulte, R. and Menzel, A.
    International Journal of Solids and Structures 136-137 38-59 (2018)
    Phenomenological constitutive models of inelastic responses based on the methods of classical plasticity provide several advantages, especially in terms of computational efficiency. For this reason, they are attractive for the analysis of complex boundary value problems comprising large computational domains. However, for the analysis of problems dominated by single crystal behavior (e.g., inclusion, granular interaction problems or inter-granular fracture), such approaches are often limited by the symmetry assumptions inherent in the stress invariants used to form yield-type criteria. On the other hand, the high computational effort associated with micro-mechanical or crystal plasticity-type models usually prevents their use in large structural simulations, multi-scale analyses, or design and property optimization computations. The goal of the present work is to establish a modeling strategy that captures micro-scale single-crystalline sma responses with sufficient fidelity at the computational cost of a phenomenological macro-scale model. Its central idea is to employ an anisotropic transformation yield criterion with sufficiently rich symmetry class—which can directly be adopted from the literature on plasticity theory—at the single crystal level. This approach is conceptually fundamentally different from the common use of anisotropic yield functions to capture tension-compression asymmetry and texture-induced anisotropy in poly-crystalline SMAs. In our model, the required anisotropy parameters are calibrated either from experimental data for single crystal responses, theoretical considerations or micro-scale computations. The model thus efficiently predicts single crystal behaviors and can be applied to the analysis of complex boundary value problems. In this work we consider the application of this approach to the modeling of shape memory alloys (SMAs), though its potential utility is much broader. Example analyses of SMA single crystals that include non-transforming precipitates and poly-crystalline aggregates are considered and the effects of both elastic and transformation anisotropy in these materials are demonstrated. © 2017 Elsevier Ltd
    view abstractdoi: 10.1016/j.ijsolstr.2017.12.002
  • 2018 • 143 Nonlinear BDDC methods with approximate solvers
    Klawonn, A. and Lanser, M. and Rheinbach, O.
    Electronic Transactions on Numerical Analysis 49 244-273 (2018)
    New nonlinear BDDC (Balancing Domain Decomposition by Constraints) domain decomposition methods using inexact solvers for the subdomains and the coarse problem are proposed. In nonlinear domain decomposition methods, the nonlinear problem is decomposed before linearization to improve concurrency and robustness. For linear problems, the new methods are equivalent to known inexact BDDC methods. The new approaches are therefore discussed in the context of other known inexact BDDC methods for linear problems. Relations are pointed out, and the advantages of the approaches chosen here are highlighted. For the new approaches, using an algebraic multigrid method as a building block, parallel scalability is shown for more than half a million (524 288) MPI ranks on the JUQUEEN IBM BG/Q supercomputer (JSC Jülich, Germany) and on up to 193 600 cores of the Theta Xeon Phi supercomputer (ALCF, Argonne National Laboratory, USA), which is based on the recent Intel Knights Landing (KNL) many-core architecture. One of our nonlinear inexact BDDC domain decomposition methods is also applied to three-dimensional plasticity problems. Comparisons to standard Newton-Krylov-BDDC methods are provided. Copyright © 2018, Kent State University.
    view abstractdoi: 10.1553/etna_vol49s244
  • 2018 • 142 ω phase acts as a switch between dislocation channeling and joint twinning- and transformation-induced plasticity in a metastable β titanium alloy
    Lai, M.J. and Li, T. and Raabe, D.
    Acta Materialia 151 67-77 (2018)
    We have investigated the twinning-induced plasticity (TWIP) and transformation-induced plasticity (TRIP) as well as the influence of ω phase on these two phenomena in a metastable β-type Ti–25Nb–0.7Ta–2Zr (at.%) alloy. We set off with two starting states: one is ω-free and the other one contains a high number density (3.20 ± 0.78 × 1024 m−3) of nanometer-sized (∼1.23 nm) ω particles. Deformation experiments demonstrate that the plastic deformation of the ω-free alloy is mediated by stress-induced β → α” martensitic transformation, {332} twinning and dislocation slip, where the former two induce joint TRIP and TWIP effects and the latter one carries the majority of the plastic strain. In the ω-enriched alloy, the ω particles fully suppress the TWIP and TRIP effects and promote localization of dislocation plasticity into specific ω-devoid channels. Atom probe tomography analysis reveals that the elemental partitioning between β and ω results in only subtle enrichment of solutes in the β matrix, which cannot sufficiently stabilize the matrix to prevent martensitic transformation and twinning. A new mechanism based on the shear modulus difference between β and ω is proposed to explain the suppression of TRIP and TWIP effects by ω particles. © 2018 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2018.03.053
  • 2018 • 141 Influence of microstructure morphology on multi-scale modeling of low-alloyed TRIP-steels
    Prüger, S. and Gandhi, A. and Balzani, D.
    Engineering Computations (Swansea, Wales) 35 499-528 (2018)
    Purpose: The purpose of this study is to quantify the impact of the variation of microstructural features on macroscopic and microscopic fields. The application of multi-scale methods in the context of constitutive modeling of microheterogeneous materials requires the choice of a representative volume element (RVE) of the considered microstructure, which may be based on some idealized assumptions and/or on experimental observations. In any case, a realistic microstructure within the RVE is either computationally too expensive or not fully accessible by experimental measurement techniques, which introduces some uncertainty regarding the microstructural features. Design/methodology/approach: In this paper, a systematical variation of microstructural parameters controlling the morphology of an RVE with an idealized microstructure is conducted and the impact on macroscopic quantities of interest as well as microstructural fields and their statistics is investigated. The study is carried out under macroscopically homogeneous deformation states using the direct micro-macro scale transition approach. Findings: The variation of microstructural parameters, such as inclusion volume fraction, aspect ratio and orientation of the inclusion with respect to the overall loading, influences the macroscopic behavior, especially the micromechanical fields significantly. Originality/value: The systematic assessment of the impact of microstructural parameters on both macroscopic quantities and statistics of the micromechanical fields allows for a quantitative comparison of different microstructure morphologies and a reliable identification of microstructural parameters that promote failure initialization in microheterogeneous materials. © 2018, Emerald Publishing Limited.
    view abstractdoi: 10.1108/EC-01-2017-0009
  • 2018 • 140 On the role of the collinear dislocation interaction in deformation patterning and laminate formation in single crystal plasticity
    Wang, D. and Diehl, M. and Roters, F. and Raabe, D.
    Mechanics of Materials 125 70-79 (2018)
    We investigate the reasons for severe deformation patterning observed in crystal plasticity simulations of an fcc nickel single crystal with initial near-Copper orientation deformed in plane strain compression. The resulting strain partitioning in the form of alternating parallel bands initiates at a very early loading stage, i.e. <0.5% global strain, and sharpens with ongoing deformation. At an applied average strain of 5.5%, the local strains finally deviate by half an order of magnitude in different regions of the initially homogeneous single crystal. We show that this microstructure lamination is the result of a complex interplay between available deformation systems, strain hardening, kinematics, and deformation energetics. Moreover, the boundary conditions play an important role as under the applied load two slip systems—which are collinear with respect to each other—have the same highest Schmid factor and therefore are preferentially activated. During strain hardening, the strong collinear interaction strength causes—depending on the initial deviation from the nominal orientation—the selection of a single prevalent slip system in clearly delimited regions. This behavior is explained by the lower global deformation energy in comparison to a homogeneous double slip behavior. We also reveal that the observed deformation pattern forms only for dislocation interaction strength values in the range predicted by discrete dislocation dynamic simulations. © 2018
    view abstractdoi: 10.1016/j.mechmat.2018.06.007
  • 2018 • 139 In-situ SEM observation of phase transformation and twinning mechanisms in an interstitial high-entropy alloy
    Wang, M. and Li, Z. and Raabe, D.
    Acta Materialia 147 236-246 (2018)
    The recently developed interstitial high-entropy alloys (iHEAs) exhibit an enhanced combination of strength and ductility. These properties are attributed to dislocation hardening, deformation-driven athermal phase transformation from the face-centered cubic (FCC) γ matrix into the hexagonal close-packed (HCP) ε phase, stacking fault formation, mechanical twinning and precipitation hardening. For gaining a better understanding of these mechanisms as well as their interactions direct observation of the deformation process is required. For this purpose, an iHEA with nominal composition of Fe-30Mn-10Co-10Cr-0.5C (at. %) was produced and investigated via in-situ and interrupted in-situ tensile testing in a scanning electron microscope (SEM) combining electron channeling contrast imaging (ECCI) and electron backscatter diffraction (EBSD) techniques. The results reveal that the iHEA is deformed by formation and multiplication of stacking faults along {111} microbands. Sufficient overlap of stacking faults within microbands leads to intrinsic nucleation of HCP ε phase and incoherent annealing twin boundaries act as preferential extrinsic nucleation sites for HCP ε formation. With further straining HCP ε nuclei grow into the adjacent deformed FCC γ matrix. γ regions with smaller grain size have higher mechanical stability against phase transformation. Twinning in FCC γ grains with a size of ∼10 μm can be activated at room temperature at a stress below ∼736 MPa. With increasing deformation, new twin lamellae continuously nucleate. The twin lamellae grow in preferred directions driven by the motion of the mobile partial dislocations. Owing to the individual grain size dependence of the activation of the dislocation-mediated plasticity, of the athermal phase transformation and of mechanical twinning at the different deformation stages, desired strain hardening profiles can be tuned and adjusted over the entire deformation regime by adequate microstructure design, providing excellent combinations of strength and ductility. © 2018 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2018.01.036
  • 2018 • 138 Coupled effect of crystallographic orientation and indenter geometry on nanoindentation of single crystalline copper
    Wang, Z. and Zhang, J. and Hassan, H.U. and Zhang, J. and Yan, Y. and Hartmaier, A. and Sun, T.
    International Journal of Mechanical Sciences 148 531-539 (2018)
    Surface pile-up topography is very significant for property extraction in nanoindentation tests. In the present work, we perform crystal plasticity finite element simulations of Berkovich nanoindentation of single crystalline copper with different crystallographic orientations, which derive quantitatively comparable mechanical properties and surface pile-up topographies with experimental data. Simulation results demonstrate that there is a coupled effect of crystallographic orientation of indented material and indenter geometry on surface pile-up behavior, due to the interaction between intrinsic dislocation slip events and extrinsic discrete stress distribution patterns. Based on the relative spatial orientation between crystallographic orientation of indented material and indenter geometry, a surface pile-up density factor mp is proposed to qualitatively characterize the propensity of surface pile-up behavior in nanoindentation tests of single crystalline copper. © 2018 Elsevier Ltd
    view abstractdoi: 10.1016/j.ijmecsci.2018.09.007
  • 2017 • 137 Dislocation interaction and twinning-induced plasticity in face-centered cubic Fe-Mn-C micro-pillars
    Choi, W.S. and Sandlöbes, S. and Malyar, N.V. and Kirchlechner, C. and Korte-Kerzel, S. and Dehm, G. and De Cooman, B.C. and Raabe, D.
    Acta Materialia 132 162-173 (2017)
    Deformation twinning contributes to a high work-hardening rate through modification of the dislocation structure and a dynamic Hall-Petch effect in polycrystalline steel. Due to the well-defined compression axis and limited deformation volume of micro-pillars, micro-compression testing is a suitable method to investigate the mechanisms of deformation twinning and the interactions of dislocations with twin boundaries. The material investigated is an austenitic Fe-22 wt%Mn-0.6 wt%C twining-induced plasticity steel. Micro-pillars oriented preferentially for deformation twinning and dislocation glide are compressed and the activated deformation systems are characterized. We observe that deformation twinning induces higher flow stresses and a more unstable work-hardening behavior than dislocation glide, while dislocation glide dominated deformation results in a stable work-hardening behavior. The higher flow stresses and unstable work-hardening behavior in micro-pillars oriented for deformation twinning are assumed to be caused by the activation of secondary slip systems and accumulated plastic deformation. © 2017 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2017.04.043
  • 2017 • 136 Thermally activated lightweight actuator based on hot extruded shape memory metal matrix composites (SMA-MMC)
    Dahnke, C. and Shapovalov, A. and Tekkaya, A.E.
    Procedia Engineering 207 1511-1516 (2017)
    Based on modified porthole dies, continuous composite extrusion allows the manufacturing of shape memory alloy metal matrix composites (SMA-MMC). In order to extend the functionality of SMA-MMC, the present work shows a new actuator concept based on integrated NiTi wires within an aluminum matrix. Due to an eccentric positioning of the wires as well as a prestraining, a bending moment is generated within the profile when the temperature is increased to a critical value. Depending on the process parameters, the occurring bending moment is able to cause an elastic or elastic-plastic deformation of the profile or specimen. © 2017 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2017.10.1083
  • 2017 • 135 Identifying Structure–Property Relationships Through DREAM.3D Representative Volume Elements and DAMASK Crystal Plasticity Simulations: An Integrated Computational Materials Engineering Approach
    Diehl, M. and Groeber, M. and Haase, C. and Molodov, D.A. and Roters, F. and Raabe, D.
    JOM 69 848-855 (2017)
    Predicting, understanding, and controlling the mechanical behavior is the most important task when designing structural materials. Modern alloy systems—in which multiple deformation mechanisms, phases, and defects are introduced to overcome the inverse strength–ductility relationship—give raise to multiple possibilities for modifying the deformation behavior, rendering traditional, exclusively experimentally-based alloy development workflows inappropriate. For fast and efficient alloy design, it is therefore desirable to predict the mechanical performance of candidate alloys by simulation studies to replace time- and resource-consuming mechanical tests. Simulation tools suitable for this task need to correctly predict the mechanical behavior in dependence of alloy composition, microstructure, texture, phase fractions, and processing history. Here, an integrated computational materials engineering approach based on the open source software packages DREAM.3D and DAMASK (Düsseldorf Advanced Materials Simulation Kit) that enables such virtual material development is presented. More specific, our approach consists of the following three steps: (1) acquire statistical quantities that describe a microstructure, (2) build a representative volume element based on these quantities employing DREAM.3D, and (3) evaluate the representative volume using a predictive crystal plasticity material model provided by DAMASK. Exemplarily, these steps are here conducted for a high-manganese steel. © 2017, The Author(s).
    view abstractdoi: 10.1007/s11837-017-2303-0
  • 2017 • 134 Crystal plasticity study on stress and strain partitioning in a measured 3D dual phase steel microstructure
    Diehl, M. and An, D. and Shanthraj, P. and Zaefferer, S. and Roters, F. and Raabe, D.
    Physical Mesomechanics 20 311-323 (2017)
    Dual phase steels are advanced high strength alloys typically used for structural parts and reinforcements in car bodies. Their good combination of strength and ductility and their lean composition render them an economically competitive option for realizing multiple lightweight design options in automotive engineering. The mechanical response of dual phase steels is the result of the strain and stress partitioning among the ferritic and martensitic phases and the individual crystallographic grains and subgrains of these phases. Therefore, understanding how these microstructural features influence the global and local mechanical properties is of utmost importance for the design of improved dual phase steel grades. While multiple corresponding simulation studies have been dedicated to the investigation of dual phase steel micromechanics, numerical tools and experiment techniques for characterizing and simulating real 3D microstructures of such complex materials have been emerged only recently. Here we present a crystal plasticity simulation study based on a 3D dual phase microstructure which is obtained by EBdD tomography, also referred to as 3D EBdD (EBdD—electron backscatter diffraction). In the present case we utilized a 3D EBdD serial sectioning approach based on mechanical polishing. Moreover, sections of the 3D microstructure are used as 2D models to study the effect of this simplification on the stress and strain distribution. The simulations are conducted using a phenomenological crystal plasticity model and a spectral method approach implemented in the Düsseldorf Advanced Material Simulation Kit (DAMAdK). © 2017, Pleiades Publishing, Ltd.
    view abstractdoi: 10.1134/S1029959917030079
  • 2017 • 133 Effect of workpiece deformation on Joule heat losses in electromagnetic forming coils
    Gies, S. and Tekkaya, A.E.
    Procedia Engineering 207 341-346 (2017)
    Coils in electromagnetic forming operations are exposed to mechanical as well as thermal loads. Especially in case of high volume production the thermal loading due to Joule heating needs to be considered in the coil and process design to prevent thermal overstressing. An analytical approach for the calculation of Joule heat losses in electromagnetic forming coils considering the changing gap width between coil and workpiece is presented. An electromagnetic sheet metal forming application using a straight one-turn coil is used as reference case to prove the accuracy of the model. A comparison of the analytical calculation and the numerical results based on a simulation with a coupling of structural, thermal, and electromagnetic effects is provided. It is proved that the coil heating in case of a deforming workpiece ranges between the heating without workpiece and the heating with rigid workpiece. It is shown that with increasing workpiece velocities the heat losses in the coil tend more and more towards the lower bound represented by a coil without workpiece.
    view abstractdoi: 10.1016/j.proeng.2017.10.785
  • 2017 • 132 Failure assessment in sheet metal forming using a phenomenological damage model and fracture criterion: Experiments, parameter identification and validation
    Heibel, S. and Nester, W. and Clausmeyer, T. and Tekkaya, A.E.
    Procedia Engineering 207 2066-2071 (2017)
    In this contribution microstructural and macroscopic experimental findings are used to calibrate the phenomenological damage model GISSMO (Generalized Incremental Stress State dependent Model) and the fracture criterion FFL/SFFL (Fracture Forming Limit line/ Shear Fracture Forming Limit line) to assess failure in sheet metal forming simulation. It is shown that macroscopic failure in a commercial dual-phase steel is initiated through a combination of ductile damage mechanisms and local shear banding at a characteristic, stress-state dependent optical or tactile measureable fracture strain. The parameter identification for both models is based on ductile fracture experiments representing characteristic stress states. GISSMO is calibrated inversely using experimental stress-strain curves, optical measured fracture strains and simulation data. The FFL and SFFL are constructed in a direct manner with the optically and tactilely measured fracture strains. Both models are validated comparatively on a cross-die cup showing ductile fracture with slight necking. The use of the fracture criterion in combination with a direct method of determining the fracture lines based on tactile strain measurements leads to an overestimation of the instant of fracture initiation. With the inversely identified parameters of the phenomenological damage model the onset of fracture initiation can be accurately predicted. © 2017 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2017.10.1065
  • 2017 • 131 Constitutive modeling of strain induced grain boundary migration via coupling crystal plasticity and phase-field methods
    Jafari, M. and Jamshidian, M. and Ziaei-Rad, S. and Raabe, D. and Roters, F.
    International Journal of Plasticity 99 19-42 (2017)
    We have developed a thermodynamically-consistent finite-deformation-based constitutive theory to describe strain induced grain boundary migration due to the heterogeneity of stored deformation energy in a plastically deformed polycrystalline cubic metal. Considering a representative volume element, a mesoscale continuum theory is developed based on the coupling between dislocation density-based crystal plasticity and phase field methods. Using the Taylor model-based homogenization method, a multiscale coupled finite-element and phase-field staggered time integration procedure is developed and implemented into the Abaqus/Standard finite element package via a user-defined material subroutine. The developed constitutive model is then used to perform numerical simulations of strain induced grain boundary migration in polycrystalline tantalum. The simulation results are shown to qualitatively and quantitatively agree with experimental results. © 2017 Elsevier Ltd.
    view abstractdoi: 10.1016/j.ijplas.2017.08.004
  • 2017 • 130 Reasons for the superior mechanical properties of medium-entropy CrCoNi compared to high-entropy CrMnFeCoNi
    Laplanche, G. and Kostka, A. and Reinhart, C. and Hunfeld, J. and Eggeler, G. and George, E.P.
    Acta Materialia 128 292-303 (2017)
    The tensile properties of CrCoNi, a medium-entropy alloy, have been shown to be significantly better than those of CrMnFeCoNi, a high-entropy alloy. To understand the deformation mechanisms responsible for its superiority, tensile tests were performed on CrCoNi at liquid nitrogen temperature (77 K) and room temperature (293 K) and interrupted at different strains. Microstructural analyses by transmission electron microscopy showed that, during the early stage of plasticity, deformation occurs by the glide of 1/2&lt;110&gt; dislocations dissociated into 1/6&lt;112&gt; Shockley partials on {111} planes, similar to the behavior of CrMnFeCoNi. Measurements of the partial separations yielded a stacking fault energy of 22 ± 4 mJ m−2, which is ∼25% lower than that of CrMnFeCoNi. With increasing strain, nanotwinning appears as an additional deformation mechanism in CrCoNi. The critical resolved shear stress for twinning in CrCoNi with 16 μm grain size is 260 ± 30 MPa, roughly independent of temperature, and comparable to that of CrMnFeCoNi having similar grain size. However, the yield strength and work hardening rate of CrCoNi are higher than those of CrMnFeCoNi. Consequently, the twinning stress is reached earlier (at lower strains) in CrCoNi. This in turn results in an extended strain range where nanotwinning can provide high, steady work hardening, leading to the superior mechanical properties (ultimate strength, ductility, and toughness) of medium-entropy CrCoNi compared to high-entropy CrMnFeCoNi. © 2017 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2017.02.036
  • 2017 • 129 Ab initio assisted design of quinary dual-phase high-entropy alloys with transformation-induced plasticity
    Li, Z. and Körmann, F. and Grabowski, B. and Neugebauer, J. and Raabe, D.
    Acta Materialia 136 262-270 (2017)
    We introduce a new class of high-entropy alloys (HEAs), i.e., quinary (five-component) dual-phase (DP) HEAs revealing transformation-induced plasticity (TRIP), designed by using a quantum mechanically based and experimentally validated approach. Ab initio simulations of thermodynamic phase stabilities of Co20Cr20Fe40-xMn20Nix (x = 0–20 at. %) HEAs were performed to screen for promising compositions showing the TRIP-DP effect. The theoretical predictions reveal several promising alloys, which have been cast and systematically characterized with respect to their room temperature phase constituents, microstructures, element distributions and compositional homogeneity, tensile properties and deformation mechanisms. The study demonstrates the strength of ab initio calculations to predict the behavior of multi-component HEAs on the macroscopic scale from the atomistic level. As a prototype example a non-equiatomic Co20Cr20Fe34Mn20Ni6 HEA, selected based on our ab initio simulations, reveals the TRIP-DP effect and hence exhibits higher tensile strength and strain-hardening ability compared to the corresponding equiatomic CoCrFeMnNi alloy. © 2017 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2017.07.023
  • 2017 • 128 Influence of compositional inhomogeneity on mechanical behavior of an interstitial dual-phase high-entropy alloy
    Li, Z. and Raabe, D.
