Prof. Dr. Markus A. Stricker
Materials Informatics and Data Science at ICAMS
- Dislocation structure analysis in the strain gradient of torsion loading: A comparison between modelling and experiment
Stricker, M. and Ziemann, M. and Walter, M. and Weygand, S.M. and Gruber, P. and Weygand, D.
Modelling and Simulation in Materials Science and Engineering 30 (2022)Complex stress states due to torsion lead to dislocation structures characteristic for the chosen torsion axis. The formation mechanism of these structures and the link to the overall plastic deformation are unclear. Experiments allow the analysis of cross sections only ex situ or are limited in spacial resolution which prohibits the identification of the substructures which form within the volume. Discrete dislocation dynamics simulations give full access to the dislocation structure and their evolution in time. By combining both approaches and comparing similar measures the dislocation structure formation in torsion loading of micro wires is explained. For the «100»torsion axis, slip traces spanning the entire sample in both simulation and experiment are observed. They are caused by collective motion of dislocations on adjacent slip planes. Thus these slip traces are not atomically sharp. Torsion loading around a «111»axis favors plasticity on the primary slip planes perpendicular to the torsion axis and dislocation storage through cross-slip and subsequent collinear junction formation. Resulting hexagonal dislocation networks patches are small angle grain boundaries. Both, experiments and discrete dislocation simulations show that dislocations cross the neutral fiber. This feature is discussed in light of the limits of continuum descriptions of plasticity. © 2022 The Author(s). Published by IOP Publishing Ltd.
view abstract 10.1088/1361-651X/ac4d77
- Achieving ultra-low friction with diamond/metal systems in extreme environments
Stoyanov, P. and Merz, R. and Stricker, M. and Kopnarski, M. and Dienwiebel, M.
Materials 14 (2021)In the search for achieving ultra-low friction for applications in extreme environments, we evaluate the interfacial processes of diamond/tungsten sliding contacts using an on-line macro-tribometer and a micro-tribometer in an ultra-high vacuum. The coefficient of friction for the tests with the on-line tribometer remained considerably low for unlubricated sliding of tungsten, which correlated well with the relatively low wear rates and low roughness on the wear track throughout the sliding. Ex situ analysis was performed by means of XPS and SEM-FIB in order to better understand the underlying mechanisms of low friction and low-wear sliding. The analysis did not reveal any evidence of tribofilm or transferfilm formation on the counterface, indicating the absence of significant bonding between the diamond and tungsten surfaces, which correlated well with the low-friction values. The minimal adhesive interaction and material transfer can possibly be explained by the low initial roughness values as well as high cohesive bonding energies of the two materials. The appearance of the wear track as well as the relatively higher roughness perpendicular to the sliding indicated that abrasion was the main wear mechanism. In order to elucidate the low friction of this tribocouple, we performed micro-tribological experiments in ultra-high vacuum conditions. The results show that the friction coefficient was reduced significantly in UHV. In addition, subsequently to baking the chamber, the coefficient of friction approached ultra-low values. Based on the results obtained in this study, the diamond/tungsten tribocouple seems promising for tribological interfaces in spacecraft systems, which can improve the durability of the components. © 2021 by the authors Licensee MDPI, Basel, Switzerland.
view abstract 10.3390/ma14143791
- Efficient implementation of atom-density representations
Musil, F. and Veit, M. and Goscinski, A. and Fraux, G. and Willatt, M.J. and Stricker, M. and Junge, T. and Ceriotti, M.
