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Martin Diehl

KU Leuven, Computer Science & Materials Engineering, Faculty Member

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RWTH Aachen University
Materials Science (Dr.-Ing.)

Technische Universität München
Mechanical Engineering (Dipl.-Ing.)
Supervisors: Christian Krempaszky; Cornelia Schwarz; Ewald Werner; Philip Eisenlohr and Franz Roters; Dierk Raabe; Ricardo Lebensohn; Bob Svendsen
Phone: +49 211 6792 187
Address: Max-Planck-Institut für Eisenforschung
Mikrostrukturphysik und Legierungsdesign
Max-Planck-Str. 1
40237 Düsseldorf
Deutschland

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Papers by Martin Diehl

An efficient and robust approach to determine material parameters of crystal plasticity constitutive laws from macro-scale stress-strain curves

International Journal of Plasticity, 2020

A severe obstacle for the routine use of crystal plasticity models is the effort associated with ... more A severe obstacle for the routine use of crystal plasticity models is the effort associated with determining their constitutive parameters. Obtaining these parameters usually requires timeconsuming micromechanical tests that allow probing of individual grains. In this study, a novel, computationally efficient, and fully automated approach is introduced which allows the identification of constitutive parameters from macroscopic tests. The approach presented here uses the response surface methodology together with a genetic algorithm to determine an optimal set of parameters. It is especially suited for complex models with a large number of parameters. The proposed approach also helps to develop a quantitative and thorough understanding of the relative influence of the different constitutive parameters and their interactions. Such general insights into parameter relations in complex models can be used to improve constitutive laws and reduce redundancy in parameter sets. The merits of the methodology are demonstrated on the examples of a dislocation-density-based crystal plasticity model for bcc steel, a phenomenological crystal plasticity model for fcc copper, and a phenomenological crystal plasticity model incorporating twinning deformation for hcp magnesium. The approach proposed is, however, modelindependent and can be also used to identify parameters of, for instance, fatigue, creep and damage models. The method has been implemented into the Düsseldorf Advanced Material Simulation Kit (DAMASK) and is available as free and open-source software. The capability of translating complex material response into a micromechanical digital twin is an essential precondition for the ongoing digitalization of material property prediction, quality control of semi-finished parts, material response in manufacturing and the long-term behavior of products and materials when in service.

Lath Martensite Microstructure Modeling: A High-Resolution Crystal Plasticity Simulation Study

This article is an open access article distributed under the terms and conditions of the Creative... more

Large-deformation crystal plasticity simulation of microstructure and microtexture evolution through adaptive remeshing

International Journal of Plasticity, 2021

The capability of high-resolution modeling of crystals subjected to large plastic strain is essen... more The capability of high-resolution modeling of crystals subjected to large plastic strain is essential in predicting many important phenomena occurring in polycrystalline materials, such as microstructure, deformation localization and in-grain texture evolution. However, due to the heterogeneity of the plastic deformation in polycrystals, the simulation mesh gets distorted during the deformation. This mesh distortion deteriorates the accuracy of the results, and after reaching high local strain levels, it is no longer possible to continue the simulation. In this work, two different adaptive remeshing approaches are introduced for simulating large deformation of 3D polycrystals with high resolution under periodic boundary conditions. In the first approach, a new geometry with a new mesh is created, and then the simulation is restarted as a new simulation in which the initial state is set based on the last deformation state that had been reached. In the second approach, the mesh is smoothened by removing the distortion part of the deformation, and then the simulation is continued after finding a new equilibrium state for the smoothed mesh and geometry. The first method is highly efficient for conducting high-resolution large-deformation simulations. On the other hand, the second method’s primary advantage is that it can overcome periodicity issues related to shear loading, and it can be used in conjunction with complex loading conditions. The merits of the methodologies are demonstrated using full-field simulations performed using a dislocation-density-based crystal plasticity model for Interstitial free (IF-) steel. Particular emphasis is put on studying the effect of resolution and adaptive meshing. The algorithms presented have been implemented into the free and open-source software package, DAMASK (Düsseldorf Advanced Material Simulation Kit).