    Materials Chemistry and Physics (2017)
    In this study we present and discuss the influence of compositional inhomogeneity on the mechanical behavior of an interstitially alloyed dual-phase non-equiatomic high-entropy alloy (Fe49.5Mn30Co10Cr10C0.5). Various processing routes including hot-rolling, homogenization, cold-rolling and recrystallization annealing were performed on the cast alloys to obtain samples in different compositional homogeneity states. Grain sizes of the alloys were also considered. Tensile testing and microstructural investigations reveal that the deformation behavior of the interstitial dual-phase high-entropy alloy samples varied significantly depending on the compositional homogeneity of the specimens probed. In the case of coarse-grains (∼300 μm) obtained for cast alloys without homogenization treatment, ductility and strain-hardening of the material was significantly reduced due to its compositional inhomogeneity. This detrimental effect was attributed to preferred deformation-driven phase transformation occurring in the Fe enriched regions with lower stacking fault energy, promoting early stress-strain localization. The grain-refined alloy (∼4 μm) with compositional heterogeneity which was obtained for recrystallization annealed alloys without homogenization treatment was characterized by almost total loss in work-hardening. This effect was attributed to large local shear strains due to the inhomogeneous planar slip. These insights demonstrate the essential role of compositional homogeneity through applying corresponding processing steps for the development of advanced high-entropy alloys. © 2017 Elsevier B.V.
    view abstractdoi: 10.1016/j.matchemphys.2017.04.050
  • 2017 • 127 Dislocation activities at the martensite phase transformation interface in metastable austenitic stainless steel: An in-situ TEM study
    Liu, J. and Chen, C. and Feng, Q. and Fang, X. and Wang, H. and Liu, F. and Lu, J. and Raabe, D.
    Materials Science and Engineering A 703 236-243 (2017)
    Understanding the mechanism of martensitic transformation is of great importance in developing advanced high strength steels, especially TRansformation-Induced Plasticity (TRIP) steels. The TRIP effect leads to enhanced work-hardening rate, postponed onset of necking and excellent formability. In-situ transmission electron microscopy has been performed to systematically investigate the dynamic interactions between dislocations and α′ martensite at microscale. Local stress concentrations, e.g. from notches or dislocation pile-ups, render free edges and grain boundaries favorable nucleation sites for α′ martensite. Its growth leads to partial dislocation emission on two independent slip planes from the hetero-interface when the austenite matrix is initially free of dislocations. The kinematic analysis reveals that activating slip systems on two independent {111} planes of austenite are necessary in accommodating the interfacial mismatch strain. Full dislocation emission is generally observed inside of austenite regions that contain high density of dislocations. In both situations, phase boundary propagation generates large amounts of dislocations entering into the matrix, which renders the total deformation compatible and provide substantial strain hardening of the host phase. These moving dislocation sources enable plastic relaxation and prevent local damage accumulation by intense slipping on the softer side of the interfacial region. Thus, finely dispersed martensite distribution renders plastic deformation more uniform throughout the austenitic matrix, which explains the exceptional combination of strength and ductility of TRIP steels. © 2017 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2017.06.107
  • 2017 • 126 A polytree-based adaptive approach to limit analysis of cracked structures
    Nguyen-Xuan, H. and Nguyen-Hoang, S. and Rabczuk, T. and Hackl, K.
    Computer Methods in Applied Mechanics and Engineering 313 1006-1039 (2017)
    We in this paper present a novel adaptive finite element scheme for limit analysis of cracked structures. The key idea is to develop a general refinement algorithm based on a so-called polytree mesh structure. The method is well suited for arbitrary polygonal elements and furthermore traditional triangular and quadrilateral ones, which are considered as special cases. Also, polytree meshes are conforming and can be regarded as a generalization of quadtree meshes. For the aim of this paper, we restrict our main interest in plane-strain limit analysis to von Mises-type materials, yet its extension to a wide class of other solid mechanics problems and materials is completely possible. To avoid volumetric locking, we propose an approximate velocity field enriched with bubble functions using Wachspress coordinates on a primal-mesh and design carefully strain rates on a dual-mesh level. An adaptive mesh refinement process is guided by an L2-norm-based indicator of strain rates. Through numerical validations, we show that the present method reaches high accuracy with low computational cost. This allows us to perform large-scale limit analysis problems favorably. © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2016.09.016
  • 2017 • 125 A Prange–Hellinger–Reissner type finite element formulation for small strain elasto-plasticity
    Schröder, J. and Igelbüscher, M. and Schwarz, A. and Starke, G.
    Computer Methods in Applied Mechanics and Engineering 317 400-418 (2017)
    In this contribution we propose a mixed variational formulation of the Prange–Hellinger–Reissner type for elasto-plasticity at small strains. Here, the displacements and the stresses are interpolated independently, which are balanced within the variational functional by the relation of the elastic strains and the partial derivative of the complementary stored energy with respect to the stresses. For the elasto-plastic material behavior a von Mises yield criterion is considered, where we restrict ourselves w.l.o.g. to linear isotropic hardening. In the proposed formulation we enforce the constraints arising from plasticity point-wise in contrast to the element-wise realization of the plastic return mapping algorithm suggested in Simo et al. (1989). The performance of the new formulation is demonstrated by the analysis of several benchmark problems. Here, we compare the point-wise treatment of elasto-plasticity with the original element-wise formulation of Simo et al. (1989). Furthermore, we derive an algorithmic consistent treatment for plane stress as well as for plane strain condition. © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2016.12.005
  • 2017 • 124 The reciprocal effects of bending and torsion on springback during 3D bending of profiles
    Staupendahl, D. and Tekkaya, A.E.
    Procedia Engineering 207 2322-2327 (2017)
    Profiles with circular cross-sections can be geometrically described by the shape of the bending line. To achieve 3D bending lines with kinematic bending processes, a continuous change of the bending plane is needed, resulting in bending force vectors that change in direction accordingly. These force vectors generate a bending moment in the forming zone and, thus, longitudinal tensile and compressive stresses. For profiles with non-circular cross-sections, the orientation of the cross-section along the bending line needs to be additionally controlled. This can be achieved by applying a specific torque to the bending process and, thus, introducing desired shear stresses into the forming zone. Up until now, this fundamental aspect of 3D profile bending has not been regarded in a coherent fashion. To take into account the reciprocal effects of the stresses applied to the forming zone and their effect on the bending moment and, thus, on springback, a comprehensive analytical process model was set up. The model is validated by experimental investigations performed using the TSS profile bending machine and comprehensive numerical investigations. Analyses were performed during plane bending as well as bending superposed with torsion. The investigations show that the applied bending force and torque not only result in stress superposition but actually also affect the development of shear strains over the cross-section of the profile. Similar to the longitudinal strains, the shear strains decrease linearly from the intrados and extrados of the profile to the neutral axis. Considering this newly observed behavior in the analytical process model, the bending moment prediction is in accordance with the experimental and numerical results. © 2017 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2017.10.1002
  • 2017 • 123 Stress state dependency of unloading behavior in high strength steels
    Sumikawa, S. and Ishiwatari, A. and Hiramoto, J. and Yoshida, F. and Clausmeyer, T. and Tekkaya, A.E.
    Procedia Engineering 207 179-184 (2017)
    Accuracy of springback prediction strongly depends on whether the unloading behavior of the material is properly considered in the material model or not. It is known that the stress-strain relationship for steel sheet during unloading is nonlinear. For accurate springback prediction, the nonlinear unloading behaviors should be observed not only under uniaxial, but also under multi-axial stress state, and properly considered in FEsimulations. In this study, unloading stress-strain curves of high strength steels under four stress states: uniaxial tension, plane strain tension, biaxial tension and shear, were experimentally obtained in several material tests. From the obtained curves with different prestrains, the average elastic moduli were calculated and converted into the equivalent modulus using the isotropic Hooke's law. Moreover, the nonlinearity of the unloading stress-strain curve was evaluated by the instantaneous stress-strain slope. The average elastic modulus and the nonlinearity obviously differ by stress states, prestrains and types of steel. The investigated steels show the stress state dependency of the unloading behavior. © 2017 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2017.10.758
  • 2017 • 122 Hydrogen-assisted failure in Ni-based superalloy 718 studied under in situ hydrogen charging: The role of localized deformation in crack propagation
    Tarzimoghadam, Z. and Ponge, D. and Klöwer, J. and Raabe, D.
    Acta Materialia 128 365-374 (2017)
    We investigated hydrogen embrittlement in Ni-based superalloy 718 by tensile testing at slow strain rate (10−4 s−1) under continuous electrochemical hydrogen charging. Hydrogen-assisted cracking mechanisms were studied via electron backscatter diffraction (EBSD) analysis and electron channeling contrast imaging (ECCI). In order to elucidate the effects of stress or strain in the cracking mechanisms, material conditions with different strength levels were investigated, including samples in solution annealed (as water quenched) and 780 °C age-hardened states. The microstructure observations in the vicinity of the cracks enabled us to establish correlations between the microstructure, crack initiation sites, and crack propagation pathways. Fracture in the hydrogen-charged samples was dominated by localized plastic deformation. Strain-controlled transgranular cracking was caused by shear localization due to hydrogen-enhanced localized plasticity (HELP) and void nucleation and coalescence along {111} slip planes in both, the solution annealed and age-hardened materials. Stress-assisted intergranular cracking in the presence of hydrogen was only observed in the high strength age-hardened material, due to slip localization at grain boundaries, grain boundary triple junction cracking, and δ/γ-matrix interface cracking. To investigate the effect of δ-phase in crack propagation along grain boundaries, the over-aged state (aged at 870 °C) with different precipitation conditions for the δ-phase was also investigated. Observations confirmed that presence of δ-phase promotes hydrogen-induced intergranular failure by initializing micro-cracks from δ/γ interfaces. © 2017 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2017.02.059
  • 2017 • 121 Material characterization for plane and curved sheets using the in-plane torsion test-an overview
    Traphöner, H. and Clausmeyer, T. and Tekkaya, A.E.
    Procedia Engineering 207 1934-1939 (2017)
    The in-plane torsion test offers a broad range of applications for the characterization of mechanical properties of sheet metal materials and components. True plastic strains up to 1.0 can be achieved. Such data can be used for the numerical analysis without extrapolation of the flow curve. The stress and strain state correspond to ideal simple shear during the entire process. The application range of the plane torsion test has been constantly expanded by different approaches and a more sophisticated evaluation has been developed. The full-field analysis of the test area makes it possible to determine an almost arbitrary number of cyclic flow curves with only one single specimen. By using a grooved specimen, the ideal simple shear state can be obtained until fracture of the material without inhomogeneities. New investigations show that the in-plane torsion test is also suitable for the determination of flow curves for curved surfaces. Investigations on curved rotationally symmetrical as well as a tubular shape were performed. Finally, first results for the local determination of the strength' arbitrary locations of a component are presented. © 2017 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2017.10.964
  • 2017 • 120 On the competition between the stress-induced formation of martensite and dislocation plasticity during crack propagation in pseudoelastic NiTi shape memory alloys
    Ungár, T. and Frenzel, J. and Gollerthan, S. and Ribárik, G. and Balogh, L. and Eggeler, G.
    Journal of Materials Research 1-10 (2017)
    The present work addresses the competition between dislocation plasticity and stress-induced martensitic transformations in crack affected regions of a pseudoelastic NiTi miniature compact tension specimen. For this purpose X-ray line profile analysis was performed after fracture to identify dislocation densities and remnant martensite volume fractions in regions along the crack path. Special emphasis was placed on characterizing sub fracture surface zones to obtain depth profiles. The stress affected zone in front of the crack-tip is interpreted in terms of a true plastic zone associated with dislocation plasticity and a pseudoelastic zone where stress-induced martensite can form. On unloading, most of the stress-induced martensite transforms back to austenite but a fraction of it is stabilized by dislocations in both, the irreversible martensite and the surrounding austenite phase. The largest volume fraction of the irreversible or remnant martensite along with the highest density of dislocations in this phase was found close to the primary crack-tip. With increasing distance from the primary crack-tip both, the dislocation density and the volume fraction of irreversible martensite decrease to lower values. Copyright © Materials Research Society 2017
    view abstractdoi: 10.1557/jmr.2017.267
  • 2017 • 119 Micromechanical modeling approach to derive the yield surface for BCC and FCC steels using statistically informed microstructure models and nonlocal crystal plasticity
    Vajragupta, N. and Ahmed, S. and Boeff, M. and Ma, A. and Hartmaier, A.
    Physical Mesomechanics 20 343-352 (2017)
    In order to describe irreversible deformation during metal forming processes, the yield surface is one of the most important criteria. Because of their simplicity and efficiency, analytical yield functions along with experimental guidelines for parameterization become increasingly important for engineering applications. However, the relationship between most of these models and microstructural features are still limited. Hence, we propose to use micromechanical modeling, which considers important microstructural features, as a part of the solution to this missing link. This study aims at the development of a micromechanical modeling strategy to calibrate material parameters for the advanced analytical initial yield function Barlat YLD 2004-18p. To accomplish this, the representative volume element is firstly created based on a method making use of the statistical description of microstructure morphology as input parameter. Such method couples particle simulations to radical Voronoi tessellations to generate realistic virtual microstructures as representative volume elements. Afterwards, a nonlocal crystal plasticity model is applied to describe the plastic deformation of the representative volume element by crystal plasticity finite element simulation. Subsequently, an algorithm to construct the yield surface based on the crystal plasticity finite element simulation is developed. The primary objectives of this proposed algorithm are to automatically capture and extract the yield loci under various loading conditions. Finally, a nonlinear least square optimization is applied to determine the material parameters of Barlat YLD 2004-18p initial yield function of representative volume element, mimicking generic properties of bcc and fcc steels from the numerical simulations. © 2017, Pleiades Publishing, Ltd.
    view abstractdoi: 10.1134/S1029959917030109
  • 2017 • 118 Towards prediction of springback in deep drawing using a micromechanical modeling scheme
    Vajragupta, N. and Ul Hassan, H. and Hartmaier, A.
    Procedia Engineering 207 60-65 (2017)
    Deep drawing is one of the most commonly used sheet metal forming processes, which can produce metal parts at a high rate. One of the major problems in deep drawing is springback, which is mainly elastic deformation occurring when the tool is removed. The focus of this work is the prediction of springback in deep drawing for DC04 steel using a micromechanical modeling scheme. A novel method is used for the characterization of material that leads to cyclic stress-strain curve. Simulations are performed with the Yoshida Uemori (YU) model for the prediction of springback for a U draw-bend geometry. The maximum deviation between the geometries of experiment and the springback simulation for hat geometry is 2.2 mm. It is shown that this micromechanical modeling scheme allows us to relate the influence of the microstructure to the springback prediction. © 2017 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2017.10.739
  • 2017 • 117 Prediction of plasticity and damage initiation behaviour of C45E + N steel by micromechanical modelling
    Wu, B. and Vajragupta, N. and Lian, J. and Hangen, U. and Wechsuwanmanee, P. and Münstermann, S.
    Materials and Design 121 154-166 (2017)
    For large-scale engineering applications, macroscopic phenomenological damage mechanics models with less complexity are usually applied due to their high computational efficiency and simple implementation procedures in finite element simulations. Compared with micromechanical models, however, they also have a significant disadvantage, namely the lack of microstructure sensitivity. This work aims to develop a method to integrate the influence of microstructural features into the parameter calibration of a stress-state-dependent damage mechanics model (the modified Bai-Wierzbicki model) for a C45E + N steel. For this purpose, virtual experiments are performed on an artificial microstructure model to derive the plasticity and damage initiation behaviour for the investigated material. A crystal plasticity model for ferrite along with an empirical strain hardening law for pearlite are assigned to the corresponding constituents in the artificial microstructure model to define their material properties. Nanoindentation tests and numerical analysis are used to calibrate the parameters of the crystal plasticity model. By applying different boundary conditions to the artificial microstructure model, both the plasticity and the damage initiation behaviour under different stress states are calibrated by the virtual experiments. In addition, this approach is also applied to investigating the influence of microstructure on plasticity and damage initiation. © 2017 Elsevier Ltd
    view abstractdoi: 10.1016/j.matdes.2017.02.032
  • 2017 • 116 Interaction between phase transformations and dislocations at incipient plasticity of monocrystalline silicon under nanoindentation
    Zhang, J. and Zhang, J. and Wang, Z. and Hartmaier, A. and Yan, Y. and Sun, T.
    Computational Materials Science 131 55-61 (2017)
    Structural phase transformation and dislocation slip are two important deformation modes of monocrystalline silicon. In the present work, we elucidate mechanisms of inhomogeneous elastic-plastic transition in spherical nanoindentation of monocrystalline silicon by means of molecular dynamics simulations. The Stillinger-Weber potential is utilized to present simultaneous phase transformations and dislocation activities in the silicon nanoindentation. And a bond angle analysis-based method is proposed to quantitatively clarify silicon phases. The influence of crystallographic orientation on the silicon nanoindentation is further addressed. Our simulation results indicate that prior to the “Pop-In” event, Si(0 1 0) undergoes inelastic deformation accompanied by the phase transformation from the Si-I to the Si-III/Si-XII, which is not occurred in Si(1 1 0) and Si(1 1 1). While the phase transformation from the Si-I to the bct-5 is the dominant mechanism of incipient plasticity for each crystallographic orientation, dislocation nucleation is also an operating deformation mode in the elastic-plastic transition of Si(0 1 0). Furthermore, interactions between phase transformations and dislocations are more pronounced in Si(0 1 0) than the other two crystallographic orientations. © 2017 Elsevier B.V.
    view abstractdoi: 10.1016/j.commatsci.2017.01.043
  • 2016 • 115 One-way and fully-coupled FE2 methods for heterogeneous elasticity and plasticity problems: Parallel scalability and an application to thermo-elastoplasticity of dual-phase steels
    Balzani, D. and Gandhi, A. and Klawonn, A. and Lanser, M. and Rheinbach, O. and Schröder, J.
    Lecture Notes in Computational Science and Engineering 113 91-112 (2016)
    In this paper, aspects of the two-scale simulation of dual-phase steels are considered. First, we present two-scale simulations applying a top-down oneway coupling to a full thermo-elastoplastic model in order to study the emerging temperature field. We find that, for our purposes, the consideration of thermomechanics at the microscale is not necessary. Second, we present highly parallel fully-coupled two-scale FE2 simulations, now neglecting temperature, using up to 458;752 cores of the JUQUEEN supercomputer at Forschungszentrum Jülich. The strong and weak parallel scalability results obtained for heterogeneous nonlinear hyperelasticity exemplify the massively parallel potential of the FE2 multiscale method. © Springer International Publishing Switzerland 2016.
    view abstractdoi: 10.1007/978-3-319-40528-5_5
  • 2016 • 114 Vessel microstructure design: A new approach for site-specific core-shell micromechanical tailoring of TRIP-assisted ultra-high strength steels
    Belde, M. and Springer, H. and Raabe, D.
    Acta Materialia 113 19-31 (2016)
    The mechanical performance of multi-phase steel microstructures critically depends on the constituents' chemical and morphological constitutions, which in combination determine the composite hardness, the onset of plasticity, internal load and strain-partitioning, as well as the stability and transformation kinetics of retained austenite in case of TRIP steels. The novel approach of utilising temporary vessel phases, hence termed vessel microstructure design, enables the tuning of constituent phase properties by linking their formation to a controllable landscape of chemical gradients. This approach hinges on the introduction of alloy carbides as a temporary container, or 'vessel' phase, deliberately producing localised enrichment of alloying elements in a structure predetermined by preliminary heat treatments, referred to as conditioning and accumulation stages. These vessel carbides, which act as reservoirs for specific alloying elements, are then partially dissolved through flash heating, leading to a self-organising landscape of alloying elements in the vicinity of the dissolving particles. The resulting three- or multiple phase microstructures then consist of confined laminates incorporating retained carbides, enveloped by retained austenite shells, embedded within a martensitic matrix. Such complex yet entirely self-organized microstructures offer unique opportunities for strain and load partitioning which we refer to as core-shell micromechanics. Different variants of these core-shell composite structures are produced and examined together with reference microstructures by tensile testing, hardness mappings, impact toughness, X-ray measurements, as well as by electron microscopy. It is found that these novel microstructures, when tempered, exhibit ultra-high strength and delayed necking, enabled by a combination of gradual strain-hardening and transformation-induced plasticity that is tuneable via control of the initial carbide structure. © 2016 Acta Materialia Inc. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2016.04.051
  • 2016 • 113 Semi-smooth Newton methods for mixed FEM discretizations of higher-order for frictional, elasto-plastic two-body contact problems
    Blum, H. and Frohne, H. and Frohne, J. and Rademacher, A.
    Computer Methods in Applied Mechanics and Engineering 309 131-151 (2016)
    In this article a semi-smooth Newton method for frictional two-body contact problems and a solution algorithm for the resulting sequence of linear systems are presented. It is based on a mixed variational formulation of the problem and a discretization by finite elements of higher-order. General friction laws depending on the normal stresses and elasto-plastic material behavior with linear isotropic hardening are considered. Numerical results show the efficiency of the presented algorithm. © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2016.06.004
  • 2016 • 112 The second Sandia Fracture Challenge: predictions of ductile failure under quasi-static and moderate-rate dynamic loading
    Boyce, B.L. and Kramer, S.L.B. and Bosiljevac, T.R. and Corona, E. and Moore, J.A. and Elkhodary, K. and Simha, C.H.M. and Williams, B.W. and Cerrone, A.R. and Nonn, A. and Hochhalter, J.D. and Bomarito, G.F. and Warner, J.E. and ...
