Prof. Dr. Alexander Hartmaier

ICAMS
Ruhr-Universität Bochum

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  • Atomistic investigation of machinability of monocrystalline 3C–SiC in elliptical vibration-assisted diamond cutting
    Zhao, L. and Zhang, J. and Zhang, J. and Hartmaier, A.
    Ceramics International 47 (2021)
    Deformation-induced characteristics of surface layer strongly rely on loading condition-related operating deformation modes. In the current study we reveal the mechanisms governing machined surface formation of hard brittle monocrystalline 3C–SiC in ultrasonic elliptical vibration-assisted diamond cutting by molecular dynamics simulations. Simulation results show different deformation modes including phase transformation, dislocation activity, and crack nucleation and propagation, as well as their correlations with surface integrity in terms of machined surface morphology and subsurface damage. In particular, molecular dynamics simulations of ordinary cutting are also carried out, which demonstrate the effectiveness of applying ultrasonic vibration of cutting tool in decreasing machining force and suppressing crack events, i.e., promoting ductile-mode cutting for achieving high surface integrity. The physical mechanism governing the machining differences between the two machining processes are also revealed. Furthermore, the effect of cutting depth on machined surface integrity under vibration-assisted cutting and ordinary cutting is addressed. © 2020 Elsevier Ltd and Techna Group S.r.l.
    view abstract10.1016/j.ceramint.2020.09.078
  • Cutting path-dependent machinability of SiCp/Al composite under multi-step ultra-precision diamond cutting
    LU, S. and ZHANG, J. and LI, Z. and ZHANG, J. and WANG, X. and HARTMAIER, A. and XU, J. and YAN, Y. and SUN, T.
    Chinese Journal of Aeronautics 34 (2021)
    Particle-tool interactions, which govern the synergetic deformation of SiC particle reinforced Al matrix composites under mechanical machining, strongly depend on the geometry of particle position residing on cutting path. In the present work, we investigate the influence of cutting path on the machinability of a SiCp/Al composite in multi-step ultra-precision diamond cutting by combining finite element simulations with experimental observations and characterization. Be consistent with experimentally characterized microstructures, the simulated SiCp/Al composite is considered to be composed of randomly distributed polygonally-shaped SiC particles with a volume fraction of 25vol%. A multi-step cutting strategy with depths of cut ranging from 2 to 10 μm is adopted to achieve an ultimate depth of cut of 10 μm. Intrinsic material parameters and extrinsic cutting conditions utilized in finite element simulations of SiCp/Al cutting are consistent with those used in corresponding experiments. Simulation results reveal different particle-tool interactions and failure modes of SiC particles, as well as their correlations with machining force evolution, residual stress distribution and machined surface topography. A detailed comparison between numerical simulation results and experimental data of multi-step diamond cutting of SiCp/Al composite reveals a substantial impact of the number of cutting steps on particle-tool interactions and machined surface quality. These findings provide guidelines for achieving high surface finish of SiCp/Al composites by ultra-precision diamond cutting. © 2020 Chinese Society of Aeronautics and Astronautics
    view abstract10.1016/j.cja.2020.07.039
  • Depth-sensing ductile and brittle deformation in 3C-SiC under Berkovich nanoindentation
    Zhao, L. and Zhang, J. and Pfetzing, J. and Alam, M. and Hartmaier, A.
    Materials and Design 197 (2021)
    The interplay between ductile and brittle deformation modes in hard brittle materials exhibits a strong size effect. In the present work, indentation depth-dependent deformation mechanisms of single-crystal 3C-SiC under Berkovich nanoindentation are elucidated by finite element simulations and corresponding experiments. A novel finite element framework, that combines a crystal plasticity constitutive model for describing dislocation slip-based ductile deformation and a cohesive zone model for capturing crack initiation and propagation-induced brittle fracture, is established. The utilized parameters in the crystal plasticity model of 3C-SiC are calibrated according to the load-displacement curves obtained from corresponding Berkovich nanoindentation experiments. Subsequent finite element simulations and experiments of nanoindentation jointly reveal co-existing microscopic plastic deformation and brittle fracture of 3C-SiC at different indentation depths, which significantly affect the observed macroscopic mechanical response and surface pile-up topography. In particular, the predicted morphology of surface cracks at an indentation depth of 500 nm agrees well with experimental observation, and the correlation of crack initiation and propagation with surface pile-up topography is theoretically analyzed. © 2020 The Authors
    view abstract10.1016/j.matdes.2020.109223
  • Amorphization-governed elasto-plastic deformation under nanoindentation in cubic (3C) silicon carbide
    Zhao, L. and Alam, M. and Zhang, J. and Janisch, R. and Hartmaier, A.
    Ceramics International 46 (2020)
    Amorphization plays an important role in ceramic deformation under mechanical loading. In the present work, we investigate the elasto-plastic deformation mechanisms of monocrystalline cubic silicon carbide (3C–SiC) in spherical nanoindentation by means of molecular dynamics simulations. The indentation-induced amorphization and its interactions with other deformation modes are emphasized. Initially, the suitable empirical potential capable of accurately characterizing the mechanical and defect properties of monocrystalline 3C–SiC, as well as the propensity of phase transformation from 3C–SiC to amorphous SiC, is rationally selected by benchmarking of different empirical potentials with experimental data and density functional theory calculations. Subsequently, the inhomogeneous elastic-plastic transitions during nanoindentation of monocrystalline 3C–SiC, as well as their dependence on crystallographic orientation, are investigated. Phase transformations including amorphization are analyzed using combined methods based on radial distribution function and bond angle distribution. Our simulation results demonstrate that before plasticity initiation-related “pop-in” event, each indented-monocrystalline 3C–SiC experiences a pure quasi-elastic deformation governed by the formation of amorphous structures. And this process of amorphization is fully reversible for small indentation depths. Further amorphization and dislocation nucleation jointly dominate the incipient plasticity in 3C–SiC nanoindentation. It is found that the indentation-induced defect zone composed of amorphous phase and dislocations is more pronounced in 3C–SiC(010) than that in the other two orientations of (110) and (111). © 2020 Elsevier Ltd and Techna Group S.r.l.
    view abstract10.1016/j.ceramint.2020.02.009
  • Anisotropic failure behavior of ordered intermetallic TiAl alloys under pure mode-I loading
    Neogi, A. and Alam, M. and Hartmaier, A. and Janisch, R.
    Modelling and Simulation in Materials Science and Engineering 28 (2020)
    Whether a metallic material fractures by brittle cleavage or by ductile rupture is primarily governed by the competition between cleavage and dislocation emission at the crack tip. The linear elastic fracture mechanics (LEFM) based criterion of Griffith, respectively the one for dislocation emission of Rice, are sufficiently reliable for determining the possible crack tip propagation mechanisms in isotropic crystalline metals. However, the applicability of these criteria is questionable when non-cubic, anisotropic solids are considered, as e.g. ordered intermetallic TiAl phases, where slip systems are limited and elastic anisotropy is pronounced. We study brittle versus ductile failure mechanisms in face-centered tetragonal TiAl and hexagonal Ti3Al using large-scale atomistic simulations and compare our findings to the predictions of LEFM-based criteria augmented by elastic anisotropy. We observe that the augmented Griffith and Rice criteria are reliable for determining the direction dependent crack tip mechanisms, if all the available dislocation slip systems are taken into account. Yet, atomistic simulations are necessary to understand crack blunting due to mixed mechanisms, or shear instabilities other than dislocation emission. The results of our systematic study can be used as basis for modifications of the Griffith/Rice criteria in order to incorporate such effects. © 2020 The Author(s). Published by IOP Publishing Ltd.
    view abstract10.1088/1361-651X/aba738
  • Anisotropy-Related Machining Characteristics in Ultra-Precision Diamond Cutting of Crystalline Copper
    Wang, Z. and Zhang, J. and Li, G. and Xu, Z. and Zhang, H. and Zhang, J. and Hartmaier, A. and Fang, F. and Yan, Y. and Sun, T.
    Nanomanufacturing and Metrology 3 (2020)
    Deformation behavior at grain levels greatly affects the machining characteristics of crystalline materials. In the present work, we investigate the influence of material anisotropy on ultra-precision diamond cutting of single crystalline and polycrystalline copper by experiments and crystal plasticity finite element simulations. Specifically,diamond turning and in situ SEM orthogonal cutting experiments are carried out to provide direct experimental evidence of the material anisotropy-dependent cutting results in terms of machined surface morphology and chip profile. Corresponding numerical simulations with the analysis of built stress further validate experimental results and reveal the mechanisms governing the material anisotropy influence.The above findings provide insight into the fabrication of ultra-smooth surfaces of polycrystalline metals by ultra-precision diamond turning. © 2020, The Author(s).
    view abstract10.1007/s41871-020-00060-9
  • 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 (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 abstract10.1016/j.precisioneng.2020.01.006
  • 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 abstract10.3390/ma13071600
  • Effect of Grain Statistics on Micromechanical Modeling: The Example of Additively Manufactured Materials Examined by Electron Backscatter Diffraction
    Biswas, A. and Prasad, M.R.G. and Vajragupta, N. and Kostka, A. and Niendorf, T. and Hartmaier, A.
    Advanced Engineering Materials 22 (2020)
    Micromechanical modeling is one of the prominent numerical tools for the prediction of mechanical properties and the understanding of deformation mechanisms of metals. As input parameters, it uses data obtained from microstructure characterization techniques, among which the electron backscatter diffraction (EBSD) technique allows us to understand the nature of microstructural features, that are usually described by statistics. Because of these advantages, the EBSD dataset is widely used for synthetic microstructure generation. However, for the statistical description of microstructural features, the population of input data must be considered. Preferably, the EBSD measurement area must be sufficiently large to cover an adequate number of grains. However, a comprehensive study of this measurement area with a crystal plasticity finite element method (CPFEM) framework is still missing although it would considerably facilitate information exchange between experimentalists and simulation experts. Herein, the influence of the EBSD measurement area and the number of grains on the statistical description of the microstructural features and studying the corresponding micromechanical simulation results for 316L stainless steel samples produced by selective laser melting is investigated. © 2020 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    view abstract10.1002/adem.201901416
  • 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 abstract10.1016/j.mtla.2020.100692
  • Elucidating the dual role of grain boundaries as dislocation sources and obstacles and its impact on toughness and brittle-to-ductile transition
    Reiser, J. and Hartmaier, A.
    Scientific Reports 10 (2020)
    In this paper, we resolve the role of grain boundaries on toughness and the brittle-to-ductile transition. On the one hand, grain boundaries are obstacles for dislocation glide. On the other hand, the intersection points of grain boundaries with the crack front are assumed to be preferred dislocation nucleation sites. Here, we will show that the single contributions of grain boundaries (obstacles vs. source) on toughness and the brittle-to-ductile transition are contradicting, and we will weight the single contributions by performing carefully designed numerical experiments by means of two-dimensional discrete dislocation dynamics modelling. In our parameter studies, we vary the following parameters: (i) the mean free path for dislocation glide, δ, combined with (ii) the (obstacle) force of the grain boundary, ϕ, and (iii) the dislocation source spacing along the crack front, λ. Our results show that for materials or microstructures for which the mean distance of the intersection points of grain boundaries with the crack front is the relevant measure for λ, a decrease of grain size results in an increase of toughness. The positive impact of grain boundaries outweighs the negative consequences of dislocation blocking. Furthermore, our results explain the evolving anisotropy of toughness in cold-worked metals and give further insight into the question of why the grain-size-dependent fracture toughness passes through a minimum (and the brittle-to-ductile transition temperature passes through a maximum) at an intermediate grain size. Finally, a relation of the grain-size-dependence of fracture toughness in the form of K(dδ, dλ) = KIC + kdδ 0.5/dλ is deduced. © 2020, The Author(s).
    view abstract10.1038/s41598-020-59405-5
  • Hydrogen embrittlement at cleavage planes and grain boundaries in bcc iron—revisiting the first-principles cohesive zone model
    Guzmán, A.A. and Jeon, J. and Hartmaier, A. and Janisch, R.
    Materials 13 (2020)
    Hydrogen embrittlement, which severely affects structural materials such as steel, comprises several mechanisms at the atomic level. One of them is hydrogen enhanced decohesion (HEDE), the phenomenon of H accumulation between cleavage planes, where it reduces the interplanar cohesion. Grain boundaries are expected to play a significant role for HEDE, since they act as trapping sites for hydrogen. To elucidate this mechanism, we present the results of first-principles studies of the H effect on the cohesive strength of α-Fe single crystal (001) and (111) cleavage planes, as well as on the Σ5(310)[001] and Σ3(112)[1¯10] symmetrical tilt grain boundaries. The calculated results show that, within the studied range of concentrations, the single crystal cleavage planes are much more sensitive to a change in H concentration than the grain boundaries. Since there are two main types of procedures to perform ab initio tensile tests, different in whether or not to allow the relaxation of atomic positions, which can affect the quantitative and qualitative results, these methods are revisited to determine their effect on the predicted cohesive strength of segregated interfaces. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/ma13245785
  • Influence of Pore Characteristics on Anisotropic Mechanical Behavior of Laser Powder Bed Fusion–Manufactured Metal by Micromechanical Modeling
    R. G. Prasad, M. and Biswas, A. and Geenen, K. and Amin, W. and Gao, S. and Lian, J. and Röttger, A. and Vajragupta, N. and Hartmaier, A.
    Advanced Engineering Materials 22 (2020)
    In recent times, additive manufacturing (AM) has proven to be an indispensable technique for processing complex 3D parts because of the versatility and ease of fabrication it offers. However, the generated microstructures show a high degree of complexity due to the complex solidification process of the melt pool. In this study, micromechanical modeling is applied to gain deeper insight into the influence of defects on plasticity and damage of 316L stainless steel specimens produced by a laser powder bed fusion (L-PBF) process. With the statistical data obtained from microstructure characterization, the complex AM microstructures are modeled by a synthetic microstructure generation tool. A damage model in combination with an element deletion technique is implemented into a nonlocal crystal plasticity model to describe anisotropic mechanical behavior, including damage evolution. The element deletion technique is applied to effectively model the growth and coalescence of microstructural pores as described by a damage parameter. Numerical simulations show that the shape of the pores not only affects the yielding and hardening behavior but also influences the porosity evolution itself. © 2020 The Authors. Published by Wiley-VCH GmbH
    view abstract10.1002/adem.202000641
  • Influence of rafted microstructures on creep in Ni-base single crystal superalloys: A 3D discrete dislocation dynamics study
    Gao, S. and Ali, M.A. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 28 (2020)
