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

Published online by Cambridge University Press:  16 October 2017

Martin Diehl Open the ORCID record for Martin Diehl [Opens in a new window]
Martin Diehl*
Affiliation:
Max-Planck-Institut für Eisenforschung GmbH, Max-Planck-Strasse 1, 40237 Düsseldorf, Germany Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba-City, Ibaraki 305-0047, Japan
*
Address all correspondence to Martin Diehl at m.diehl@mpie.de
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Abstract

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.

Type
Prospective Articles
Information
MRS Communications , Volume 7 , Issue 4 , December 2017 , pp. 735 - 746
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Copyright © Materials Research Society 2017 

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References

1. Roters, F., Eisenlohr, P., Hantcherli, L., Tjahjanto, D.D., Bieler, T.R., and Raabe, D.: Overview of constitutive laws, kinematics, homogenization, and multiscale methods in crystal plasticity finite element modeling: Theory, experiments, applications. Acta Mater. 58, 1152 (2010).CrossRefGoogle Scholar
2. Roters, F., Eisenlohr, P., Bieler, T.R., and Raabe, D.: Crystal Plasticity Finite Element Methods in Materials Science and Engineering (Wiley–VCH, Weinheim, 2010).CrossRefGoogle Scholar
3. Dawson, P.R.: Crystal plasticity. In Computational Materials Science, edited by Raabe, D. (Wiley–VCH, Weinheim, 2005), p. 115.Google Scholar
4. Chaboche, J.L.: Continuum damage mechanics 1. General concepts. J. Appl. Mech. 55, 59 (1988).CrossRefGoogle Scholar
5. Voyiadjis, G.Z. (editor): Handbook of Damage Mechanics (Springer, New York, 2015).CrossRefGoogle Scholar
6. Miehe, C., Welschinger, F., and Hofacker, M.: Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations. Int. J. Numer. Methods Eng. 83, 1273 (2010).CrossRefGoogle Scholar
7. Steinbach, I.: Phase-field models in materials science. Model. Simul. Mater. Sci. Eng. 17, 073001 (2009).CrossRefGoogle Scholar
8. Provatas, N. and Elder, K.: Phase-Field Methods in Materials Science and Engineering (Wiley–VCH, Weinheim, 2010).CrossRefGoogle Scholar
9. Moelans, N., Blanpain, B., and Wollants, P.: An introduction to phase-field modeling of microstructure evolution. Calphad 32, 268 (2008).CrossRefGoogle Scholar
10. Chen, L.-Q.: Introduction to the phase-field method of microstructure evolution. In Computational Materials Science, edited by Raabe, D. (Wiley–VCH, Weinheim, 2005), p. 37.Google Scholar
11. Wolfram, S., ed.: Theory and applications of cellular automata. In Advanced Series on Complex Systems (World Scientific, Singapore, 1, 1986), p. 485.Google Scholar
12. Hallberg, H.: Approaches to modeling of recrystallization. Metals 1, 16 (2011).CrossRefGoogle Scholar
13. Raabe, D.: Cellular automata in materials science with particular reference to recrystallization simulation. Annu. Rev. Mater. Res. 32, 53 (2002).CrossRefGoogle Scholar
14. Han, F., Tang, B., Kou, H., Li, J., and Feng, Y.: Cellular automata modeling of static recrystallization based on the curvature driven subgrain growth mechanism. J. Mater. Sci. 48, 7142 (2013).CrossRefGoogle Scholar
15. Moelans, N., Wendler, F., and Nestler, B.: Comparative study of two phase-field models for grain growth. Comput. Mater. Sci. 46, 479 (2009).CrossRefGoogle Scholar