    International Journal of Fracture 198 5-100 (2016)
    Ductile failure of structural metals is relevant to a wide range of engineering scenarios. Computational methods are employed to anticipate the critical conditions of failure, yet they sometimes provide inaccurate and misleading predictions. Challenge scenarios, such as the one presented in the current work, provide an opportunity to assess the blind, quantitative predictive ability of simulation methods against a previously unseen failure problem. Rather than evaluate the predictions of a single simulation approach, the Sandia Fracture Challenge relies on numerous volunteer teams with expertise in computational mechanics to apply a broad range of computational methods, numerical algorithms, and constitutive models to the challenge. This exercise is intended to evaluate the state of health of technologies available for failure prediction. In the first Sandia Fracture Challenge, a wide range of issues were raised in ductile failure modeling, including a lack of consistency in failure models, the importance of shear calibration data, and difficulties in quantifying the uncertainty of prediction [see Boyce et al. (Int J Fract 186:5–68, 2014) for details of these observations]. This second Sandia Fracture Challenge investigated the ductile rupture of a Ti–6Al–4V sheet under both quasi-static and modest-rate dynamic loading (failure in (Formula presented.) 0.1 s). Like the previous challenge, the sheet had an unusual arrangement of notches and holes that added geometric complexity and fostered a competition between tensile- and shear-dominated failure modes. The teams were asked to predict the fracture path and quantitative far-field failure metrics such as the peak force and displacement to cause crack initiation. Fourteen teams contributed blind predictions, and the experimental outcomes were quantified in three independent test labs. Additional shortcomings were revealed in this second challenge such as inconsistency in the application of appropriate boundary conditions, need for a thermomechanical treatment of the heat generation in the dynamic loading condition, and further difficulties in model calibration based on limited real-world engineering data. As with the prior challenge, this work not only documents the ‘state-of-the-art’ in computational failure prediction of ductile tearing scenarios, but also provides a detailed dataset for non-blind assessment of alternative methods. © 2016, The Author(s).
    view abstractdoi: 10.1007/s10704-016-0089-7
  • 2016 • 111 A variational formulation for thermomechanically coupled low cycle fatigue at finite strains
    Canadija, M. and Mosler, J.
    International Journal of Solids and Structures 100-101 388-398 (2016)
    In this paper, a constitutive model suitable for the analysis of Low Cycle Thermo-Mechanical Fatigue in metals is elaborated. The model is based on finite strain elastoplasticity coupled to continuum damage theory. It is embedded into a thermodynamical framework allowing to consistently capture the interplay between mechanics and thermal effects. It is shown that the fully coupled constitutive model can be re-written into a variationally consistent manner such that all (state) variables follow jointly and naturally from minimizing an incrementally defined functional. By discretizing this time-continuous functional in time by means of implicit integration schemes a numerically efficient implementation is proposed. In order to predict the temperature increase caused by plastic deformations realistically, the pre-loading history of the considered specimen is accounted for by non-zero initial internal variables. A comparison of the results predicted by the novel constitutive model to those corresponding to experiments (Ultimet alloy) shows that the predictive capabilities of the final model are excellent. © 2016
    view abstractdoi: 10.1016/j.ijsolstr.2016.09.009
  • 2016 • 110 Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations
    Cereceda, D. and Diehl, M. and Roters, F. and Raabe, D. and Perlado, J.M. and Marian, J.
    International Journal of Plasticity 78 242-265 (2016)
    We use a physically-based crystal plasticity model to predict the yield strength of body-centered cubic (bcc) tungsten single crystals subjected to uniaxial loading. Our model captures the thermally-activated character of screw dislocation motion and full non-Schmid effects, both of which are known to play critical roles in bcc plasticity. The model uses atomistic calculations as the sole source of constitutive information, with no parameter fitting of any kind to experimental data. Our results are in excellent agreement with experimental measurements of the yield stress as a function of temperature for a number of loading orientations. The validated methodology is employed to calculate the temperature and strain-rate dependence of the yield strength for 231 crystallographic orientations within the standard stereographic triangle. We extract the strain-rate sensitivity of W crystals at different temperatures, and finish with the calculation of yield surfaces under biaxial loading conditions that can be used to define effective yield criteria for engineering design models. © 2015 Elsevier Ltd.
    view abstractdoi: 10.1016/j.ijplas.2015.09.002
  • 2016 • 109 Optimal control of static elastoplasticity in primal formulation
    De Los Reyes, J.C. and Herzog, R. and Meyer, C.
    SIAM Journal on Control and Optimization 54 3016-3039 (2016)
    An optimal control problem of static plasticity with linear kinematic hardening and von Mises yield condition is studied. The problem is treated in its primal formulation, where the state system is a variational inequality of the second kind. First-order necessary optimality conditions are obtained by means of an approximation by a family of control problems with state system regularized by Huber-type smoothing, and a subsequent limit analysis. The equivalence of the optimality conditions with the C-stationarity system for the equivalent dual formulation of the problem is proved. Numerical experiments are presented, which demonstrate the viability of the Huber-type smoothing approach. © 2016 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/130920861
  • 2016 • 108 Plasticity of the ω-Al7Cu2Fe phase
    Laplanche, G. and Bonneville, J. and Joulain, A. and Gauthier-Brunet, V. and Dubois, S.
    Journal of Alloys and Compounds 665 144-151 (2016)
    Polycrystalline samples with the Al0.693Cu0.201Fe0.106 composition, corresponding to the tetragonal P4/mnc ω-Al7Cu2Fe crystallographic structure, were synthesised by spark plasma sintering and deformed in compression under constant strain-rate conditions, ε = 2 × 10-4 s-1, over the temperature range 650 K-1000 K. A brittle-to-ductile transition is evidenced between 700 K and 750 K. The stress-strain curves exhibit a yield point followed by softening or steady state conditions only. The upper yield stress, σUYS, shows a strong temperature dependence suggesting that the rate controlling deformation mechanisms are highly thermally activated. The strain-rate sensitivity of stress characterised either by stress exponents, nexp, or by activation volumes, Vexp, was measured by the load relaxation technique. High nexp values, i.e., larger than 7, associated with low Vexp, typically smaller than 1 nm3, are measured. The Gibbs free activation energy, ΔG, deduced by integrating Vexp with respect to stress varies from nearly 2 eV at 790 K to 4 eV at 1000 K. Because plasticity of the ω-Al7Cu2Fe phase takes place at temperatures at which diffusion processes are considered as dominant, the results are interpreted in the frame of dislocation climb models proposed to account for high temperature plasticity of crystalline phases. © 2016 Published by Elsevier B.V.
    view abstractdoi: 10.1016/j.jallcom.2015.12.161
  • 2016 • 107 Metastable high-entropy dual-phase alloys overcome the strength-ductility trade-off
    Li, Z. and Pradeep, K.G. and Deng, Y. and Raabe, D. and Tasan, C.C.
    Nature 534 227-230 (2016)
    Metals have been mankind's most essential materials for thousands of years; however, their use is affected by ecological and economical concerns. Alloys with higher strength and ductility could alleviate some of these concerns by reducing weight and improving energy efficiency. However, most metallurgical mechanisms for increasing strength lead to ductility loss, an effect referred to as the strength-ductility trade-off. Here we present a metastability-engineering strategy in which we design nanostructured, bulk high-entropy alloys with multiple compositionally equivalent high-entropy phases. High-entropy alloys were originally proposed to benefit from phase stabilization through entropy maximization. Yet here, motivated by recent work that relaxes the strict restrictions on high-entropy alloy compositions by demonstrating the weakness of this connection, the concept is overturned. We decrease phase stability to achieve two key benefits: interface hardening due to a dual-phase microstructure (resulting from reduced thermal stability of the high-temperature phase); and transformation-induced hardening (resulting from the reduced mechanical stability of the room-temperature phase). This combines the best of two worlds: extensive hardening due to the decreased phase stability known from advanced steels and massive solid-solution strengthening of high-entropy alloys. In our transformation-induced plasticity-assisted, dual-phase high-entropy alloy (TRIP-DP-HEA), these two contributions lead respectively to enhanced trans-grain and inter-grain slip resistance, and hence, increased strength. Moreover, the increased strain hardening capacity that is enabled by dislocation hardening of the stable phase and transformation-induced hardening of the metastable phase produces increased ductility. This combined increase in strength and ductility distinguishes the TRIP-DP-HEA alloy from other recently developed structural materials. This metastability-engineering strategy should thus usefully guide design in the near-infinite compositional space of high-entropy alloys.
    view abstractdoi: 10.1038/nature17981
  • 2016 • 106 Crystal plasticity study of monocrystalline stochastic honeycombs under in-plane compression
    Ma, D. and Eisenlohr, P. and Epler, E. and Volkert, C.A. and Shanthraj, P. and Diehl, M. and Roters, F. and Raabe, D.
    Acta Materialia 103 796-808 (2016)
    We present a study on the plastic deformation of single crystalline stochastic honeycombs under in-plane compression using a crystal plasticity constitutive description for face-centered cubic (fcc) materials, focusing on the very early stage of plastic deformation, and identifying the interplay between the crystallographic orientation and the cellular structure during plastic deformation. We observe that despite the stochastic structure, surprisingly, the slip system activations in the honeycombs are almost identical to their corresponding bulk single crystals at the early stage of the plastic deformation. On the other hand, however, the yield stresses of the honeycombs are nearly independent of their crystallographic orientations. Similar mechanical response is found in compression testing of nanoporous gold micro-pillars aligned with various crystallographic orientations. The macroscopic stress tensors of the honeycombs show the same anisotropy as their respective bulk single crystals. Locally, however, there is an appreciable fluctuation in the local stresses, which are even larger than for polycrystals. This explains why the Taylor/Schmid factor associated with the crystallographic orientation is less useful to estimate the yield stresses of the honeycombs than the bulk single crystals and polycrystals, and why the plastic deformation occurs at smaller strains in the honeycombs than their corresponding bulk single crystals. Besides these findings, the observations of the crystallographic reorientation suggest that conventional orientation analysis tools, such as inverse pole figure and related tools, would in general fail to study the plastic deformation mechanism of monocrystalline cellular materials. © 2015 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2015.11.016
  • 2016 • 105 Loss of ellipticity for non-coaxial plastic deformations in additive logarithmic finite strain plasticity
    Neff, P. and Ghiba, I.-D.
    International Journal of Non-Linear Mechanics 81 122-128 (2016)
    In this paper we consider the additive logarithmic finite strain plasticity formulation from the view point of loss of ellipticity in elastic unloading. We prove that even if an elastic energy FW(F)=W(logU) defined in terms of logarithmic strain logU, where U=FTF, happens to be everywhere rank-one convex as a function of F, the new function FW(F)=W(logU-logUp) need not remain rank-one convex at some given plastic stretch Up (viz. EploglogUp). This is in complete contrast to multiplicative plasticity (and infinitesimal plasticity) in which FW(FFp-1) remains rank-one convex at every plastic distortion Fp if FW(F) is rank-one convex (usymu-εp 2 remains convex). We show this disturbing feature of the additive logarithmic plasticity model with the help of a recently introduced family of exponentiated Hencky energies. © 2016 Elsevier Ltd.
    view abstractdoi: 10.1016/j.ijnonlinmec.2016.01.003
  • 2016 • 104 The exponentiated Hencky-logarithmic strain energy: Part III—coupling with idealized multiplicative isotropic finite strain plasticity
    Neff, P. and Ghiba, I.-D.
    Continuum Mechanics and Thermodynamics 28 477-487 (2016)
    We investigate an immediate application in finite strain multiplicative plasticity of the family of isotropic volumetric–isochoric decoupled strain energies (Formula Presented) based on the Hencky-logarithmic (true, natural) strain tensor log U. Here, μ &gt; 0 is the infinitesimal shear modulus, κ = 2μ+3λ/3 &gt; 0 is the infinitesimal bulk modulus with λ the first Lamé constant, k, k are additional dimensionless material parameters, F = ∇ϕ is the gradient of deformation, U = √FT F is the right stretch tensor, and devn log U = log U –1/ntr(log U) · 1 is the deviatoric part of the strain tensor log U. Based on the multiplicative decomposition Fn = Fe Fp, we couple these energies with some isotropic elasto-plastic flow rules Fpd/dt[Fp −1] ∈ −∂χ (dev3 ∑e) defined in the plastic distortion Fp, where ∂χ is the subdifferential of the indicator function χ of the convex elastic domain εe (∑e, 1/3σy 2) in the mixed-variant ∑e-stress space, ∑e = Fe T DFe Wiso (Fe), and Wiso (Fe) represents the isochoric part of the energy. While WeH may loose ellipticity, we show that loss of ellipticity is effectively prevented by the coupling with plasticity, since the ellipticity domain of WeH on the one hand and the elastic domain in ∑e -stress space on the other hand are closely related. Thus, the new formulation remains elliptic in elastic unloading at any given plastic predeformation. In addition, in this domain, the true stress–true strain relation remains monotone, as observed in experiments. © Springer-Verlag Berlin Heidelberg 2015.
    view abstractdoi: 10.1007/s00161-015-0449-y
  • 2016 • 103 Size and orientation dependent mechanical behavior of body-centered tetragonal Sn at 0.6 of the melting temperature
    Philippi, B. and Kirchlechner, C. and Micha, J.S. and Dehm, G.
    Acta Materialia 115 76-82 (2016)
    Although, tin is one of the most prominent metals in soldering, very little is known about its mechanical behavior. In addition, possible size-effects of tin can become restricting for the ongoing miniaturization of microelectronic devices. Due to the low melting temperature of 505.15 K and the body-centered tetragonal crystal structure, differences in the mechanical behavior compared to face-centered cubic and body-centered cubic metals can be expected. Since Tin is especially interesting because of its multiple different slip systems, post mortem slip step analysis allowed to determine the activated slip systems and thus, to calculate size dependent critical resolved shear stresses. The measured size scaling exponent (-1.07 ± 0.06) is close to model-predictions of -1, irrespective of the activated families of slip systems in different orientations. Furthermore, an exceptional low scatter of the flow stress in various samples and no apparent hardening is found. It is concluded, that the activation of dislocation sources instead of dislocation-dislocation interactions are responsible for the observed behavior. This is in line with complementary μLaue diffraction experiments which indicate an unresolvable low density of geometrical necessary dislocations. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2016.05.055
  • 2016 • 102 Ab initio-guided design of twinning-induced plasticity steels
    Raabe, D. and Roters, F. and Neugebauer, J. and Gutierrez-Urrutia, I. and Hickel, T. and Bleck, W. and Schneider, J.M. and Wittig, J.E. and Mayer, J.
    MRS Bulletin 41 320-325 (2016)
    The twinning-induced plasticity effect enables designing austenitic Fe-Mn-C-based steels with >70% elongation with an ultimate tensile strength >1 GPa. These steels are characterized by high strain hardening due to the formation of twins and complex dislocation substructures that dynamically reduce the dislocation mean free path. Both mechanisms are governed by the stacking-fault energy (SFE) that depends on composition. This connection between composition and substructure renders these steels ideal model materials for theory-based alloy design: Ab initio-guided composition adjustment is used to tune the SFE, and thus, the strain-hardening behavior for promoting the onset of twinning at intermediate deformation levels where the strain-hardening capacity provided by the dislocation substructure is exhausted. We present thermodynamic simulations and their use in constitutive models, as well as electron microscopy and combinatorial methods that enable validation of the strain-hardening mechanisms. Copyright © 2016 Materials Research Society.
    view abstractdoi: 10.1557/mrs.2016.63
  • 2016 • 101 Effect of intercritical deformation on microstructure and mechanical properties of a low-silicon aluminum-added hot-rolled directly quenched and partitioned steel
    Tan, X.-D. and Xu, Y.-B. and Ponge, D. and Yang, X.-L. and Hu, Z.-P. and Peng, F. and Ju, X.-W. and Wu, D. and Raabe, D.
    Materials Science and Engineering A 656 200-215 (2016)
    Here, we applied hot-rolling in conjunction with direct quenching and partitioning (HDQ&P) processes with different rolling schedules to a low-C low-Si Al-added steel. Ferrite was introduced into the steel by intercritical rolling and air cooling after hot-rolling. The effect of intercritcal deformation on the microstructure evolution and mechanical properties was investigated. The promotion of austenite stabilization and the optimization of the TRIP effect due to a moderate degree of intercritical deformation were systematically explored. The results show that the addition of 1.46 wt% of Al can effectively promote ferrite formation. An intercritical deformation above 800 °C can result in a pronounced bimodal grain size distribution of ferrite and some elongated ferrite grains containing sub-grains. The residual strain states of both austenite and ferrite and the occurrence of bainite transformation jointly increase the retained austenite fraction due to its mechanical stabilization and the enhanced carbon partitioning into austenite from its surrounding phases. An intercritical deformation below 800 °C can profoundly increase the ferrite fraction and promote the recrystallization of deformed ferrite. The formation of this large fraction of ferrite enhances the carbon enrichment in the untransformed austenite and retards the bainite transformation during the partitioning process and finally enhances martensite transformation and decreases the retained austenite fraction. The efficient TRIP effect of retained austenite and the possible strain partitioning of bainite jointly improve the work hardening and formability of the steel and lead to the excellent mechanical properties with relatively high tensile strength (905 MPa), low yield ratio (0.60) and high total elongation (25.2%). © 2016 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2016.01.040
  • 2016 • 100 Implementation of incremental variational formulations based on the numerical calculation of derivatives using hyper dual numbers
    Tanaka, M. and Balzani, D. and Schröder, J.
    Computer Methods in Applied Mechanics and Engineering 301 216-241 (2016)
    In this paper, novel implementation schemes for the automatic calculation of internal variables, stresses and consistent tangent moduli for incremental variational formulations (IVFs) describing inelastic material behavior are proposed. IVFs recast inelasticity theory as an equivalent optimization problem where the incremental stress potential within a discrete time interval is minimized in order to obtain the values of internal variables. In the so-called Multilevel Newton-Raphson method for the inelasticity theory, this minimization problem is typically solved by using second derivatives with respect to the internal variables. In addition to that, to calculate the stresses and moduli further second derivatives with respect to deformation tensors are required. Compared with classical formulations such as the return mapping method, the IVFs are relatively new and their implementation is much less documented. Furthermore, higher order derivatives are required in the algorithms demanding increased implementation efforts. Therefore, even though IVFs are mathematically and physically elegant, their application is not standard. Here, novel approaches for the implementation of IVFs using HDNs of second and higher order are presented to arrive at a fully automatic and robust scheme with computer accuracy. The proposed formulations are quite general and can be applied to a broad range of different constitutive models, which means that once the proposed schemes are implemented as a framework, any other dissipative material model can be implemented in a straightforward way by solely modifying the constitutive functions. These include the Helmholtz free energy function, the dissipation potential function and additional side constraints such as e.g. the yield function in the case of plasticity. Its uncomplicated implementation for associative finite strain elasto-plasticity and performance is illustrated by some representative numerical examples. © 2015 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2015.12.010
  • 2016 • 99 Assessment of strain hardening in copper single crystals using in situ SEM microshear experiments
    Wieczorek, N. and Laplanche, G. and Heyer, J.-K. and Parsa, A.B. and Pfetzing-Micklich, J. and Eggeler, G.
    Acta Materialia 113 320-334 (2016)
    The effect of a pre-strain on the plasticity of copper single crystals subjected to in situ microshear deformation in a scanning electron microscope (SEM) is investigated. Pre-strains of 6.5 and 20% are imposed using [1 0 0] tensile testing. During tensile pre-deformation, several slip systems are activated and irregularly spaced slip bands form. A trace analysis revealed the presence of several slip bands on the tensile specimen near the grips while one family of slip bands parallel to the (1 1 1) crystallographic plane were detected in the middle of the tensile specimen. From the middle of the pre-deformed tensile specimens double microshear samples were prepared using focused ion beam (FIB) machining such that the [0 -1 -1] (1 -1 1) slip system could be directly activated. The results show how microshear behavior reacts to different levels of tensile pre-deformation. Sudden deformation events (SDEs) are observed during microshear testing. The critical stress associated with the first SDE is shown to increase with increasing pre-deformation as a result of an increasing number of slip bands introduced during pre-deformation per shear zone. The results allow also to obtain information on the interaction between dislocations activated during microshearing ([0 -1 -1] (1 -1 1)) and those which were introduced during tensile pre-deformation ([1 0 -1] (1 1 1) and [1 -1 0] (1 1 1)). When these slip systems interact glissile junctions and Lomer-Cottrell locks are likely to form. In the light of this analysis, we rationalize the occurrence of sudden deformation events based on piled up dislocation assemblies which overcome Lomer-Cottrell lock barriers. © 2016 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2016.04.055
  • 2016 • 98 A crystal plasticity model for twinning- and transformation-induced plasticity
    Wong, S.L. and Madivala, M. and Prahl, U. and Roters, F. and Raabe, D.
    Acta Materialia 118 140-151 (2016)
    A dislocation density-based crystal plasticity model incorporating both transformation-induced plasticity (TRIP) and twinning-induced plasticity (TWIP) is presented. The approach is a physically-based model which reflects microstructure investigations of ε-martensite, twins and dislocation structures in high manganese steels. Validation of the model was conducted using experimental data for a TRIP/TWIP Fe-22Mn-0.6C steel. The model is able to predict, based on the difference in the stacking fault energies, the activation of TRIP and/or TWIP deformation mechanisms at different temperatures. © 2016 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2016.07.032
  • 2016 • 97 A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations
    Zhang, H. and Diehl, M. and Roters, F. and Raabe, D.