Journal of Chemical Physics 154 (2021)Physically motivated and mathematically robust atom-centered representations of molecular structures are key to the success of modern atomistic machine learning. They lie at the foundation of a wide range of methods to predict the properties of both materials and molecules and to explore and visualize their chemical structures and compositions. Recently, it has become clear that many of the most effective representations share a fundamental formal connection. They can all be expressed as a discretization of n-body correlation functions of the local atom density, suggesting the opportunity of standardizing and, more importantly, optimizing their evaluation. We present an implementation, named librascal, whose modular design lends itself both to developing refinements to the density-based formalism and to rapid prototyping for new developments of rotationally equivariant atomistic representations. As an example, we discuss smooth overlap of atomic position (SOAP) features, perhaps the most widely used member of this family of representations, to show how the expansion of the local density can be optimized for any choice of radial basis sets. We discuss the representation in the context of a kernel ridge regression model, commonly used with SOAP features, and analyze how the computational effort scales for each of the individual steps of the calculation. By applying data reduction techniques in feature space, we show how to reduce the total computational cost by a factor of up to 4 without affecting the model's symmetry properties and without significantly impacting its accuracy. © 2021 Author(s).
view abstract 10.1063/5.0044689
- Machine learning for metallurgy II. A neural-network potential for magnesium
Stricker, M. and Yin, B. and Mak, E. and Curtin, W.A.
Physical Review Materials 4 (2020)Interatomic potentials are essential for studying fundamental mechanisms of deformation and failure in metals and alloys because the relevant defects (dislocations, cracks, etc.) are far above the scales accessible to first-principles studies. Existing potentials for non-fcc metals and nearly all alloys are, however, not sufficiently quantitative for many crucial phenomena. Here machine learning in the Behler-Parrinello neural-network framework is used to create a broadly applicable potential for pure hcp magnesium (Mg). Lightweight Mg and its alloys are technologically important while presenting a diverse range of slip systems and crystal surfaces relevant to both plasticity and fracture that present a significant challenge for any potential. The machine learning potential is trained on first-principles density-functional theory (DFT) computable metallurgically relevant properties and is then shown to well predict metallurgically crucial dislocation and crack structures and competing phenomena. Extensive comparisons to an existing very good modified embedded atom method potential are made. These results demonstrate that a single machine learning potential can represent the wide scope of phenomena required for metallurgical studies. The DFT database is openly available for use in any other machine learning method. The method is naturally extendable to alloys, which are necessary for engineering applications but where ductility and fracture are controlled by complex atomic-scale mechanisms that are not well predicted by existing potentials. © 2020 American Physical Society.
view abstract 10.1103/PhysRevMaterials.4.103602
- Prismatic Slip in Magnesium
Stricker, M. and Curtin, W.A.
Journal of Physical Chemistry C 124 (2020)Magnesium is the lowest-density structural metal but has low ductility that limits applications. The low ductility is related to the hexagonally close-packed crystal structure where activation of nonbasal slip is required for general plasticity. Here, our recent neural network potential (NNP) for Mg, trained using Kohn-Sham density functional theory (DFT), is used to examine slip of a dislocations on the prismatic plane. The generalized stacking fault surface energies (GSFEs) for basal and prismatic slip are computed and agree better with Kohn-Sham density functional theory (KS-DFT) than orbital-free density functional theory (OF-DFT) and modified embedded atom method (MEAM), which predict spurious minima. Consistent with the generalized stacking fault energy (GSFE), direct simulations of the prismatic a»screw dislocation show it is unstable to dissociate into the a basal screw dislocation; this is mostly consistent with OF-DFT while MEAM predicts stability. Prismatic slip is thus achieved by a double-cross-slip process of the stable basal dislocations driven by a resolved shear stress on the orthogonal prismatic plane; this is consistent with the process deduced from experiments. The Nudged Elastic Band method is used with the NNP to examine the atomistic path and the stress-dependent enthalpy barrier for this mechanism; this requires many tens of thousands of atoms. The basal-prismatic cross-slip occurs in increments of c/2 via basal constriction, cross-slip on the prism plane, cross-slip back onto the basal plane, and lateral motion of the created jogs to extend the new basal dislocation. Comparisons with experimental deductions show some agreement and some notable disagreement. Resolution of the differences points toward further large-scale studies that require the accuracy and efficiency of KS-DFT-trained NNP, an approach that is also naturally extendable to the important domain of Mg alloys. © 2020 American Chemical Society. All rights reserved.
view abstract 10.1021/acs.jpcc.0c09665
- A mechanism-based homogenization of a dislocation source model for bending
Schmitt, S. and Stricker, M. and Gumbsch, P. and Schulz, K.