16. Hildebrand, F.E. and Miehe, C.: A phase field model for the formation and evolution of martensitic laminate microstructure at finite strains. Phil. Mag. 92, 4250 (2012).CrossRefGoogle Scholar
17. Levitas, V.I.: Phase field approach to martensitic phase transformations with large strains and interface stresses. J. Mech. Phys. Solids 70, 154 (2014).CrossRefGoogle Scholar
18. Vannozzi, C., Fiorentino, D., D'Amore, M., Rumshitzki, D.S., Dress, A., and Mauri, R.: Cellular automata model of phase transition in binary mixtures. Ind. Eng. Chem. Res. 45, 2892 (2006).CrossRefGoogle Scholar
19. Warren, J.A., Carter, W.C., and Kobayashi, R.: A phase field model of the impingement of solidifying particles. Physica A 261, 159 (1998).CrossRefGoogle Scholar
20. Gránásy, L., Pusztai, T., Börzsönyi, T., Tóth, G., Tegze, G., Warren, J.A., and Douglas, J.F.: Phase field theory of crystal nucleation and polycrystalline growth: a review. J. Mater. Res. 21, 309 (2006).CrossRefGoogle Scholar
21. Cortie, M.B.: Simulation of metal solidification using a cellular automaton. Metall. Trans. B 24, 1045 (1993).CrossRefGoogle Scholar
22. Asle Zaeem, M., Yin, H., and Felicelli, S.D.: Modeling dendritic solidification of Al-3%Cu using cellular automaton and phase-field methods. Appl. Math. Model. 37, 3495 (2013).CrossRefGoogle Scholar
23. Bishop, J.E. and Lim, H.: Continuum approximations. In Multiscale Materials Modeling for Nanomechanics, edited by Weinberger, C.R. and Tucker, G.J. (Springer International Publishing, Cham, 2016), p. 89.CrossRefGoogle Scholar
24. Kadanoff, L.P.: Statistical Physics. Statics, Dynamics and Renormalization (World Scientific, Singapur, 2011).Google Scholar
25. Koyama, M., Rohwerder, M., Tasan, C.C., Bashir, A., Akiyama, E., Takai, K., Raabe, D., and Tsuzaki, K.: Recent progress in microstructural hydrogen mapping in steels: Quantification, kinetic analysis, and multi-scale characterisation. Mater. Sci. Technol. 33, 1481 (2017).CrossRefGoogle Scholar
26. Kugler, G. and Turk, R.: Study of the influence of initial microstructure topology on the kinetics of static recrystallization using a cellular automata model. Comput. Mater. Sci. 37, 284 (2006).CrossRefGoogle Scholar
27. Pagenkopf, J., Butz, A., Wenk, M., and Helm, D.: Virtual testing of dual-phase steels: Effect of martensite morphology on plastic flow behavior. Mater. Sci. Eng. A 674, 672 (2016).CrossRefGoogle Scholar
28. Zhang, H., Diehl, M., Roters, F., and Raabe, D.: A virtual laboratory for initial yield surface determination using high resolution crystal plasticity simulations. Int. J. Plas. 80, 111 (2016).CrossRefGoogle Scholar
29. Kraska, M., Doig, M., Tikhomirov, D., Raabe, D., and Roters, F.: Virtual material testing for stamping simulations based on polycrystal plasticity. Comput. Mater. Sci. 46, 383 (2009).CrossRefGoogle Scholar
30. Dunne, F.P.E., Rugg, D., and Walker, A.: Lengthscale-dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys. Int. J. Plas. 23, 1061 (2007).CrossRefGoogle Scholar
31. Cuddihy, M.A., Stapleton, A., Williams, S., and Dunne, F.P.E.: On cold dwell facet fatigue in titanium alloy aero-engine components. Int. J. Fatique 97, 177 (2017).CrossRefGoogle Scholar