    International Journal of Plasticity 80 111-138 (2016)
    We present a virtual laboratory to investigate the anisotropic yield behavior of polycrystalline materials by using high resolution crystal plasticity simulations. Employing a fast spectral method solver enables us to conduct a large number of full-field virtual experiments with different stress states to accurately identify the yield surface of the probed materials. Based on the simulated yield stress points, the parameters for many commonly used yield functions are acquired simultaneously with a nonlinear least square fitting procedure. Exemplarily, the parameters of four yield functions frequently used in sheet metal forming, namely Yld91, Yld2000-2D, Yld2004-18p, and Yld2004-27p are adjusted to accurately describe the yield behavior of an AA3014 aluminum alloy at two material states, namely with a recrystallization texture and a cold rolling texture. The comparison to experimental results proves that the methodology presented, combining accuracy with efficiency, is a promising micromechanics-based tool for probing the mechanical anisotropy of polycrystalline metals and for identifying the parameters of advanced yield functions. © 2016 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.ijplas.2016.01.002
  • 2015 • 96 Second-order sufficient optimality conditions for optimal control of static elastoplasticity with hardening
    Betz, T. and Meyer, C.
    ESAIM - Control, Optimisation and Calculus of Variations 21 271-300 (2015)
    The paper is concerned with the optimal control of static elastoplasticity with linear kinematic hardening. This leads to an optimal control problem governed by an elliptic variational inequality (VI) of first kind in mixed form. Based on Lp-regularity results for the state equation, it is shown that the control-to-state operator is Bouligand differentiable. This enables to establish second-order sufficient optimality conditions by means of a Taylor expansion of a particularly chosen Lagrange function. © EDP Sciences, SMAI 2014.
    view abstractdoi: 10.1051/cocv/2014024
  • 2015 • 95 Formulation of nonlocal damage models based on spectral methods for application to complex microstructures
    Boeff, M. and Gutknecht, F. and Engels, P.S. and Ma, A. and Hartmaier, A.
    Engineering Fracture Mechanics 147 373-387 (2015)
    The increasing interest in modelling local deformations and damage evolution within materials with complex microstructures leads to an increasing demand for efficient numerical methods. A method designed to study damage evolution within the microstructure should be able to deal with complex geometries and to capture system sizes that are large enough to rectify the assumptions made when naming them representative volume elements (RVEs). We introduce a nonlocal damage model into the framework of a spectral solver and study initiation and evolution of damage on the microstructural scale, where regions susceptible to damage are identified. © 2015.
    view abstractdoi: 10.1016/j.engfracmech.2015.06.030
  • 2015 • 94 Nanotribology in austenite: Plastic plowing and crack formation
    Brinckmann, S. and Dehm, G.
    Wear 338-339 436-440 (2015)
    Especially during the run-in phase of metal friction, plasticity develops in the contact zone. If well controlled, the plasticity will lead to an improved microstructure that exhibits low wear rates during machine operation. We investigate the plasticity due to a single stroke of a micrometer-sized asperity to understand fundamentally tribology induced plasticity and microstructure formation. We find that the local crystal orientation has a significant influence on the development and spread of plasticity. Additionally, the complex three-dimensional stress state results in the formation of non-obvious plastic slip patterns. Finally, we observe crack formation in the scratch track even during the single stroke experiments. © 2015 Elsevier Ltd.
    view abstractdoi: 10.1016/j.wear.2015.05.001
  • 2015 • 93 Linking atomistic, kinetic Monte Carlo and crystal plasticity simulations of single-crystal tungsten strength
    Cereceda, D. and Diehl, M. and Roters, F. and Shanthraj, P. and Raabe, D. and Perlado, J.M. and Marian, J.
    GAMM Mitteilungen 38 213-227 (2015)
    Understanding and improving the mechanical properties of tungsten is a critical task for the materials fusion energy program. The plastic behavior in body-centered cubic (bcc) metals like tungsten is governed primarily by screw dislocations on the atomic scale and by ensembles and interactions of dislocations at larger scales. Modeling this behavior requires the application of methods capable of resolving each relevant scale. At the small scale, atomistic methods are used to study single dislocation properties, while at the coarse-scale, continuum models are used to cover the interactions between dislocations. In this work we present a multiscale model that comprises atomistic, kinetic Monte Carlo (kMC) and continuum-level crystal plasticity (CP) calculations. The function relating dislocation velocity to applied stress and temperature is obtained from the kMC model and it is used as the main source of constitutive information into a dislocation-based CP framework. The complete model is used to perform material point simulations of single-crystal tungsten strength. We explore the entire crystallographic orientation space of the standard triangle. Non-Schmid effects are inlcuded in the model by considering the twinning-antitwinning (T/AT) asymmetry in the kMC calculations. We consider the importance of ?111?{110} and 111 {112} slip systems in the homologous temperature range from 0.08T<inf>m</inf> to 0.33T<inf>m</inf>, where T<inf>m</inf> =3680 K is the melting point in tungsten. © 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/gamm.201510012
  • 2015 • 92 Size and orientation effects in partial dislocation-mediated deformation of twinning-induced plasticity steel micro-pillars
    Choi, W.S. and De Cooman, B.C. and Sandlöbes, S. and Raabe, D.
    Acta Materialia 98 391-404 (2015)
    Abstract Bulk and micro-pillar single crystals were used to investigate the twinning-induced plasticity mechanism in austenitic Fe-22 wt%Mn-0.6 wt%C TWIP steel. Compression of micro-pillars oriented either for deformation-induced twinning or for perfect dislocation glide was carried out for pillars with diameters in the range of 600 nm to 4 μm. The same size dependence of the critical resolved shear stress was observed for both orientations. The critical micro-pillar diameter for size-independent plasticity was approximately 7.6 μm. Partial dislocation-mediated formation of twins and ε-martensite was observed in micro-pillars oriented for twinning by transmission electron microscopy. The elastic-plastic transition in micro-pillars oriented for deformation twinning did not involve twinning, and dislocation-dislocation interactions were a necessary precondition for twin formation. © 2015 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2015.06.065
  • 2015 • 91 Design of a twinning-induced plasticity high entropy alloy
    Deng, Y. and Tasan, C.C. and Pradeep, K.G. and Springer, H. and Kostka, A. and Raabe, D.
    Acta Materialia 94 124-133 (2015)
    We introduce a liquid metallurgy synthesized, non-equiatomic Fe<inf>40</inf>Mn<inf>40</inf>Co<inf>10</inf>Cr<inf>10</inf> high entropy alloy that is designed to undergo mechanically-induced twinning upon deformation at room temperature. Microstructure characterization, carried out using SEM, TEM and APT shows a homogeneous fcc structured single phase solid solution in the as-cast, hot-rolled and homogenized states. Investigations of the deformation substructures at specific strain levels with electron channeling contrast imaging (ECCI) combined with EBSD reveal a clear change in the deformation mechanisms of the designed alloy starting from dislocation slip to twinning as a function of strain. Such twinning induced plasticity has only been observed under cryogenic conditions in the equiatomic FeMnNiCoCr high entropy alloy. Thus, despite the decreased contribution of solid solution strengthening, the tensile properties of the introduced lean alloy at room temperature are found to be comparable to that of the well-studied five component FeMnNiCoCr system. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2015.04.014
  • 2015 • 90 The relaxed linear micromorphic continuum: Existence, uniqueness and continuous dependence in dynamics
    Ghiba, I.-D. and Neff, P. and Madeo, A. and Placidi, L. and Rosi, G.
    Mathematics and Mechanics of Solids 20 1171-1197 (2015)
    We study well-posedness for the relaxed linear elastic micromorphic continuum model with symmetric Cauchy force-stresses and curvature contribution depending only on the micro-dislocation tensor. In contrast to classical micromorphic models our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. Another interesting feature concerns the prescription of boundary values for the micro-distortion field: only tangential traces may be determined which are weaker than the usual strong anchoring boundary condition. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch, and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. © The Author(s) 2014.
    view abstractdoi: 10.1177/1081286513516972
  • 2015 • 89 Investigating the influence of crystal orientation on bending size effect of single crystal beams
    Gupta, S. and Ma, A. and Hartmaier, A.
    Computational Materials Science 101 201-210 (2015)
    Influence of crystal orientation on bending size effect has been numerically investigated for single crystal beams. This work is inspired by the experimental observations of Hayashi et al. (2011), where they observed a significant difference in bending size effect for two different crystal orientations. We have used a higher order non-local crystal plasticity model which can account for different hardening contributions by SSDs (statistically stored dislocations) and GNDs (geometrically necessary dislocations) simultaneously. It was found that strain hardening together with an additional kinematic hardening caused by accumulation of GNDs and the number of activated slip systems can be seen as the origin of the orientation dependence of bending size effect. We have also observed a pronounced orientation dependence of spring back size effect, which can be explained on the basis of number of the activated slip systems and equivalent plastic strain. Simulation results showing enhanced or diminished bending size effect for different crystal orientations reveal the importance of crystal orientation for precise micro-bending operations. © 2015 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.commatsci.2014.12.038
  • 2015 • 88 ICME for Crashworthiness of TWIP Steels: From Ab Initio to the Crash Performance
    Güvenç, O. and Roters, F. and Hickel, T. and Bambach, M.
    JOM 67 120-128 (2015)
    During the last decade, integrated computational materials engineering (ICME) emerged as a field which aims to promote synergetic usage of formerly isolated simulation models, data and knowledge in materials science and engineering, in order to solve complex engineering problems. In our work, we applied the ICME approach to a crash box, a common automobile component crucial to passenger safety. A newly developed high manganese steel was selected as the material of the component and its crashworthiness was assessed by simulated and real drop tower tests. The crashworthiness of twinning-induced plasticity (TWIP) steel is intrinsically related to the strain hardening behavior caused by the combination of dislocation glide and deformation twinning. The relative contributions of those to the overall hardening behavior depend on the stacking fault energy (SFE) of the selected material. Both the deformation twinning mechanism and the stacking fault energy are individually well-researched topics, but especially for high-manganese steels, the determination of the stacking-fault energy and the occurrence of deformation twinning as a function of the SFE are crucial to understand the strain hardening behavior. We applied ab initio methods to calculate the stacking fault energy of the selected steel composition as an input to a recently developed strain hardening model which models deformation twinning based on the SFE-dependent dislocation mechanisms. This physically based material model is then applied to simulate a drop tower test in order to calculate the energy absorption capacity of the designed component. The results are in good agreement with experiments. The model chain links the crash performance to the SFE and hence to the chemical composition, which paves the way for computational materials design for crashworthiness. © 2014, The Minerals, Metals & Materials Society.
    view abstractdoi: 10.1007/s11837-014-1192-8
  • 2015 • 87 Correlations between microstructure and room temperature tensile behavior of a duplex TNB alloy for systematically heat treated samples
    Kabir, M.R. and Bartsch, M. and Chernova, L. and Kelm, K. and Wischek, J.
    Materials Science and Engineering A 635 13-22 (2015)
    The mechanical properties of TiAl alloys are very sensitive to the inherent microstructure. For an in-depth understanding of microstructural influences on mechanical properties a duplex type TNB (Nb-containing TiAl) alloy has been investigated. For varying the microstructure of this alloy controlled heat treatments (HT) have been performed with eight distinct maximum temperatures, ranging from 1230. °C to 1300. °C with a 10. °C temperature increment. The series of annealing processes resulted in duplex microstructures with a gradual change of the ratio of globular grains and lamellar colonies, keeping the global chemical composition unchanged. Microstructure of each sample was characterized using SEM and TEM before and after mechanical testing to correlate the morphology and microstructure features to the tensile properties. Quantitative data analysis from these results revealed how the evolution of duplex microstructures influences the room temperature tensile properties: i.e. the elastic stiffness, room temperature ductility, work hardening, fracture stress, and fracture strain. The results are discussed with respect to deformation mechanisms as understood from the tensile test results and fracture surface investigations. From the observed correlations between microstructure and properties an optimized constellation of globular and lamellar microstructure for relevant properties can be predicted. Furthermore, the required heat-treatment window for properties targeted can be defined. © 2015 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2015.03.041
  • 2015 • 86 Spatially and kinetically resolved mapping of hydrogen in a twinning-induced plasticity steel by use of Scanning Kelvin Probe Force Microscopy
    Koyama, M. and Bashir, A. and Rohwerder, M. and Merzlikin, S.V. and Akiyama, E. and Tsuzaki, K. and Raabe, D.
    Journal of the Electrochemical Society 162 C638-C647 (2015)
    The hydrogen distribution in a hydrogen-charged Fe-18Mn-1.2C (wt%) twinning-induced plasticity austenitic steel was studied by Scanning Kelvin Probe Force Microscopy (SKPFM). We observed that 1-2 days after the hydrogen-charging, hydrogen showed a higher activity at twin boundaries than inside the matrix. This result indicates that hydrogen at the twin boundaries is diffusible at room temperature, although the twin boundaries act as deeper trap sites compared to typical diffusible hydrogen trap sites such as dislocations. After about 2 weeks the hydrogen activity in the twin boundaries dropped and was indistinguishable from that in the matrix. These SKPFM results were supported by thermal desorption spectrometry and scanning electron microscopic observations of deformation-induced surface cracking parallel to deformation twin boundaries. With this joint approach, two main challenges in the field of hydrogen embrittlement research can be overcome, namely, the detection of hydrogen with high local and chemical sensitivity and the microstructure-dependent and spatially resolved observation of the kinetics of hydrogen desorption. © 2015 The Electrochemical Society.
    view abstractdoi: 10.1149/2.0131512jes
  • 2015 • 85 Well-posedness for dislocation based gradient visco-plasticity with isotropic hardening
    Kraynyukova, N. and Nesenenko, S. and Neff, P. and Chełmiński, K.
    Nonlinear Analysis: Real World Applications 25 96-111 (2015)
    In this work we establish the well-posedness for infinitesimal dislocation based gradient viscoplasticity with isotropic hardening for general subdifferential plastic flows. We assume an additive split of the displacement gradient into non-symmetric elastic distortion and non-symmetric plastic distortion. The thermodynamic potential is augmented with a term taking the dislocation density tensor Curlp into account. The constitutive equations in the models we study are assumed to be of self-controlling type. Based on the self-controlling property the existence of solutions of quasi-static initial-boundary value problems under consideration is shown using a time-discretization technique and a monotone operator method. © 2015 Elsevier Ltd.
    view abstractdoi: 10.1016/j.nonrwa.2015.03.004
  • 2015 • 84 A study of deformation and phase transformation coupling for TRIP-assisted steels
    Ma, A. and Hartmaier, A.
    International Journal of Plasticity 64 40-55 (2015)
    A constitutive model for Transformation Induced Plasticity (TRIP) assisted steels is proposed that considers the elastic-plastic deformation of ferrite and austenite, the austenite-martensite phase transformation and the elastic deformation of martensite. Within this model, an explicit relation between martensite nucleation and plastic deformation within an austenite grain has been established based on the inverse Nishiyama-Wassermann (NW) relationship. In particular, strain-induced martensite nucleation and stress-assisted martensite growth have been included in one model with the help of a thermodynamic principle. With this model, we found consistently with experiment that the TRIP effect enhances the effective work hardening rate and hence is beneficial for improving strength and ductility of steels. The mechanical anisotropy produced by stress-assisted and strain-induced phase transformations are significantly different. Furthermore, we observed that austenite grains transform to martensite more quickly under tension than under compression. © 2014 Elsevier Ltd.
    view abstractdoi: 10.1016/j.ijplas.2014.07.008
  • 2015 • 83 On the identification of superdislocations in the γ′-phase of single-crystal Ni-base superalloys - An application of the LACBED method to complex microstructures
    Müller, J. and Eggeler, G. and Spiecker, E.
    Acta Materialia 87 34-44 (2015)
    Ni-base superalloys are used for turbine blades, which operate in the creep range at temperatures above 1000 °C. One of the objectives of modern materials science is to analyze the combination of elementary deformation and microstructural coarsening processes and to identify physically based micromechanical models which allow one to predict the mechanical behavior on the macroscale. High-temperature creep of single-crystal Ni-base superalloys is governed by dislocation plasticity in the well-known γ/γ′-microstructure. For a comprehensive description of plasticity, it is important to understand the nucleation, glide and climb of superdislocations in the γ′-phase. The rate-controlling dislocation processes have to be identified and therefore a reliable Burgers vector analysis of superdislocations is essential. Superdislocations exhibit complex dislocation cores, typically comprising superpartial dislocations and planar defects. Therefore, conventional Burgers vector analysis based on the invisibility criterion often fails, due to the presence of pronounced residual contrast. In the present work, large-angle convergent-beam electron diffraction (LACBED) is employed for Burgers vector determination of two characteristic superdislocations, of the standard <1 1 0> and the more complex <1 0 0> type. LACBED results are compared with results obtained using the conventional invisibility analysis. While both techniques work for the standard superdislocation, the conventional analysis fails to analyze the <1 0 0> superdislocation, which shows pronounced residual contrast even under conditions of g · b = 0 and g · b × u = 0. In contrast, the LACBED technique allows for an unambiguous determination of the Burgers vector, including its magnitude and absolute sense. In the present study, the use of LACBED to identify dislocations in the complex microstructure of an Ni-base superalloy is outlined and the better performance of LACBED as compared to the conventional gb-analysis is discussed. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2014.12.029
  • 2015 • 82 An energy-barrier-based computational micro-sphere model for phase-transformations interacting with plasticity
    Ostwald, R. and Bartel, T. and Menzel, A.
    Computer Methods in Applied Mechanics and Engineering 293 232-265 (2015)
    We extend a newly introduced framework for the simulation of shape memory alloys undergoing martensite-austenite phase-transformations by allowing for the evolution of individual plastic deformations in each phase considered. The goal is to obtain a generalised model which will facilitate the reflection of the characteristic macroscopic behaviour of SMA as well as TRIP steels. Particularly, we show that the incorporation of plasticity effects interacting with phase-transformations allows to capture the typical multi-cyclic stress-strain responses. As a basis, we use a scalar-valued phase-transformation model where a Helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase. The incorporation of plasticity phenomena is established by enhancing the deviatoric contributions of the Helmholtz free energy functions of the material phases considered, where the plastic driving forces acting in each phase are derived from the overall free energy potential of the mixture. The resulting energy landscape of the constitutive model is obtained from the contributions of the individual constituents, where the actual energy barriers are computed by minimising parametric intersection curves of elliptic paraboloids. With the energy barriers at hand, we use a statistical physics based approach to determine the resulting evolution of volume fractions due to acting thermo-mechanical loads. Though the model allows to take into account an arbitrary number of solid phases of the underlying material, we restrict the investigations to the simulation of phase-transformations between an austenitic parent phase and a martensitic tension and compression phase. The scalar-valued model is embedded into a computational micro-sphere formulation in order to simulate three-dimensional boundary value problems. The systems of evolution equations are solved in a staggered manner, where a newly proposed, physically motivated plasticity inheritance law accounts for the inheritance of plastic deformations due to evolving phases. © 2015 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2015.04.008
  • 2015 • 81 The influence of stacking fault energy on the microstructural and strain-hardening evolution of Fe-Mn-Al-Si steels during tensile deformation
    Pierce, D.T. and Jiménez, J.A. and Bentley, J. and Raabe, D. and Wittig, J.E.
    Acta Materialia 100 178-190 (2015)
    Understanding the relationship between the stacking-fault energy (SFE), deformation mechanisms, and strain-hardening behavior is important for alloying and design of high-Mn austenitic transformation- and twinning-induced plasticity (TRIP/TWIP) steels. The present study investigates the influence of SFE on the microstructural and strain-hardening evolution of three TRIP/TWIP alloys (Fe-22/25/28Mn-3Al-3Si wt.%). The SFE is increased by systemically increasing the Mn content from 22 to 28 wt.%. The Fe-22Mn-3Al-3Si alloy, with a SFE of 15 mJ m-2, deforms by planar dislocation glide and strain-induced ε<inf>hcp</inf>-/α<inf>bcc</inf>-martensite formation which occurs from the onset of plastic deformation, resulting in improved work-hardening at low strains but lower total elongation. With an increased SFE of 21 mJ m-2 in the Fe-25Mn-3Al-3Si alloy, both mechanical twinning and ε<inf>hcp</inf>-martensite formation are activated during deformation, and result in the largest elongation of the three alloys. A SFE of 39 mJ m-2 enables significant dislocation cross slip and suppresses ε<inf>hcp</inf>-martensite formation, causing reduced work-hardening during the early stages of deformation in the Fe-28Mn-3Al-3Si alloy while mechanical twinning begins to enhance the strain-hardening after approximately 10% strain. The increase in SFE from 15 to 39 mJ m-2 results in significant changes in the deformation mechanisms and, at low strains, decreased work-hardening, but has a relatively small influence on strength and ductility. © 2015 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2015.08.030
  • 2015 • 80 Transition from shear to stress-assisted diffusion of copper-chromium nanolayered thin films at elevated temperatures
    Raghavan, R. and Wheeler, J.M. and Harzer, T.P. and Chawla, V. and Djaziri, S. and Thomas, K. and Philippi, B. and Kirchlechner, C. and Jaya, B.N. and Wehrs, J. and Michler, J. and Dehm, G.
    Acta Materialia 100 73-80 (2015)
    The mechanical behavior of Cu-Cr nanolayered films and an alloy film of nominal composition Cu<inf>20</inf>Cr<inf>80</inf> at.% was studied by microcompression testing at temperatures from 25 °C to 300 °C. Comparing nanolayered films, plastic deformation and failure occurred at consistently higher stress levels in the film with the smaller layer thicknesses. Plasticity in the nanolayered films always initiated in the softer Cu layers followed by a finite strain-hardening response in the stress-strain curves. Failure indicated by a strain-softening response following the higher peak strength due to shearing and tearing at columnar boundaries of Cr was observed in the nanolayered films at 25 °C and 100 °C. A transition from shearing and crack formation across the Cu-Cr interfaces leading to anomalous grain growth or beading of the nanocrystalline Cu layers was observed at elevated temperatures of 200 °C and 300 °C. On the other hand, the Cu<inf>20</inf>Cr<inf>80</inf> at.% alloy film exhibited failure by columnar buckling consistently at elevated temperatures, but shearing promoted by buckling at the highest strengths among the films at ambient temperature. © 2015 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2015.08.016
  • 2015 • 79 Homogenization of plasticity equations with two-scale convergence methods
    Schweizer, B. and Veneroni, M.