    Ni-base single-crystal superalloys exhibit a dynamic evolution of their microstructure during operation at elevated temperatures. The rafting of γ′ precipitates changes the mechanical behavior in a way that was understood insufficiently. In this work, we combine a phase-field method with a discrete dislocation dynamics model to clarify the influence of different rafted microstructures with the same initial dislocation density and configuration on creep behavior. The unrafted and rafted microstructures of Ni-base single crystal superalloys are simulated by a phase-field crystal plasticity method. By introducing these microstructures into a 3D discrete dislocation dynamics (DDD) model, the creep behavior under uniaxial loads of 350 and 250 MPa along [100] direction at 950 °C is studied. Due to the negative lattice mismatch of Ni-base superalloys, the N-type rafting with the formation of plate-like γ′ precipitates occurs under uniaxial tensile loads along {100} direction at high temperatures, while the P-type rafting with the formation of rod-like γ′ precipitates occurs under compressive loads. Taking the cuboidal, N-type rafted and P-type rafted microstructures as the initial and fixed microstructures for the same loading conditions, it is found from DDD simulations that the rafted microstructures result in smaller creep deformation than the cuboidal microstructure. The reason for this is that the coalescence of γ′ precipitates during the rafting diminishes the width of some γ channels, so as to increase the local Orowan stresses which retard the dislocation glide. For tensile loads, the N-type rafted microstructure has the best creep resistance. For a low compressive load, the P-type rafting shows a better creep resistance than N-type rafting. © 2019 IOP Publishing Ltd.
    view abstract10.1088/1361-651X/ab5e40
  • Influence of trapped gas on pore healing under hot isostatic pressing in nickel-base superalloys
    Prasad, M.R.G. and Gao, S. and Vajragupta, N. and Hartmaier, A.
    Crystals 10 (2020)
    Under the typical hot isostatic pressing (HIP) processing conditions, plastic deformation by dislocation slip is considered the primary mechanism for pore shrinkage, according to experimental observations and deformation mechanism maps. In the present work, a crystal plasticity model has been used to investigate the influence of applied pressure and holding time on porosity reduction in a nickel-base single crystal superalloy. The influence of trapped gas on pore shrinkage is modeled by coupling mechanical deformation with pore–gas interaction. In qualitative agreement with experimental investigations, we observe that increasing the applied pressure or the holding time can effectively reduce porosity. Furthermore, the effect of pore shape on the shrinkage is observed to depend on a combination of elastic anisotropy and the complex distribution of stresses around the pore. Simulation results also reveal that, for pores of the same shape, smaller pores (radius < 0.1 µm) have a higher shrinkage rate in comparison to larger pores (radius ≥ 0.1 µm), which is attributed to the increasing pore surface energies with decreasing pore sizes. It is also found that, for smaller initial gas-filled pores (radius < 0.1 µm), HIP can result in very high gas pressures (on the order of GPa). Such high pressures either act as a driving force for argon to diffuse into the surrounding metal during HIP itself, or it can result in pore re-opening during subsequent annealing or mechanical loading. These results demonstrate that the micromechanical model can quantitatively evaluate the individual influences of HIP processing conditions and pore characteristics on pore annihilation, which can help optimize the HIP process parameters in the future. © 2020 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/cryst10121147
  • Inverse method to determine fatigue properties of materials by combining cyclic indentation and numerical simulation
    Sajjad, H.M. and ul Hassan, H. and Kuntz, M. and Schäfer, B.J. and Sonnweber-Ribic, P. and Hartmaier, A.
    Materials 13 (2020)
    The application of instrumented indentation to assess material properties like Young's modulus and microhardness has become a standard method. In recent developments, indentation experiments and simulations have been combined to inverse methods, from which further material parameters such as yield strength, work hardening rate, and tensile strength can be determined. In this work, an inverse method is introduced by which material parameters for cyclic plasticity, i.e., kinematic hardening parameters, can be determined. To accomplish this, cyclicVickers indentation experiments are combined with finite element simulations of the indentation with unknown material properties, which are then determined by inverse analysis. To validate the proposed method, these parameters are subsequently applied to predict the uniaxial stress-strain response of a material with success. The method has been validated successfully for a quenched and tempered martensitic steel and for technically pure copper, where an excellent agreement between measured and predicted cyclic stress-strain curves has been achieved. Hence, the proposed inverse method based on cyclic nanoindentation, as a quasi-nondestructive method, could complement or even substitute the resource-intensive conventional fatigue testing in the future for some applications. © 2020 by the authors.
    view abstract10.3390/ma13143126
  • Micro-, macromechanical and aeroelastic investigation of glass - fiber based, lightweight turbomachinery components
    Iseni, S. and Prasad, M.R.G. and Hartmaier, A. and Holeczek, K. and Modeler, N. and di Mare, F.
    Proceedings of the ASME Turbo Expo 10A-2020 (2020)
    A major technical challenge for modern aero engines is the development of designs which reduce noise and emission whilst increasing aerodynamic efficiency and ensuring aeroelastic stability of low-temperature engine components such as fans and low-pressure compressors. Composites are used in aviation due to their excellent stiffness and strength properties, which also enable additional flexibility in the design process. The weight reduction of the turbomachine components, due to composite materials and lighter engines, is especially relevant for the design and developments of hybrid-electric or distributed propulsion systems [1]. To accomplish this, a representative volume element (RVE) of a glass-fiber reinforced polymer is created, describing the geometrical arrangement of the textile reinforcement structure within the polymer matrix. For both phases, realistic linear elastic properties are assumed. This RVE will be investigated with the finite element method under various loading conditions to assess its anisotropic elastic properties and also its damping behaviour for elastic waves. To study the influence of delamination on the mechanical properties, small defects will be introduced into the model at the interface between reinforcement and matrix. Based on this micromechanical approach, a constitutive model for the composite will be formulated that describes the anisotropic properties as well as the damping behaviour. This constitutive model is then used to describe the material response in a macro-mechanical model, which serves as the basis for an aeroelastic analysis of a 1/3-scaled high-speed fan using a conventional (Ti-6Al -4V) and fiber composite material. Copyright © 2020 ASME
    view abstract10.1115/GT2020-14951
  • Micromechanical modeling of DP600 steel: From microstructure to the sheet metal forming process
    Vajragupta, N. and Maassen, S. and Clausmeyer, T. and Brands, D. and Schröder, J. and Hartmaier, A.
    Procedia Manufacturing 47 (2020)
    This study proposes a micromechanical modeling scheme to predict relevant mechanical behavior of DP600 steel for the sheet metal forming process. This study can be divided into two parts which are the prediction of the advanced anisotropic initial yield function by means of microstructure-based simulations and the investigation of microstructure changes during the sheet metal forming process. Firstly, based on the quantitative microstructure characterization of DP600 steel by EBSD analysis, the obtained statistical information of important microstructural features is used to generate a microstructure model with the help of an advanced dynamic microstructure generator (ADMG), which combines a particle simulation method with radical Voronoi tessellation. In the next step, finite element simulations with a non-local crystal plasticity model for the individual grains are conducted. With the help of these simulations, the crystal plasticity parameters are adapted to match the experiments. The resulting parameterized microstructure model of DP600 steel is then applied to various loading conditions to investigate the corresponding mechanical responses. For the second part, macroscopic simulations of the bending process are performed and local deformation fields of the location of interest are captured and imposed as boundary conditions on the microstructure model to study the changes in the microstructural features. © 2020 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (https://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 23rd International Conference on Material Forming.
    view abstract10.1016/j.promfg.2020.04.347
  • Nanocutting mechanism of 6H-SiC investigated by scanning electron microscope online observation and stress-assisted and ion implant-assisted approaches
    Xu, Z. and Liu, L. and He, Z. and Tian, D. and Hartmaier, A. and Zhang, J. and Luo, X. and Rommel, M. and Nordlund, K. and Zhang, G. and Fang, F.
    International Journal of Advanced Manufacturing Technology 106 (2020)
    Nanocutting mechanism of single crystal 6H-SiC is investigated through a novel scanning electron microscope setup in this paper. Various undeformed chip thicknesses on (0001) < 1–100 > orientation are adopted in the nanocutting experiments. Phase transformation and dislocation activities involved in the 6H-SiC nanocutting process are also characterized and analyzed. Two methods of stress-assisted and ion implant-assisted nanocutting are studied to improve 6H-SiC ductile machining ability. Results show that stress-assisted method can effectively decrease the hydrostatic stress and help to activate dislocation motion and ductile machining; ion implant-induced damages are helpful to improve the ductile machining ability from MD simulation and continuous nanocutting experiments under the online observation platform. © 2020, Springer-Verlag London Ltd., part of Springer Nature.
    view abstract10.1007/s00170-019-04886-6
  • 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 abstract10.1016/j.mtcomm.2020.101314
  • 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 (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 abstract10.1107/S1600576719017138
  • 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 abstract10.3390/ma13030735
  • 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 (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 abstract10.1007/s10853-020-04801-5
  • 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 abstract10.1016/j.jmatprotec.2019.116400
  • Ab initio study of the combined effects of alloying elements and h on grain boundary cohesion in ferritic steels
    Subramanyam, A.P.A. and Guzmán, A.A. and Vincent, S. and Hartmaier, A. and Janisch, R.
    Metals 9 (2019)
    Hydrogen enhanced decohesion is expected to play a major role in ferritic steels, especially at grain boundaries. Here, we address the effects of some common alloying elements C, V, Cr, and Mn on the H segregation behaviour and the decohesion mechanism at a Σ5(310)[001] 36.9° grain boundary in bcc Fe using spin polarized density functional theory calculations. We find that V, Cr, and Mn enhance grain boundary cohesion. Furthermore, all elements have an influence on the segregation energies of the interstitial elements as well as on these elements’ impact on grain boundary cohesion. V slightly promotes segregation of the cohesion enhancing element C. However, none of the elements increase the cohesion enhancing effect of C and reduce the detrimental effect of H on interfacial cohesion at the same time. At an interface which is co-segregated with C, H, and a substitutional element, C and H show only weak interaction, and the highest work of separation is obtained when the substitute is Mn. © 2019 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/met9030291
  • 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 (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 abstract10.1016/j.jmapro.2019.01.007
  • 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 (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 abstract10.1016/j.wear.2019.04.024
  • Influence of excess volumes induced by Re and W on dislocation motion and creep in ni-base single crystal superalloys: A 3D discrete dislocation dynamics study
    Gao, S. and Yang, Z. and Grabowski, M. and Rogal, J. and Drautz, R. and Hartmaier, A.
    Metals 9 (2019)
    A comprehensive 3D discrete dislocation dynamics model for Ni-base single crystal superalloys was used to investigate the influence of excess volumes induced by solute atoms Re and W on dislocation motion and creep under different tensile loads at 850 °C. The solute atoms were distributed homogeneously only in g matrix channels. Their excess volumes due to the size difference from the host Ni were calculated by density functional theory. The excess volume affected dislocation glide more strongly than dislocation climb. The relative positions of dislocations and solute atoms determined the magnitude of back stresses on the dislocation motion. Without diffusion of solute atoms, it was found that W with a larger excess volume had a stronger strengthening effect than Re. With increasing concentration of solute atoms, the creep resistance increased. However, a low external stress reduced the influence of different excess volumes and different concentrations on creep. © 2019 by the authors. Licensee MDPI, Basel, Switzerland.
    view abstract10.3390/met9060637
  • Influence of Microstructural Features on the Strain Hardening Behavior of Additively Manufactured Metallic Components
    Biswas, A. and Prasad, M.R.G. and Vajragupta, N. and ul Hassan, H. and Brenne, F. and Niendorf, T. and Hartmaier, A.
    Advanced Engineering Materials 21 (2019)
    Additive manufacturing (AM) has recently become one of the key manufacturing processes in the era of Industry 4.0 because of its highly flexible production scheme. Due to complex thermal cycles during the manufacturing process itself and special solidification conditions, the microstructure of AM components often exhibits elongated grains together with a pronounced texture. These microstructural features significantly contribute to an anisotropic mechanical behavior. In this work, the microstructure and mechanical properties of additively manufactured samples of 316L stainless steel are characterized experimentally and a micromechanical modeling approach is employed to predict the macroscopic properties. The objective of this work is to study the effects of texture and microstructural morphology on yield strength and strain hardening behavior of face-centered cubic additively manufactured metallic components. To incorporate the texture in synthetic representative volume elements (RVE), the proposed approach considers both the crystallographic and grain boundary textures. The mechanical behavior of these RVEs is modeled using crystal plasticity finite element method, which incorporates size effects through the implementation of strain gradients. © 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
    view abstract10.1002/adem.201900275
  • MD simulation of stress-assisted nanometric cutting mechanism of 3C silicon carbide
    Liu, L. and Xu, Z. and Tian, D. and Hartmaier, A. and Luo, X. and Zhang, J. and Nordlund, K. and Fang, F.
    Industrial Lubrication and Tribology 71 (2019)
    Purpose: This paper aims to reveal the mechanism for improving ductile machinability of 3C-silicon carbide (SiC) and associated cutting mechanism in stress-assisted nanometric cutting. Design/methodology/approach: Molecular dynamics simulation of nano-cutting 3C-SiC is carried out in this paper. The following two scenarios are considered: normal nanometric cutting of 3C-SiC; and stress-assisted nanometric cutting of 3C-SiC for comparison. Chip formation, phase transformation, dislocation activities and shear strain during nanometric cutting are analyzed. Findings: Negative rake angle can produce necessary hydrostatic stress to achieve ductile removal by the extrusion in ductile regime machining. In ductile-brittle transition, deformation mechanism of 3C-SiC is combination of plastic deformation dominated by dislocation activities and localization of shear deformation. When cutting depth is greater than 10 nm, material removal is mainly achieved by shear. Stress-assisted machining can lead to better quality of machined surface. However, there is a threshold for the applied stress to fully gain advantages offered by stress-assisted machining. Stress-assisted machining further enhances plastic deformation ability through the active dislocations’ movements. Originality/value: This work describes a stress-assisted machining method for improving the surface quality, which could improve 3C-SiC ductile machining ability. © 2019, Emerald Publishing Limited.
    view abstract10.1108/ILT-03-2019-0096
  • Micromechanical modeling of fatigue crack nucleation around non-metallic inclusions in martensitic high-strength steels
    Schäfer, B.J. and Sonnweber-Ribic, P. and Ul-Hassan, H. and Hartmaier, A.
    Metals 9 (2019)
    Martensitic high-strength steels are prone to exhibit premature fatigue failure due to fatigue crack nucleation at non-metallic inclusions and other microstructural defects. This study investigates the fatigue crack nucleation behavior of the martensitic steel SAE 4150 at different microstructural defects by means of micromechanical simulations. Inclusion statistics based on experimental data serve as a reference for the identification of failure-relevant inclusions and defects for the material of interest. A comprehensive numerical design of experiment was performed to systematically assess the influencing parameters of the microstructural defects with respect to their fatigue crack nucleation potential. In particular, the effects of defect type, inclusion-matrix interface configuration, defect size, defect shape and defect alignment to loading axis on fatigue damage behavior were studied and discussed in detail. To account for the evolution of residual stresses around inclusions due to previous heat treatments of the material, an elasto-plastic extension of the micromechanical model is proposed. The non-local Fatemi-Socie parameter was used in this study to quantify the fatigue crack nucleation potential. The numerical results of the study exhibit a loading level-dependent damage potential of the different inclusion-matrix configurations and a fundamental influence of the alignment of specific defect types to the loading axis. These results illustrate that the micromechanical model can quantitatively evaluate the different defects, which can make a valuable contribution to the comparison of different material grades in the future. © 2019 by the authors.