Acta Materialia 164 (2019)The homogenization of dislocation dynamics including the mechanisms of dislocation nucleation is a great challenge in dislocation based continuum formulations. Due to the loss of the local and temporal resolution in a continuum model, physical nucleation mechanisms have to be incorporated in an average sense. Consequences can be the over- or underestimation of the macroscopic production rate of dislocation density which results in artificial softening or hardening phenomena. In this paper, we derive a mechanism-based homogenization of a dislocation source model based on the theory of critical thickness, which accounts for the relation between the external loading condition and the resulting dislocation density production rate. The formulation is applied to pure and cantilever bending problems, validated in comparison to discrete dislocation dynamics simulations, and discussed for the discrete-continuum transition regime. © 2018 Acta Materialia Inc.
view abstract 10.1016/j.actamat.2018.11.013
- Comparison of K-doped and pure cold-rolled tungsten sheets: As-rolled condition and recrystallization behaviour after isochronal annealing at different temperatures
Lied, P. and Bonnekoh, C. and Pantleon, W. and Stricker, M. and Hoffmann, A. and Reiser, J.
International Journal of Refractory Metals and Hard Materials 85 (2019)Severely deformed cold-rolled tungsten is a promising structural material for future fusion reactor applications due to high melting temperature and excellent mechanical properties. However, the fine-grained microstructure after deformation is not stable at temperatures above 800 °C, leading to brittle material behaviour. In this study, we utilize potassium-doping to inhibit recrystallization of tungsten sheets, a mechanism well known from incandescent lamp wires. We produced K-doped tungsten sheets by warm-rolling and subsequent cold-rolling with five different logarithmic strains up to 4.6, and equivalently rolled pure tungsten sheets. Both sets of materials are compared using EBSD and microhardness testing. In both materials, the hardness increases and the grain size along normal direction decreases with strain; the densities of low and high angle boundaries increase in particular during cold-rolling. The K-doped W sheet reaches the highest hardness with 772 ± 8 HV0.1, compared to the pure W sheet with 711 ± 14 HV0.1. All boundaries taken into account, a Hall-Petch relation describes the hardness evolution nicely, except a deviation of the K-doped tungsten sheet rolled to highest strain with its much higher hardness. The similar structural and mechanical properties of both materials in the as-rolled condition allow further studies of recrystallization behaviour of the new K-doped material with a benchmark against the equivalent pure tungsten sheets. Isochronal annealing for 1 h was performed at different temperatures between 700 °C and 2200 °C. A sharp decrease in hardness to intermediate values is observed at around 900 °C for both materials, presumably reflecting extended recovery. A second decrease is observed at 1400 °C for pure tungsten, approaching the hardness of a single crystal and indicating recrystallization and severe growth of grains. For K-doped tungsten, however, the occurrence of the second decrease is shifted to higher temperatures from 1400 °C to 1800 °C with increasing strain and an intermediate hardness is maintained up to 1800 °C. We refer this dependence of the recrystallization resistance on strain in the K-doped material to the dispersion of K-bubbles, resulting in increased Zener pinning forces retarding boundary motion. © 2019
view abstract 10.1016/j.ijrmhm.2019.105047
- DAMASK – The Düsseldorf Advanced Material Simulation Kit for modeling multi-physics crystal plasticity, thermal, and damage phenomena from the single crystal up to the component scale
Roters, F. and Diehl, M. and Shanthraj, P. and Eisenlohr, P. and Reuber, C. and Wong, S.L. and Maiti, T. and Ebrahimi, A. and Hochrainer, T. and Fabritius, H.-O. and Nikolov, S. and Friák, M. and Fujita, N. and Grilli, N. and Janssens, K.G.F. and Jia, N. and Kok, P.J.J. and Ma, D. and Meier, F. and Werner, E. and Stricker, M. and Weygand, D. and Raabe, D.