32. Goerler, J.V., Lopez-Galilea, I., Mujica Roncery, L., Shchyglo, O., Theisen, W., and Steinbach, I.: Topological phase inversion after long-term thermal exposure of nickel-base superalloys: Experiment and phase-field simulation. Acta Mater. 124, 158 (2017).CrossRefGoogle Scholar
33. Goetz, R.L. and Seetharaman, V.: Static recrystallization kinetics with homogeneous and heterogeneous nucleation using a cellular automata model. Metall. Mater. Trans. A 29, 2307 (1998).CrossRefGoogle Scholar
34. Raabe, D. and Becker, R.C.: Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium. Model. Simul. Mater. Sci. Eng. 8, 445 (2000).CrossRefGoogle Scholar
35. Güvenc, O., Henke, T., Laschet, G., Böttger, B., Apel, M., Bambach, M., and Hirt, G.: Modelling of static recrystallization kinetics by coupling crystal plasticity FEM an multiphase field simulations. Comput. Meth. Mater. Sci. 13, 368 (2003).Google Scholar
36. Han, F., Tang, B., Kou, H., Cheng, L., Li, J., and Feng, Y.: Static recrystallization simulations by coupling cellular automata and crystal plasticity finite element method using a physically based model for nucleation. J. Mater. Sci. 49, 3253 (2014).CrossRefGoogle Scholar
37. Lim, H., Abdeljawad, F, Owen, S.J., Hanks, B.W., Foulk, J.W., and Battaile, C.C.: Incorporating physically-based microstructures in materials modeling: Bridging phase field and crystal plasticity frameworks. Modelling Simul. Mater. Sci. Eng. 24, 045016 (2016).CrossRefGoogle Scholar
38. Moulinec, H. and Suquet, P.: A fast numerical method for computing the linear and nonlinear properties of composites. C. R. Acad. Sci. II 318, 1417 (1994).Google Scholar
39. Lebensohn, R.A.: N-site modeling of a 3D viscoplastic polycrystal using fast Fourier transform. Acta Mater. 49, 2723 (2001).CrossRefGoogle Scholar
40. Vidyasagar, A., Tan, W.L., and Kochmann, D.M.: Predicting the effective response of bulk polycrystalline ferroelectric ceramics via improved spectral phase field methods. J. Mech. Phys. Solids 106, 133 (2017).CrossRefGoogle Scholar
41. Hernández Encinas, L., Hoya White, S., Martín Del Rey, A., and Rodríguez Sánchez, G.: Modelling forest fire spread using hexagonal cellular automata. Appl. Math. Model. 31, 1213 (2007).CrossRefGoogle Scholar
42. Reina, C. and Conti, S.: Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of F=FeFp . J. Mech. Phys. Solids 67, 40 (2014).CrossRefGoogle Scholar
43. Abrivard, G., Busso, E.P., Forest, S., and Appolaire, B.: Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part I: Theory and numerical implementation. Phil. Mag. 92, 3618 (2012).CrossRefGoogle Scholar
44. Abrivard, G., Busso, E.P., Forest, S., and Appolaire, B.: Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part II: Application to recrystallisation. Phil. Mag. 92, 3643 (2012).CrossRefGoogle Scholar
45. Chen, L., Chen, J., Lebensohn, R.A., Ji, Y.Z., Heo, T.W., Bhattacharyya, S., Chang, K., Mathaudhu, S., Liu, Z.K., and Chen, L.-Q.: An integrated fast Fourier transform-based phase-field and crystal plasticity approach to model recrystallization of three dimensional polycrystals. Comput. Methods Appl. Mech. Eng. 285, 829 (2015).CrossRefGoogle Scholar
46. Hiebeler, J.: Recovery and recrystallization during hot deformation in austenitic steel. Ph.D. Thesis, Bochum, 2016.Google Scholar