    view abstract10.3390/met9121258
  • Micromechanical modelling of coupled crystal plasticity and hydrogen diffusion
    Hassan, H.U. and Govind, K. and Hartmaier, A.
    Philosophical Magazine 99 (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 abstract10.1080/14786435.2018.1530466
  • Micromechanical modelling of the cyclic deformation behavior of martensitic sae 4150-a comparison of different kinematic hardening models
    Schäfer, B.J. and Song, X. and Sonnweber-Ribic, P. and Hassan, H.U. and Hartmaier, A.
    Metals 9 (2019)
    A fundamental prerequisite for the micromechanical simulation of fatigue is the appropriate modelling of the effective cyclic properties of the considered material. Therefore, kinematic hardening formulations on the slip system level are of crucial importance due to their fundamental relevance in cyclic material modelling. The focus of this study is the comparison of three different kinematic hardening models (Armstrong Frederick, Chaboche, and Ohno-Wang). In this work, investigations are performed on the modelling and prediction of the cyclic stress-strain behavior of the martensitic high-strength steel SAE 4150 for two different total strain ratios (R Ɛ = -1 and R Ɛ = 0). In the first step, a three-dimensional martensitic microstructure model is developed by using multiscale Voronoi tessellations. Based on this martensitic representative volume element, micromechanical simulations are performed by a crystal plasticity finite element model. For the constitutive model calibration, a new multi-objective calibration procedure incorporating a sensitivity analysis as well as an evolutionary algorithm is presented. The numerical results of different kinematic hardening models are compared to experimental data with respect to the appropriate modelling of the Bauschinger effect and the mean stress relaxation behavior at R Ɛ = 0. It is concluded that the Ohno-Wang model is superior to the Armstrong Frederick and Chaboche kinematic hardening model at R Ɛ = -1 as well as at R Ɛ = 0. © 2019 by the authors.
    view abstract10.3390/met9030368
  • Micromechanical modelling of the influence of strain ratio on fatigue crack initiation in a martensitic steel-a comparison of different fatigue indicator parameters
    Schäfer, B.J. and Sonnweber-Ribic, P. and ul Hassan, H. and Hartmaier, A.
    Materials 12 (2019)
    Micromechanical fatigue lifetime predictions, in particular for the high cycle fatigue regime, require an appropriate modelling of mean stress effects in order to account for lifetime reducing positive mean stresses. Focus of this micromechanical study is the comparison of three selected fatigue indicator parameters (FIPs), with respect to their applicability to different total strain ratios. In this work, investigations are performed on the modelling and prediction of the fatigue crack initiation life of the martensitic high-strength steel SAE 4150 for two different total strain ratios. First, multiple martensitic statistical volume elements (SVEs) are generated by multiscale Voronoi tessellations. Micromechanical fatigue simulations are then performed on these SVEs by means of a crystal plasticity model to obtain microstructure dependent fatigue responses. In order to account for the material specific fatigue damage zone, a non-local homogenisation scheme for the FIPs is introduced for lath martensitic microstructures. The numerical results of the different non-local FIPs are compared with experimental fatigue crack initiation results for two different total strain ratios. It is concluded that the multiaxial fatigue criteria proposed by Fatemi-Socie is superior for predicting fatigue crack initiation life to the energy dissipation criteria and the accumulated plastic slip criteria for the investigated total strain ratios. © 2019 by the authors.
    view abstract10.3390/ma12182852
  • Modeling Macroscopic Material Behavior With Machine Learning Algorithms Trained by Micromechanical Simulations
    Reimann, D. and Nidadavolu, K. and ul Hassan, H. and Vajragupta, N. and Glasmachers, T. and Junker, P. and Hartmaier, A.
    Frontiers in Materials 6 (2019)
    Micromechanical modeling of material behavior has become an accepted approach to describe the macroscopic mechanical properties of polycrystalline materials in a microstructure-sensitive way. The microstructure is modeled by a representative volume element (RVE), and the anisotropic mechanical behavior of individual grains is described by a crystal plasticity model. Such micromechanical models are subjected to mechanical loads in a finite element (FE) simulation and their macroscopic behavior is obtained from a homogenization procedure. However, such micromechanical simulations with a discrete representation of the material microstructure are computationally very expensive, in particular when conducted for 3D models, such that it is prohibitive to apply them for process simulations of macroscopic components. In this work, we suggest a new approach to develop microstructure-sensitive, yet flexible and numerically efficient macroscopic material models by using micromechanical simulations for training Machine Learning (ML) algorithms to capture the mechanical response of various microstructures under different loads. In this way, the trained ML algorithms represent a new macroscopic constitutive relation, which is demonstrated here for the case of damage modeling. In a second application of the combination of ML algorithms and micromechanical modeling, a proof of concept is presented for the application of trained ML algorithms for microstructure design with respect to desired mechanical properties. The input data consist of different stress-strain curves obtained from micromechanical simulations of uniaxial testing of a wide range of microstructures. The trained ML algorithm is then used to suggest grain size distributions, grain morphologies and crystallographic textures, which yield the desired mechanical response for a given application. For validation purposes, the resulting grain microstructure parameters are used to generate RVEs, accordingly and the macroscopic stress-strain curves for those microstructures are calculated and compared with the target quantities. The two examples presented in this work, demonstrate clearly that ML methods can be trained by micromechanical simulations, which capture material behavior and its relation to microstructural mechanisms in a physically sound way. Since the quality of the ML algorithms is only as good as that of the micromechanical model, it is essential to validate these models properly. Furthermore, this approach allows a hybridization of experimental and numerical data. © Copyright © 2019 Reimann, Nidadavolu, ul Hassan, Vajragupta, Glasmachers, Junker and Hartmaier.
    view abstract10.3389/fmats.2019.00181
  • 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 abstract10.3390/ma12111767
  • New flat-punch indentation creep testing approach for characterizing the local creep properties at high temperatures
    Matschkal-Amberger, D. and Kolb, M. and Neumeier, S. and Gao, S. and Hartmaier, A. and Durst, K. and Göken, M.
    Materials and Design 183 (2019)
    An indentation creep testing approach has been developed which allows measuring creep properties at high temperatures. In contrast to existing indentation or impression creep experiments, the approach described here allows to achieve a quite high spatial resolution, as flat punch indenters with a diameter of only 20 μm are used. First indentation creep tests have been performed on single crystalline nickel and nickel binary solid solution alloys with Re, Ta or W as alloying elements, respectively. The indentation creep tests have been carried out at a temperature of 650 °C and stress levels in the range of 85 to 400 MPa. Using crystal plasticity finite element modeling, the indentation creep response is converted into equivalent uniaxial creep properties. It is shown that the conversion parameters, evaluated for differently oriented single crystals, can be chosen independently of the creep rate exponent in the power law creep regime. It is found that the indentation creep results agree well with conventional uniaxial creep tests. Furthermore, the results show that Ta is the most effective solid solution strengthener of all tested solid-solution strengtheners at 650 °C because of the large atomic size mismatch, followed by W and Re. © 2019 The Authors
    view abstract10.1016/j.matdes.2019.108090
  • On the numerical modeling of nucleation and growth of microstructurally short cracks in polycrystals under cyclic loading
    Boeff, M. and Hassan, H.U. and Hartmaier, A.
    Journal of Materials Research (2019)
    In the scope of this work, a micromechanical model based on the crystal plasticity finite element method is proposed and applied to describe the nucleation and growth of microstructurally short fatigue cracks in polycrystalline materials under cyclic loads. The microstructure is generated in the form of a representative volume element of a polycrystalline material with equiaxed grains having columnar structure along thickness and random crystallographic texture. With this model, we investigate the influence of loading amplitude on the crack growth behavior. It is shown that for smaller strain amplitudes, a single crack nucleates and propagates, while for larger strain amplitudes several independent crack nucleation sites form, from which microcracks start propagating. It is also observed that the global plastic strain amplitude decreases from the initial to the final cycle, during total strain-controlled loading. However, this can even increase the crack growth rate because the crack advance is governed by the local plastic slip which accumulates at the crack tip over the number of cycles. With this work, it is shown that micromechanical modeling can strongly improve our understanding of the mechanisms of short-crack nucleation and growth under fatigue loading. © 2019 Materials Research Society.
    view abstract10.1557/jmr.2019.270
  • Parameterization of a Non-local Crystal Plasticity Model for Tempered Lath Martensite Using Nanoindentation and Inverse Method
    Engels, J.K. and Vajragupta, N. and Hartmaier, A.
    Frontiers in Materials 6 (2019)
    Crystal plasticity (CP) models have proven to accurately describe elasto-plastic behavior on micro- and nanometer length scales in numerous applications. However, their parameterization requires a series of experiments and inverse analysis of the results. In this regard, nanoindentation promises to be a well-suited tool for realizing a parameterization approach to determine all model parameters. The objective of this work is to develop a parameterization technique for a non-local CP model by means of an accessible and reproducible workflow. To determine its feasibility, tempered lath martensite with two different carbon contents is used as testing material. The workflow combines nanoindentation tests with finite element simulations. First, indentation into single packets of tempered lath martensitic specimen is yielding the load-displacement curves and the residual imprint topology on the surface with the help of atomic force microscopy. In a second step, a finite element simulation of the indentation using non-local crystal plasticity as constitutive model is performed with estimated model parameters. In the next step, non-local CP parameters are systematically adapted in an optimization scheme to reach optimal agreement with experiments. As a final validation step, it is successfully demonstrated that the CP model parameterized by nanoindentation is able to determine the macroscopic stress-strain response of polycrystals. Two observations are made: on the one hand, the material properties locally scatter very strongly, which is caused by fluctuations in microstructure and chemistry. On the other hand, a novel method has been demonstrated, were an inverse analysis is used to parameterize a non-local CP model for highly complex microstructures as those of tempered lath martensite. The novelty of this study is the application of nanoindentation and optimization scheme to parameterize a higher-order CP model of oligocrystals with a complex microstructure like the tempered lath martensite as well as the topology identification method developed and employed for both experiment and numerics. © Copyright © 2019 Engels, Vajragupta and Hartmaier.
    view abstract10.3389/fmats.2019.00247
  • Studying grain boundary strengthening by dislocation-based strain gradient crystal plasticity coupled with a multi-phase-field model
    Amin, W. and Ali, M.A. and Vajragupta, N. and Hartmaier, A.
    Materials 12 (2019)
    One ambitious objective of Integrated Computational Materials Engineering (ICME) is to shorten the materials development cycle by using computational materials simulation techniques at different length scales. In this regard, the most important aspects are the prediction of the microstructural evolution during material processing and the understanding of the contributions of microstructural features to the mechanical response of the materials. One possible solution to such a challenge is to apply the Phase Field (PF) method because it can predict the microstructural evolution under the influence of different internal or external stimuli, including deformation. To accomplish this, it is necessary to take into account plasticity or, specifically, non-homogeneous plastic deformation, which is particularly important for investigating the size effects in materials emerging at the micron length scale. In this work, we present quasi-2D simulations of plastic deformation in a face centred cubic system using a finite strain formulation. Our model consists of dislocation-based strain gradient crystal plasticity implemented into a PF code. We apply this model to study the influence of grain size on the mechanical behavior of polycrystals, which includes dislocation storage and annihilation. Furthermore, the initial state of the material before deformation is also considered. The results show that a dislocation-based strain gradient crystal plasticity model can capture the Hall-Petch effect in many aspects. The model reproduced the correct functional dependence of the flow stress of the polycrystal on grain size without assigning any special properties to the grain boundaries. However, the predicted Hall-Petch coefficients are significantly smaller than those found typically in experiments. In any case, we found a good qualitative agreement between our findings and experimental results. © 2019 by the authors.
    view abstract10.3390/ma12182977
  • The brittle-to-ductile transition in cold rolled tungsten plates: Impact of crystallographic texture, grain size and dislocation density on the transition temperature
    Bonnekoh, C. and Jäntsch, U. and Hoffmann, J. and Leiste, H. and Hartmaier, A. and Weygand, D. and Hoffmann, A. and Reiser, J.
    International Journal of Refractory Metals and Hard Materials 78 (2019)
    The aim of this paper is to elucidate the mechanisms controlling the brittle-to-ductile transition (BDT) in pre-deformed, textured, polycrystalline body-centred cubic (bcc) metals by the example of cold rolled tungsten (W). For this purpose, five sheets were rolled out from one and the same sintered ingot, by various levels, representing degrees of deformation of 1.8, 2.5, 3.0, 3.4, and 4.1 (this refers to 83.5%, 91.8%, 95.0%, 96.7%, and 98.3% in the technical notation). Toughness tests show that the BDT temperature decreases with increasing degree of deformation from 115 °C ± 15 °C (388 K ± 15 K) down to −65 °C ± 15 °C (208 K ± 15 K). This is an improvement of >600 K compared with a sintered ingot. In this paper we perform an in-depth analysis of the microstructure of the five sheets mentioned above. This analysis includes the assessment of (i) crystallographic texture, (ii) grain size and (iii) dislocation density. A comparison between microstructural features and experimental data confirms our working hypothesis which states that the BDT is controlled by the glide of screw dislocations and that the transition temperature decreases with decreasing spacing, λ of dislocation sources along the crack front. Sources for dislocations may be the intersection points of grain boundaries with the crack front (BDT-temperature-grain-size-relation) or dislocation multiplication processes such as e.g., the expansion of open and closed loops (impact of dislocation density). © 2018 Elsevier Ltd
    view abstract10.1016/j.ijrmhm.2018.09.010
  • The interaction between grain boundary and tool geometry in nanocutting of a bi-crystal copper
    Wang, Z. and Sun, T. and Zhang, H. and Li, G. and Li, Z. and Zhang, J. and Yan, Y. and Hartmaier, A.
    International Journal of Extreme Manufacturing 1 (2019)