format_quoteMicrostructures in pure nickel evolve significantly between strains 0.8 to 2.7, revealing crucial insights into strain localization and microstructure evolution.format_quote

Modeling and simulation of microstructure in metallic systems based on multi-physics approaches

npj Computational Materials, 2022

The complex interplay between chemistry, microstructure, and behavior of many engineering materia... more The complex interplay between chemistry, microstructure, and behavior of many engineering materials has been investigated predominantly by experimental methods. Parallel to the increase in computer power, advances in computational modeling methods have resulted in a level of sophistication which is comparable to that of experiments. At the continuum level, one class of such models is based on continuum thermodynamics, phase-field methods, and crystal plasticity, facilitating the account of multiple physical mechanisms (multi-physics) and their interaction during microstructure evolution. This paper reviews the status of simulation approaches and software packages in this field and gives an outlook towards promising research directions.

Coupling crystal plasticity and cellular automaton models to study meta-dynamic recrystallization during hot rolling at high strain rates

by Martin Diehl and Karo Sedighiani

Materials Science and Engineering: A, 2022

Predicting microstructure and (micro-)texture evolution during thermo-mechanical processing requi... more Predicting microstructure and (micro-)texture evolution during thermo-mechanical processing requires the combined simulation of plastic deformation and recrystallization. Here, a simulation approach based on the coupling of a full-field dislocation density based crystal plasticity model and a cellular automaton model is presented. A regridding/remeshing procedure is used to transfer data between the deformed mesh of the large-strain crystal plasticity model and the regular grid of the cellular automaton. Moreover, a physics based nucleation criterion has been developed based on dislocation density difference and changes in orientation due to deformation. The developed framework is used to study meta-dynamic recrystallization during double-hit compression tests and multi-stand rolling in high-resolution representative volume elements. These simulations reveal a good agreement with experimental results in terms of texture evolution, mechanical behaviour and growth kinetics, while enabling insights regarding the effect of nucleation on kinetics and crystallographic texture evolution.

$Fig. 2. (a) The flow stress o3; as a function of the strain 3, for different strain rates ¢ =5, 10, 15, and 20s"! annealing time f,. and (b) the recrystallized volume fraction X as a function of the$

$Fig. 3. (a) The flow stress o3, as a function of the strain e,, for annealing time of t, = 20 s and different deformation temperatures T, =1223, 1273, 1323, and 1373 K and (b) the recrystallized volume fraction X as a function of the annealing time t, for the corresponding deformation temperatures T,.$

$Fig. 4. (a) The flow stress o3, as a function of the strain 3, for different annealing times t, = 0, 2.5, 5, 7.5 and 10s and (b) the recrystallized volume fraction X as a functior of the annealing time 1,.$

$Fig. 5. (a) Flow stress o33 as a function of the strain ¢33 for different annealing temperatures T, =1223, 1273, 1273, and 1373 K and (b) the recrystallized volume fraction X as. function of the annealing time , for corresponding annealing temperatures Ty. texta$

$Fig. 9. (a) Recrystallized volume fraction, X, for the different cases of uniaxial compression followed by annealing: homogeneous stored energy with random nucleation (ideal case), homogeneous stored energy with non-random nucleation, inhomogeneous stored energy with random nucleation and inhomogeneous stored energy with non-random nucleation and (b) corresponding JMAK plots.$

Crystal plasticity simulation of in-grain microstructural evolution during large deformation of IF-steel