47. Zhao, P., Song En Low, T., Wang, Y., and Niezgoda, S.R.: An integrated full-field model of concurrent plastic deformation and microstructure evolution: application to 3D simulation of dynamic recrystallization in polycrystalline copper. Int. J. Plas. 80, 38 (2016).CrossRefGoogle Scholar
48. Bos, C., Mecozzi, M.G., and Sietsma, J.: A microstructure model for recrystallisation and phase transformation during the dual-phase steel annealing cycle. Comput. Mater. Sci. 48, 692 (2010).CrossRefGoogle Scholar
49. Shanthraj, P., Sharma, L., Svendsen, B., Roters, F., and Raabe, D.: A phase field model for damage in elasto-viscoplastic materials. Comput. Methods Appl. Mech. Eng. 312, 167 (2016).CrossRefGoogle Scholar
50. Shanthraj, P., Diehl, M., Eisenlohr, P., Roters, F., and Raabe, D.: Spectral solvers for crystal plasticity and multi-physics. In Handbook of Mechanics of Materials, edited by C.-H. Hsueh, S. Schmauder, C.-S. Chen, K. K. Chawla, N. Chawla, W. Chen, and Y. Kagawa (Springer Nature Singapore, Singapore, 2017).Google Scholar
51. Diehl, M., Wicke, M., Shanthraj, P., Roters, F., Brueckner-Foit, A., and Raabe, D.: Coupled crystal plasticity–phase field fracture simulation study on damage evolution around a void: Pore shape versus crystallographic orientation. JOM 69, 872 (2017).CrossRefGoogle Scholar
52. Bache, M.R., Dunne, F.P.E., and Madrigal, C.: Experimental and crystal plasticity studies of deformation and crack nucleation in a titanium alloy. J. Strain Anal. Eng. 45, 391 (2010).CrossRefGoogle Scholar
53. Schwarze, C., Gupta, A., Hickel, T., and Darvishi Kamachali, R.: Phase-field study of ripening and rearrangement of precipitates under chemomechanical coupling. Phys. Rev. B. 95, 174101 (2017).CrossRefGoogle Scholar
54. Raabe, D. and Hantcherli, L.: 2D cellular automaton simulation of the recrystallization texture of an IF sheet steel under consideration of Zener pinning. Comput. Mater. Sci. 34, 299 (2005).CrossRefGoogle Scholar
55. Gaubert, A., Le Bouar, Y., and Finel, A.: Coupling phase field and viscoplasticity to study rafting in Ni-based superalloys. Phil. Mag. 90, 375 (2010).CrossRefGoogle Scholar
56. Reuber, C., Eisenlohr, P., Roters, F., and Raabe, D.: Dislocation density distribution around an indent in single-crystalline nickel: Comparing nonlocal crystal plasticity finite element predictions with experiments. Acta Mater. 71, 333 (2014).CrossRefGoogle Scholar
57. Cereceda, D., Diehl, M., Roters, F., Raabe, D., Perlado, J.M., and Marian, J.: Unraveling the temperature dependence of the yield strength in single-crystal Tungsten using atomistically-informed crystal plasticity calculations. Int. J. Plas. 78, 242 (2016).CrossRefGoogle Scholar
58. Köster, A., Ma, A., and Hartmaier, A.: Atomistically informed crystal plasticity model for body-centered cubic iron. Acta Mater. 60, 3894 (2012).CrossRefGoogle Scholar
59. Queyreau, S., Monnet, G., and Devincre, B.: Slip systems interactions in alpha-iron determined by dislocation dynamics simulations. Int. J. Plas. 25, 361 (2009).CrossRefGoogle Scholar
60. Devincre, B.: Dislocation dynamics simulations of slip systems interactions and forest strengthening in ice single crystal. Phil. Mag. 93, 235 (2013).CrossRefGoogle Scholar
61. Devincre, B., Kubin, L., and Hoc, T.: Physical analyses of crystal plasticity by DD simulations. Scr. Mater. 54, 741 (2006).CrossRefGoogle Scholar