    Applicable Analysis 94 375-398 (2015)
    We investigate the deformation of heterogeneous plastic materials. The model uses internal variables and kinematic hardening, elastic and plastic strain are used in an infinitesimal strain theory. For periodic material properties with periodicity length scale (Formula presented.) , we obtain the limiting system as (Formula presented.). The limiting two-scale plasticity model coincides with well-known effective models. Our direct approach relies on abstract tools from two-scale convergence (regarding convex functionals and monotone operators) and on higher order estimates for solution sequences. © 2014, © 2014 Taylor & Francis.
    view abstractdoi: 10.1080/00036811.2014.896992
  • 2015 • 78 Effects of retained austenite volume fraction, morphology, and carbon content on strength and ductility of nanostructured TRIP-assisted steels
    Shen, Y.F. and Qiu, L.N. and Sun, X. and Zuo, L. and Liaw, P.K. and Raabe, D.
    Materials Science and Engineering A 636 551-564 (2015)
    With a suite of multi-modal and multi-scale characterization techniques, the present study unambiguously proves that a substantially-improved combination of ultrahigh strength and good ductility can be achieved by tailoring the volume fraction, morphology, and carbon content of the retained austenite (RA) in a transformation-induced-plasticity (TRIP) steel with the nominal chemical composition of 0.19C-0.30Si-1.76Mn-1.52Al (weight percent, wt%). After intercritical annealing and bainitic holding, a combination of ultimate tensile strength (UTS) of 1100. MPa and true strain of 50% has been obtained, as a result of the ultrafine RA lamellae, which are alternately arranged in the bainitic ferrite around junction regions of ferrite grains. For reference, specimens with a blocky RA, prepared without the bainitic holding, yield a low ductility (35%) and a low UTS (800. MPa). The volume fraction, morphology, and carbon content of RA have been characterized using various techniques, including the magnetic probing, scanning electron microscopy (SEM), electron-backscatter-diffraction (EBSD), and transmission electron microscopy (TEM). Interrupted tensile tests, mapped using EBSD in conjunction with the kernel average misorientation (KAM) analysis, reveal that the lamellar RA is the governing microstructure component responsible for the higher mechanical stability, compared to the blocky one. By coupling these various techniques, we quantitatively demonstrate that in addition to the RA volume fraction, its morphology and carbon content are equally important in optimizing the strength and ductility of TRIP-assisted steels. © 2015 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2015.04.030
  • 2015 • 77 Nanolaminate transformation-induced plasticity-twinning-induced plasticity steel with dynamic strain partitioning and enhanced damage resistance
    Wang, M.-M. and Tasan, C.C. and Ponge, D. and Dippel, A.-Ch. and Raabe, D.
    Acta Materialia 85 216-228 (2015)
    Conventional martensitic steels have limited ductility due to insufficient microstructural strain-hardening and damage resistance mechanisms. It was recently demonstrated that the ductility and toughness of martensitic steels can be improved without sacrificing the strength, via partial reversion of the martensite back to austenite. These improvements were attributed to the presence of the transformation-induced plasticity (TRIP) effect of the austenite phase, and the precipitation hardening (maraging) effect in the martensitic matrix. However, a full micromechanical understanding of this ductilizing effect requires a systematic investigation of the interplay between the two phases, with regards to the underlying deformation and damage micromechanisms. For this purpose, in this work, a Fe-9Mn-3Ni-1.4Al-0.01C (mass%) medium-Mn TRIP maraging steel is produced and heat-treated under different reversion conditions to introduce well-controlled variations in the austenite-martensite nanolaminate microstructure. Uniaxial tension and impact tests are carried out and the microstructure is characterized using scanning and transmission electron microscopy based techniques and post mortem synchrotron X-ray diffraction analysis. The results reveal that (i) the strain partitioning between austenite and martensite is governed by a highly dynamical interplay of dislocation slip, deformation-induced phase transformation (i.e. causing the TRIP effect) and mechanical twinning (i.e. causing the twinning-induced plasticity effect); and (ii) the nanolaminate microstructure morphology leads to enhanced damage resistance. The presence of both effects results in enhanced strain-hardening capacity and damage resistance, and hence the enhanced ductility. © 2014 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2014.11.010
  • 2015 • 76 Identification of fully coupled anisotropic plasticity and damage constitutive equations using a hybrid experimental-numerical methodology with various triaxialities
    Yue, Z.M. and Soyarslan, C. and Badreddine, H. and Saanouni, K. and Tekkaya, A.E.
    International Journal of Damage Mechanics 24 683-710 (2015)
    A hybrid experimental-numerical methodology is presented for the parameter identification of a mixed nonlinear hardening anisotropic plasticity model fully coupled with isotropic ductile damage accounting for microcracks closure effects. In this study, three test materials are chosen: DP1000, CP1200, and AL7020. The experiments involve the tensile tests with smooth and notched specimens and two types of shear tests. The tensile tests with smooth specimens are conducted in different directions with respect to the rolling direction. This helps to determine the plastic anisotropy parameters of the material when the ductile damage is still negligible. Also, in-plane torsion tests with a single loading cycle are used to determine separately the isotropic and kinematic hardening parameters. Finally, tensile tests with notched specimens and Shouler and Allwood shear tests are used for the damage parameters identification. These are conducted until the final fracture with the triaxiality ratio• lying between 0 and 1 / 3 (i.e. 0• 1/3). The classical force-displacement curves are chosen as the experimental responses. However, for the tensile test with notched specimens, the distribution of displacement components is measured using a full field measurement technique (ARAMIS system). These experimental results are directly used by the identification methodology in order to determine the values of material parameters involved in the constitutive equations. The inverse identification methodology combines an optimization algorithm which is coded within MATLAB together with the finite element (FE) code ABAQUS/Explicit. After optimization, good agreement between experimental and numerically predicted results in terms of force-displacement curves is obtained for the three studied materials. Finally, the applicability and validity of the determined material parameters are proved with additional validation tests. © 2014 The Author(s) Reprints and permissions.
    view abstractdoi: 10.1177/1056789514546578
  • 2015 • 75 A study on the geometry of dislocation patterns in the surrounding of nanoindents in a TWIP steel using electron channeling contrast imaging and discrete dislocation dynamics simulations
    Zhang, J.-L. and Zaefferer, S. and Raabe, D.
    Materials Science and Engineering A 636 231-242 (2015)
    Electron channeling contrast imaging under controlled diffraction conditions (cECCI) enables observation of crystal defects, especially dislocations, stacking faults and nano-twins, close to the surface of bulk samples. In this work cECCI has been employed to observe defects around nanoindents into the surface of {100}-, {110}-, {111}-oriented grains in a Fe-22Mn-0.65C (wt%) TWIP steel sample (fcc crystal structure, stacking fault energy ~20. mJ/m) using a cone-spherical indenter. The dislocation patterns show four- and two-fold symmetries for the {100}- and {110}-orientation, and a three-fold symmetry for the {111}-orientation which is, however, difficult to observe. Discrete dislocation dynamics (DDD) simulations of the indentation were carried out to complement the static experimental investigations. The simulations were carried out with both, cross-slip disabled and enabled conditions, where the former were found to match to the experimental results better, as may be expected for an fcc material with low stacking fault energy. The 3-dimensional geometry of the dislocation patterns of the different indents was analysed and discussed with respect to pattern formation mechanisms. The force-displacement curves obtained during indentation showed a stronger strain hardening for the {111} oriented crystal than that for the other orientations. This is in contrast to the behaviour of, for example, copper and is interpreted to be due to planar slip. Irrespective of orientation and indentation depth the radius of the plastically deformed area was found to be approximately 4 times larger than that of the indenter contact area. © 2015 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2015.03.078
  • 2014 • 74 Recycling of aluminum chips by hot extrusion with subsequent cold extrusion
    Haase, M. and Tekkaya, A.E.
    Procedia Engineering 81 652-657 (2014)
    In this paper, the direct conversion of AA6060 aluminum alloy machining chips into finished products by hot extrusion with subsequent cold extrusion is investigated. For hot extrusion, two different types of extrusion dies, a conventional flat-face die and an experimental die, are used. The experimental die combines the process of equal channel angular pressing with the process of hot extrusion in a single die, which increases the strain and pressure affecting the chips during extrusion, both critical factors for achieving sound chip bonding. Subsequently, the chip-based extrudates are machined to fabricate chip-based preforms for the cold extrusion experiments. In order to investigate different processing routes, forward rod extrusion and backward can extrusion trials were conducted. In all steps, cast material was processed similar to the chips as a reference. The results showed that the quality of the chip-based finished parts strongly depends on the bonding quality between the individual chips, determined during the hot extrusion process. © 2014 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2014.10.055
  • 2014 • 73 Analytical prediction of roughness after ball burnishing of thermally coated surfaces
    Hiegemann, L. and Weddeling, C. and Khalifa, N.B. and Tekkaya, A.E.
    Procedia Engineering 81 1921-1926 (2014)
    An analytical model to predict the roughness of a thermally sprayed coating after a ball burnishing process is presented. Based on the observation of a roughness peak, a correlation between the leveling during rolling and the surface pressure under the rolling ball as well as a material parameter is derived. Ball burnishing experiments on thermally coated surfaces were carried out to verify the model. A good correspondence between the experimental data and the calculated values is presented. © 2014 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2014.10.257
  • 2014 • 72 Formability limits by fracture in sheet metal forming
    Isik, K. and Silva, M.B. and Tekkaya, A.E. and Martins, P.A.F.
    Journal of Materials Processing Technology 214 1557-1565 (2014)
    The aim of this paper is twofold: first, to revisit the forming limit diagram (FLD) in the light of fundamental concepts of plasticity, damage and ductile fracture mechanics and, second, to propose a new experimental methodology to determine the formability limits by fracture in sheet metal forming. The first objective makes use of the theory of plasticity applied to proportional strain loading paths, under plane stress conditions, to analyze the fracture forming limit line (FFL) and to introduce the shear fracture forming limit line (SFFL). The second objective makes use of single point incremental forming (SPIF), torsion and plane shear tests to determine the experimental values of the in-plane strains at the onset of fracture. Results show that the proposed methodology provides an easy and efficient procedure to characterize the formability limits by fracture in sheet metal forming. In particular, the paper shows that the FFL determined by means of tensile and conventional sheet formability tests is identical to that determined from SPIF tests on conical and pyramidal truncated specimens. The new proposed approach is expected to have impact in the established methodologies to outline the formability limits on the basis of the forming limit curves (FLC's) at the onset of necking. © 2014 Elsevier B.V.
    view abstractdoi: 10.1016/j.jmatprotec.2014.02.026
  • 2014 • 71 Cyclic plasticity and lifetime of the nickel-based Alloy C-263: Experiments, models and component simulation
    Maier, G. and Hübsch, O. and Riedel, H. and Somsen, C. and Klöwer, J. and Mohrmann, R.
    MATEC Web of Conferences 14 (2014)
    The present work deals with the thermomechanical fatigue and low-cycle fatigue behavior of C-263 in two different material conditions. Microstructural characteristics and fracture modes are investigated with light and electron microscopy. The experimental results indicate that viscoplastic deformations depend on the heat treatment or rather on the current state of the microstructure. The measured data are used to adjust the parameters of a Chaboche type model and a fracture-mechanics based model for fatigue lifetime prediction. The Chaboche model is able to describe the essential phenomena of time and temperature dependent cyclic plasticity including the complex cyclic hardening during thermo-cyclic loading of both material conditions with a unique set of material parameters. This could be achieved by including an additional internal variable into the Chaboche model which accounts for changes in the precipitation microstructure during high temperature loading. Furthermore, the proposed lifetime model is well suited for a common fatigue life prediction of both investigated heats. The deformation and lifetime models are implemented into a user defined material routine. In this work, the material routine is applied for the lifetime prediction of a critical power plant component using the finite element method. © 2014 Owned by the authors, published by EDP Sciences.
    view abstractdoi: 10.1051/matecconf/20141416006
  • 2014 • 70 A unifying perspective: The relaxed linear micromorphic continuum
    Neff, P. and Ghiba, I.-D. and Madeo, A. and Placidi, L. and Rosi, G.
    Continuum Mechanics and Thermodynamics 26 639-681 (2014)
    We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of the microstructure and to predict nonpolar size effects. It is intended for the homogenized description of highly heterogeneous, but nonpolar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models, our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models. © 2013 Springer-Verlag Berlin Heidelberg.
    view abstractdoi: 10.1007/s00161-013-0322-9
  • 2014 • 69 Alloy Design, Combinatorial Synthesis, and Microstructure–Property Relations for Low-Density Fe-Mn-Al-C Austenitic Steels
    Raabe, D. and Springer, H. and Gutierrez-Urrutia, I. and Roters, F. and Bausch, M. and Seol, J.-B. and Koyama, M. and Choi, P.-P. and Tsuzaki, K.
    JOM 66 1845-1856 (2014)
    We present recent developments in the field of austenitic steels with up to 18% reduced mass density. The alloys are based on the Fe-Mn-Al-C system. Here, two steel types are addressed. The first one is a class of low-density twinning-induced plasticity or single phase austenitic TWIP (SIMPLEX) steels with 25–30 wt.% Mn and <4–5 wt.% Al or even <8 wt.% Al when naturally aged. The second one is a class of κ-carbide strengthened austenitic steels with even higher Al content. Here, κ-carbides form either at 500–600°C or even during quenching for >10 wt.% Al. Three topics are addressed in more detail, namely, the combinatorial bulk high-throughput design of a wide range of corresponding alloy variants, the development of microstructure–property relations for such steels, and their susceptibility to hydrogen embrittlement. © 2014, The Minerals, Metals & Materials Society.
    view abstractdoi: 10.1007/s11837-014-1032-x
  • 2014 • 68 Construction of statistically similar representative volume elements - Comparative study regarding different statistical descriptors
    Scheunemann, L. and Schröder, J. and Balzani, D. and Brands, D.
    Procedia Engineering 81 1360-1365 (2014)
    Advanced high strength steels, such as dual-phase steel (DP steel), provide advantages for engineering applications compared to conventional high strength steel. The main constituents of DP steel on the microscopic level are martensitic inclusions embedded in a ferritic matrix. A way to include these heterogeneities on the microscale into the modeling of the material is the FE2- method. Herein, in every integration point of a macroscopic finite element problem a microscopic boundary value problem is attached, which consists of a representative volume element (RVE) often defined as a segment of a real microstructure. From this representation, high computational costs arise due to the complexity of the discretization which can be circumvented by the use of a Statistically Similar RVE (SSRVE), which is governed by similar statistical features as the real target microstructure but shows a lower complexity. For the construction of such SSRVEs, an optimization problem is constructed which consists of a least-square functional taking into account the differences of statistical measures evaluated for the real microstructure and the SSRVE. This functional is minimized to identify the SSRVE for which the similarity in a statistical sense is optimal. The choice of the statistical measures considered in the least-square functional however play an important role. We focus on the construction of SSRVEs based on the volume fraction, lineal-path function and spectral density and check the performance in virtual tests. Here the response of the individual SSRVEs is compared with the real target microstructure. Further higher order measures, some specific Minkowski functionals, are investigated regarding their applicability and efficiency in the optimization process. © 2014 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2014.10.157
  • 2014 • 67 Two-scale modeling of DP steel incorporating distributed properties inside micro-constituents
    Schröder, J. and Gandhi, A. and Balzani, D.
    Procedia Engineering 81 1390-1395 (2014)
    Advanced High Strength Steels (AHSS) are increasingly used in the industry due to their excellent strength and formability properties enabling weight savings. In this wide class of steel we restrict ourselves to the modeling of Dual Phase (DP) steels which are, at the microscale, characterized by a hard martensitic inclusion phase embedded in a soft ferritic matrix phase. During the production process the martensite transforms from austenite by rapidly cooling down the material and thereby causing a volume jump leading to initial plastic strains associated with eigenstresses of higher order. A technique to incorporate theses distributed properties in the ferrite matrix is proposed and implemented using the direct micro-macro transition approach. © 2014 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2014.10.162
  • 2014 • 66 Simulation of composite hot extrusion with high reinforcing Volumes
    Schwane, M. and Citrea, T. and Dahnke, C. and Haase, M. and Khalifa, N.B. and Tekkaya, A.E.
    Procedia Engineering 81 1265-1270 (2014)
    Experimental results, which indicate a significant influence of the reinforcing elements on the material flow during composite extrusion with high reinforcing volumes, are presented. In order to analyze the process numerically, finite element simulations with models taking into account the reinforcing elements were carried out. The results are discussed with regard to the material flow and the load of the reinforcing elements. © 2014 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2014.10.108
  • 2014 • 65 Modeling the microstructure influence on fatigue life variability in structural steels
    Sharaf, M. and Kucharczyk, P. and Vajragupta, N. and Münstermann, S. and Hartmaier, A. and Bleck, W.
    Computational Materials Science 94 258-272 (2014)
    The endurance and HCF lifetime of multiphase steel components depend mainly on the phase of fatigue microcrack initiation and early propagation. A numerical study, which quantitatively describes the influence of microstructural features on the initiation and growth of cyclic microcracks, is presented within the context of microstructure-sensitive modeling. The implementation of kinematic hardening on each slip system in a crystal plasticity model allows for capturing the local accumulation of plastic microdeformation representing slip irreversibility occurring in the crack incubation phase. A load increasing testing technique with continuous temperature measurement and interrupted cyclic bending experiments deliver information about the endurance strength of a structural steel and allow for metallographic observation of cyclic microcrack propagation and thereby provide the experimental basis for the numerical simulations. The material model is implemented in cyclic computations with statistically representative volume elements, which are based on experimental microstructure description using the electron backscatter diffraction technique (EBSD). The extreme value distributions of the computed accumulation of local dislocation slip are then correlated to the microstructure in an approach to assess and explore the validity extent of microstructure-sensitive modeling using fatigue indicator parameters (FIPs) to correlate to the endurance limit and fatigue life under high-cycle fatigue conditions. The eligibility of consideration of the stresses normal to the planes of localized plastic damage assisting fatigue crack formation into these FIPs is investigated. © 2014 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.commatsci.2014.05.059
  • 2014 • 64 Forming of lightweight metal components: Need for new technologies
    Tekkaya, A.E. and Ben Khalifa, N. and Grzancic, G. and Hölker, R.
    Procedia Engineering 81 28-37 (2014)
    Contributing to lightweight design in the field of metal forming, four different strategies are introduced - The material, component, functional, and conditional lightweight strategy. Their main objective is the reduction of a component's weight and the saving of our available resources. Regarding each approach, innovative forming technologies are presented and their contribution to lightweight success is depicted. On the one hand, this article covers conventional processes like e.g. extrusion, which are used for processing hybrid lightweight materials. On the other hand, new forming technologies are introduced to serve lightweight requirements like e.g. load adaption. Finally, the importance of numerical damage modeling regarding lightweight design is shown. © 2014 The Authors. Published by Elsevier Ltd.
    view abstractdoi: 10.1016/j.proeng.2014.09.125
  • 2014 • 63 The modeling scheme to evaluate the influence of microstructure features on microcrack formation of DP-steel: The artificial microstructure model and its application to predict the strain hardening behavior
    Vajragupta, N. and Wechsuwanmanee, P. and Lian, J. and Sharaf, M. and Münstermann, S. and Ma, A. and Hartmaier, A. and Bleck, W.
    Computational Materials Science 94 198-213 (2014)
    Due to the existence of constituents with strong distinction in mechanical properties, dual phase steels exhibit remarkably high-energy absorption along with excellent combination of strength and ductility. Furthermore, these constituents also affect deformation and microcrack formation in which various mechanisms can be observed. Thus, a reliable microstructure-based simulation approach for describing these deformations and microcrack initiation is needed. Under this framework of modeling scheme development, several work packages have been carried out. These work packages includes algorithm to generate the artificial microstructure model, a procedure to derive plasticity parameters for each constituent, and characterization of the microcrack formation and initiation criteria determination. However, due to the complexity of topic and in order to describe each work package in detail, this paper focused only on the approach to generate the artificial microstructure model and its application to predict the strain hardening behavior. The approach was based on the quantitative results of metallographic microstructure analysis and their statistical representation. The dual phase steel was first characterized by EBSD analysis to identify individual phase grain size distribution functions. The results were then input into a multiplicatively weighted Voronoi tessellation based algorithm to generate artificial microstructure geometry models. Afterwards, nanoindentation was performed to calibrate crystal plasticity parameters of ferrite and empirical approach based on local chemical composition was used to approximate flow curve of martensite. By assigning the artificial microstructure model with plasticity description of each constituent, strain-hardening behavior of DP-steel was then predicted. © 2014 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.commatsci.2014.04.011
  • 2014 • 62 Correlations of plasticity in sheared glasses
    Varnik, F. and Mandal, S. and Chikkadi, V. and Denisov, D. and Olsson, P. and Vågberg, D. and Raabe, D. and Schall, P.
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 89 (2014)
    In a recent paper [Mandal, Phys. Rev. E 88, 022129 (2013)PLEEE81539-375510. 1103/PhysRevE.88.022129], the nature of spatial correlations of plasticity in hard-sphere glasses was addressed both via computer simulations and in experiments. It was found that the experimentally obtained correlations obey a power law, whereas the correlations from simulations are better fitted by an exponential decay. We here provide direct evidence - via simulations of a hard-sphere glass in two dimensions (2D) - that this discrepancy is a consequence of the finite system size in the 3D simulations. By extending the study to a 2D soft disk model at zero temperature [Durian, Phys. Rev. Lett. 75, 4780 (1995)PRLTAO0031-900710.1103/PhysRevLett.75.4780], the robustness of the power-law decay in sheared amorphous solids is underlined. Deviations from a power law occur when either reducing the packing fraction towards the supercooled regime in the case of hard spheres or changing the dissipation mechanism from contact dissipation to a mean-field-type drag in the case of soft disks. © 2014 American Physical Society.
    view abstractdoi: 10.1103/PhysRevE.89.040301
  • 2014 • 61 In situ observation of collective grain-scale mechanics in Mg and Mg-rare earth alloys
    Wang, F. and Sandlöbes, S. and Diehl, M. and Sharma, L. and Roters, F. and Raabe, D.