Acta Materialia, 2022

High-resolution three-dimensional crystal plasticity simulations are used to investigate deformat... more High-resolution three-dimensional crystal plasticity simulations are used to investigate deformation heterogeneity and microstructure evolution during cold rolling of interstitial free (IF-) steel. A Fast Fourier Transform (FFT)-based spectral solver is used to conduct crystal plasticity simulations using a dislocationdensity-based crystal plasticity model. The in-grain texture evolution and misorientation spread are consistent with experimental results obtained using electron backscatter diffraction (EBSD) experiments. The crystal plasticity simulations show that two types of strain localization features develop during the large strain deformation of IF-steel. The first type forms band-like areas with large strain accumulation that appear as river patterns extending across the specimen. In addition to these river-like patterns, a second type of strain localization with rather sharp and highly localized in-grain shear bands is identified. These localized features are dependent on the crystallographic orientation of the grain and extend within a single grain. In addition to the strain localization, the evolution of in-grain orientation gradients, misorientation features, dislocation density, kernel average misorientation, and stress in major texture components are discussed.

$Fig. 7. Correlation matrix showing the dependence between different pairs of variables. The subplots show a scatter plot of a pair of variables with a linear regression fit. The displayed values present the correlation coefficient between the GOS and GAM with volume fraction of various texture components. Each diagonal subplot contains the distribution of a variable as a histogram.$

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

Computational Materials Science, 2019

Crystal Plasticity (CP) modeling is a powerful and well established computational materials scien... more 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 multipurpose 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-https://doi. T 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.

$Fig. 13. 3D Dual Phase (DP) microstructures consisting of 1000 grains. Both microstructures have a second phase volume fraction of 15.6% (indicated in black color). Colors represent crystallographic orientations.$

$Fig. 35. Strain in loading direction mapped onto the microstructure in de formed configuration. Gray color indicates the average strain of ¢ = 0.12. Fig. 34. 3D model obtained from serial sectioning Electron Backscatter Diffraction (EBSD) used for the Dual Phase (DP) steel simulations. The di- mensions are 70.0 {1m x 20.0 1m x 2.9 um. Color indicates Inverse Pole Figure (IPF) along the horizontal loading direction.$

$Fig. 64. 3D von Miszs stress field maps obtained from spectral method calculations applying in-plane uniaxial tension at strains that are close to experimental fractur values obtained for endocuticle of the lobster (a), and the crab (b-d). Representative Volume Elements (RVEs) (a) and (b) represent geometries as found in nature while (c) and (d) represent hypothetical cases where structural parameters of the pore canals were altered by removing the pore canal reinforcement phase anc modifying the pore canal volumes. Figure adopted from [317] with permission from the Institute of Chemical Engineering-BAS.$

On the interaction of precipitates and tensile twins in magnesium alloys

Acta Materialia, 2019

Although magnesium alloys deform extensively through shear strains and crystallographic reorienta... more Although magnesium alloys deform extensively through shear strains and crystallographic reorientations associated with the growth of twins, little is known about the strengthening mechanisms associated with this deformation mode. A crystal plasticity based phase field model for twinning is employed in this work to study the strengthening mechanisms resulting from the interaction between twin growth and precipitates. The full-field simulations reveal in great detail the pinning and de-pinning of a twin boundary at individual precipitates, resulting in a maximum resistance to twin growth when the precipitate is partially embedded in the twin. Furthermore, statistically representative precipitate distributions are used to systematically investigate the influence of key microstructural parameters such as precipitate orientation, volume fraction, size, and aspect ratio on the resistance to twin growth. The results indicate that the effective critical resolved shear stress (CRSS) for twin growth increases linearly with precipitate volume fraction and aspect ratio. For a constant volume fraction of precipitates, reduction of the precipitate size below a critical level produces a strong increase in the CRSS due to the OROWAN-like strengthening mechanism between the twin interface and precipitates. Above this level the CRSS is size independent. The results are quantitatively and qualitatively comparable with experimental measurements and predictions of mean-field strengthening models. Based on the results, guidelines for the design of high strength magnesium alloys are discussed.