Computational Materials Science 158 (2019)Crystal Plasticity (CP) modeling is a powerful and well established computational materials science tool to investigate mechanical structure–property relations in crystalline materials. It has been successfully applied to study diverse micromechanical phenomena ranging from strain hardening in single crystals to texture evolution in polycrystalline aggregates. However, when considering the increasingly complex microstructural composition of modern alloys and their exposure to—often harsh—environmental conditions, the focus in materials modeling has shifted towards incorporating more constitutive and internal variable details of the process history and environmental factors into these structure–property relations. Technologically important fields of application of enhanced CP models include phase transformations, hydrogen embrittlement, irradiation damage, fracture, and recrystallization. A number of niche tools, containing multi-physics extensions of the CP method, have been developed to address such topics. Such implementations, while being very useful from a scientific standpoint, are, however, designed for specific applications and substantial efforts are required to extend them into flexible multi-purpose tools for a general end-user community. With the Düsseldorf Advanced Material Simulation Kit (DAMASK) we, therefore, undertake the effort to provide an open, flexible, and easy to use implementation to the scientific community that is highly modular and allows the use and straightforward implementation of different types of constitutive laws and numerical solvers. The internal modular structure of DAMASK follows directly from the hierarchy inherent to the employed continuum description. The highest level handles the partitioning of the prescribed field values on a material point between its underlying microstructural constituents and the subsequent homogenization of the constitutive response of each constituent. The response of each microstructural constituent is determined, at the intermediate level, from the time integration of the underlying constitutive laws for elasticity, plasticity, damage, phase transformation, and heat generation among other coupled multi-physical processes of interest. Various constitutive laws based on evolving internal state variables can be implemented to provide this response at the lowest level. DAMASK already contains various CP-based models to describe metal plasticity as well as constitutive models to incorporate additional effects such as heat production and transfer, damage evolution, and athermal transformations. Furthermore, the implementation of additional constitutive laws and homogenization schemes, as well as the integration of a wide class of suitable boundary and initial value problem solvers, is inherently considered in its modular design. © 2018 The Author(s)
view abstract 10.1016/j.commatsci.2018.04.030
- Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity
Sudmanns, M. and Stricker, M. and Weygand, D. and Hochrainer, T. and Schulz, K.
Journal of the Mechanics and Physics of Solids 132 (2019)Modeling dislocation multiplication due to interaction and reactions on a mesoscopic scale is an important task for the physically meaningful description of stage II hardening in face-centered cubic crystalline materials. In recent Discrete Dislocation Dynamics simulations it is observed that dislocation multiplication is exclusively the result of mechanisms, which involve dislocation reactions between different slip systems. These findings contradict multiplication models in dislocation based continuum theories, in which density increase is related to plastic slip on the same slip system. An application of these models for the density evolution on individual slip systems results in self-replication of dislocation density. We introduce a formulation of dislocation multiplication in a dislocation based continuum formulation of plasticity derived from a mechanism-based homogenization of cross-slip and glissile reactions in three-dimensional face-centered cubic systems. As a key feature, the presented model includes the generation of dislocations based on an interplay of dislocation density on different slip systems. This particularly includes slip systems with vanishing shear stress. The results show, that the proposed dislocation multiplication formulation allows for a physically meaningful microstructural evolution without self-replication of dislocations density. The results are discussed in comparison to discrete dislocation dynamics simulations exposing the coupling of different slip systems as the central characteristic for the increase of dislocation density on active and inactive slip systems. © 2019 Elsevier Ltd
view abstract 10.1016/j.jmps.2019.103695
- Dislocation multiplication in stage II deformation of fcc multi-slip single crystals
Stricker, M. and Sudmanns, M. and Schulz, K. and Hochrainer, T. and Weygand, D.