62. Bertin, N., Tomé, C.N., Beyerlein, I.J., Barnett, M.R., and Capolungo, L.: On the strength of dislocation interactions and their effect on latent hardening in pure magnesium. Int. J. Plas. 62, 72 (2014).CrossRefGoogle Scholar
63. Stricker, M.: Die Übertragung von mikrostrukturellen Eigenschaften aus der diskreten Versetzungsdynamik in Kontinuumsbeschreibungen. Ph.D. Thesis, Karlsruhe, 2017.Google Scholar
64. Stricker, M. and Weygand, D.: Dislocation multiplication mechanisms—glissile junctions and their role on the plastic deformation at the microscale. Acta Mater. 99, 130 (2015).CrossRefGoogle Scholar
65. Jones, R.E., Zimmerman, J.A., and Po, G.: Comparison of dislocation density tensor fields derived from discrete dislocation dynamics and crystal plasticity simulations of torsion. J. Mater Sci. Res. 5, 44 (2016).Google Scholar
66. Groh, S., Marin, E.B., Horstemeyer, M.F., and Zbib, H.M.: Multiscale modeling of the plasticity in an aluminum single crystal. Int. J. Plas. 25, 1456 (2009).CrossRefGoogle Scholar
67. Wong, S.L., Madivala, M., Prahl, U., Roters, F., and Raabe, D.: A crystal plasticity model for twinning- and transformation-induced plasticity. Acta Mater. 118, 140 (2016).CrossRefGoogle Scholar
68. Zhao, P., Shen, C., Li, J., and Wang, Y.: Effect of nonlinear and noncollinear transformation strain pathways in phase-field modeling of nucleation and growth during martensite transformation. NPJ Comput. Mater. 3, 19 (2017).CrossRefGoogle Scholar
69. Shchyglo, O., Hammerschmidt, T., Čak, M., Drautz, R., and Steinbach, I.: Atomistically informed extended Gibbs energy description for phase-field simulation of tempering of martensitic steel. Materials 9, 669 (2016).CrossRefGoogle ScholarPubMed
70. Hickel, T., Kattner, U.R., and Fries, S.G.: Computational thermodynamics: recent developments and future potential and prospects. Phys. Status Solidi (b) 251, (2014). http://onlinelibrary.wiley.com/doi/10.1002/pssb.201470101/full CrossRefGoogle Scholar
71. Amodeo, J., Begau, C., and Bitzek, E.: Atomistic simulations of compression tests on Ni3Al nanocubes. Mater. Res. Lett. 2, 140 (2014).CrossRefGoogle Scholar
72. Senger, J., Weygand, D., Kraft, O., and Gumbsch, P.: Dislocation microstructure evolution in cyclically twisted microsamples: a discrete dislocation dynamics simulation. Model. Simul. Mater. Sci. Eng. 19, 074004 (2011).CrossRefGoogle Scholar
73. Karlsson, B. and Sundström, B.O.: Inhomogeneity in plastic deformation of two-phase steels. Mater. Sci. Eng. 16, 161 (1974).CrossRefGoogle Scholar
74. Choi, S.-H., Kim, E.-Y., Woo, W., Han, S.H., and Kwak, J.H.: The effect of crystallographic orientation on the micromechanical deformation and failure behaviors of DP980 steel during uniaxial tension. Int. J. Plas. 45, 85 (2013).CrossRefGoogle Scholar
75. Wang, L., Barabash, R.I., Yang, Y., Bieler, T.R., Crimp, M.A., Eisenlohr, P., Liu, W., and Ice, G.E.: Experimental characterization and crystal plasticity modeling of heterogeneous deformation in polycrystalline α-Ti. Metall. Mater. Trans. A 42, 626 (2011).CrossRefGoogle Scholar
76. Tasan, C.C., Diehl, M., Yan, D., Zambaldi, C., Shanthraj, P., Roters, F., and Raabe, D.: Integrated experimental-numerical analysis of stress and strain partitioning in multi-phase alloys. Acta Mater. 81, 386 (2014).CrossRefGoogle Scholar