Coupled Crystal Plasticity–Phase Field Fracture Simulation Study on Damage Evolution Around a Void: Pore Shape Versus Crystallographic Orientation

by Martin Diehl and Dierk Raabe

Various mechanisms such as anisotropic plastic flow, damage nucleation, and crack propagation gov... more Various mechanisms such as anisotropic plastic flow, damage nucleation, and crack propagation govern the overall mechanical response of structural materials. Understanding how these mechanisms interact, i.e. if they amplify mutually or compete with each other, is an essential prerequisite for the design of improved alloys. This study shows—by using the free and open source software DAMASK (the Dü sseldorf Advanced Material Simulation Kit)—how the coupling of crystal plasticity and phase field fracture methods can increase the understanding of the complex interplay between crystallographic orientation and the geometry of a void. To this end, crack initiation and propagation around an experimentally obtained pore with complex shape is investigated and compared to the situation of a simplified spherical void. Three different crystallographic orientations of the aluminum matrix hosting the defects are considered. It is shown that crack initiation and propagation depend in a non-trivial way on crystallographic orientation and its associated plastic behavior as well as on the shape of the pore.

A virtual laboratory using high resolution crystal plasticity simulations to determine the initial yield surface for sheet metal forming operations

International Journal of Plasticity, 2016

We present a virtual laboratory to investigate the anisotropic yield behavior of polycrystalline ... more We present a virtual laboratory to investigate the anisotropic yield behavior of polycrystalline materials by using high resolution crystal plasticity simulations. Employing a fast spectral method solver enables us to conduct a large number of full-field virtual experiments with different stress states to accurately identify the yield surface of the probed materials. Based on the simulated yield stress points, the parameters for many commonly used yield functions are acquired simultaneously with a nonlinear least square fitting procedure. Exemplarily, the parameters of four yield functions frequently used in sheet metal forming, namely Yld91, Yld2000-2D, Yld2004-18p, and Yld2004-27p are adjusted to accurately describe the yield behavior of an AA3014 aluminum alloy at two material states, namely with a recrystallization texture and a cold rolling texture. The comparison to experimental results proves that the methodology presented, combining accuracy with efficiency, is a promising micromechanics-based tool for probing the mechanical anisotropy of polycrystalline metals and for identifying the parameters of advanced yield functions.

Numerically robust spectral methods for crystal plasticity simulations of heterogeneous materials

International Journal of Plasticity, 2015

Efficient spectral methods are developed to predict the micromechanical behaviour of plastically ... more Efficient spectral methods are developed to predict the micromechanical behaviour of plastically deforming heterogeneous materials. The direct and mixed variational conditions for mechanical equilibrium and strain compatibility are formulated in a framework that couples them to a general class of non-linear solution methods. Locally evolving microme-chanical fields in a sheared polycrystalline material governed by a phenomenological crystal plasticity constitutive law are used to validate the methods, and their performance at varying material heterogeneities is benchmarked. The results indicate that the solution method has a dominant influence on performance and stability at large material heteroge-neities, and significant improvements over the conventional fixed-point approach are obtained when higher-order solution methods are employed. Optimal solution strategies are devised based on this and applied to an idealised dual-phase polycrystalline aggregate.

format_quoteSimulations showed convergence at maximum shear value of 0.4 and stiffness contrast between 10⁻¹ and 10⁴ for elastic and plastic inclusion cases.format_quote

Crystal plasticity study of monocrystalline stochastic honeycombs under in-plane compression