    Anisotropy is one central influencing factor on achievable ultimate machined surface integrity of metallic materials. Specifically, grain boundary has a strong impact on the deformation behaviour of polycrystalline materials and correlated material removal at the microscale. In the present work, we perform molecular dynamics simulations and experiments to elucidate the underlying grain boundary-associated mechanisms and their correlations with machining results of a bi-crystal Cu under nanocutting using a Berkovich tool. Specifically, crystallographic orientations of simulated bi-crystal Cu with a misorientation angle of 44.1° are derived from electron backscatter diffraction characterization of utilized polycrystalline copper specimen. Simulation results reveal that blocking of dislocation motion at grain boundaries, absorption of dislocations by grain boundaries and dislocation nucleation from grain boundaries are operating deformation modes in nanocutting of the bi-crystal Cu. Furthermore, heterogeneous grain boundary-associated mechanisms in neighbouring grains lead to strong anisotropic machining behaviour in the vicinity of the grain boundary. Simulated machined surface morphology and machining force evolution in the vicinity of grain boundary qualitatively agree well with experimental results. It is also found that the geometry of Berkovich tool has a strong impact on grain boundary-associated mechanisms and resultant ploughing-induced surface pile-up phenomenon. © 2019 The Author(s). Published by IOP Publishing Ltd on behalf of the IMMT
    view abstract10.1088/2631-7990/ab4b68
  • A phenomenological creep model for nickel-base single crystal superalloys at intermediate temperatures
    Gao, S. and Wollgramm, P. and Eggeler, G. and Ma, A. and Schreuer, J. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 26 (2018)
    For the purpose of good reproduction and prediction of creep deformation of nickel-base single crystal superalloys at intermediate temperatures, a phenomenological creep model is developed, which accounts for the typical γ/γ′ microstructure and the individual thermally activated elementary deformation processes in different phases. The internal stresses from γ/γ′ lattice mismatch and deformation heterogeneity are introduced through an efficient method. The strain hardening, the Orowan stress, the softening effect due to dislocation climb along γ/γ′ interfaces and the formation of dislocation ribbons, and the Kear-Wilsdorf-lock effect as key factors in the main flow rules are formulated properly. By taking the cube slip in slip systems and twinning mechanisms into account, the creep behavior for [110] and [111] loading directions are well captured. Without specific interaction and evolution of dislocations, the simulations of this model achieve a good agreement with experimental creep results and reproduce temperature, stress and crystallographic orientation dependences. It can also be used as the constitutive relation at material points in finite element calculations with complex boundary conditions in various components of superalloys to predict creep behavior and local stress distributions. © 2018 IOP Publishing Ltd.
    view abstract10.1088/1361-651X/aabdbe
  • Analysis of hydrogen diffusion and trapping in ultra-high strength steel grades
    Schaffner, T. and Hartmaier, A. and Kokotin, V. and Pohl, M.
    Journal of Alloys and Compounds 746 (2018)
    The transport behavior of hydrogen in ultra-high strength steel grades (UHSS) has been analyzed by several test and evaluation methods. In particular, permeation and desorption measurements have been performed to evaluate material specific parameters such as the effective diffusion coefficient, the reversible trap density and the reversible trap activation energy. Subjects of this study were a dual phase steel grade (DP) with a ferritic-martensitic microstructure and a martensitic steel grade (MS). The results of the permeation measurements indicate that the influence of irreversible traps might be negligible for the investigated UHSS compared to other impact factors. The evaluated reversible trap densities were some orders of magnitude higher than those known for pure iron reflecting the more complex microstructure. The major influence on hydrogen trapping is attributed to reversible traps like grain boundaries and dislocations based on the results of desorption measurements. © 2018 Elsevier B.V.
    view abstract10.1016/j.jallcom.2018.02.264
  • 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 (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 abstract10.1016/j.ijmecsci.2018.09.007
  • Fracture ab initio: A force-based scaling law for atomistically informed continuum models
    Möller, J.J. and Bitzek, E. and Janisch, R. and Ul Hassan, H. and Hartmaier, A.
    Journal of Materials Research 33 (2018)
    In fracture mechanics, established methods exist to model the stability of a crack tip or the kinetics of crack growth on both the atomic and the macroscopic scale. However, approaches to bridge the two scales still face the challenge in terms of directly converting the atomic forces at which bonds break into meaningful continuum mechanical failure stresses. Here we use two atomistic methods to investigate cleavage fracture of brittle materials: (i) we analyze the forces in front of a sharp crack and (ii) we study the bond breaking process during rigid body separation of half crystals without elastic relaxation. The comparison demonstrates the ability of the latter scheme, which is often used in ab initio density functional theory calculations, to model the bonding situation at a crack tip. Furthermore, we confirm the applicability of linear elastic fracture mechanics in the nanometer range close to crack tips in brittle materials. Based on these observations, a fracture mechanics model is developed to scale the critical atomic forces for bond breaking into relevant continuum mechanical quantities in the form of an atomistically informed scale-sensitive traction separation law. Such failure criteria can then be applied to describe fracture processes on larger length scales, e.g., in cohesive zone models or extended finite element models. Copyright © Materials Research Society 2018 This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (.
    view abstract10.1557/jmr.2018.384
  • In situ TEM observation of rebonding on fractured silicon carbide
    Zhang, Z. and Cui, J. and Wang, B. and Jiang, H. and Chen, G. and Yu, J. and Lin, C. and Tang, C. and Hartmaier, A. and Zhang, J. and Luo, J. and Rosenkranz, A. and Jiang, N. and Guo, D.
    Nanoscale 10 (2018)
    Silicon carbide (SiC) is widely used in harsh environments and under extreme conditions, including at high-power, higherature, high-current, high-voltage and high-frequency. The rebonding and self-matching of stack faults (SFs) is highly desirable to avoid catastrophic failure for SiC devices, especially for specific applications in the aerospace and nuclear power industries. In this study, a novel approach was developed using an eyebrow hair to pick up and transfer nanowires (NWs), in order to obtain in situ transmission electron microscope (TEM) images of the rebonding and self-matching of SFs at atomic resolution. During rebonding and healing, the electron beam was shut off. Rebonding on the fractured surfaces of monocrystalline and amorphous SiC NWs was observed by in situ TEM at room temperature. The fracture strength was 1.7 GPa after crack-healing, restoring 12.9% of that of a single crystal NW. Partial recrystallization along the <111> orientation and the self-matching of SFs are responsible for the rebonding of the monocrystalline NW. In comparison, the fracture strengths were 6.7 and 5.5 GPa for the first and second rebonding, respectively recovering 67% and 55% of that of an amorphous NW. Atomic diffusion contributed enormously to the rebonding on fractured surfaces of an amorphous NW, resulting in a healed surface consisting of an amorphous phase and crystallites. This rebonding function provides new insight into the fabrication of high-performance SiC devices for the aerospace, optoelectronic and semiconductor industries. © 2018 The Royal Society of Chemistry.
    view abstract10.1039/c8nr00341f
  • Mechanical twinning induced alteration in the kinetics of martensitic phase transformation in TRIP-maraging steels
    Gupta, S. and Ma, A. and Hartmaier, A.
    International Journal of Solids and Structures 155 (2018)
    A computational study is conducted to examine the influence of mechanical twins on the kinetics of martensitic transformation in TRIP-maraging steel. Simulations are performed using a non-local crystal plasticity (CP) phase transformation model describing the deformation behavior of TRIP-maraging steel. This work is inspired by the experimental observations of Wang et al. (2014), where authors reported a twinning induced stability against the phase transformation in austenite islands embedded in the martensitic matrix. Finite element (FE) analysis is used to simulate the stability of austenite against the phase transformation in the presence and absence of mechanical twins, respectively. Depending on the parent crystal orientation, macroscopic outcome of FE calculations manifested a slower/faster transformation kinetics for austenitic islands with mechanical twins as compared to islands without twins which is found to be in a good qualitative agreement to experimental observations. Models with two austenite islands of different sizes confirmed the twinning induced alteration in the transformation kinetics. Microscopic observations from the simulations demonstrated that the twin orientations generated during mechanical twinning are less or more favorable for the strain induced or stress assisted transformations. This directly indicates that the basis of the alteration in the transformation kinetics could be the strong orientation dependence of the martensitic transformation. Thus, a model based analysis was used to explain the experimental findings related to phase transformation kinetics of TRIP-maraging steels. © 2018 Elsevier Ltd
    view abstract10.1016/j.ijsolstr.2018.07.021
  • Molecular dynamics simulation of silicon ion implantation into diamond and subsequent annealing
    Fu, X. and Xu, Z. and He, Z. and Hartmaier, A. and Fang, F.
    Nuclear Instruments and Methods in Physics Research, Section B: Beam Interactions with Materials and Atoms (2018)
    Ion implantation is one of the best methods to manufacture silicon-vacancy (SiV) centers in diamond, which can be used as qubits. In this work, molecular dynamics (MD) simulation was conducted to analyze the damage evolution and distribution during the process of silicon ion implantation into bulk diamond and subsequent annealing. Tersoff-ZBL (Ziegler-Biersack-Littmark) potential was used to describe the atomic interaction. Identify Diamond Structure (IDS) and Wigner-Seitz defect analysis methods were used to calculate damages and vacancies. After 2393 K annealing, about 42.5% of ion induced IDS damages were recovered. During the temperature cooling down from 2393 K to 293 K, the movements of silicon atoms along the implantation direction were sensitive to the temperature variation, while vacancies were almost insensitive. MD simulation is helpful to illustrate the ion implant induced damages’ dynamic evolution and Si-V related defects, which can assist a deeper understanding of SiV center's manufacturing. © 2018 Elsevier B.V.
    view abstract10.1016/j.nimb.2018.04.027
  • Numerically efficient microstructure-based calculation of internal stresses in superalloys
    Gao, S. and Gogilan, U. and Ma, A. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 26 (2018)
    According to the classical Eshelby inclusion problem, we introduce a new linear relation to calculate internal stresses in γ/γ′ microstructures of superalloys via an effective stiffness method. To accomplish this, we identify regions with almost uniform deformation behavior within the microstructure. Assigning different eigenstrains to these regions results in a characteristic internal stress state. The linear relation between eigenstrains and internal stresses, as proposed by Eshelby for simpler geometries, is shown to be a valid approximation to the solution for complex microstructures. The fast Fourier transformation method is chosen as a very efficient numerical solver to determine the effective stiffness matrix. Numerical validation shows that this generalized method with the effective stiffness matrix is efficient to obtain appropriate internal stresses and that it can be used to consider the influence of internal stresses on plasticity and creep kinetics in superalloys. © 2017 IOP Publishing Ltd.
    view abstract10.1088/1361-651X/aa9ba3
  • On Shear Testing of Single Crystal Ni-Base Superalloys
    Eggeler, G. and Wieczorek, N. and Fox, F. and Berglund, S. and Bürger, D. and Dlouhy, A. and Wollgramm, P. and Neuking, K. and Schreuer, J. and Agudo Jácome, L. and Gao, S. and Hartmaier, A. and Laplanche, G.
    Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science (2018)
    Shear testing can contribute to a better understanding of the plastic deformation of Ni-base superalloy single crystals. In the present study, shear testing is discussed with special emphasis placed on its strengths and weaknesses. Key mechanical and microstructural results which were obtained for the high-temperature (T ≈ 1000 °C) and low-stress (τ ≈ 200 MPa) creep regime are briefly reviewed. New 3D stereo STEM images of dislocation substructures which form during shear creep deformation in this regime are presented. It is then shown which new aspects need to be considered when performing double shear creep testing at lower temperatures (T < 800 °C) and higher stresses (τ > 600 MPa). In this creep regime, the macroscopic crystallographic [11−2](111) shear system deforms significantly faster than the [01−1](111) system. This represents direct mechanical evidence for a new planar fault nucleation scenario, which was recently suggested (Wu et al. in Acta Mater 144:642–655, 2018). The double shear creep specimen geometry inspired a micro-mechanical in-situ shear test specimen. Moreover, the in-situ SEM shear specimen can be FIB micro-machined from prior dendritic and interdendritic regions. Dendritic regions, which have a lower γ′ volume fraction, show a lower critical resolved shear stress. © 2018 The Author(s)
    view abstract10.1007/s11661-018-4726-9
  • 3D discrete dislocation dynamics study of creep behavior in Ni-base single crystal superalloys by a combined dislocation climb and vacancy diffusion model
    Gao, S. and Fivel, M. and Ma, A. and Hartmaier, A.
    Journal of the Mechanics and Physics of Solids 102 (2017)
    A three-dimensional (3D) discrete dislocation dynamics (DDD) creep model is developed to investigate creep behavior under uniaxial tensile stress along the crystallographic [001] direction in Ni-base single crystal superalloys, which takes explicitly account of dislocation glide, climb and vacancy diffusion, but neglects phase transformation like rafting of γ′ precipitates. The vacancy diffusion model takes internal stresses by dislocations and mismatch strains into account and it is coupled to the dislocation dynamics model in a numerically efficient way. This model is helpful for understanding the fundamental creep mechanisms in superalloys and clarifying the effects of dislocation glide and climb on creep deformation. In cases where the precipitate cutting rarely occurs, e.g. due to the high anti-phase boundary energy and the lack of superdislocations, the dislocation glide in the γ matrix and the dislocation climb along the γ/γ′ interface dominate plastic deformation. The simulation results show that a high temperature or a high stress both promote dislocation motion and multiplication, so as to cause a large creep strain. Dislocation climb accelerated by high temperature only produces a small plastic strain, but relaxes the hardening caused by the filling γ channels and lets dislocations further glide and multiply. The strongest variation of vacancy concentration occurs in the horizontal channels, where more mixed dislocations exit and tend to climb. The increasing internal stresses due to the increasing dislocation density are easily overcome by dislocations under a high external stress that leads to a long-term dislocation glide accompanied by multiplication. © 2017 Elsevier Ltd
    view abstract10.1016/j.jmps.2017.02.010
  • A Study on Microstructural Parameters for the Characterization of Granular Porous Ceramics Using a Combination of Stochastic and Mechanical Modeling
    Kulosa, M. and Neumann, M. and Boeff, M. and Gaiselmann, G. and Schmidt, V. and Hartmaier, A.
    International Journal of Applied Mechanics 9 (2017)
    To correlate the mechanical properties of granular porous materials with their microstructure, typically porosity is being considered as the dominant parameter. In this work, we suggest the average coordination number, i.e., the average number of connections that each grain of the porous material has to its neighboring grains, as additional - and possibly even more fundamental - microstructural parameter. In this work, a combination of stochastic and mechanical modeling is applied to study microstructural influences on the elastic properties of porous ceramics. This is accomplished by generating quasi-two-dimensional (2D) and fully three-dimensional (3D) representative volume elements (RVEs) with tailored microstructural features by a parametric stochastic microstructure model. In the next step, the elastic properties of the RVEs are characterized by finite element analysis. The results reveal that the average coordination number exhibits a very strong correlation with the Young's modulus of the material in both 2D and 3D RVEs. Moreover, it is seen that quasi-2D RVEs with the same average coordination number, but largely different porosities, only differ very slightly in their elastic properties such that the correlation is almost unique. This finding is substantiated and discussed in terms of the load distribution in microstructures with different porosities and average coordination numbers. © 2017 World Scientific Publishing Europe Ltd.
    view abstract10.1142/S1758825117500697
  • 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 (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 abstract10.1016/j.commatsci.2017.01.043
  • 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 (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 abstract10.1134/S1029959917030109
  • Micromechanical modeling of fatigue crack initiation in polycrystals
    Boeff, M. and Hassan, H.U. and Hartmaier, A.