77. Pinna, C., Lan, Y., Kiu, M.F., Efthymiadis, P., Lopez-Pedrosa, M., and Farrugia, D.: Assessment of crystal plasticity finite element simulations of the hot deformation of metals from local strain and orientation measurements. Int. J. Plas. 73, 24 (2015).CrossRefGoogle Scholar
78. Zhu, B. and Militzer, M.: 3D phase field modelling of recrystallization in a low-carbon steel. Model. Simul. Mater. Sci. Eng. 20, 085011 (2012).CrossRefGoogle Scholar
79. Haase, C., Kühbach, M., Barrales-Mora, L.A., Wong, S.L, Roters, F., Molodov, D.A., and Gottstein, G.: Recrystallization behavior of a high-manganese steel: Experiments and simulations. Acta Mater. 100, 155 (2015).CrossRefGoogle Scholar
80. Contieri, R.J., Zanotello, M., and Caram, R.: Simulation of cp-Ti recrystallization and grain growth by a cellular automata algorithm: Simulated versus experimental results. Mater. Res. 20, 688 (2017).CrossRefGoogle Scholar
81. Abdolvand, H. and Daymond, M.R.: Multi-scale modeling and experimental study of twin inception and propagation in hexagonal close-packed materials using a crystal plasticity finite element approach. Part I: Average behavior. J. Mech. Phys. Solids 61, 783 (2013).CrossRefGoogle Scholar
82. Wan, V.V.C., Cuddihy, M.A., Jiang, J., MacLachlan, D.W., and Dunne, F.P.E.: An hr-EBSD and computational crystal plasticity investigation of microstructural stress distributions and fatigue hotspots in polycrystalline copper. Acta Mater. 115, 45 (2016).CrossRefGoogle Scholar
83. Groeber, M.A. and Jackson, M.A.: DREAM.3D: A digital representation environment for the analysis of microstructure in 3D. Integr. Mater. Manuf. Innov. 3, 5 (2014).CrossRefGoogle Scholar
84. Zeghadi, A., Nguyen, F., Forest, S., Gourgues, A.-F., and Bouaziz, O.: Ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure. Part 1: Anisotropic elastic behaviour. Phil. Mag. 87, 1401 (2007).CrossRefGoogle Scholar
85. Zeghadi, A., Forest, S., Gourgues, A.-F., and Bouaziz, O.: Ensemble averaging stress–strain fields in polycrystalline aggregates with a constrained surface microstructure. Part 2: Crystal plasticity. Phil. Mag. 87, 1425 (2007).CrossRefGoogle Scholar
86. Diehl, M., Shanthraj, P., Eisenlohr, P., and Roters, F.: Neighborhood influences on stress and strain partitioning in dual-phase microstructures. An investigation on synthetic polycrystals with a robust spectral-based numerical method. Meccanica 51, 429 (2016).CrossRefGoogle Scholar
87. Wang, L., Li, M., Almer, J., Bieler, T., and Barabash, R.: Microstructural characterization of polycrystalline materials by synchrotron X-rays. Front. Mater. Sci. 7, 156 (2013).CrossRefGoogle Scholar
88. Zhang, C., Li, H., Eisenlohr, P., Liu, W.J., Boehlert, C.J., Crimp, M.A., and Bieler, T.R.: Effect of realistic 3D microstructure in crystal plasticity finite element analysis of polycrystalline Ti-5Al-2.5Sn. Int. J. Plas. 69, 21 (2015).CrossRefGoogle Scholar
89. Abdolvand, H., Majkut, M., Oddershede, J., Wright, J.P., and Daymond, M.R.: Study of 3-D stress development in parent and twin pairs of a hexagonal close-packed polycrystal: Part II—crystal plasticity finite element modeling. Acta Mater. 93, 235 (2015).CrossRefGoogle Scholar