Acta Materialia, 2016

We present a study on the plastic deformation of single crystalline stochastic honeycombs under i... more We present a study on the plastic deformation of single crystalline stochastic honeycombs under in-plane compression using a crystal plasticity constitutive description for face-centered cubic (fcc) materials , focusing on the very early stage of plastic deformation, and identifying the interplay between the crystallographic orientation and the cellular structure during plastic deformation. We observe that despite the stochastic structure, surprisingly, the slip system activations in the honeycombs are almost identical to their corresponding bulk single crystals at the early stage of the plastic deformation. On the other hand, however, the yield stresses of the honeycombs are nearly independent of their crystallographic orientations. Similar mechanical response is found in compression testing of nanoporous gold micro-pillars aligned with various crystallographic orientations. The macroscopic stress tensors of the honeycombs show the same anisotropy as their respective bulk single crystals. Locally, however, there is an appreciable fluctuation in the local stresses, which are even larger than for polycrystals. This explains why the Taylor/Schmid factor associated with the crystallographic orientation is less useful to estimate the yield stresses of the honeycombs than the bulk single crystals and polycrystals, and why the plastic deformation occurs at smaller strains in the honeycombs than their corresponding bulk single crystals. Besides these findings, the observations of the crystallographic reorientation suggest that conventional orientation analysis tools, such as inverse pole figure and related tools, would in general fail to study the plastic deformation mechanism of monocrystalline cellular materials.

Analytical bounds of in-plane Young's modulus and full-field simulations of two-dimensional monocrystalline stochastic honeycomb structures

In this study, we focus on the interplay between the honeycomb structure and the crystallographic... more In this study, we focus on the interplay between the honeycomb structure and the crystallographic orientation. Specifically, the in-plane Young's moduli of monocrystalline stochastic honeycombs are calculated by a numerical and an analytical approach. The in-plane Young's moduli of the honeycombs were calculated numerically using a solution scheme for the full-field mechanical equilibrium based on spectral methods and anisotropic crystal elasticity. The analytical approach formulates two alternative assumptions, i.e. uniform force and uniform strain per strut, considers the elastic anisotropy of the base material, and depends on the two-variable distribution of the strut length and inclination angle as the structural parameters characterizing the stochastic honeycombs. The uniform strain assumption agrees closely with the numerical simulation results and constitutes an improvement compared to analytical solutions proposed in previous studies.

Review and outlook: mechanical, thermodynamic, and kinetic continuum modeling of metallic materials at the grain scale

MRS Communications, 2017

Continuum modeling approaches are well established in materials science and engineering of metals... more Continuum modeling approaches are well established in materials science and engineering of metals. They enable the quantitative investigation of diverse questions related to the improved understanding of mechanics and microstructure evolution of various material classes. Applicable to time and length scales relevant in manufacturing and service, continuum modeling approaches are widely used to study engineering-related phenomena such as recrystallization, strain localization, fracture initiation, and phase transformations. However, focusing on individual physical aspects hampers the wider routine use of continuum modeling tools for many engineering applications. With the advent of multi-physics modeling tools developed with the help of and parametrized by (sub-)micrometer-scale simulations and experiments, a huge variety of applications such as hot rolling, bake-hardening, and case-hardening comes within reach for full-field integrated computational materials engineering. Moreover, the integration of experimentally characterized microstructures and the use of user friendly simulation and evaluation tools render powerful modeling approaches feasible for a broad materials science user community. The state of the art and future trends of mechanical, thermodynamic, and kinetic continuum modeling of metallic materials at the grain scale are outlined in this prospective article.

High-Resolution Crystal Plasticity Simulations

In this work the possibilities and capabilities of high-resolution crystal plasticity simulations... more In this work the possibilities and capabilities of high-resolution crystal plasticity simulations are presented and discussed. Giving several examples, it is shown how the application of crystal plasticity simulations helps to understand the micro-mechanical behaviour of crystalline materials. To avoid the high computational costs associated with crystal plasticity simulations that arise from (i) the evaluation of the selected constitutive law, and (ii) the solution of the associated mechanical boundary value problem, both contributions to the runtime have to be kept small. This is done by (i) employing a rather simple—and therefore fast—constitutive model, and by (ii) using an effective spectral method employing fast Fourier transforms for solving the partial differential equations describing the mechanical behaviour. Here, an improved spectral solver incorporated into the Düsseldorf Advanced Material Simulation Kit (DAMASK) is used. Coupled experimental–numerical analyses performed on dual phase steel and magnesium microstructures shows that for highly resolved microstructure discretisations even a comparably simple phenomenological crystal plasticity model is able to predict behaviour in good agreement with experimental observations. Both simulation series complement the experimental investigations to achieve a better understanding of the experimental results. The influence of the subsurface microstructure on the observed local stress and strain values on a 2D observation plane is investigated with the help of synthetic dual phase steel microstructures and the size of the influenced sub-surface region in dependence on the strain heterogeneity is quantified. A comparison of microstruc-ture generation approaches proves that the use of the fast standard Voronoi tessel-lation does not introduce a strong bias on the observed stress and strain partitioning in single phase materials at the continuum level. It can be assumed that the standard Voronoi tessellation can also be used without restriction for crystal plasticity simulations. The investigation on strain pattern formation in hexagonal water ice displays the capabilities and limits of the phenomenological material point model in predicting complex patterning phenomena.