    Acta Materialia 80 77-93 (2014)
    The microstructure evolution of pure Mg and two Mg-rare-earth alloys (Mg-3 wt.% Dy and Mg-3 wt.% Er) was studied during in situ compression tests by electron backscatter diffraction and electron channelling contrast imaging. Strain localization and the formation of an early stage shear band ("pre-shear band") were observed in pure Mg during compressive deformation below 5% engineering strain. In the experiments percolative grain clusters with prevalent basal slip as a precursor for shear band formation was observed. This collective grain-cluster shear behaviour was analysed in more detail using crystal plasticity simulations, revealing a percolation of intense basal slip activity across grain boundaries as the mechanism for shear band initiation. Plane trace analysis, Schmid factor calculation and deformation transfer analysis at the grain boundaries were performed for the activated twins. It appears that many activated tension twins exhibit pronounced non-Schmid behaviour. Twinning appears to be a process of accommodating local strain rather than a response to macroscopic strain. © 2014 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2014.07.048
  • 2014 • 60 Temperature dependent transition of intragranular plastic to intergranular brittle failure in electrodeposited Cu micro-tensile samples
    Wimmer, A. and Smolka, M. and Heinz, W. and Detzel, T. and Robl, W. and Motz, C. and Eyert, V. and Wimmer, E. and Jahnel, F. and Treichler, R. and Dehm, G.
    Materials Science and Engineering A 618 398-405 (2014)
    Smaller grain sizes are known to improve the strength and ductility of metals by the Hall-Petch effect. Consequently, metallic thin films and structures which must sustain mechanical loads in service are deposited under processing conditions that lead to a fine grain size. In this study, we reveal that at temperatures as low as 473. K the failure mode of 99.99. at% pure electro-deposited Cu can change from ductile intragranular to brittle intergranular fracture. The embrittlement is accompanied by a decrease in strength and elongation to fracture. Chemical analyses indicate that the embrittlement is caused by impurities detected at grain boundaries. In situ micromechanical experiments in the scanning electron microscope and atomistic simulations are performed to study the underlying mechanisms. © 2014 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2014.09.029
  • 2014 • 59 Synthesis, characterization, and nanoindentation response of single crystal Fe-Cr-Ni alloys with FCC and BCC structures
    Xia, Y.Z. and Bei, H. and Gao, Y.F. and Catoor, D. and George, E.P.
    Materials Science and Engineering A 611 177-187 (2014)
    Fe-based alloys are used extensively in many structural applications including under irradiation conditions in the nuclear industry. In this study, model Fe-Cr, Fe-Ni and Fe-Cr-Ni alloys that are the basis of many structural steels were synthesized as single crystals and characterized. The compositions investigated were Fe-15Cr, Fe-30Cr, Fe-30Ni and Fe-15Cr-15Ni (at%). Several key mechanical properties were determined which will be useful in further studies of irradiation/deformation-induced defects. Incipient plasticity and slip characteristics were investigated by nanoindentation on (001) and (1-10) surfaces, and hardness, modulus, pop-in behavior and theoretical strength were determined. The slip trace patterns after microindentation were imaged in a microscope. A novel slip trace analysis was developed and the underlying deformation mechanisms identified. The analysis shows that under both (001) and (1-10) indentations, the activated slip system for the BCC alloys is {112} for the FCC alloys the activated slip plane is {111}. These results were confirmed with finite element simulations using a slip-based crystal-plasticity model. Finally, the effects of heterogeneous pop-in mechanisms are discussed in the context of incipient plasticity in the four different alloys. © 2014 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2014.05.079
  • 2013 • 58 Existence theorems in the geometrically non-linear 6-parameter theory of elastic plates
    Bîrsan, M. and Neff, P.
    Journal of Elasticity 112 185-198 (2013)
    In this paper we show the existence of global minimizers for the geometrically non-linear equations of elastic plates, in the framework of the general 6-parameter shell theory. A characteristic feature of this model for shells is the appearance of two independent kinematic fields: the translation vector field and the rotation tensor field (representing in total 6 independent scalar kinematic variables). For isotropic plates, we prove the existence theorem by applying the direct methods of the calculus of variations. Then, we generalize our existence result to the case of anisotropic plates. © 2012 Springer Science+Business Media B.V.
    view abstractdoi: 10.1007/s10659-012-9405-2
  • 2013 • 57 Incipient plasticity and deformation mechanisms in single-crystal Mg during spherical nanoindentation
    Catoor, D. and Gao, Y.F. and Geng, J. and Prasad, M.J.N.V. and Herbert, E.G. and Kumar, K.S. and Pharr, G.M. and George, E.P.
    Acta Materialia 61 2953-2965 (2013)
    Incipient plasticity in Mg single crystals was investigated using the pop-ins generated during spherical nanoindentation on (0 0 0 1), (1 0 -1 2) and (1 0 -1 0) surfaces. Representative deformed regions extracted from underneath indents by means of focused ion beam machining were examined by transmission electron microscopy (TEM) to identify the deformation mechanisms. Anisotropic elastic Hertzian contact theory was used to calculate indentation Schmid factors and the relevant resolved shear stresses at pop-in from the load-displacement curves. The pop-in statistics in conjunction with the TEM analysis showed that the most likely deformation mechanism responsible for pop-in is slip via 〈a〉 dislocations even in the case of indentation along the c-axis. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2013.01.055
  • 2013 • 56 Microbanding mechanism in an Fe-Mn-C high-Mn twinning-induced plasticity steel
    Gutierrez-Urrutia, I. and Raabe, D.
    Scripta Materialia 69 53-56 (2013)
    We study the microbanding mechanism in an Fe-22Mn-0.6C (wt.%) twinning-induced plasticity steel. Dislocation substructures were examined by electron channeling contrast imaging and electron backscatter diffraction. We observe a pronounced effect of the strain path on microbanding, which is explained in terms of Schmid's law. Microbands created under shear loading have a non-crystallographic character. This is attributed to the microbanding mechanism and its relation with the dislocation substructure. Further insights into the dislocation configuration of microbands are provided.© 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.scriptamat.2013.03.010
  • 2013 • 55 B-and strong stationarity for optimal control of static plasticity with hardening
    Herzog, R. and Meyer, C. and Wachsmuth, G.
    SIAM Journal on Optimization 23 321-352 (2013)
    Optimal control problems for the variational inequality of static elastoplasticity with linear kinematic hardening are considered. The control-to-state map is shown to be weakly directionally differentiable, and local optimal controls are proved to verify an optimality system of B-stationary type. For a modified problem, local minimizers are shown to even satisfy an optimality system of strongly stationary type. © 2013 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/110821147
  • 2013 • 54 Simulation of shear banding in heterophase co-deformation: Example of plane strain compressed Cu-Ag and Cu-Nb metal matrix composites
    Jia, N. and Roters, F. and Eisenlohr, P. and Raabe, D. and Zhao, X.
    Acta Materialia 61 4591-4606 (2013)
    The co-deformation and shear localization in heterophase alloys is studied using two-dimensional crystal plasticity finite element simulations on plane strain compressed Cu-Ag and Cu-Nb metal matrix composites. The aim is to study the fundamentals of micromechanics, co-deformation and shear banding in materials with heterophase interfaces. It is observed that, depending on the initial orientations of the crystals, co-deformation of the constituent heterophases often proceeds via collective mechanisms, i.e. by pronounced shear banding triggered by stress concentration at the interfaces. This phenomenon leads to highly localized strains within the bands, exceeding the average strain in part by two orders of magnitude. Shear band development is related to the inherent mechanical properties of each crystal and also to the properties of the abutting crystals. The predicted topology and nature of the cross-phase shear bands, i.e. the extreme local strains, significant bending of the interface regions, and sharp strain localization that propagates across the interfaces, agree well with experimental observations in cold-rolled composites. The simulations reveal that cross-phase shear banding leads to large and highly localized values of stress and strain at heterophase interfaces. Such information is essential for a better understanding of the micromechanical boundary conditions inside co-deformed composites and the associated shear-induced chemical mixing. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2013.04.029
  • 2013 • 53 Simulation of electromagnetic forming of a cross-shaped cup by means of a viscoplasticity model coupled with damage at finite strains
    Kiliclar, Y. and Demir, O.K. and Vladimirov, I.N. and Kwiatkowski, L. and Reese, S. and Tekkaya, A.E.
    Key Engineering Materials 554-557 2363-2368 (2013)
    In the field of sheet metal forming conventional forming processes are well established. However, a quasi-static forming process combined with a high speed forming process can enhance the forming limits of a single one. In this paper, the investigation of the process chain quasi-static deep drawing - electromagnetic forming by means of a new coupled damage-viscoplasticity model for large deformations is performed. The finite strain constitutive model, used in the finite element simulation combines nonlinear kinematic and isotropic hardening and is derived in a thermodynamically consistent setting. This anisotropic viscoplastic model is based on the multiplicative decomposition of the deformation gradient in the context of hyperelasticity. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. The coupling of damage and plasticity is carried out in a constitutive manner according to the effective stress concept. The constitutive equations of the material model are integrated in an explicit manner and implemented as a user material subroutine in the commercial finite element package LS-DYNA with the electromagnetical module. The aim of the work is to show the increasing formability of the sheet by combining quasistatic deep drawing processes with high speed electromagnetic forming. Copyright © 2013 Trans Tech Publications Ltd.
    view abstractdoi: 10.4028/www.scientific.net/KEM.554-557.2363
  • 2013 • 52 Hydrogen-assisted failure in a twinning-induced plasticity steel studied under in situ hydrogen charging by electron channeling contrast imaging
    Koyama, M. and Akiyama, E. and Tsuzaki, K. and Raabe, D.
    Acta Materialia 61 4607-4618 (2013)
    We investigated the hydrogen embrittlement of a Fe-18Mn-1.2%C (wt.%) twinning-induced plasticity steel, focusing on the influence of deformation twins on hydrogen-assisted cracking. A tensile test under ongoing hydrogen charging was performed at low strain rate (1.7 × 10-6 s -1) to observe hydrogen-assisted cracking and crack propagation. Hydrogen-stimulated cracks and deformation twins were observed by electron channeling contrast imaging. We made the surprising observation that hydrogen-assisted cracking was initiated both at grain boundaries and also at deformation twins. Also, crack propagation occurred along both types of interfaces. Deformation twins were shown to assist intergranular cracking and crack propagation. The stress concentration at the tip of the deformation twins is suggested to play an important role in the hydrogen embrittlement of the Fe-Mn-C twining-induced plasticity steel. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2013.04.030
  • 2013 • 51 Understanding the detection of carbon in austenitic high-Mn steel using atom probe tomography
    Marceau, R.K.W. and Choi, P. and Raabe, D.
    Ultramicroscopy 132 239-247 (2013)
    A high-Mn TWIP steel having composition Fe-22Mn-0.6C (wt%) is considered in this study, where the need for accurate and quantitative analysis of clustering and short-range ordering by atom probe analysis requires a better understanding of the detection of carbon in this system. Experimental measurements reveal that a high percentage of carbon atoms are detected as molecular ion species and on multiple hit events, which is discussed with respect to issues such as optimal experimental parameters, correlated field evaporation and directional walk/migration of carbon atoms at the surface of the specimen tip during analysis. These phenomena impact the compositional and spatial accuracy of the atom probe measurement and thus require careful consideration for further cluster-finding analysis. © 2013 Elsevier B.V.
    view abstractdoi: 10.1016/j.ultramic.2013.01.010
  • 2013 • 50 The influences of temperature and microstructure on the tensile properties of a CoCrFeMnNi high-entropy alloy
    Otto, F. and Dlouhý, A. and Somsen, C. and Bei, H. and Eggeler, G. and George, E.P.
    Acta Materialia 61 5743-5755 (2013)
    An equiatomic CoCrFeMnNi high-entropy alloy, which crystallizes in the face-centered cubic (fcc) crystal structure, was produced by arc melting and drop casting. The drop-cast ingots were homogenized, cold rolled and recrystallized to obtain single-phase microstructures with three different grain sizes in the range 4-160 μm. Quasi-static tensile tests at an engineering strain rate of 10-3 s-1 were then performed at temperatures between 77 and 1073 K. Yield strength, ultimate tensile strength and elongation to fracture all increased with decreasing temperature. During the initial stages of plasticity (up to ∼2% strain), deformation occurs by planar dislocation glide on the normal fcc slip system, {1 1 1}〈1 1 0〉, at all the temperatures and grain sizes investigated. Undissociated 1/2〈1 1 0〉 dislocations were observed, as were numerous stacking faults, which imply the dissociation of several of these dislocations into 1/6〈1 1 2〉 Shockley partials. At later stages (∼20% strain), nanoscale deformation twins were observed after interrupted tests at 77 K, but not in specimens tested at room temperature, where plasticity occurred exclusively by the aforementioned dislocations which organized into cells. Deformation twinning, by continually introducing new interfaces and decreasing the mean free path of dislocations during tensile testing ("dynamic Hall-Petch"), produces a high degree of work hardening and a significant increase in the ultimate tensile strength. This increased work hardening prevents the early onset of necking instability and is a reason for the enhanced ductility observed at 77 K. A second reason is that twinning can provide an additional deformation mode to accommodate plasticity. However, twinning cannot explain the increase in yield strength with decreasing temperature in our high-entropy alloy since it was not observed in the early stages of plastic deformation. Since strong temperature dependencies of yield strength are also seen in binary fcc solid solution alloys, it may be an inherent solute effect, which needs further study. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2013.06.018
  • 2013 • 49 On dislocation involvement in Ti-Nb gum metal plasticity
    Plancher, E. and Tasan, C.C. and Sandloebes, S. and Raabe, D.
    Scripta Materialia 68 805-808 (2013)
    The excellent mechanical properties of the Ti-Nb-based gum metal were originally proposed to arise from a "dislocation-free" giant fault mechanism; however, the involvement of lattice dislocations in the process is still under debate. To address this issue, gum metal deformation mechanisms are investigated systematically on cast specimens, employing postmortem and in situ analysis techniques. The results demonstrate that a giant fault mechanism (which appears to be a phase-transformation-assisted nanotwinning mechanism) governs gum metal plasticity without direct assistance from dislocations during the process. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.scriptamat.2013.01.034
  • 2013 • 48 Revealing the strain-hardening behavior of twinning-induced plasticity steels: Theory, simulations, experiments
    Steinmetz, D.R. and Jäpel, T. and Wietbrock, B. and Eisenlohr, P. and Gutierrez-Urrutia, I. and Saeed-Akbari, A. and Hickel, T. and Roters, F. and Raabe, D.
    Acta Materialia 61 494-510 (2013)
    We present a multiscale dislocation density-based constitutive model for the strain-hardening behavior in twinning-induced plasticity (TWIP) steels. The approach is a physics-based strain rate- and temperature-sensitive model which reflects microstructural investigations of twins and dislocation structures in TWIP steels. One distinct advantage of the approach is that the model parameters, some of which are derived by ab initio predictions, are physics-based and known within an order of magnitude. This allows more complex microstructural information to be included in the model without losing the ability to identify reasonable initial values and bounds for all parameters. Dislocation cells, grain size and twin volume fraction evolution are included. Particular attention is placed on the mechanism by which new deformation twins are nucleated, and a new formulation for the critical twinning stress is presented. Various temperatures were included in the parameter optimization process. Dissipative heating is also considered. The use of physically justified parameters enables the identification of a universal parameter set for the example of an Fe-22Mn-0.6C TWIP steel. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2012.09.064
  • 2012 • 47 In-Situ TEM Straining Experiments: Recent Progress in Stages and Small-Scale Mechanics
    Dehm, G. and Legros, M. and Kiener, D.
    In-Situ Electron Microscopy: Applications in Physics, Chemistry and Materials Science 227-254 (2012)
    doi: 10.1002/9783527652167.ch10
  • 2012 • 46 Adiabatic temperature increase associated with deformation twinning and dislocation plasticity
    Eisenlohr, A. and Gutierrez-Urrutia, I. and Raabe, D.
    Acta Materialia 60 3994-4004 (2012)
    We studied local deformation and temperature effects associated with mechanical twinning in Fe-3 wt.% Si at room temperature. During tensile testing, two large stress drops occurred. They were accompanied by local strain and temperature bursts, which we mapped via simultaneous displacement and temperature field characterization. To identify the microstructural origin of these phenomena, we performed high resolution electron backscatter scanning diffraction and electron channeling contrast imaging measurements. The microstructure at the positions where strong adiabatic heating occurred was characterized by the formation of primary twins and high dislocation activity within a range of about 10 μm around the twin-matrix interface. We suggest that the local temperature and strain jumps result from the formation and dissipative motion of lattice dislocations that accommodate twinning. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2012.03.008
  • 2012 • 45 Grain size effect on strain hardening in twinning-induced plasticity steels
    Gutierrez-Urrutia, I. and Raabe, D.
    Scripta Materialia 66 992-996 (2012)
    We investigate the influence of grain size on the strain hardening of two Fe-22Mn-0.6C (wt.%) twinning-induced plasticity steels with average grain sizes of 3 and 50 μm, respectively. The grain size has a significant influence on the strain hardening through the underlying microstructure. The dislocation substructure formed in the early deformation stages determines the density of nucleation sites for twins per unit grain boundary area which controls the developing twin substructure. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.scriptamat.2012.01.037
  • 2012 • 44 C-stationarity for optimal control of static plasticity with linear kinematic hardening
    Herzog, R. and Meyer, C. and Wachsmuth, G.
    SIAM Journal on Control and Optimization 50 3052-3082 (2012)
    An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. Existence and uniqueness of the plastic multiplier is rigorously proved, which allows for the reformulation of the forward system using a complementarity condition. In order to derive necessary optimality conditions, a family of regularized optimal control problems is analyzed, wherein the static plasticity problems are replaced by their viscoplastic approximations. By passing to the limit in the optimality conditions for the regularized problems, necessary optimality conditions of C-stationarity type are obtained. © 2012 Society for Industrial and Applied Mathematics.
    view abstractdoi: 10.1137/100809325
  • 2012 • 43 Orientation dependence of shear banding in face-centered-cubic single crystals
    Jia, N. and Eisenlohr, P. and Roters, F. and Raabe, D. and Zhao, X.
    Acta Materialia 60 3415-3434 (2012)
    We present crystal plasticity finite element simulations of plane strain compression of α-Brass single crystals with different initial orientations. The aim is to study the fundamentals of mesoscale structure and texture development in face-centered-cubic (fcc) metals with low stacking fault energy (SFE). Shear banding depends on the initial orientation of the crystals. In Copper and Brass-R-oriented crystals which show the largest tendency to form shear bands, an inhomogeneous texture distribution induced by shear banding is observed. To also understand the influence of the micromechanical boundary conditions on shear band formation, simulations on Copper-oriented single crystals with varying sample geometry and loading conditions are performed. We find that shear banding can be understood in terms of a mesoscopic softening mechanism. The predicted local textures and the shear banding patterns agree well with experimental observations in low SFE fcc crystals. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2012.03.005
  • 2012 • 42 Atomistically informed crystal plasticity model for body-centered cubic iron
    Koester, A. and Ma, A. and Hartmaier, A.
    Acta Materialia 60 3894-3901 (2012)
    The glide of screw dislocations with non-planar dislocation cores dominates the plastic deformation behavior in body-centered cubic iron. This yields a strong strain rate and temperature dependence of the flow stress, the breakdown of Schmid's law and a dependence of dislocation mobility on stress components that do not contribute to the mechanical driving force of dislocation glide. We developed a constitutive plasticity model that takes all these effects into account. The model is based on the crystal plasticity approach and parameterized by performing molecular statics calculations using a semi-empirical potential. The atomistic studies yield quantitative relations between local stress tensor components and the mobility of dislocations. Together with experimental stress-strain curves obtained for two different orientations of iron single crystals taken from the literature, the constitutive law is completely parameterized. The model is validated by comparing numerical single crystal tension tests for a third orientation to the equivalent experimental data from the literature. We also provide results for the temperature and strain rate dependence of the new atomistically informed constitutive model. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2012.03.053
  • 2012 • 41 The stacking fault energy and its dependence on the interstitial content in various austenitic steels
    Mujica, L. and Weber, S. and Theisen, W.
    Materials Science Forum 706-709 2193-2198 (2012)
    The stacking fault energy (SFE) is an intrinsic property of metals and is involved in the deformation mechanism of different kind of steels, such as TWIP (twinning induced plasticity), TRIP (transformation induced plasticity), HNS (high nitrogen), and high strength steels. The dependence of the SFE on the content of interstitial elements (C, N) is not yet fully understood, and different tendencies have been found by different authors. In order to study the influence of the interstitial elements on the SFE, experimental measurements extracted from literature were collected and analyzed to predict the individual and combined effect of carbon and nitrogen in different systems. The referenced austenitic steels are Fe-22Mn-C, Fe-30Ni-C, Fe-15Cr-17Mn-N, Fe-18Cr-16Ni-10Mn-N, Fe-18Cr-9Mn-C-N, Fe-18Mn-18Cr-C-N and Fe-(20-30)Mn-12Cr-C-N. The calculation of the SFE is based on the Gibbs free energy of the austenite to ε-martensite transformation (ΔG γ→ε), which is calculated by means of the Calphad method. The revision of the measured values reveals that on different ranges of interstitial contents the SFE behaves differently. At lower values (C, N or C+N up to 0.4%), a local minimum or maximum is found in most of the systems. At higher concentration levels, a proportional dependence seems to occur. These observations agree with the theory of the dependence of SFE on the free electron concentration. Alloying with Mn or Ni has a strong influence on the electronic configuration and magnetic properties of the austenite and therefore on the SFE. The results of this study provide valuable information for materials design, especially in the context of alloying with C, N or C+N. © 2012 Trans Tech Publications, Switzerland.
    view abstractdoi: 10.4028/www.scientific.net/MSF.706-709.2193
  • 2012 • 40 Welding of twinning-induced plasticity steels
    Mújica Roncery, L. and Weber, S. and Theisen, W.