Journal of the Mechanics and Physics of Solids 119 (2018)Dislocation multiplication in plasticity research is often connected to the picture of a Frank-Read source. Although it is known that this picture is not applicable after easy glide deformation, plasticity theories often assume Frank-Read-type models for dislocation multiplication. By analyzing discrete dislocation dynamics simulations in a bulk like setting, a new view on dislocation multiplication is presented. It is observed that only two mechanisms provide a source for dislocations: cross-slip and glissile junctions. Both source mechanisms involve a change of glide system and transfer of dislocation density (line length) from the primary dislocation(s) slip system(s) to the one of the new dislocation. The motion of dislocations is found to be highly restricted by other dislocations and therefore the contribution to plastic deformation of each individual dislocation is small. Also a substantial fraction of the physical dislocation line length is annihilated by the collinear reaction, lowering dislocation storage during plastic deformation. Furthermore, multiplication events involve the loss of a substantial amount of dislocation length and curvature (sudden changes in line orientation) due to the topology changes in the dislocation network of the respective mechanisms. The findings are discussed in light of continuum dislocation theories, which currently barely account for dislocation density transfer to other systems and the limited contribution of plastic strain from individual dislocations. © 2018 Elsevier Ltd
view abstract 10.1016/j.jmps.2018.07.003
- Irreversibility of dislocation motion under cyclic loading due to strain gradients
Stricker, M. and Weygand, D. and Gumbsch, P.
Scripta Materialia 129 (2017)Mechanisms that make dislocation motion irreversible are associated with the formation of dislocation junctions and cross-slip, leaving dislocations trapped inside the specimen. Using Discrete Dislocation Dynamics simulations, we identify another mechanism that produces irreversible plastic deformation and leaves no or only very few dislocations inside the sample: Under cyclic loading, dislocations which pass the neutral plane during loading (pile-up formation), generate a slip step upon unloading. The explanation is an intrinsic asymmetry between the backward and forward motion. An additional bias may be introduced by the geometry of the specimen due to the shortening of the line length of dislocations. © 2016 Acta Materialia Inc.
view abstract 10.1016/j.scriptamat.2016.10.029
- On slip transmission and grain boundary yielding
Stricker, M. and Gagel, J. and Schmitt, S. and Schulz, K. and Weygand, D. and Gumbsch, P.
Meccanica 51 (2016)Dislocation-grain boundary interaction plays a key role in the plasticity of polycrystalline materials. Capturing the effect of discrete dislocations interacting with a grain boundary in continuum models is not yet achieved. To date several approaches exist, but they have shortcomings in capturing the influence of dislocation–dislocation interaction across a grain boundary and the parameters which control grain boundary yield are phenomenologically motivated. In this work we show that grain boundary yielding is not inherently connected to physical dislocation transmission and that a realistic model needs to incorporate the interaction of dislocations across grain boundaries to capture the true strain distribution in the individual grains. By comparing discrete dislocation dynamics simulations of a single crystal with an artificial grain boundary to continuum dislocation dynamics results, a clear influence on the strain profile from the elastic interaction of dislocations belonging to different grains is shown. Our results demonstrate that continuum models like gradient plasticity need to extend their grain boundary modeling to incorporate dislocation interactions because a single yield criterion is not sufficient. © 2015, Springer Science+Business Media Dordrecht.
view abstract 10.1007/s11012-015-0192-2
- Dislocation multiplication mechanisms - Glissile junctions and their role on the plastic deformation at the microscale
Stricker, M. and Weygand, D.