Crystal Plasticity Study on Stress and Strain Partitioning in a Measured 3D Dual Phase Steel Microstructure

Physical Mesomechanics, 2017

Dual phase (DP) steels are advanced high strength alloys typically used for structural parts and ... more Dual phase (DP) steels are advanced high strength alloys typically used for structural parts and reinforcements in car bodies. Their good combination of strength and ductility and their lean composition render them an economically competitive option for realizing multiple lightweight design options in automotive engineering. The mechanical response of DP steels is the result of the strain and stress partitioning among the ferritic and martensitic phases and the individual crystallographic grains and subgrains of these phases. Therefore, understanding how these microstruc-tural features influence the global and local mechanical properties is of utmost importance for the design of improved DP steel grades. While multiple corresponding simulation studies have been dedicated to the investigation of DP steel micromechanics, numerical tools and experiment techniques for characterizing and simulating real 3D microstructures of such complex materials have been emerged only recently. Here we present a crystal plasticity simulation study based on a 3D DP microstructure which is obtained by EBSD tomogra-phy, also referred to as 3D EBSD (EBSD—electron backscatter diffraction). In the present case we utilized a 3D EBSD serial sectioning approach based on mechanical polishing. Moreover, sections of the 3D mi

A Flexible and Efficient Output File Format for Grain-Scale Multiphysics Simulations

Integrating Materials and Manufacturing Innovation, 2016

Modern high-performing structural materials gain their excellent properties from the complex inte... more Modern high-performing structural materials gain their excellent properties from the complex interactions of various constituent phases, grains, and subgrain structures that are present in their microstructure. To further understand and improve their properties, simulations need to take into account multiple aspects in addition to the composite nature. Crystal plasticity simulations incorporating additional physical effects such as heat generation and distribution, damage evolution, phase transformation, or changes in chemical composition enable the compilation of comprehensive structure–property relationships of such advanced materials under combined thermo-chemo-mechanical loading conditions. Capturing the corresponding thermo-chemo-mechanical response at the microstructure scale usually demands specifically adopted constitutive descriptions per phase. Furthermore, to bridge from the essential microstructure scale to the component scale, which is often of ultimate interest, a sophisticated (computational) homogenization scheme needs to be employed. A modular simulation toolbox that allows the problem-dependent use of various constitutive models and/or homogenization schemes in one concurrent simulation requires a flexible and adjustable file format to store the resulting heterogeneous data. Besides dealing with heterogeneous data, a file format suited for microstructure simulations needs to be able to deal with large (and growing) amounts of data as (i) the spatial resolution of routine simulations is ever increasing and (ii) more and more quantities are taken into account to characterize a material. To cope with such demands, a flexible and adjustable data layout based on HDF5 is proposed. The key feature of this data structure is the decoupling of spatial position and data, such that spatially variable information can be efficiently accommodated. For position-dependent operations, e.g., spatially resolved visualization, the spatial link is restored through explicit mappings between simulation results and their spatial position.