    Journal of Materials Research (2017)
    Fatigue is an important mechanism for the failure of components in many engineering applications and a significant proportion of the fatigue life is spent in the crack initiation phase. Although a large number of research work addresses fatigue life and fatigue crack growth, the problem of modeling crack initiation remains a major challenge in the scientific and engineering community. In the present work, a micromechanical model is developed and applied to study fatigue crack initiation. In particular, the effect of different hardening mechanisms on fatigue crack initiation is investigated. To accomplish this, a model describing the evolution of the particular dislocation structures observed under cyclic plastic deformation is implemented and applied on randomly generated representative microstructures to investigate fatigue crack initiation. Finally, a method is presented to calculate the S–N curve for the polycrystalline materials. With this work, it is demonstrated how the micromechanical modeling can support the understanding of damage and failure mechanisms occurring during fatigue. Copyright © Materials Research Society 2017
    view abstract10.1557/jmr.2017.384
  • The shear instability energy: A new parameter for materials design?
    Kanani, M. and Hartmaier, A. and Janisch, R.
    Modelling and Simulation in Materials Science and Engineering 25 (2017)
    Reliable and predictive relationships between fundamental microstructural material properties and observable macroscopic mechanical behaviour are needed for the successful design of new materials. In this study we establish a link between physical properties that are defined on the atomic level and the deformation mechanisms of slip planes and interfaces that govern the mechanical behaviour of a metallic material. To accomplish this, the shear instability energy Γ is introduced, which can be determined via quantum mechanical ab initio calculations or other atomistic methods. The concept is based on a multilayer generalised stacking fault energy calculation and can be applied to distinguish the different shear deformation mechanisms occurring at TiAl interfaces during finite-temperature molecular dynamics simulations. We use the new parameter Γ to construct a deformation mechanism map for different interfaces occurring in this intermetallic. Furthermore, Γ can be used to convert the results of ab initio density functional theory calculations into those obtained with an embedded atom method type potential for TiAl. We propose to include this new physical parameter into material databases to apply it for the design of materials and microstructures, which so far mainly relies on single-crystal values for the unstable and stable stacking fault energy. © 2017 IOP Publishing Ltd.
    view abstract10.1088/1361-651X/aa865a
  • Towards prediction of springback in deep drawing using a micromechanical modeling scheme
    Vajragupta, N. and Ul Hassan, H. and Hartmaier, A.
    Procedia Engineering 207 (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 abstract10.1016/j.proeng.2017.10.739
  • A crystal plasticity smooth-particle hydrodynamics approach and its application to equal-channel angular pressing simulation
    Ma, A. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 24 (2016)
    A crystal plasticity (CP) modelling approach based on smooth-particle hydrodynamics (SPH) has been developed to study severe plastic deformation of crystalline materials. The method has been implemented and validated by comparing the stress distribution and stress evolution of several SPH and FEM simulations for an anisotropic elastic material. The findings show that the SPH method produces an efficient and numerically robust solution for solid-mechanics boundary value problems. Furthermore, the approach has been extended to incorporate a CP model and employed to simulate FCC polycrystals under the equal-channel angular pressing (ECAP) condition. It was found that the polycrystal contains four distinct regions with different deformation mechanisms. For the case that friction between deformable particles and boundary particles was neglected, more than one half of the grains suffered severe plastic deformation. The CP-SPH developed here thus is demonstrated to be a powerful tool to study grain refinement under severe plastic deformation. © 2016 IOP Publishing Ltd.
    view abstract10.1088/0965-0393/24/8/085011
  • A CSF-SPH method for simulating drainage and imbibition at pore-scale resolution while tracking interfacial areas
    Sivanesapillai, R. and Falkner, N. and Hartmaier, A. and Steeb, H.
    Advances in Water Resources 95 (2016)
    We present a conservative smoothed particle hydrodynamics (SPH) model to study the flow of multiple, immiscible fluid phases in porous media using direct pore-scale simulations. Particular focus is put on continuously tracking the evolution of interfacial areas, which are considered to be important morphological quantities affecting multiphase transport in porous media. In addition to solving the Navier–Stokes equations, the model accounts for the effects of capillarity at interfaces and contact lines. This is done by means of incorporating the governing interfacial mass and momentum balances using the continuum surface force (CSF) method, thus rendering model calibration routines unnecessary and minimizing the set of constitutive and kinematic assumptions. We address the application of boundary conditions at rigid solid surfaces and study the predictive capability of the model as well as optimal choices for numerical parameters using an extensive model validation procedure. We demonstrate the applicability of the model to simulate multiphase flows involving partial wettability, dynamic effects, large density ratios (up to 1000), large viscosity ratios (up to 100), as well as fragmentation and coalescence of fluid phases. The model is used to study the evolution of fluid–fluid interfacial areas during saturation-controlled primary drainage and main imbibition of heterogeneous pore spaces at low capillary numbers. A variety of pore-scale effects, such as wetting phase entrapment and fragmentation due to snap-off, are observed. Specific fluid–fluid interfacial area is observed to monotonically increase during primary drainage and hysteretic effects are apparent during main imbibition. © 2015
    view abstract10.1016/j.advwatres.2015.08.012
  • Direction-dependent mechanical characterization of cellulose-based composite vulcanized fiber
    Scholz, R. and Mittendorf, R. M. and Engels, J. K. and Hartmaier, A. and Kunne, B. and Walther, F.
    Materials Testing 58 (2016)
    Vulcanized fiber is a macromolecular cellulose-based composite material manufactured using the parchmentizing process. The cellulose is produced from the chemical digestion of plant-based raw materials (wood, cotton) or textile waste. Chemical additives used during manufacturing are completely removed. After the process, vulcanized fiber possesses improved properties concerning mechanical strength and abrasion as well as corrosion resistance in comparison to its raw materials. Concerning its economic life cycle assessment, low density, electrical insulating capability and balanced properties, vulcanized fiber has a potential, up to now unused, as a light and renewable structural material for applications in automotive or civil engineering industries. Research activities concerning the mechanical properties are insufficient and existing standards are out-of-date. In this work, for the first time a direction-dependent characterization of the process-related anisotropic mechanical properties of the material is realized with the aim to formulate an adequate material model for numerical simulations in the next step.
    view abstract10.3139/120.110929
  • Influence of the twin microstructure on the mechanical properties in magnetic shape memory alloys
    Reinholz, B. and Brinckmann, S. and Hartmaier, A. and Muntifering, B. and Knowlton, W.B. and Müllner, P.
    Acta Materialia 108 (2016)
    The microstructure evolution, i.e. Reorientation of martensite variants, is an important deformation mechanism in shape-memory alloys. This microstructure evolution occurs by the motion of twin boundaries and the nucleation and annihilation of twins in the hierarchical microstructure. An appropriate discrete disclination model for the description of the internal elastic fields and microstructure evolution is introduced for representative volume elements. The model is applied to an experimentally characterized microstructure, i.e. Conjugation boundary, and the predicted mechanical response is verified by comparison to experimental measurements. The influence of the twin microstructure on the homogenized stress-strain curve is studied. It is found that regular twinned microstructures have a low strain energy and a high resistance against deformation. These simulations also reason the origin of the microstructural stability of conjugation boundaries. © 2016 Acta Materialia Inc.Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2016.02.007
  • Microstructure design of tempered martensite by atomistically informed full-field simulation: From quenching to fracture
    Borukhovich, E. and Du, G. and Stratmann, M. and Boeff, M. and Shchyglo, O. and Hartmaier, A. and Steinbach, I.
    Materials 9 (2016)
    Martensitic steels form a material class with a versatile range of properties that can be selected by varying the processing chain. In order to study and design the desired processing with the minimal experimental effort, modeling tools are required. In this work, a full processing cycle from quenching over tempering to mechanical testing is simulated with a single modeling framework that combines the features of the phase-field method and a coupled chemo-mechanical approach. In order to perform the mechanical testing, the mechanical part is extended to the large deformations case and coupled to crystal plasticity and a linear damage model. The quenching process is governed by the austenite-martensite transformation. In the tempering step, carbon segregation to the grain boundaries and the resulting cementite formation occur. During mechanical testing, the obtained material sample undergoes a large deformation that leads to local failure. The initial formation of the damage zones is observed to happen next to the carbides, while the final damage morphology follows the martensite microstructure. This multi-scale approach can be applied to design optimal microstructures dependent on processing and materials composition. © 2016 by the authors.
    view abstract10.3390/ma9080673
  • Springback prediction and reduction in deep drawing under influence of unloading modulus degradation
    ul Hassan, H. and Maqbool, F. and Güner, A. and Hartmaier, A. and Ben Khalifa, N. and Tekkaya, A.E.
    International Journal of Material Forming 9 (2016)
    Springback is considered as one of the major problems in deep drawing of high-strength steels (HSS) and advanced high-strength steels (AHSS) which occurs during the unloading of part from the tools. With an ever increasing demand on the automotive manufactures for the production of lightweight automobile structures and increased crash performance, the use of HSS and AHSS is becoming extensive. For the accurate prediction of springback, unloading behavior of dual phase steels DP600, DP1000 and cold rolled steel DC04 for the deep drawing process is investigated and a strategy for the reduction of springback based on variable blankholder force is also presented. Cyclic tension compression tests and LS-Opt software are used for the identification of material parameters for Yoshida-Uemori (YU) model. Degradation of the Young’s modulus is found to be 28 and 26 and 14 % from the initial Young’s modulus for DP600, DP1000 and for the DC04 respectively for the saturated value. A finite element model is generated in LS-DYNA based on the kinematic hardening material model, namely Yoshida-Uemori (YU) model. The validation of numerical simulations is also carried out by the real deep drawing experiments. The springback could be predicted with the maximum deviation of 1.1 mm for these materials. For DP1000, the maximum springback is reduced by 24.5 %, for DP600 33.3 and 48.7 % for DC04 by the application of monotonic blankholder force instead of a constant blankholder force of 80 kN. It is concluded that despite the reduction of Young’s modulus, the springback can be reduced for these materials by increasing the blankholder force only in last 13 % of the punch travel. © 2015, Springer-Verlag France.
    view abstract10.1007/s12289-015-1248-5
  • Stacking fault based analysis of shear mechanisms at interfaces in lamellar TiAl alloys
    Kanani, M. and Hartmaier, A. and Janisch, R.
    Acta Materialia 106 (2016)
    The interfaces in lamellar TiAl alloys have a strong influence on the strength and deformability of the microstructure. It is widely accepted that their number and spacing can be used to tune these properties. However, the results of molecular dynamics simulations of sliding at γ/γ interfaces in lamellar TiAl alloys presented here suggest that important factors, namely the sequence of different interface types as well as the orientation of in-plane directions with respect to the loading axis, have to be included into meso-scale models. Simulations of bicrystal shear show significant differences in the deformation behavior of the different interfaces, as well as pronounced in-plane anisotropy of the shear strength of the individual interfaces. The critical stresses derived from bicrystal shear simulations are of the same order of magnitude as the one for nucleation and motion of twins in a γ-single crystal, showing that these mechanisms are competitive. In total four different deformation mechanisms, interface migration, twin nucleation and migration, dislocation nucleation, and rigid grain boundary sliding are observed. Their occurrence can be understood based on a multilayer generalized stacking fault energy analysis. This link between physical properties, geometry and deformation mechanism can provide guidelines for future alloy development. © 2016 Published by Elsevier Ltd on behalf of Acta Materialia Inc.
    view abstract10.1016/j.actamat.2015.11.047
  • A study of deformation and phase transformation coupling for TRIP-assisted steels
    Ma, A. and Hartmaier, A.
    International Journal of Plasticity 64 (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 abstract10.1016/j.ijplas.2014.07.008
  • Atomistic investigation of wear mechanisms of a copper bi-crystal
    Zhang, J. and Begau, C. and Geng, L. and Hartmaier, A.
    Wear 332-333 (2015)
    In the present work, we investigate the wear mechanisms of a Cu bi-crystal containing a random high angle grain boundary by means of molecular dynamics simulations. The underlying deformation behavior of the material is analyzed and further related to the observed characteristics of mechanical response and resulting morphology of the worn surface. In particular, the grain boundary-associated mechanisms are characterized by advanced analysis techniques for lattice defects. Our simulation results indicate that in addition to dislocation slip and dislocation-grain boundary interactions, grain boundary migration plays an important role in the plastic deformation of Cu bi-crystal. It is found that the wear behavior of Cu depends on the crystallographic orientation of the worn surface and can be altered quite significantly by the presence of a grain boundary. © 2015 Elsevier B.V.
    view abstract10.1016/j.wear.2015.02.023
  • 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 (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 abstract10.1016/j.engfracmech.2015.06.030
  • Influence of misfit stresses on dislocation glide in single crystal superalloys: A three-dimensional discrete dislocation dynamics study
    Gao, S. and Fivel, M. and Ma, A. and Hartmaier, A.
    Journal of the Mechanics and Physics of Solids 76 (2015)
    In the characteristic γ/γ′ microstructure of single crystal superalloys, misfit stresses occur due to a significant lattice mismatch of those two phases. The magnitude of this lattice mismatch depends on the chemical composition of both phases as well as on temperature. Furthermore, the lattice mismatch of γ and γ′ phases can be either positive or negative in sign. The internal stresses caused by such lattice mismatch play a decisive role for the micromechanical processes that lead to the observed macroscopic athermal deformation behavior of these high-temperature alloys. Three-dimensional discrete dislocation dynamics (DDD) simulations are applied to investigate dislocation glide in γ matrix channels and shearing of γ′ precipitates by superdislocations under externally applied uniaxial stresses, by fully taking into account internal misfit stresses. Misfit stress fields are calculated by the fast Fourier transformation (FFT) method and hybridized with DDD simulations. For external loading along the crystallographic [001] direction of the single crystal, it was found that the different internal stress states for negative and positive lattice mismatch result in non-uniform dislocation movement and different dislocation patterns in horizontal and vertical γ matrix channels. Furthermore, positive lattice mismatch produces a lower deformation rate than negative lattice mismatch under the same tensile loading, but for an increasing magnitude of lattice mismatch, the deformation resistance always diminishes. Hence, the best deformation performance is expected to result from alloys with either small positive, or even better, vanishing lattice mismatch between γ and γ′ phase. © 2014 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.jmps.2014.11.015
  • Interplanar potential for tension-shear coupling at grain boundaries derived from ab initio calculations
    Pang, X.Y. and Janisch, R. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 24 (2015)