Acta Materialia 99 (2015)Dislocation junctions are considered to control the hardening behavior of crystalline materials during plastic deformation. Here the influence of the glissile junction on the plastic deformation of microscale samples is investigated, based on discrete dislocation dynamics simulation results. It is found that with increasing dislocation density ρ, sample size d, which can be collapsed into a single dimensionless parameter dρ, and an increasing number of activated slip systems due to different global crystallographic orientations, the glissile junction forms frequently and can bow out easily, acting as an effective source. The resulting new dislocations are mobile and contribute to the macroscopic plastic deformation on the order of 30-60%. In the size regime from 0.5 to 2 μm and dislocation densities in the range of 1012-1014m-2, the glissile junction is therefore an important source for generating mobile dislocation density. Furthermore a significant correlation between stress drops and activity of dislocations originating from glissile junctions is found. A rate formulation is proposed to include these findings in crystal plasticity or continuum dislocation density frameworks. © 2015 Acta Materialia Inc. All rights reserved.
view abstract 10.1016/j.actamat.2015.07.073
- Equivalent plastic strain gradient plasticity with grain boundary hardening and comparison to discrete dislocation dynamics
Bayerschen, E. and Stricker, M. and Wulfinghoff, S. and Weygand, D. and Böhlke, T.
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471 (2015)The gradient crystal plasticity framework of Wulfinghoff et al. (Wulfinghoff et al. 2013 Int. J. Plasticity 51, 33-46. (doi:10.1016/j.ijplas.2013.07.001)), incorporating an equivalent plastic strain yeq and grain boundary (GB) yielding, is extended with GB hardening. By comparison to averaged results from many discrete dislocation dynamics (DDD) simulations of an aluminium-Type tricrystal under tensile loading, the new hardening parameter of the continuum model is calibrated. Although the GBs in the discrete simulations are impenetrable, an infinite GB yield strength, corresponding to microhard GB conditions, is not applicable in the continuum model. A combination of a finite GB yield strength with an isotropic bulk Voce hardening relation alone also fails to model the plastic strain profiles obtained by DDD. Instead, a finite GB yield strength in combination with GB hardening depending on the equivalent plastic strain at the GBs is shown to give a better agreement to DDD results. The differences in the plastic strain profiles obtained in DDD simulations by using different orientations of the central grain could not be captured. This indicates that the misorientationdependent elastic interaction of dislocations reaching over the GBs should also be included in the continuum model. © 2015 The Author(s) Published by the Royal Society. All rights reserved.
view abstract 10.1098/rspa.2015.0388
- Nanoscale sliding friction phenomena at the interface of diamond-like carbon and tungsten
Stoyanov, P. and Romero, P.A. and Merz, R. and Kopnarski, M. and Stricker, M. and Stemmer, P. and Dienwiebel, M. and Moseler, M.
Acta Materialia 67 (2014)Macroscopic tribometry is linked to classical atomistic simulations in order to improve understanding of the nanoscale interfacial processes during sliding of hydrogenated DLC (a-C:H) against a metal (W) in dry and lubricated conditions. Experimentally, using an online tribometer, wear and roughness measurements are performed after each sliding cycle, which are then correlated with the frictional resistance. Ex situ analysis is also performed on the worn surfaces (i.e. plates and counterfaces) using X-ray photoelectron spectroscopy, Auger electron spectroscopy and cross-sectional transmission electron microscopy imaging of the near-surface region. Then, in order to elucidate the atomistic level processes that contribute to the observed microstructural evolution in the experiments, classical molecular dynamics are performed, employing a bond order potential for the tungsten-carbon-hydrogen system. Macroscopic tribometry shows that dry sliding of a-C:H against W results in higher frictional resistance and significantly more material transfer compared with lubricated conditions. Similarly, the molecular dynamic simulations exhibit higher average shear stresses and clear material transfer for dry conditions compared with simulations with hexadecane as a lubricant. In the lubricated simulations, the lower shear stress and the absence of a material transfer are attributed to hexadecane monolayers that are partially tethered to the a-C:H surface and significantly reduce adhesion and mechanical mixing between the sliding partners. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.
view abstract 10.1016/j.actamat.2013.12.029
Computational Materials Science
Machine Learned Interatomic Potentials
Scale Bridging Materials design