Neighborhood influences on stress and strain partitioning in dual-phase microstructures An investigation on synthetic polycrystals with a robust spectral-based numerical method

The mechanical response of multiphase metallic materials is governed by the strain and stress par... more The mechanical response of multiphase metallic materials is governed by the strain and stress partitioning behavior among their phases, crystals, and subgrains. Despite knowledge about the existence of these complex and long-ranging interactions, the experimental characterization of such materials is often limited to surface observations of microstructure evolution and strain partitioning, i.e. ignoring the influence of the underlying features. Hence, for the interpretation of the observed surface behavior it is imperative to understand how it might be influenced by the subsurface microstruc-ture. In the present study, we therefore systematically change the subsurface microstructure of synthetic dual-phase polycrystals and investigate the altered response of a 2D region of interest. The series of high-resolution crystal plasticity simulations are conducted with a fast and efficient spectral-based iterative scheme for calculating the mechanical response of complex crystalline materials. To overcome the slow convergence of the conventional spectral-based solver when dealing with heterogeneous materials of large contrast in stiffness (or strength), direct and mixed variational conditions for mechanical equilibrium and strain compatibility have been formulated such that they can be combined with a general class of non-linear solution methods. The different solution techniques have been implemented into DAMASK, the Düsseldorf Advanced Material Simulation Kit, and the ones showing the best performance are used in this study. The results show that the subsurface microstructure has a dominant influence on the observed stress and strain partitioning. Additionally, it can be seen that the zone of influence increases with increasing heterogeneity of the microstructure.

Unraveling the temperature dependence of the yield strength in single-crystal tungsten using atomistically-informed crystal plasticity calculations

International Journal of Plasticity, 2016

We use a physically-based crystal plasticity model to predict the yield strength of body-centered... more We use a physically-based crystal plasticity model to predict the yield strength of body-centered cubic (bcc) tungsten single crystals subjected to uniaxial loading. Our model captures the thermally-activated character of screw dislocation motion and full non-Schmid effects, both of which are known to play critical roles in bcc plasticity. The model uses atomistic calculations as the sole source of constitutive information, with no parameter fitting of any kind to experimental data. Our results are in excellent agreement with experimental measurements of the yield stress as a function of temperature for a number of loading orientations. The validated methodology is employed to calculate the temperature and strain-rate dependence of the yield strength for 231 crystallographic orientations within the standard stereographic triangle. We extract the strain-rate sensitivity of W crystals at different temperatures, and finish with the calculation of yield surfaces under biaxial loading conditions that can be used to define effective yield criteria for engineering design models.

Linking atomistic, kinetic Monte Carlo and crystal plasticity simulations of single-crystal Tungsten strength

GAMM-Mitteilungen, 2015

Understanding and improving the mechanical properties of tungsten is a critical task for the mate... more Understanding and improving the mechanical properties of tungsten is a critical task for the materials fusion energy program. The plastic behavior in body-centered cubic (bcc) metals like tungsten is governed primarily by screw dislocations on the atomic scale and by ensembles and interactions of dislocations at larger scales. Modeling this behavior requires the application of methods capable of resolving each relevant scale. At the small scale, atomistic methods are used to study single dislocation properties, while at the coarse-scale, continuum models are used to cover the interactions between dislocations. In this work we present a multiscale model that comprises atomistic, kinetic Monte Carlo (kMC) and continuum-level crystal plasticity (CP) calculations. The function relating dislocation velocity to applied stress and temperature is obtained from the kMC model and it is used as the main source of constitutive information into a dislocation-based CP framework. The complete model is used to perform material point simulations of single-crystal tungsten strength. We explore the entire crystallographic orientation space of the standard triangle. Non-Schmid effects are inlcuded in the model by considering the twinning-antitwinning (T/AT) asymmetry in the kMC calculations. We consider the importance of 〈111〉{110} and 〈111〉{112} slip systems in the homologous temperature range from 0.08Tm to 0.33Tm, where Tm =3680 K is the melting point in tungsten.