    Scripta Materialia 66 997-1001 (2012)
    This work focuses on the technical and technological aspects of fusion welding of high-manganese steels exhibiting twinning-induced plasticity (TWIP) for both similar and dissimilar joints. Changes in the alloy chemistry resulting from evaporation and dilution are discussed with respect to stacking fault energy and austenite stability. The influence of fusion welding on grain size and strength is also discussed. Conclusions are drawn with respect to optimization processes for fusion welding of TWIP steel. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.scriptamat.2011.11.041
  • 2012 • 39 Phase-transformations interacting with plasticity - A micro-sphere model applied to TRIP steel
    Ostwald, R. and Bartel, T. and Menzel, A.
    Computational Materials Science 64 12-16 (2012)
    We present an efficient model for the simulation of polycrystalline materials, particularly accounting for the interactions of solid to solid phase-transformations and plasticity. The underlying one-dimensional model is embedded into a micro-sphere formulation in order to simulate three-dimensional boundary value problems. Representative numerical examples are provided for both the micro-level and the macro-level. Moreover, a finite element implementation of the model is presented and discussed. © 2012 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.commatsci.2012.05.015
  • 2012 • 38 Bond order potentials for fracture, wear, and plasticity
    Pastewka, L. and Mrovec, M. and Moseler, M. and Gumbsch, P.
    MRS Bulletin 37 493-503 (2012)
    Coulson's bond order is a chemically intuitive quantity that measures the difference in the occupation of bonding and anti-bonding orbitals. Both empirical and rigorously derived bond order expressions have evolved in the course of time and proven very useful for atomistic modeling of materials. The latest generation of empirical formulations has recently been augmented by screening-function approaches. Using friction and wear of diamond and diamond-like carbon as examples, we demonstrate that such a screened bond order scheme allows for a faithful description of dynamical bond-breaking processes in materials far from equilibrium. The rigorous bond order expansions are obtained by systematic coarse-graining of the tight binding approximation and form a bridge between the electronic structure and the atomistic modeling hierarchies. They have enabled bottom-up derivations of bond order potentials for covalently bonded semiconductors, transition metals, and multicomponent intermetallics. The recently developed magnetic bond order potential gives a correct description of both directional covalent bonds and magnetic interactions in iron and is able to correctly predict the stability of bulk Fe polymorphs as well as the intricate properties of dislocation cores. The bond order schemes hence represent a family of reliable and powerful models that can be applied in large-scale simulations of complex processes involving fracture, wear, and plasticity. © 2012 Materials Research Society.
    view abstractdoi: 10.1557/mrs.2012.94
  • 2012 • 37 Atomic scale effects of alloying, partitioning, solute drag and austempering on the mechanical properties of high-carbon bainitic-austenitic TRIP steels
    Seol, J.-B. and Raabe, D. and Choi, P.-P. and Im, Y.-R. and Park, C.-G.
    Acta Materialia 60 6183-6199 (2012)
    Understanding alloying and thermal processing at an atomic scale is essential for the optimal design of high-carbon (0.71 wt.%) bainitic-austenitic transformation-induced plasticity (TRIP) steels. We investigate the influence of the austempering temperature, chemical composition (especially the Si:Al ratio) and partitioning on the nanostructure and mechanical behavior of these steels by atom probe tomography. The effects of the austempering temperature and of Si and Al on the compositional gradients across the phase boundaries between retained austenite and bainitic ferrite are studied. We observe that controlling these parameters (i.e. Si, Al content and austempering temperature) can be used to tune the stability of the retained austenite and hence the mechanical behavior of these steels. We also study the atomic scale redistribution of Mn and Si at the bainitic ferrite/austenite interface. The observations suggest that either para-equilibrium or local equilibrium-negligible partitioning conditions prevail depending on the Si:Al ratio during bainite transformation. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2012.07.064
  • 2012 • 36 Performance of mixed and enhanced finite elements for strain localization in hypoplasticity
    Trinh, B.T. and Hackl, K.
    International Journal for Numerical and Analytical Methods in Geomechanics 36 1125-1150 (2012)
    Displacement and mixed finite element formulations of shear localization in materials are presented. The formulations are based on hypoplastic constitutive laws for soils and the mixed enhanced treatment involving displacement, strain and stress rates as independently varied fields. Included in these formulations are the standard displacement method, the three-field mixed formulation, the enhanced assumed strain method and the mixed enhanced strain method. Several numerical examples demonstrating the capability and performance of the different finite element formulations are presented. The numerical results are compared with available experimental data for Hostun RF sand and numerical results for Karlsruhe sand on biaxial tests. © 2011 John Wiley & Sons, Ltd.
    view abstractdoi: 10.1002/nag.1042
  • 2012 • 35 Atomistic simulation of the influence of nanomachining-induced deformation on subsequent nanoindentation
    Zhang, J.J. and Sun, T. and Hartmaier, A. and Yan, Y.D.
    Computational Materials Science 59 14-21 (2012)
    In this paper it is demonstrated how nanoindentation can be used to assess the subsurface damage induced by nanomachining. To accomplish this, a characteristic difference in the nanoindentation response between plastically deformed and undeformed material is exploited. Classical molecular dynamics simulations are performed to investigate the elementary mechanisms of the irreversible plastic processes that occur during nanomachining of a copper single crystal. To mimic the experimental characterization of subsurface damage, we perform nanoindentation simulations into the machined surface. The results show that the critical contact pressure required for dislocation nucleation, i.e. the pop-in load, decreases continuously with increasing machining depth, while the indentation hardness seems widely unaffected by prior nanomachining. © 2012 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.commatsci.2012.02.024
  • 2011 • 34 First-principles investigation of the effect of carbon on the stacking fault energy of Fe-C alloys
    Abbasi, A. and Dick, A. and Hickel, T. and Neugebauer, J.
    Acta Materialia 59 3041-3048 (2011)
    The intrinsic stacking fault energy (SFE) is a critical parameter that defines the type of plasticity mechanisms in austenitic high-Mn steels. We have performed ab initio investigations to study the effect of interstitial carbon atoms on the SFE of face-centred cubic (fcc) Fe-C alloys. Simulating the stacking fault explicitly, we observe a strong dependence of the SFE on the position of carbon atoms with respect to the stacking-fault layer and the carbon concentration. To determine the SFE for realistic carbon distributions we consider two scenarios, assuming (i) an equilibration of the carbon atoms in response to the stacking fault formation and (ii) a homogeneous distribution of the C atoms when creating the stacking fault (i.e. diffusion is suppressed). This distinction allows us to interpret two sets of apparently contradicting experimental data sets, where some find an almost negligible dependence on the carbon concentration while others report a large carbon dependence. In particular, our results for the second scenario show a significant increase in the SFE as a function of carbon concentration. These trends are consistently found for the explicit calculations as well as for the computationally much more efficient axial next-nearest-neighbour Ising approach. They will be decisive for the selection of specific plasticity mechanisms in steels (such as twin formation, martensitic transformations and dislocation gliding). © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2011.01.044
  • 2011 • 33 A dislocation density-based crystal plasticity constitutive model for prismatic slip in α-titanium
    Alankar, A. and Eisenlohr, P. and Raabe, D.
    Acta Materialia 59 7003-7009 (2011)
    A new constitutive plasticity model for prismatic slip in hexagonal α-titanium is developed. In the concept pure edge and screw dislocation densities evolve on the {101̄0}〈12̄10〉 slip systems. The model considers that the screw dislocation segments have a spread out core, leading to a much higher velocity of edge compared with screw dislocations. This enables the model to describe the observed transition in strain hardening from stage I to stage II in single crystals oriented for prismatic slip. Good agreement is found between the experimentally observed and simulated stress-strain behavior. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2011.07.053
  • 2011 • 32 On the thermomechanical coupling in finite strain plasticity theory with non-linear kinematic hardening by means of incremental energy minimization
    Canadija, M. and Mosler, J.
    International Journal of Solids and Structures 48 1120-1129 (2011)
    The thermomechanical coupling in finite strain plasticity theory with non-linear kinematic hardening is analyzed within the present paper. This coupling is of utmost importance in many applications, e.g., in those showing low cycle fatigue (LCF) under large strain amplitudes. Since the by now classical thermomechanical coupling originally proposed by Taylor and Quinney cannot be used directly in case of kinematic hardening, the change in heat as a result of plastic deformation is computed by applying the first law of thermodynamics. Based on this balance law, together with a finite strain plasticity model, a novel variationally consistent method is elaborated. Within this method and following Stainier and Ortiz (2010), all unknown variables are jointly and conveniently computed by minimizing an incrementally defined potential. In sharp contrast to previously published works, the evolution equations are a priori enforced by employing a suitable parameterization of the flow rule and the evolution equations. The advantages of this parameterization are, at least, twofold. First, it leads eventually to an unconstrained stationarity problem which can be directly applied to any yield function being positively homogeneous of degree one, i.e., the approach shows a broad range of application. Secondly, the parameterization provides enough flexibility even for a broad range of non-associative models such as kinematic hardening of Armstrong-Frederick-type. Different to Stainier and Ortiz (2010), the continuous variational problem is approximated by a standard, fully-implicit time integration. The applicability of the resulting numerical implementation is finally demonstrated by analyzing the thermodynamically coupled response for a loading cycle. © 2011 Elsevier Ltd.
    view abstractdoi: 10.1016/j.ijsolstr.2010.12.018
  • 2011 • 31 A regularization framework for damage-plasticity models via gradient enhancement of the free energy
    Dimitrijevic, B.J. and Hackl, K.
    International Journal for Numerical Methods in Biomedical Engineering 27 1199-1210 (2011)
    We present a framework for the regularization of coupled damage-plasticity models through gradient enhancement of the Helmholtz-free-energy function. This enhancement is achieved introducing new variables, coupled to the gradients of the inelastic variables and thus regularizing the model. The variational formulation of the model results in a pure minimization problem. Numerical examples, which show the performance of the proposed gradient-enhanced model, are presented. It is shown that the pathological mesh dependence of the coupled inelastic model is efficiently removed, together with the difficulties of numerical calculations in the softening range. © 2009 John Wiley & Sons, Ltd.
    view abstractdoi: 10.1002/cnm.1350
  • 2011 • 30 Dislocation and twin substructure evolution during strain hardening of an Fe-22 wt.% Mn-0.6 wt.% C TWIP steel observed by electron channeling contrast imaging
    Gutierrez-Urrutia, I. and Raabe, D.
    Acta Materialia 59 6449-6462 (2011)
    We study the kinetics of the substructure evolution and its correspondence to the strain hardening evolution of an Fe-22 wt.% Mn-0.6 wt.% C TWIP steel during tensile deformation by means of electron channeling contrast imaging (ECCI) combined with electron backscatter diffraction (EBSD). The contribution of twin and dislocation substructures to strain hardening is evaluated in terms of a dislocation mean free path approach involving several microstructure parameters, such as the characteristic average twin spacing and the dislocation substructure size. The analysis reveals that at the early stages of deformation (strain below 0.1 true strain) the dislocation substructure provides a high strain hardening rate with hardening coefficients of about G/40 (G is the shear modulus). At intermediate strains (below 0.3 true strain), the dislocation mean free path refinement due to deformation twinning results in a high strain rate with a hardening coefficient of about G/30. Finally, at high strains (above 0.4 true strain), the limited further refinement of the dislocation and twin substructures reduces the capability for trapping more dislocations inside the microstructure and, hence, the strain hardening decreases. Grains forming dislocation cells develop a self-organized and dynamically refined dislocation cell structure which follows the similitude principle but with a smaller similitude constant than that found in medium to high stacking fault energy alloys. We attribute this difference to the influence of the stacking fault energy on the mechanism of cell formation. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2011.07.009
  • 2011 • 29 Existence and regularity of the plastic multiplier in static and quasistatic plasticity
    Herzog, R. and Meyer, C. and Wachsmuth, G.
    GAMM Mitteilungen 34 39-44 (2011)
    Existence of the plastic multiplier with L1 spatial regularity for quasistatic and static plasticity is proved for arbitrary continuous and convex yield functions and linear hardening laws. L2 regularity is shown in the particular cases of kinematic hardening, or combined kinematic and isotropic hardening. © 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/gamm.201110006
  • 2011 • 28 An incremental minimization principle suitable for the analysis of low cycle fatigue in metals: A coupled ductile-brittle damage model
    Kintzel, O. and Mosler, J.
    Computer Methods in Applied Mechanics and Engineering 200 3127-3138 (2011)
    The present paper is concerned with a novel variational constitutive update suitable for the analysis of low cycle fatigue in metals. The underlying constitutive model originally advocated in [1] accounts for plastic deformation as well as for damage accumulation. The latter is captured by a combination of two constitutive models. While the first of those is associated with ductile damage, the second material law is related to a quasi-brittle response. The complex overall model falls into the range of so-called generalized standard materials and thus, it is thermodynamically consistent. However, since the evolution equations are non-associative, it does not show an obvious variational structure. By enforcing the flow rule as well as the evolution equations through a suitable parameterization, a minimization principle can be derived nevertheless. Discretized in time, this principle is employed for developing an effective numerical implementation. Since the mechanical subproblems corresponding to ductile damage and that of quasi-brittle damage are uncoupled, an efficient staggered scheme can be elaborated. Within both steps, Newton's method is applied. While the evolution of the quasi-brittle damage requires only the computation of a one-dimensional optimization problem, the ductile damage model is defined by a numerically more expensive tensor-valued variable. For further increasing the numerical performance of the respective minimization principle, a closed-form solution for the inverse of the Hessian matrix is derived. By numerically analyzing the prediction of mesocrack initiation in low-cycle fatigue simulations, the performance of the resulting algorithm is demonstrated. © 2011 Elsevier B.V.
    view abstractdoi: 10.1016/j.cma.2011.07.006
  • 2011 • 27 Dislocation storage in single slip-oriented Cu micro-tensile samples: New insights via X-ray microdiffraction
    Kirchlechner, C. and Kiener, D. and Motz, C. and Labat, S. and Vaxelaire, N. and Perroud, O. and Micha, J.-S. and Ulrich, O. and Thomas, O. and Dehm, G. and Keckes, J.
    Philosophical Magazine 91 1256-1264 (2011)
    Synchrotron X-ray microdiffraction was used to characterize the deformation structure of single crystalline Cu micro-tensile specimens which were oriented for single slip. The 3-m thick samples were strained in situ in a scanning electron microscope (SEM). Electron microscopy observations revealed glide steps at the surface indicating single slip. While the slip steps at the surface must have formed by the predominant activation of the primary glide system, analysis of Laue peak streaking directions revealed that, even at low strains, dislocations had been activated and stored on an unpredicted slip system. Furthermore, the Laue scans showed that multiple slip takes over at a later state of deformation. © 2011 Taylor & Francis.
    view abstractdoi: 10.1080/14786431003785639
  • 2011 • 26 FETI-DP domain decomposition methods for elasticity with structural changes: P-elasticity
    Klawonn, A. and Neff, P. and Rheinbach, O. and Vanis, S.
    ESAIM: Mathematical Modelling and Numerical Analysis 45 563-602 (2011)
    We consider linear elliptic systems which arise in coupled elastic continuum mechanical models. In these systems, the strain tensor εP:= sym (P-1∇u) is redefined to include a matrix valued inhomogeneity P(x) which cannot be described by a space dependent fourth order elasticity tensor. Such systems arise naturally in geometrically exact plasticity or in problems with eigenstresses. The tensor field P induces a structural change of the elasticity equations. For such a model the FETI-DP method is formulated and a convergence estimate is provided for the special case that P-T = ∇ψ is a gradient. It is shown that the condition number depends only quadratic-logarithmically on the number of unknowns of each subdomain. The dependence of the constants of the bound on P is highlighted. Numerical examples confirm our theoretical findings. Promising results are also obtained for settings which are not covered by our theoretical estimates. © EDP Sciences, SMAI, 2010.
    view abstractdoi: 10.1051/m2an/2010067
  • 2011 • 25 The evolution of laminates in finite crystal plasticity: A variational approach
    Kochmann, D.M. and Hackl, K.
    Continuum Mechanics and Thermodynamics 23 63-85 (2011)
    The analysis and simulation of microstructures in solids has gained crucial importance, virtue of the influence of all microstructural characteristics on a material's macroscopic, mechanical behavior. In particular, the arrangement of dislocations and other lattice defects to particular structures and patterns on the microscale as well as the resultant inhomogeneous distribution of localized strain results in a highly altered stress-strain response. Energetic models predicting the mechanical properties are commonly based on thermodynamic variational principles. Modeling the material response in finite strain crystal plasticity very often results in a non-convex variational problem so that the minimizing deformation fields are no longer continuous but exhibit small-scale fluctuations related to probability distributions of deformation gradients to be calculated via energy relaxation. This results in fine structures that can be interpreted as the observed microstructures. In this paper, we first review the underlying variational principles for inelastic materials. We then propose an analytical partial relaxation of a Neo-Hookean energy formulation, based on the assumption of a first-order laminate microstructure, thus approximating the relaxed energy by an upper bound of the rank-one-convex hull. The semi-relaxed energy can be employed to investigate elasto-plastic models with a single as well as multiple active slip systems. Based on the minimization of a Lagrange functional (consisting of the sum of energy rate and dissipation potential), we outline an incremental strategy to model the time-continuous evolution of the laminate microstructure, then present a numerical scheme by means of which the microstructure development can be computed, and show numerical results for particular examples in single- and double-slip plasticity. We discuss the influence of hardening and of slip system orientations in the present model. In contrast to many approaches before, we do not minimize a condensed energy functional. Instead, we incrementally solve the evolution equations at each time step and account for the actual microstructural changes during each time step. Results indicate a reduction in energy when compared to those theories based on a condensed energy functional. © 2010 Springer-Verlag.
    view abstractdoi: 10.1007/s00161-010-0174-5
  • 2011 • 24 Scanning transmission electron microscope observations of defects in as-grown and pre-strained Mo alloy fibers
    Phani, P.S. and Johanns, K.E. and Duscher, G. and Gali, A. and George, E.P. and Pharr, G.M.
    Acta Materialia 59 2172-2179 (2011)
    Compression testing of micro-pillars has recently been of great interest to the small-scale mechanics community. Previous compression tests on single crystal Mo alloy micro-pillars produced by directional solidification of eutectic alloys showed that as-grown pillars yield at strengths close to the theoretical strength while pre-strained pillars yield at considerably lower stresses. In addition, the flow behavior changes from stochastic to deterministic with increasing pre-strain. In order to gain a microstructural insight into this behavior, an aberration corrected scanning transmission electron microscope was used to study the defect structures in as-grown and pre-strained single crystal Mo alloy fibers. The as-grown fibers were found to be defect free over large lengths while the highly pre-strained (16%) fibers had high defect densities that were uniform throughout. Interestingly, the fibers with intermediate pre-strain (4%) exhibited an inhomogeneous defect distribution. The observed defect structures and their distributions are correlated with the previously reported stress-strain behavior. Some of the mechanistic interpretations of Bei et al. are examined in the light of new microstructural observations. © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2010.12.018
  • 2011 • 23 Powder metallurgy processing and compressive properties of Ti3AlC2/Al composites
    Wang, W.J. and Gauthier-Brunet, V. and Bei, G.P. and Laplanche, G. and Bonneville, J. and Joulain, A. and Dubois, S.
    Materials Science and Engineering A 530 168-173 (2011)
    Al-matrix material composites are produced from pure Al and 40vol.% Ti3AlC2 powders using hot isostatic pressing technique. It is demonstrated that the nanocrystallized-Ti3AlC2 agglomerates, uniformly distributed in the Al matrix, form a hard continuous skeleton. The mechanical properties of the composites are evaluated over the temperature range of 20-500°C by performing compression tests at constant strain rate. The monotonic temperature dependence of the proof stress at 0.2% plastic strain suggests that the same thermally activated mechanism controls the composite plastic deformation over the entire temperature range. The yield stress of the composite, about twice as high as that of the Al matrix in the investigated temperature range proves that Ti3AlC2 particles constitute efficient reinforcement particles for Al matrix. SEM observations indicate that plastic deformation of 40Ti3AlC2/60Al composite takes place in the Al matrix while Ti3AlC2 particle agglomerates undergo substantial fracture. © 2011 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2011.09.068
  • 2011 • 22 Analysis of the plastic anisotropy and pre-yielding of (γ/ α2)-phase titanium aluminide microstructures by crystal plasticity simulation
    Zambaldi, C. and Roters, F. and Raabe, D.
    Intermetallics 19 820-827 (2011)
    The plastic deformation of lamellar microstructures composed of the two phases γ-TiAl and α2-Ti3Al is highly orientation dependent. In this paper we present a homogenized model that takes into account the micromechanical effect of the plate-like morphologies that are often observed in two-phase titanium aluminide alloys. The model is based on crystal elasto-viscoplasticity and 18 deformation systems were implemented that have been identified to govern the plastic flow of the lamellar microstructures. The model is validated against experiments on polysynthetically twinned (PST) crystals and shows good agreement with the data. On a larger length scale, the model is applied to a 64-grain aggregate to investigate the mechanical response of two different kinds of microstructures. Different magnitudes of the kinematic constraints exerted by the densely spaced and highly aligned interfaces are shown to affect the macroscopic flow behavior of the microstructures. The phenomenon of pronounced microplasticity of fully lamellar material as well as the stress variation inside two-phase microstructures are studied quantitatively. © 2011 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.intermet.2011.01.012
  • 2010 • 21 A two-dimensional dislocation dynamics model of the plastic deformation of polycrystalline metals
    Ahmed, N. and Hartmaier, A.