    Based on ab initio density functional theory (DFT) calculations we derive an analytical expression for the interplanar potential of grain boundaries and single crystals as a function of coupled tensile and shear displacements. This energy function captures even details of the grain boundary behaviour, such as the tension-softening of the shear instability of aluminium grain boundaries, with good accuracy. The good agreement between the analytical model and the DFT calculations is achieved by introducing two new characteristic parameters, namely the position of the generalised unstable stacking fault with respect to the stable stacking fault, and the ratio of stable and unstable generalised stacking fault energies. One of the potentials' parameters also serves as a criterion to judge if a grain boundary deforms via crack propagation or dislocation nucleation. We suggest this potential function for application in continuum models, where constitutive relationships for grain boundaries need to be derived from a sound physical model. © 2016 IOP Publishing Ltd.
    view abstract10.1088/0965-0393/24/1/015007
  • 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 (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 abstract10.1016/j.commatsci.2014.12.038
  • Large scale Molecular Dynamics simulation of microstructure formation during thermal spraying of pure copper
    Wang, T. and Begau, C. and Sutmann, G. and Hartmaier, A.
    Surface and Coatings Technology 280 (2015)
    Thermal spray processes are widely used for the manufacture of advanced coating systems, e.g. metallic coatings for wear and corrosion protection. The desired coating properties are closely related to the microstructure, which is highly influenced by the processing parameters, such as temperature, size and velocity of the sprayed particles. In this paper, large scale Molecular Dynamics simulations are conducted to investigate the microstructure formation mechanisms during the spraying process of hot nano-particles onto a substrate at room temperature using pure copper as a benchmark material representing for a wider class of face-centered-cubic metals. To evaluate the influence of processing parameters on the coating morphology, a number of simulations are performed in which the initial temperature, size and velocity of copper particles are systematically varied in order to investigate the thermal and microstructural evolution during impaction. Two distinct types of microstructural formation mechanisms, resulting in different coating morphologies, are observed in the present investigation, which are either governed by plastic deformation or by the process of melting and subsequent solidification. Furthermore, a thermodynamically motivated model as a function of the particle temperature and velocity is developed, which predicts the microstructural mechanisms observed in the simulations. The results provide an elementary insight into the microstructure formation mechanisms on an atomistic scale, which can serve as basic input for continuum modeling of thermal spray process. © 2015 Published by Elsevier B.V.
    view abstract10.1016/j.surfcoat.2015.08.034
  • Primary combination of phase-field and discrete dislocation dynamics methods for investigating athermal plastic deformation in various realistic Ni-base single crystal superalloy microstructures
    Gao, S. and Kumar Rajendran, M. and Fivel, M. and Ma, A. and Shchyglo, O. and Hartmaier, A. and Steinbach, I.
    Modelling and Simulation in Materials Science and Engineering 23 (2015)
    Three-dimensional discrete dislocation dynamics (DDD) simulations in combination with the phase-field method are performed to investigate the influence of different realistic Ni-base single crystal superalloy microstructures with the same volume fraction of γ;precipitates on plastic deformation at room temperature. The phase-field method is used to generate realistic microstructures as the boundary conditions for DDD simulations in which a constant high uniaxial tensile load is applied along different crystallographic directions. In addition, the lattice mismatch between the γand γ;phases is taken into account as a source of internal stresses. Due to the high antiphase boundary energy and the rare formation of superdislocations, precipitate cutting is not observed in the present simulations. Therefore, the plastic deformation is mainly caused by dislocation motion in γ; matrix channels. From a comparison of the macroscopic mechanical response and the dislocation evolution for different microstructures in each loading direction, we found that, for a given γ;phase volume fraction, the optimal microstructure should possess narrow and homogeneous γ; matrix channels. © 2015 IOP Publishing Ltd Printed in the UK.
    view abstract10.1088/0965-0393/23/7/075003
  • Atomistic study of the influence of lattice defects on the thermal conductivity of silicon
    Wang, T. and Madsen, G.K.H. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 22 (2014)
    Lattice defects such as vacancies, voids and dislocations are inevitably present in any material of technological interest. In this work, non-equilibrium molecular dynamics simulations are conducted to investigate how the monatomic vacancies and nanovoids influence the lattice thermal conductivity of silicon. The results show a clear non-linear decrease of the thermal conductivity with increasing defect volume fraction. Furthermore, it is found that for a given volume fraction of defects, a random distribution shows a lower lattice thermal conductivity. To develop a fundamental understanding of these observations, the spectral energy densities for all phonon branches obtained from 2D Fourier transformations of the atomic trajectories are analyzed. This yields the mean phonon group velocities and relaxation times, which are the main physical quantities contributing to the lattice thermal conductivity. Our analysis reveals that the phonon relaxation time is the most important parameter for describing the degrading of the thermal transport behavior in the defected structures. © 2014 IOP Publishing Ltd.
    view abstract10.1088/0965-0393/22/3/035011
  • Coupled atomistic-continuum study of the effects of C atoms at α-Fe dislocation cores
    Chockalingam, K. and Janisch, R. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 22 (2014)
    The influence of carbon at dislocation cores in α-Fe is studied to determine the Peierls stress, i.e. the critical stress required to move the dislocation at 0 K. The effect of carbon on both edge and screw dislocations is investigated. A coupled molecular statics (MS) and extended finite element method (XFEM) is employed for this study, where the dislocation core is modeled atomistically. The results on pure Fe are found to be in good agreement with a fully atomistic study. The coupled approach captures the right core behavior and significantly reduces the size of the atomistic region, while describing the behavior of a single dislocation in an infinite anisotropic elastic medium. Furthermore, mechanical boundary conditions can be applied consistently. It was found that the influence of carbon on edge dislocations is much stronger than that on screw dislocations, and that carbon causes a directionally dependent Peierls stress in the case of a screw dislocation. Even though the increase of the Peierls stress is much more pronounced for edge dislocations, the total value does not reach the level of the Peierls stress for screw dislocations, either with or without carbon at the core. Hence, we conclude that the motion of screw dislocations remains the rate limiting factor for plastic deformation of α-Fe. © 2014 IOP Publishing Ltd.
    view abstract10.1088/0965-0393/22/7/075007
  • Hydrogen embrittlement of a carbon segregated σ5 (310) [001] symmetrical tilt grain boundary in α-Fe
    Tahir, A.M. and Janisch, R. and Hartmaier, A.
    Materials Science and Engineering A 612 (2014)
    The physical and mechanical properties of a σ5 (310) [001] symmetrical tilt grain boundary (STGB) in body centred cubic (bcc) Fe are investigated by means of ab initio calculations with respect to the effect of a varying number of C and H atoms at the grain boundary. The obtained results show that with increasing number of C atoms the grain boundary energy is lowered, and the segregation energy remains negative up to a full coverage of the grain boundary with C. Thus, in a bcc Fe-C system with a sufficient amount of interstitial C, the C segregated state should be considered as the ground state of this interface. Ab initio uni-axial tensile tests of the grain boundary reveal that the work of separation as well as the theoretical strength of the σ5 (310) [001] STGB increases significantly with increasing C content. The improved cohesion due to C is mainly a chemical effect, but the mechanical contribution is also cohesion enhancing. The presence of hydrogen changes the cohesion enhancing mechanical contribution of C to an embrittling contribution, and also reduces the beneficial chemical contribution to the cohesion. When hydrogen is present together with C at the grain boundary, the reduction in strength amounts to almost 20% for the co-segregated case and to more than 25% if C is completely replaced by H. Compared to the strength of the STGB in pure iron, however, the influence of H is negligible. Hence, H embrittlement can only be understood in the three component Fe-C-H system. © 2014 Elsevier B.V.
    view abstract10.1016/j.msea.2014.06.071
  • Interface properties in lamellar TiAl microstructures from density functional theory
    Kanani, M. and Hartmaier, A. and Janisch, R.
    Intermetallics 54 (2014)
    The deformability and strength of lamellar two-phase (γ and α2) TiAl alloys strongly depends on the mechanical properties of the different interfaces in such microstructures. We carried out ab-initio density functional theory calculations of interface energy and strength for all known interface variants as well as the corresponding single crystal slip/cleavage planes to obtain a comprehensive database of key mechanical quantities. This data collection can be used for meso-scale simulations of deformation and fracture in TiAl. In spite of the different atomic configurations of the lamellar interfaces and the single crystal planes, the calculated values for the tensile strength are in the same range and can be considered as equal in a meso-scale model. Analysis of generalized stacking fault energy surfaces showed that the shear strength is directional dependent, however, the [112̄] direction is an invariant easy gliding direction in all investigated systems. The probability of different dislocation dissociation reactions as part of a shear deformation mechanism are discussed as well. © 2014 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.intermet.2014.06.001
  • 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 (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 abstract10.1016/j.commatsci.2014.05.059
  • Multiscale modeling of nanoindentation: From Atomistic to continuum models
    Engels, P.S. and Begau, C. and Gupta, S. and Schmaling, B. and Ma, A. and Hartmaier, A.
    Solid Mechanics and its Applications 203 (2014)
    Nanoindentation revealed a number of effects, like pop-in behavior or indentation size effects, that are very different from the classical mechanical behavior of bulk materials and that have therefore sparked a lot of research activities. In this contribution a multiscale approach is followed to understand the mechanisms behind this peculiar material behavior during nanoindentation. Atomistic simulations reveal the mechanisms of dislocation nucleation and multiplication during the very start of plastic deformation. From mesoscale dislocation density based models we gain advanced insight into how plastic zones develop and spread through materials with heterogeneous dislocation microstructures. Crystal plasticity models on the macroscale, finally, are able to reproduce load-indentation curves and remaining imprint topologies in a way that is directly comparable to experimental results and, thus, allows for the determination of true material properties by inverse methods. The complex interplay of the deformation mechanisms occurring on different length scales is described and the necessity to introduce the knowledge about fundamental deformation mechanisms into models on higher length scales is highlighted. © Springer Science+Business Media Dordrecht 2014.
    view abstract10.1007/978-94-007-6919-9_15
  • On the influence of isotropic and kinematic hardening caused by strain gradients on the deformation behaviour of polycrystals
    Ma, A. and Hartmaier, A.
    Philosophical Magazine 94 (2014)
    During the deformation of polycrystals, pronounced strain gradients may occur at grain boundaries between grains whose misorientations lead to a large mismatch in their deformation behaviour. Hence, even under globally uniaxial and homogeneous strains, internal stresses will arise that must be characterized by nonlocal plasticity models. In this work, such a nonlocal constitutive model is formulated based on the concept of densities of geometrically necessary superdislocations in an isotropic elastic-plastic medium. Since the deformation of individual grains is considered, crystal plasticity models are applied that take into account plastic slip on crystallographic planes. This new nonlocal constitutive model is applied to describe the deformation of a polycrystal under the influence of plastic strain gradients caused by isotropic and kinematic strain hardening. It is found that isotropic hardening originating from plastic strain gradients amplifies deformation heterogeneities stemming from different Schmid factors in neighbouring grains. However, the kinematic hardening resulting from plastic strain gradients tends to reduce such deformation heterogeneity. Thus, the capability of a polycrystal to deform uniformly is determined by the competition between isotropic and kinematic hardening. Finally, the model is applied to explain why grain refinement is an efficient way to improve material strength and ductility at the same time. © 2013 Taylor & Francis.
    view abstract10.1080/14786435.2013.847290
  • 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 (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 abstract10.1016/j.commatsci.2014.04.011
  • Transition of effective hydraulic properties from low to high Reynolds number flow in porous media
    Sivanesapillai, R. and Steeb, H. and Hartmaier, A.
    Geophysical Research Letters 41 (2014)
    We numerically analyze fluid flow through porous media up to a limiting Reynolds number of O(103). Due to inertial effects, such processes exhibit a gradual transition from laminar to turbulent flow for increasing magnitudes of Re. On the macroscopic scale, inertial transition implies nonlinearities in the relationship between the effective macroscopic pressure gradient and the filter velocity, typically accounted for in terms of the quadratic Forchheimer equation. However, various inertia-based extensions to the linear Darcy equation have been discussed in the literature; most prominently cubic polynomials in velocity. The numerical results presented in this contribution indicate that inertial transition, as observed in the apparent permeability, hydraulic tortuosity, and interfacial drag, is inherently of sigmoidal shape. Based on this observation, we derive a novel filtration law which is consistent with Darcy's law at small Re, reproduces Forchheimer's law at large Re, and exhibits higher-order leading terms in the weak inertia regime. © 2014. American Geophysical Union. All Rights Reserved.
    view abstract10.1002/2014GL060232
  • Ab initio calculation of traction separation laws for a grain boundary in molybdenum with segregated C impurites
    Tahir, A.M. and Janisch, R. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 21 (2013)
    We have determined the influence of carbon on mechanical properties such as grain boundary energy, work of separation (WoS) and fracture strength of the Σ5(3 1 0)[0 0 1] symmetrical tilt grain boundary (STGB) in molybdenum with ab initio methods. From our ab initio results, we derived traction-separation laws that can be used in continuum simulations of fracture employing cohesive zones. Our results show that with an increasing number of C atoms at the grain boundary, the energy of the grain boundary is lowered, indicating a strong driving force for segregation. Uni-axial tensile tests of the grain boundary reveal that there is only a small effect of segregated C atoms on the cohesive energy or WoS of the grain boundary, while the strength of the Σ5(3 1 0)[0 0 1] STGB increases by almost 30% for a complete monolayer of C. This increase in strength is accompanied by an increase in grain boundary stiffness and a decrease of the interface excess volume. The characteristic parameters are combined in the concentration-dependent traction-separation laws. A study of the scaling behaviour of the different investigated systems shows that the energy-displacement curves can be well described by the universal binding energy relationship even for different C concentrations. These findings open the way for significant simplification of the calculation of ab initio traction separation laws for grain boundaries with and without impurities. © 2013 IOP Publishing Ltd.
    view abstract10.1088/0965-0393/21/7/075005
  • Mechanisms of anisotropic friction in nanotwinned Cu revealed by atomistic simulations
    Zhang, J.J. and Hartmaier, A. and Wei, Y.J. and Yan, Y.D. and Sun, T.
    Modelling and Simulation in Materials Science and Engineering 21 (2013)