    Journal of the Mechanics and Physics of Solids 58 2054-2064 (2010)
    Two-dimensional dislocation dynamics (2D-DD) simulations under fully periodic boundary conditions are employed to study the relation between microstructure and strength of a material. The material is modeled as an elastic continuum that contains a defect microstructure consisting of a preexisting dislocation population, dislocation sources, and grain boundaries. The mechanical response of such a material is tested by uniaxially loading it up to a certain stress and allowing it to relax until the strain rate falls below a threshold. The total plastic strain obtained for a certain stress level yields the quasi-static stressstrain curve of the material. Besides assuming FrankRead-like dislocation sources, we also investigate the influence of a pre-existing dislocation density on the flow stress of the model material. Our results show that despite its inherent simplifications the 2D-DD model yields material behavior that is consistent with the classical theories of Taylor and HallPetch. Consequently, if set up in a proper way, these models are suited to study plastic deformation of polycrystalline materials. © 2010 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.jmps.2010.09.005
  • 2010 • 20 Bending of single crystal microcantilever beams of cube orientation: Finite element model and experiments
    Demir, E. and Roters, F. and Raabe, D.
    Journal of the Mechanics and Physics of Solids 58 1599-1612 (2010)
    The aim of this work is to investigate the microstructure evolution, stressstrain response and strain hardening behavior of microscale beams. For that purpose, two single crystal cantilever beams in the size dependent regime were manufactured by ion beam milling and beams were bent with an indenter device. A crystal plasticity material model for large deformations was implemented in a finite element framework to further investigate the effect of boundary constraints. Simulations were performed using bulk material properties of single crystal copper without any special treatment for the strain gradients. The difference between the slopes of the experimental and the simulated force displacement curves suggested negligible amount of strain gradient hardening compared to the statistical hardening mechanisms. © 2010 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.jmps.2010.07.007
  • 2010 • 19 The mechanical size effect as a mean-field breakdown phenomenon: Example of microscale single crystal beam bending
    Demir, E. and Raabe, D. and Roters, F.
    Acta Materialia 58 1876-1886 (2010)
    Single crystalline copper beams with thicknesses between 0.7 and 5 μm are manufactured with a focused ion beam technique and bent in a nanoindenter. The yield strengths of the beams show a mechanical size effect (smaller-is-stronger). The geometrically necessary dislocation (GND) densities estimated from misorientation maps do not explain the observed size effect. Also, accumulation of GNDs principally requires pre-straining. We hence introduce a mean-field breakdown theory and generalize it to small-scale mechanical tests other than bending. The mean-field breakdown limit is defined in terms of a microstructural correlation measure (characteristic dislocation bow-out length) below which the local availability of dislocation sources and not the density of GNDs dominates the mechanical size effect. This explains why a size dependence can occur for samples that are not pre-strained (by using a very small critical strain to define the yield strength). After pre-straining, when GNDs build up, they can contribute to the flow stress. The mean-field breakdown theory can also explain the large scatter typically observed in small-scale mechanical tests as the availability of sufficiently soft sources at scales around or below the correlation length does not follow statistical laws but highly depends on the position where the probe is taken. © 2009 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2009.11.031
  • 2010 • 18 Existence and uniqueness for rate-independent infinitesimal gradient plasticity with isotropic hardening and plastic spin
    Ebobisse, F. and Neff, P.
    Mathematics and Mechanics of Solids 15 691-703 (2010)
    Existence and uniqueness for infinitesimal dislocation based rate-independent gradient plasticity with linear isotropic hardening and plastic spin are shown using convex analysis and variational inequality methods. The dissipation potential is extended non-uniquely from symmetric plastic rates to non-symmetric plastic rates and three qualitatively different formats for the dissipation potential are distinguished. © 2010 The Author(s).
    view abstractdoi: 10.1177/1081286509342269
  • 2010 • 17 Investigation of the fatigue behavior of Al thin films with different microstructure
    Heinz, W. and Pippan, R. and Dehm, G.
    Materials Science and Engineering A 527 7757-7763 (2010)
    Cyclic compressive and tensile stresses occur in metallic films and interconnects applied in sensors and microelectronic devices when exposed to temperature changes. The stresses are induced by differences in the thermal expansion coefficients of the adjacent materials. Repeated cycling leads to damage evolution and, eventually, to failure. In this study we report on a successful strategy how to avoid thermal stress induced fatigue damage. We analysed the deformation structures of 0.2-2μm thick Al films subjected to thermal cycling between 100°C and 450°C up to 10,000 times. The investigations reveal that a reduction in film thickness or controlling the Al texture and the Al/substrate interface structure can be used to prevent thermo-mechanical fatigue damage. The findings are explained by orientation dependent plasticity and differences in dislocation mechanisms for different interface structures, and less accumulated plastic strain for thinner films. The approach is expected to apply in general for metallic films on substrates. © 2010 Elsevier B.V.
    view abstractdoi: 10.1016/j.msea.2010.08.046
  • 2010 • 16 Determining Burgers vectors and geometrically necessary dislocation densities from atomistic data
    Hua, J. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 18 (2010)
    We describe a novel analysis method to quantify the Burgers vectors of dislocations in atomistic ensembles and to calculate densities of geometrically necessary and statistically stored dislocations. This is accomplished by combining geometrical methods to determine dislocation cores and the slip vector analysis, which yields the relative slip of the atoms in dislocation cores and indicates the Burgers vectors of the dislocations. To demonstrate its prospects, the method is applied to investigate the density of geometrically necessary dislocations under a spherical nanoindentation. It is seen that this local information about dislocation densities provides useful information to bridge the gap between atomistic methods and continuum descriptions of plasticity, in particular for non-local plasticity. © 2010 IOP Publishing Ltd.
    view abstractdoi: 10.1088/0965-0393/18/4/045007
  • 2010 • 15 Numerical investigation of room-temperature deformation behavior of a duplex type γtiAl alloy using a multi-scale modeling approach
    Kabir, M.R. and Chernova, L. and Bartsch, M.
    Acta Materialia 58 5834-5847 (2010)
    Room-temperature deformation of a niobium-rich TiAl alloy with duplex microstructure has been numerically investigated. The model links the microstructural features at micro- and meso-scale by the two-level (FE 2) multi-scale approach. The deformation mechanisms of the considered phases were described in the micro-mechanical crystal-plasticity model. Initial material parameters for the model were taken from the literature and validated using tensile experiments at macro-scale. For the niobium-rich TiAl alloy further adaptation of the crystal plasticity parameters is proposed. Based on these model parameters, the influences of the grain orientation, grain size, and texture on the global mechanical behavior have been investigated. The contributions of crystal deformation modes (slips and dislocations in the phases) to the mechanical response are also analyzed. The results enable a quantitative prediction of relationships between microstructure and mechanical behavior on global and local scale, including an assessment of possible crack initiation sites. The model can be used for microstructure optimization to obtain better material properties. © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.actamat.2010.06.058
  • 2010 • 14 A novel isotropic quasi-brittle damage model applied to LCF analyses of Al2024
    Kintzel, O. and Khan, S. and Mosler, J.
    International Journal of Fatigue 32 1948-1959 (2010)
    The current paper deals with the assessment and the numerical simulation of low cycle fatigue of an aluminum 2024 alloy. According to experimental observations, the material response of Al2024 is highly direction-dependent showing a material behavior between ductile and brittle. In particular, in its corresponding (small transversal) S-direction, the material behavior can be characterized as quasi-brittle. For the modeling of such a mechanical response, a novel, fully coupled isotropic ductile-brittle continuum damage mechanics model is proposed. Since the resulting model shows a large number of material parameters, an efficient, hybrid parameter identification strategy is discussed. Within this strategy, as many parameters as possible have been determined a priori by exploiting analogies to established theories (like Paris' law), while the remaining free unknowns are computed by solving an optimization problem. Comparisons between the experimentally observed and the numerically simulated lifetimes reveal the prediction capability of the proposed model. © 2010 Elsevier Ltd. All rights reserved.
    view abstractdoi: 10.1016/j.ijfatigue.2010.07.001
  • 2010 • 13 Comparison of finite element and fast Fourier transform crystal plasticity solvers for texture prediction
    Liu, B. and Raabe, D. and Roters, F. and Eisenlohr, P. and Lebensohn, R.A.
    Modelling and Simulation in Materials Science and Engineering 18 (2010)
    We compare two full-field formulations, i.e. a crystal plasticity fast Fourier transform-based (CPFFT) model and the crystal plasticity finite element model (CPFEM) in terms of the deformation textures predicted by both approaches. Plane-strain compression of a 1024-grain ensemble is simulated with CPFFT and CPFEM to assess the models in terms of their predictions of texture evolution for engineering applications. Different combinations of final textures and strain distributionsare obtained with the CPFFT and CPFEM models for this 1024-grain polycrystal. To further understand these different predictions, the correlation between grain rotations and strain gradients is investigated through the simulation of plane-strain compression of bicrystals. Finally, a study of the influence of the initial crystal orientation and the crystallographic neighborhood on grain rotations and grain subdivisions is carried out by means of plane-strain compression simulations of a 64-grain cluster. © 2010 IOP Publishing Ltd.
    view abstractdoi: 10.1088/0965-0393/18/8/085005
  • 2010 • 12 Effect of strain hardening on texture development in cold rolled Al-Mg alloy
    Liu, W.C. and Man, C.-S. and Raabe, D.
    Materials Science and Engineering A 527 1249-1254 (2010)
    The hot band of a continuous cast Al-Mg alloy possesses a typical deformed structure and a strong β fiber rolling texture. The hot band was heat-treated at 260 °C for 3 h to generate different degrees of strain hardening. The hot band and its counterpart after recovery treatment were cold rolled to different reductions along the original transverse direction. The effect of strain hardening on texture evolution was investigated by X-ray diffraction. The results show that a high degree of strain hardening reduces the formation rate of the β fiber rolling texture. © 2009 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.msea.2009.09.059
  • 2010 • 11 On the implementation of rate-independent standard dissipative solids at finite strain - Variational constitutive updates
    Mosler, J. and Bruhns, O.T.
    Computer Methods in Applied Mechanics and Engineering 199 417-429 (2010)
    This paper is concerned with an efficient, variationally consistent, implementation for rate-independent dissipative solids at finite strain. More precisely, focus is on finite strain plasticity theory based on a multiplicative decomposition of the deformation gradient. Adopting the formalism of standard dissipative solids which allows to describe constitutive models by means of only two potentials being the Helmholtz energy and the yield function (or equivalently, a dissipation functional), finite strain plasticity is recast into an equivalent minimization problem. In contrast to previous models, the presented framework covers isotropic and kinematic hardening as well as isotropic and anisotropic elasticity and yield functions. Based on this approach a novel numerical implementation representing the main contribution of the paper is given. In sharp contrast to by now classical approaches such as the return-mapping algorithm and analogously to the theoretical part, the numerical formulation is variationally consistent, i.e., all unknown variables follow naturally from minimizing the energy of the considered system. Consequently, several different numerically efficient and robust optimization schemes can be directly employed for solving the resulting minimization problem. Extending previously published works on variational constitutive updates, the advocated model does not rely on any material symmetry and therefore, it can be applied to a broad range of different plasticity theories. As two examples, an anisotropic Hill-type and a Barlat-type model are implemented. Numerical examples demonstrate the applicability and the performance of the proposed implementation. © 2009 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.cma.2009.07.006
  • 2010 • 10 Parallel simulation of an infinitesimal elasto-plastic Cosserat model
    Neff, P. and Müller, W. and Wieners, C.
    GAMM Mitteilungen 33 79-94 (2010)
    We review the continuous and fully-discrete problem setting of an elasto-plastic Cosserat model, which is an enhanced continuum model with independent rotational degrees of freedom. The continuous model is defined by a variational inequality, and for the discrete model a corresponding non-smooth nonlinear variational problem is derived which can be solved with a generalized Newton method. We present numerical results for two representative geometries, where we test the convergence for different finite element discretizations, we study the parameter dependency, and we demonstrate the efficiency of the parallel solution method for very large problem sizes. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
    view abstractdoi: 10.1002/gamm.201010007
  • 2010 • 9 Development of Mn-Cr-(C-N) corrosion resistant twinning induced plasticity steels: Thermodynamic and diffusion calculations, production, and characterization
    Roncery, L.M. and Weber, S. and Theisen, W.
    Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 41 2471-2479 (2010)
    In this work, the development of corrosion-resistant twinning induced plasticity steels is presented, supported by thermodynamic and diffusion calculations within the (Fe-Mn-Cr)-(C-N) alloy system. For the calculations, ambient pressure and primary austenitic solidification were considered as necessary to avoid nitrogen degassing in all processing steps. Manganese is used as an austenite stabilizer, chromium is used to increase nitrogen solubility and provide corrosion resistance, and carbon and nitrogen are used as interstitial elements to provide mechanical strength. Isopleths of the different elements vs temperature as well as isothermal sections were calculated to determine the proper amount of Mn, Cr, total interstitial content, and the C/N ratio. Scheil and diffusion calculations were used to predict the extent of microsegregations and additionally to evaluate the effect of diffusion annealing treatments. The materials were produced in laboratory scale, being followed by thermomechanical processing and the characterization of the microstructure. Tensile tests were performed with three different alloys, exhibiting yield strengths of 460 Mpa to 480 MPa and elongations to fracture between 85 pct and 100 pct. © The Minerals, Metals & Materials Society and ASM International 2010.
    view abstractdoi: 10.1007/s11661-010-0334-z
  • 2010 • 8 Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
    Roters, F. and Eisenlohr, P. and Hantcherli, L. and Tjahjanto, D.D. and Bieler, T.R. and Raabe, D.
    Acta Materialia 58 1152-1211 (2010)
    This article reviews continuum-based variational formulations for describing the elastic-plastic deformation of anisotropic heterogeneous crystalline matter. These approaches, commonly referred to as crystal plasticity finite-element models, are important both for basic microstructure-based mechanical predictions as well as for engineering design and performance simulations involving anisotropic media. Besides the discussion of the constitutive laws, kinematics, homogenization schemes and multiscale approaches behind these methods, we also present some examples, including, in particular, comparisons of the predictions with experiments. The applications stem from such diverse fields as orientation stability, microbeam bending, single-crystal and bicrystal deformation, nanoindentation, recrystallization, multiphase steel (TRIP) deformation, and damage prediction for the microscopic and mesoscopic scales and multiscale predictions of rolling textures, cup drawing, Lankfort (r) values and stamping simulations for the macroscopic scale. © 2009 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2009.10.058
  • 2010 • 7 Periodic homogenization of the Prandtlreuss model with hardening
    Schweizer, B. and Veneroni, M.
    Journal of Multiscale Modeling 2 69-106 (2010)
    We study the n-dimensional wave equation with an elastoplastic nonlinear stressstrain relation. We investigate the case of heterogeneous materials, i.e., x-dependent parameters that are periodic at the scale η>0. We study the limit η→0 and derive the plasticity equations for the homogenized material. We prove the well-posedness for the original and the effective system with a finite-element approximation. The approximate solutions are also used in the homogenization proof which is based on oscillating test functions and an adapted version of the div-curl Lemma. © 2010 Imperial College Press.
    view abstractdoi: 10.1142/S1756973710000291
  • 2010 • 6 Finite deformation plasticity coupled with isotropic damage: Formulation in principal axes and applications
    Soyarslan, C. and Tekkaya, A.E.
    Finite Elements in Analysis and Design 46 668-683 (2010)
    A local, isotropic damage coupled hyperelasticplastic framework is formulated in principal axes. It is shown that, in a functional setting, treatment of many damage growth models, including those originated from phenomenological models (with formal thermodynamical derivations), micro-mechanics or fracture criteria, proposed in the literature, is possible. As a model problem, a Lemaitre-variant damage model with quasi-unilateral damage evolutionary forms is given with special emphasis on the feasibility of formulations in principal axes. To this end, closed form expression for the inelastic tangent moduli, consistent with the linearization of the closest point projection algorithm, is derived. It is shown that, generally, even in the absence of quasi-unilateral damage evolutionary conditions, the consistent tangent moduli are unsymmetric. The model is implemented as a user defined material subroutine (UMAT) for ABAQUS/Standard. The predictive capability of the selected model problem is studied through axi-symmetric application problems involving forward extrusion of a cylindrical billet, upsetting of a tapered specimen and tension of a notched specimen, in which characteristic failure mechanisms are observed. © 2010 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.finel.2010.03.006
  • 2010 • 5 A damage coupled orthotropic finite plasticity model for sheet metal forming: CDM approach
    Soyarslan, C. and Tekkaya, A.E.
    Computational Materials Science 48 150-165 (2010)
    A framework for orthotropic finite plasticity coupled with a Lemaitre type isotropic ductile damage is presented in a thermodynamically sound setting for sheet metal forming. The finite plasticity utilizes Green-Naghdi type additive decomposition in the logarithmic Lagrangean strain space, which allows adaptation of the return mapping schemes of damage coupled infinitesimal plasticity. Hydrostatic stress state and principal stress state dependent unilateral damage evolutionary conditions are efficiently formulated without need for repetitive tensor transformations, taking advantage of the eigenvalue equivalence in between the stress measure conjugate to the logarithmic Lagrangean strain and the Kirchhoff stress. For the sake of completeness a Perzyna type viscous regularization is also elaborated. A three-step, staggered local integration algorithm, composed of elastic prediction, plastic correction and damage deterioration, is performed for return mapping at integration points. To this end, the framework is implemented as a VUMAT subroutine for ABAQUS/Explicit and used in a set of simulations. Besides proving the applicability range of the methodology, the outcomes show that Lemaitre model, once enhanced with unilateral damage evolutionary conditions, gives physically meaningful results in cup drawing simulations. © 2010 Elsevier B.V. All rights reserved.
    view abstractdoi: 10.1016/j.commatsci.2009.12.022
  • 2010 • 4 Adaptive least squares finite element methods in elasto-plasticity
    Starke, G.
    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 5910 LNCS 671-678 (2010)
    In computational mechanics applications, one is often interested not only in accurate approximations for the displacements but also for the stress tensor. Least squares finite element methods are perfectly suited for such problems since they approximate both process variables simultaneously in suitable finite element spaces. We consider an least squares formulation for the incremental formulation of elasto-plasticity using a plastic flow rule of von Mises type. The nonlinear least squares functional constitutes an a posteriori error estimator on which an adaptive refinement strategy may be based. The variational formulation under plane strain and plane stress conditions is investigated in detail. Standard conforming elements are used for the displacement approximation while the stress is represented by Raviart-Thomas elements. The algebraic least squares problems arising from the finite element discretization are nonlinear and nonsmooth and may be solved by generalized Newton methods. © 2010 Springer-Verlag Berlin Heidelberg.
    view abstractdoi: 10.1007/978-3-642-12535-5_80
  • 2010 • 3 Crystal plasticity modelling and experiments for deriving microstructure-property relationships in γ-TiAl based alloys
    Zambaldi, C. and Raabe, D.
    Journal of Physics: Conference Series 240 (2010)
    Single-crystals of γ-TiAl cannot be grown for the compositions present inside the two-phase γ/α 2-microstructures that show good mechanical properties. Therefore the single crystal constitutive behaviour of γ-TiAl was studied by nanoindentation experiments in single phase regions of these microstructures. The experiments were extensively characterized by a combined experimental approach to clarify the orientation dependent mechanical response during nanoindentation. They further were analyzed by a three-dimensional crystal plasticity finite element model that incorporated the deformation behaviour of γ-TiAl. The spatially resolved activation of competing deformation mechanisms during indentation was used to assess their relative strengths. On the length-scale of multi-grain aggregates two kinds of microstructures were investigated. The lamellar microstructure was analyzed in terms of kinematic constraints perpendicular to densely spaced lamellar boundaries which lead to pronounced plastic anisotropy. Secondly, the mechanical behaviour of massively transformed microstructures was modelled by assuming a lower degree of kinematic constraints. This resulted in less plastic anisotropy on a single grain scale and lower compatibility stresses in a 64-grain aggregate. On the macroscopic length scale, the results could possibly explain the pre-yielding of lamellar microstructures. © 2010 IOP Publishing Ltd.
    view abstractdoi: 10.1088/1742-6596/240/1/012140
  • 2010 • 2 Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation
    Zambaldi, C. and Raabe, D.
    Acta Materialia 58 3516-3530 (2010)
    Single crystals of γ-TiAl cannot be grown in the near-stoichiometric compositions that are present inside two-phase γ / α2-microstructures with attractive mechanical properties. Therefore, the single-crystal constitutive behavior of γ-TiAl was studied by nanoindentation experiments in single-phase regions of these γ / α2-microstructures. The experiments were characterized by orientation microscopy and atomic force microscopy to quantify the orientation-dependent mechanical response during nanoindentation. Further, they were analyzed by a three-dimensional crystal plasticity finite element model that incorporated the deformation behavior of γ-TiAl. The spatially resolved activation of competing deformation mechanisms during indentation was used to assess their relative strengths. A convention was defined to unambiguously relate any indentation axis to a crystallographic orientation. Experiments and simulations were combined to study the orientation-dependent surface pile-up. The characteristic pile-up topographies were simulated throughout the unit triangle of γ-TiAl and represented graphically in the newly introduced inverse pole figure of pile-up patterns. Through this approach, easy activation of ordinary dislocation glide in stoichiometric γ-TiAl was confirmed independently from dislocation observation by transmission electron microscopy. © 2010 Acta Materialia Inc.
    view abstractdoi: 10.1016/j.actamat.2010.02.025
  • 2010 • 1 Influence of crystal anisotropy on elastic deformation and onset of plasticity in nanoindentation: A simulational study
    Ziegenhain, G. and Urbassek, H.M. and Hartmaier, A.
    Journal of Applied Physics 107 (2010)
    Using molecular-dynamics simulation we simulate nanoindentation into the three principal surfaces-the (100), (110), and (111) surface-of Cu and Al. In the elastic regime, the simulation data agree fairly well with the linear elastic theory of indentation into an elastically anisotropic substrate. With increasing indentation depth, the effect of pressure hardening becomes visible. When the critical stress for dislocation nucleation is reached, even the elastically isotropic Al shows a strong dependence of the force-displacement curves on the surface orientation. After the load drop, when plasticity has set in, the influence of the surface orientation is lost, and the contact pressure (hardness) becomes independent of the surface orientation. © 2010 American Institute of Physics.
    view abstractdoi: 10.1063/1.3340523