    The nature of nanocrystalline materials determines that their deformation at the grain level relies on the orientation of individual grains. In this work, we investigate the anisotropic response of nanotwinned Cu to frictional contacts during nanoscratching by means of molecular dynamics simulations. Nanotwinned Cu samples containing embedded twin boundaries parallel, inclined and perpendicular to scratching surfaces are adopted to address the effects of crystallographic orientation and inclination angle of aligned twin boundaries cutting the scratching surface. The transition in deformation mechanisms, the evolution of friction coefficients and the friction-induced microstructural changes are analyzed in detail and are related to the loading conditions and the twinned microstructures of the materials. Furthermore, the effect of twin spacing on the frictional behavior of Cu samples is studied. Our simulation results show that the crystallographic orientation strongly influences the frictional response in different ways for samples with different twin spacing, because the dominant deformation mode varies upon scratching regions of different orientations. A critical inclination angle of 26.6° gives the lowest yield strength and the highest friction coefficient, at which the plasticity is dominated by twin boundary migration and detwinning. It is demonstrated that the anisotropic frictional response of nanotwinned Cu originates from the heterogeneous localized deformation, which is strongly influenced by crystallographic orientation, twin boundary orientation and loading condition. © 2013 IOP Publishing Ltd.
    view abstract10.1088/0965-0393/21/6/065001
  • On the crystallographic anisotropy of nanoindentation in pseudoelastic NiTi
    Pfetzing-Micklich, J. and Somsen, C. and Dlouhy, A. and Begau, C. and Hartmaier, A. and Wagner, M.F.-X. and Eggeler, G.
    Acta Materialia 61 (2013)
    We use a nanoindenter with a Berkovich tip to study local mechanical properties of two polycrystalline intermetallics with a B2 crystal structure, NiAl and NiTi. We use orientation imaging scanning electron microscopy to select a relevant number of grains with appropriate sizes and surface normals parallel to 〈0 0 1〉, 〈1 0 1〉 and 〈1 1 1〉. As a striking new result, we find a strong crystallographic orientation dependence for NiTi. This anisotropy is less pronounced in the case of NiAl. For NiTi, the indentation force required to impose a specific indentation depth is highest for indentation experiments performed in the 〈0 0 1〉 direction and lowest along the 〈1 1 1〉 direction. We consider transmission electron microscopy results from cross-sections below the indents and use molecular dynamics simulations and resolved shear stress calculations to discuss how this difference can be accounted for in terms of elementary deformation and transformation processes, related to dislocation plasticity (NiAl and NiTi), and in terms of the stress-induced formation and growth of martensite (NiTi). Our results show that the crystallographic anisotropy during nanoindentation of NiTi is governed by the orientation dependence of the martensitic transformation; dislocation plasticity appears to be less important. © 2012 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2012.09.081
  • A micromechanical damage simulation of dual phase steels using XFEM
    Vajragupta, N. and Uthaisangsuk, V. and Schmaling, B. and Münstermann, S. and Hartmaier, A. and Bleck, W.
    Computational Materials Science 54 (2012)
    As a result of their microstructures being made up by constituents with strong distinctions in mechanical properties, multiphase steels exhibit high energy absorption as well as an excellent combination of strength and ductility. Furthermore, the microstructural composition influences the failure behaviour of such kind of steels because of the occurrence of different fracture mechanisms in parallel. When the failure behaviour of dual phase (DP) steels is investigated, several types of failures are typically observed, such as the ductile failure of ferrite, the brittle failure of martensite and the interface debonding between phases. Hence, a reliable microstructure-based simulation approach must be developed that describes material deformation and failure under any given loading condition. In this work, two different damage mechanics methods were employed to study the interaction between failure modes in DP steels by means of a representative volume element (RVE). In order to consider the characteristics of a real microstructure, all involved phases were modelled with a precise volume fraction. Firstly, the extended finite element method (XFEM) was used to study the damage onset and progression in martensitic regions without prescribing the crack path. Secondly, a damage curve was derived and employed for the ductile ferritic phase. By combining these two damage models in the RVE model on microscopic scale, development of different failures modes in DP steels could be investigated. © 2011 Elsevier B.V. All rights reserved.
    view abstract10.1016/j.commatsci.2011.10.035
  • A novel approach to study dislocation density tensors and lattice rotation patterns in atomistic simulations
    Begau, C. and Hua, J. and Hartmaier, A.
    Journal of the Mechanics and Physics of Solids 60 (2012)
    Crystal plasticity caused by the nucleation and interaction of dislocations is an important aspect in crystal deformation. Recent nanoindentation experiments in single crystals of copper or aluminum revealed large deviations in the lattice rotation and an inhomogeneous distribution of the dislocation density in the plastic zone under the indenter tip. Molecular dynamics simulations offer the possibility to study the origin of these phenomena on an atomistic scale, but require sophisticated analysis routines in order to deal with the massive amount of generated data. Here a new efficient approach to analyze atomistic data on the fly during the simulation is introduced. This approach allows us to identify the dislocation network including Burgers vectors on the timescale of picoseconds and below. This data does not only reveal the evolution of dislocation structures, but it offers the possibility to quantify local dislocation density tensors calculated on an atomic level. The numerical results are compared with experimental data from the literature. The presented approach provides useful insight into the active deformation mechanisms during plastic deformation that will help us to bridge simulations on atomic scales and continuum descriptions. © 2012 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.jmps.2011.12.005
  • A scheme to combine molecular dynamics and dislocation dynamics
    Brinckmann, S. and Mahajan, D.K. and Hartmaier, A.
    Modelling and Simulation in Materials Science and Engineering 20 (2012)
    Many engineering challenges occur on multiple interacting length scales, e.g. during fracture atoms separate on the atomic scale while plasticity develops on the micrometer scale. To investigate the details of these events, a concurrent multiscale model is required which studies the problem at appropriate length- and time-scales: the atomistic scale and the dislocation dynamics scale. The AtoDis multiscale model is introduced, which combines atomistics and dislocation dynamicsinto a fully dynamic model that is able to simulate deformation mechanisms at finite temperature. The model uses point forces to ensure mechanical equilibrium and kinematic continuity at the interface. By resolving each interface atom analytically, and not numerically, the framework uses a coarse FEM mesh and intrinsically filters out atomistic vibrations. This multiscale model allows bi-directional dislocation transition at the interface of both models with no remnant atomic disorder. Thereby, the model is able to simulate a larger plastic zone than conventional molecular dynamics while reducing the need for constitutive dislocation dynamics equations. This contribution studies dislocation nucleation at finite temperature and investigates the absorption of dislocations into the crack wake. © 2012 IOP Publishing Ltd.
    view abstract10.1088/0965-0393/20/4/045001
  • 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 (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 abstract10.1016/j.commatsci.2012.02.024
  • Atomistically informed crystal plasticity model for body-centered cubic iron
    Koester, A. and Ma, A. and Hartmaier, A.
    Acta Materialia 60 (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 abstract10.1016/j.actamat.2012.03.053
  • Continuum simulation of the evolution of dislocation densities during nanoindentation
    Engels, P. and Ma, A. and Hartmaier, A.
    International Journal of Plasticity 38 (2012)
    When nanoindenting dislocation-free regions of single crystals a so-called pop-in phenomenon is commonly observed. Molecular dynamics (MD) studies have revealed homogeneous nucleation of dislocations in a perfect crystal as a mechanism causing such pop-in behavior. In this work we transfer this knowledge gained on the atomic scale into a dislocation nucleation model that is applied within a dislocation density based crystal plasticity description. Furthermore, we develop a non-local formulation of a crystal plasticity model that is devised to yield a valid description of plasticity also in situations where the dislocation density is small or even vanishing and where conventional plasticity models fail. This is accomplished by studying the evolution of statistically stored and geometrically necessary dislocation densities separately. We apply this non-local crystal plasticity model to investigate the evolution of dislocation densities in the early stages of nanoindentation. The results of our continuum model show good agreement with MD simulations for cases where nanoindentation into an initially dislocation-free crystal is studied, i.e. where a pop-in occurs when the critical stress underneath the indenter reaches the critical value for homogeneous dislocation nucleation. After thus validating our model we study the influence of pre-existing homogeneous and local dislocation densities. Both cases show a good qualitative agreement with recent experimental findings and it is concluded that pre-existing local dislocations densities reduce the load at which a pop-in occurs and - more importantly - change the mechanism from homogeneous dislocation nucleation to rapid dislocation multiplication. In general, our results show that continuum plasticity formulations can be extended such that applications to nanoscale volumes become possible. © 2012 Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.ijplas.2012.05.010
  • Determination of plastic material properties by analysis of residual imprint geometry of indentation
    Schmaling, B. and Hartmaier, A.
    Journal of Materials Research 27 (2012)
    A method is presented for the identification of plastic material properties, i.e., yield strength and work hardening rate, using the residual imprint geometry formed by a spheroconical indentation. A corresponding finite element simulation with the same tip geometry and maximum as applied in the indentation experiment yields a numerical imprint profile. Then, the imprint profiles resulting from simulation and experiment are compared, and the material parameters of the simulation are varied by an optimization procedure until a satisfying agreement between simulation and experiment is established. At this stage, the material parameters used for the simulation represent the true material properties. It is shown that this procedure yields unique results that are furthermore verified by independent uniaxial straining experiments. Finally, the reliability of this method with special emphasis on its sensitivity with respect to measurement errors of the imprint geometry is demonstrated. Hence, it is concluded that the residual imprint can be regarded as the fingerprint of a material that contains sufficient information on plastic material behavior to uniquely extract values for yield strength and work hardening rate. © Materials Research Society 2012.
    view abstract10.1557/jmr.2012.212
  • Influence of Microstructural Features on the Propagation of Microstructurally Short Fatigue Cracks in Structural Steels
    Sharaf, M. and Lian, J. and Vajragupta, N. and Münstermann, S. and Bleck, W. and Schmaling, B. and Ma, A. and Hartmaier, A.
    Fatigue of Materials II: Advances and Emergences in Understanding (2012)
    Cyclically loaded structural steel components are usually designed to endure macroscopic stress amplitudes close to the material's endurance strength where microcracks initiate due to microstructural inhomogeneities and exhibit strong interactions with the various microstructural features in their neighborhood upon propagating. The current study presents a microstructural model with a capability to quantitatively describe the influence of microstructural features on the growth of cyclic cracks in the decisive, very early fatigue behavior stage. The FE model is based on the crystal plasticity theory and accounts for relative grain orientations. Both the extended finite element method (XFEM) and a coupled damage mechanics approach are used to describe crack opening behavior. The model is implemented to simulate real microcracking events produced in interrupted cyclic multiple-step tests under metallographic observation with temperature change measurements. Furthermore, the model is implemented on virtually created microstructures with altered grain sizes and orientations based on statistical EBSD analysis. © 2013 The Minerals, Metals, & Materials Society. All rights reserved.
    view abstract10.1002/9781118533383.ch18
  • Mechanisms of crazing in glassy polymers revealed by molecular dynamics simulations
    Mahajan, D.K. and Hartmaier, A.
    Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 86 (2012)
    Mechanisms leading to initiation of crazing type failure in a glassy polymer are not clearly understood. This is mainly due to the difficulty in characterizing the stress state and polymer configuration sufficiently locally at the craze initiation site. Using molecular dynamics simulations, we have now been able to access this information and have shown that the local heterogeneous deformation leads to craze initiation in glassy polymers. We found that zones of high plastic activity are constrained by their neighborhood and become unstable, initiating crazing from these sites. Furthermore, based on the constant flow stresses observed in the unstable zones, we conclude that microcavitation is the essential local deformation mode to trigger crazing in glassy polymers. Our results demonstrate the basic difference in the local deformation mode as well as the conditions that lead to either shear-yielding or crazing type failures in glassy polymers. We anticipate our paper to help in devising a new criterion for craze initiation that not only considers the stress state, but also considers local deformation heterogeneities that form the necessary condition for crazing in glassy polymers. © 2012 American Physical Society.
    view abstract10.1103/PhysRevE.86.021802
  • The mechanical shear behavior of Al single crystals and grain boundaries
    Pang, X. and Ahmed, N. and Janisch, R. and Hartmaier, A.
    Journal of Applied Physics 112 (2012)
    To investigate the mechanical shear properties of interfaces in metals, we have determined the γ-surfaces of different special tilt and twist grain boundaries in aluminum by means of ab initio calculations. From the γ-surfaces, we obtained minimum energy paths and barriers, as well as the theoretical shear strength. For the [110] tilt grain boundaries, there is a pronounced easy-sliding direction along the tilt axis. The theoretical shear strength scales with the height of the slip barrier and exhibits a relation with the misorientation angle: the closer the angle to 90°, the higher the shear stress. There is no simple relationship with the periodicity of the grain boundary, i.e., the Σ value or the grain boundary energy. © 2012 American Institute of Physics.
    view abstract10.1063/1.4736525
  • Twin boundary spacing-dependent friction in nanotwinned copper
    Zhang, J. and Wei, Y. and Sun, T. and Hartmaier, A. and Yan, Y. and Li, X.
    Physical Review B - Condensed Matter and Materials Physics 85 (2012)
    The deformation mechanisms of nanotwinned Cu subjected to nanoscratching are investigated by means of molecular dynamics simulations. Scratching simulations on nanotwinned single-crystalline Cu with the twin planes parallel and perpendicular to the scratching direction are performed. Since the detwinning mechanism is completely suppressed in the former case, no apparent correlation between frictional coefficient and the twin spacing is observed. In samples where the twin planes are perpendicular to the scratching direction, the friction increases as the twin spacing decreases, and then decreases as the twin spacings become even smaller. It results from the competitive plastic deformation between the inclined dislocations and the detwinning mechanism. Subsequent simulations for nanotwinned polycrystalline Cu unveil that in addition to the grain-boundary-associated deformation mechanism, dislocation-mediated detwinning plays a significant role in the plastic deformation of nanotwinned Cu. The twin boundary spacing in turn affects nanotwinned materials to resist scratching via plastic deformation. We demonstrate via the nanoscratching tests that there exists a critical twin boundary spacing for which the friction coefficient is maximized and that this transition results from the competing deformation mechanisms in those nanotwinned materials. © 2012 American Physical Society.
    view abstract10.1103/PhysRevB.85.054109
  • Atomistic processes of dislocation generation and plastic deformation during nanoindentation
    Begau, C. and Hartmaier, A. and George, E.P. and Pharr, G.M.
    Acta Materialia 59 (2011)
    To enable plastic deformation during nanoindentation of an initially defect-free crystal, it is necessary first to produce dislocations. While it is now widely accepted that the nucleation of the first dislocations occurs at the start of the pop-in event frequently observed in experiments, it is unclear how these initial dislocations multiply during the early stages of plastic deformation and produce pop-in displacements that are typically much larger than the magnitude of the Burgers vector. This uncertainty about the complex interplay between dislocation multiplication and strain hardening during nanoindentation makes a direct correlation between force-displacement curves and macroscopic material properties difficult. In this paper, we study the early phase of plastic deformation during nanoindentation with the help of large-scale molecular dynamics simulations. A skeletonization method to simplify defect structures in atomistic simulations enables the direct observation and quantitative analysis of dislocation nucleation and multiplication processes occurring in the bulk as well as at the surface. © 2010 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2010.10.016
  • Atomistically informed continuum model for body centered cubic iron
    Koester, A. and Ma, A. and Hartmaier, A.
    Materials Research Society Symposium Proceedings 1296 (2011)
    Plastic deformation in body centered cubic iron is dominated by glide of screw dislocations with non-planar dislocation cores. This causes a strong strain rate and temperature dependence of flow stress, the breakdown of Schmid's law and a dependence of dislocation mobility on shear stress components that do not contribute to the mechanical driving force for dislocation glide. Based on the framework of crystal plasticity, we developed a constitutive plasticity model that takes all these phenomena into account. To parameterize this continuum plasticity model molecular statics simulations using a semi-empirical potential have been performed. These atomistic calculations yielded quantitative relationships for the influence of all components of the local stress tensor on dislocation mobility. Together with experimental data from the literature on the kinetics of screw dislocations in bcc iron the constitutive relation presented here has been developed. As application example of the model, we calculated the tension compression asymmetry and the strain rate dependence of the hardening behavior within a bcc iron crystal. © 2011 Materials Research Society.
    view abstract10.1557/opl.2011.1445
  • Influence of dislocation density on the pop-in behavior and indentation size effect in CaF2 single crystals: Experiments and molecular dynamics simulations
    Lodes, M.A. and Hartmaier, A. and Göken, M. and Durst, K.
    Acta Materialia 59 (2011)
    In this work, the indentation size effect and pop-in behavior are studied for indentations in undeformed and locally pre-deformed CaF2 single crystals, using both nanoindentation experiments and molecular dynamics simulations. To study the influence of dislocation density on the indentation behavior, small-scale indentations are carried out inside the plastic zone of larger indentations. This experiment is mimicked in the simulations by indenting a small sphere into the center of the residual impression of a larger sphere. The undeformed material shows the well-known pop-in behavior followed by the indentation size effect. Pre-deforming the material leads to a reduction in the indentation size effect both for experiments and simulations, which is in accordance with the Nix-Gao theory. Furthermore, the pop-in load is reduced in the experiments, whereas a smooth transition from elastic to plastic deformation is found in the simulations. There, plasticity is initiated by the movement of pre-existing dislocation loops in the vicinity of the plastic zone. The simulations thus give a detailed insight into the deformation mechanism during indentation and highlight the importance of the dislocation microstructure for the indentation size effect and dislocation nucleation. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2011.03.050
  • Mechanisms of grain boundary softening and strain-rate sensitivity in deformation of ultrafine-grained metals at high temperatures
    Ahmed, N. and Hartmaier, A.
    Acta Materialia 59 (2011)
    Two-dimensional dislocation dynamics and diffusion kinetics simulations are employed to study the different mechanisms of plastic deformation of ultrafine-grained (UFG) metals at different temperatures. Besides conventional plastic deformation by dislocation glide within the grains, we also consider grain boundary (GB)-mediated deformation and recovery mechanisms based on the absorption of dislocations into GBs. The material is modeled as an elastic continuum that contains a defect microstructure consisting of a pre-existing dislocation population, dislocation sources and GBs. The mechanical response of the material to an external load is calculated with this model over a wide range of temperatures. We find that at low homologous temperatures, the model material behaves in agreement with the classical Hall-Petch law. At high homologous temperatures, however, a pronounced GB softening and, moreover, a high strain-rate sensitivity of the model material is found. Qualitatively, these numerical results agree well with experimental results known from the literature. Thus, we conclude that dynamic recovery processes at GBs and GB diffusion are the rate-limiting processes during plastic deformation of UFG metals. © 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
    view abstract10.1016/j.actamat.2011.03.056
  • Micro-shear deformation of pure copper
    Pfetzing-Micklich, J. and Brinckmann, S. and Dey, S.R. and Otto, F. and Hartmaier, A. and Eggeler, G.
    Materialwissenschaft und Werkstofftechnik 42 (2011)
    In this paper a new micro-shear experiment is introduced using a double shear specimen machined by a focused ion beam technique. The micro-shear specimen is structured from pure copper promoting (111) [101] slip. Comparing scanning electron microscopy images before and after deformation provides evidence for localized shear. Load-displacement data identify a load plateau and characterize the localized shear process (critical shear-stress for activation of (111) [101] slip: 170 MPa). Copyright © 2011 WILEY-VCH Verlag GmbH & Co. KGaA.
    view abstract10.1002/mawe.201100715
  • On the formation of vacancies by edge dislocation dipole annihilation in fatigued copper
    Brinckmann, S. and Sivanesapillai, R. and Hartmaier, A.
    International Journal of Fatigue 33 (2011)
    Fatigue experiments on copper have shown that vacancy production leads to the evolution of extrusions, which are the preferred sites for fatigue crack initiation. However, experimental, analytical and numerical results for the critical edge-dislocation dipole annihilation distance vastly differ. This study performs molecular statics and molecular dynamics simulations at elevated temperature to investigate the discrepancies in annihilation distance. Vacancy forming edge dislocation dipoles are stable if their spacing exceeds 2 lattice spacings. If the dislocation dipole is perpendicular to the free surface in a thin sheet of material, jogs on edge dislocations lead to dipole annihilation. Our main conclusion is that dislocation generation, glide and stable edge dislocation dipoles are sufficient to lead to that extrusion growth, which results in fatigue crack initiation.
    view abstract10.1016/j.ijfatigue.2011.05.004
  • Simulation of fracture in heterogeneous elastic materials with cohesive zone models
    Prechtel, M. and Ronda, P.L. and Janisch, R. and Hartmaier, A. and Leugering, G. and Steinmann, P. and Stingl, M.
    International Journal of Fracture 168 (2011)
    In brittle composite materials, failure mechanisms like debonding of the matrix-fiber interface or fiber breakage can result in crack deflection and hence in the improvement of the damage tolerance. More generally it is known that high values of fracture energy dissipation lead to toughening of the material. Our aim is to investigate the influence of material parameters and geometrical aspects of fibers on the fracture energy as well as the crack growth for given load scenarios. Concerning simulations of crack growth the cohesive element method in combination with the Discontinuous Galerkin method provides a framework to model the fracture considering strength, stiffness and failure energy in an integrated manner. Cohesive parameters are directly determined by DFT supercell calculations. We perform studies with prescribed crack paths as well as free crack path simulations. In both cases computational results reveal that fracture energy depends on both the material parameters but also the geometry of the fibers. In particular it is shown that the dissipated energy can be increased by appropriate choices of cohesive parameters of the interface and geometrical aspects of the fiber. In conclusion, our results can help to guide the manufacturing process of materials with a high fracture toughness. © 2010 Springer Science+Business Media B.V.
    view abstract10.1007/s10704-010-9552-z
  • Solubility of carbon in α-iron under volumetric strain and close to the Σ5(3 1 0)[0 0 1] grain boundary: Comparison of DFT and empirical potential methods
    Hristova, E. and Janisch, R. and Drautz, R. and Hartmaier, A.
    Computational Materials Science 50 (2011)
    The solubility of carbon in α-Fe as a function of lattice strain and in the vicinity of the ∑5(310)[001] symmetrical tilt grain boundary is calculated with ab initio methods based on density-functional theory (DFT). The results are compared to four different empirical potentials: the embedded-atom method (EAM) potentials of Lau et al. [1], Ruda et al. [2] and Hepburn et al. [3], and the modified embedded-atom method (MEAM) potential of Lee [4]. The results confirm that the solubility of carbon in body-centered-cubic (bcc) Fe increases under local volume expansion and provide quantitative data for the excess enthalpy to be used in thermodynamic databases. According to our study the excess enthalpy obtained from DFT is more strain-sensitive than the ones obtained from the tested empirical potentials. The comparison of the applied methods furthermore reveals that among the empirical potentials the MEAM is most appropriate to describe the solubility of C in bcc Fe under strain. The differences between the four empirical potentials stem from different parameterizations of the EAM potentials and, in the case of the MEAM, from the altogether different formalism that also includes angular dependent terms in the binding energy. © 2010 Elsevier B.V. All rights reserved.
    view abstract10.1016/j.commatsci.2010.11.006
  • 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 (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 abstract10.1016/j.jmps.2010.09.005
  • Ab initio tensile tests of Al bulk crystals and grain boundaries: Universality of mechanical behavior
    Janisch, R. and Ahmed, N. and Hartmaier, A.
    Physical Review B - Condensed Matter and Materials Physics 81 (2010)
    We have performed ab initio tensile tests of bulk Al along different tensile axes, as well as perpendicular to different grain boundaries to determine mechanical properties such as interface energy, work of separation, and theoretical strength. We show that all the different investigated geometries exhibit energy-displacement curves that can be brought into coincidence in the spirit of the well known universal binding energy relationship curve. This simplifies significantly the calculation of ab initio tensile strengths for the whole parameter space of grain boundaries. © 2010 The American Physical Society.
    view abstract10.1103/PhysRevB.81.184108
  • 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 abstract10.1088/0965-0393/18/4/045007
  • Development of a method to determine Burgers vectors from atomistic data
    Hua, J. and Hartmaier, A.
    Journal of Physics: Conference Series 240 (2010)
    Large-scale molecular dynamics simulations have been widely used to investigate the mechanical behaviour of materials. But complex datasets, involving the positions of millions of atoms, generated during the simulations make quantitative data analysis quite a challenge. This paper presents a novel method to determine not only dislocations in the crystal, but also to quantify their Burgers vectors. This is achieved by combining geometrical methods to determine the atoms lying in the dislocations cores, like for example the common neighbour analysis or the bond angle analysis, with the slip vector analysis. The first methods are used to filter out the atoms lying in undisturbed regions of the crystal; the latter method yields the relative slip of the remaining atoms and thus indicates the Burgers vector of those atoms lying in the dislocation cores. The validity of the method is demonstrated here on a single edge dislocation in a relatively small sample. Furthermore a way will be sketched how this analysis can be used to determine densities of statistically stored and geometrically necessary dislocations, respectively. Hence, this method can be expected to provide valuable input for strain gradient plasticity models. © 2010 IOP Publishing Ltd.
    view abstract10.1088/1742-6596/240/1/012010
  • How dislocation substructures evolve during long-term creep of a 12% Cr tempered martensitic ferritic steel
    Pešička, J. and Aghajani, A. and Somsen, C. and Hartmaier, A. and Eggeler, G.
    Scripta Materialia 62 (2010)
    We document the evolution of dislocation densities in tempered martensite ferritic steels during long-term aging and creep. Scanning transmission electron microscopy in combination with a high-angle annular dark-field detector is used to study dislocations in a 12% Cr steel. During aging, the dislocation density quickly decreases by a factor 2 and then remains constant. Long-term creep results in an initial decrease by a factor 10, and after this sharp drop, the dislocation density continues to decrease. © 2009 Acta Materialia Inc.
    view abstract10.1016/j.scriptamat.2009.10.037
  • 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 abstract10.1063/1.3340523
  • Modeling size effects on fracture toughness by dislocation dynamics
    Zeng, X.H. and Hartmaier, A.
    Acta Materialia 58 (2010)
    The effects of grain size and of crack-tip blunting radius on the fracture toughness of tungsten polycrystals are studied by using a combined dislocation dynamics/cohesive zone model (CZM). Two-dimensional dislocation dynamics are employed to analyze crack-tip plasticity and crack propagation is characterized by a CZM. The geometry of the crack and the corresponding boundary conditions are described by means of a boundary element method with dislocation dipoles as fundamental solution. Grain boundaries are introduced as obstacles for dislocation motion. Numerical experiments reveal that the fracture toughness decreases with grain size, because grain boundaries confine the plastic zone. This effect is particularly pronounced at small loading rates, where the unconfined plastic zone is large. Our results also show that fracture toughness scales with the tip radius as the stress concentration at the crack tip is reduced and the plastic zone is enlarged. © 2009 Acta Materialia Inc.
    view abstract10.1016/j.actamat.2009.09.005
  • Multiscale simulations on the grain growth process in nanostructured materials
    Kamachali, R.D. and Hua, J. and Steinbach, I. and Hartmaier, A.
    International Journal of Materials Research 101 (2010)
    In this work, multi-phase field and molecular dynamics simulations have been used to investigate nanoscale grain growth mechanisms. Based on experimental observations, the combination of grain boundary expansion and vacancy diffusion has been considered in the multi-phase field model. The atomistic mechanism of boundary movement and the free volume redistribution during the growth process have been investigated using molecular dynamics simulations. According to the multi-phase field results, linear grain growth in nanostructured materials at low temperature can be explained by vacancy diffusion in the stress field around the grain boundaries. Molecular dynamics simulations confirm the observation of linear grain growth for nanometresized grains. The activation energy of grain boundary motion in this regime has been determined to be of the order of onetenth of the self-diffusion activation energy, which is consistent with experimental data. Based on the simulation results, the transition from linear to normal grain growth is discussed in detail and a criterion for this transition is proposed. © Carl Hanser Verlag GmbH & Co. KG.
    view abstract10.3139/146.110419
  • Phase-field model with plastic flow for grain growth in nanocrystalline material
    Steinbach, I. and Song, X. and Hartmaier, A.
    Philosophical Magazine 90 (2010)
    A phase-field model is presented which considers the accumulation of structural defects in grain boundaries by an isotropic eigenstrain associated with the grain boundaries. It is demonstrated that the elastic energy caused by dilatation of the grain boundary with respect to the bulk crystal contributes largely to the grain boundary energy. The sign of this contribution can be both positive and negative dependent on the local stress state in the grain boundary. Self-diffusion of atoms is taken into account to relax the stress caused by the dilatation of the grain boundary. Application of the model to discontinuous grain growth in pure nanocrystalline cobalt material is presented. Linear grain growth is found in the nanocrystalline state, which is explained by the interpretation of grain boundary motion as a diffusive process defining an upper limit of the grain boundary velocity independent of the grain boundary curvature but dependent on temperature. The transition to regular grain growth at a critical temperature, as observed experimentally, is explained by the drop of theoretical grain boundary velocity due to its mean curvature during coarsening of the nanograin structure below the maximum velocity.
    view abstract10.1080/14786430903074763
  • constitutive models

  • crystal plasticity

  • dislocation dynamics

  • dislocations

  • finite element method

  • machine learning

  • mechanical properties

  • micromechanics

  • microstructure

  • modelling and simulation

  • molecular dynamics

  • multiscale modeling

  • nanoindentation

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