90. Pokharel, R., Lind, J., Li, S.F., Kenesei, P., Lebensohn, R.A., Suter, R.M., and Rollett, A.D.: In-situ observation of bulk 3D grain evolution during plastic deformation in polycrystalline Cu. Int. J. Plas. 67, 217 (2015).CrossRefGoogle Scholar
91. Turner, T.J., Shade, P.A., Bernier, J.V., Li, S.F., Schuren, J.C., Lind, J., Lienert, U., Kenesei, P., Suter, R.M., Blank, B., and Almer, J.: Combined near- and far-field high-energy diffraction microscopy dataset for Ti-7Al tensile specimen elastically loaded in situ. Integr. Mater. Manuf. Innov. 5, 5 (2016).CrossRefGoogle Scholar
92. Maire, E. and Withers, P.J.: Quantitative X-ray tomography. Int. Mater. Rev. 59, 1 (2014).CrossRefGoogle Scholar
93. McDonald, S.A., Reischig, P., Holzner, C., Lauridsen, E.M., Withers, P.J., Merkle, A.P., and Feser, M.: Non-destructive mapping of grain orientations in 3D by laboratory X-ray microscopy. Sci. Rep. 5, 14665 (2015).CrossRefGoogle ScholarPubMed
94. Zaefferer, S., Wright, S.I., and Raabe, D.: Three-dimensional orientation microscopy in a focused ion beam–scanning electron microscope: A new dimension of microstructure characterization. Metall. Mater. Trans. A 39, 374 (2008).CrossRefGoogle Scholar
95. Diehl, M., An, D., Shanthraj, P., Zaefferer, S., Roters, F., and Raabe, D.: Crystal plasticity study on stress and strain partitioning in a measured 3D dual phase steel microstructure. Phys. Mesomech. 20, 311 (2017).CrossRefGoogle Scholar
96. Moreland, K.: Diverging color maps for scientific visualization. In Proc. Adv. in Vis. Comut. 5th Int. Symp. Part II, edited by Bebis, G., Boyle, R., Parvin, B., Koracin, D., Kuno, Y., Wang, J., Pajarola, R., Lindstrom, P., Hinkenjann, A., Encarnação, M.L., Silva, C.T., and Coming, D. (Springer, Berlin/Heidelberg, 2009), p. 92.Google Scholar
97. Borland, D. and Taylor, R.M.: Rainbow color map (still) considered harmful. IEEE Comput. Graph. Appl. 27, 14 (2007).CrossRefGoogle ScholarPubMed
98. Liedl, U., Traint, S., and Werner, E.: An unexpected feature of the stress–strain diagram of dual-phase steel. Comput. Mater. Sci. 25, 122 (2002).CrossRefGoogle Scholar
99. De Geus, T.W.J., Peerlings, R.H.J., and Geers, M.G.D.: Microstructural topology effects on the onset of ductile failure in multi-phase materials—A systematic computational approach. Int. J. Solids Struct. 67, 326 (2015).CrossRefGoogle Scholar
100. Kalidindi, S.R. and De Graef, M.: Materials data science: Current status and future outlook. Annu. Rev. Mater. Res. 45, 171 (2015).CrossRefGoogle Scholar
101. Chowdhury, A., Kautz, E., Yener, B., and Lewis, D.: Image driven machine learning methods for microstructure recognition. Comput. Mater. Sci. 123, 176 (2016).CrossRefGoogle Scholar
102. DeCost, B.L. and Holm, E.A.: A computer vision approach for automated analysis and classification of microstructural image data. Comput. Mater. Sci. 110, 133 (2015).CrossRefGoogle Scholar
103. Azimi, S.M., Britz, D., Engstler, M., Fritz, M., and Mücklich, F.: Advanced steel microstructure classification by deep learning methods (2017). arXiv:1706.06480.Google Scholar
104. Gomberg, J.A., Medford, A.J., and Kalidindi, S.R.: Extracting knowledge from molecular mechanics simulations of grain boundaries using machine learning. Acta Mater. 133, 100 (2017).CrossRefGoogle Scholar
105. Folk, M., Heber, G., Koziol, Q., Pourmal, E., and Robinson, D.: An overview of the HDF5 technology suite and its applications. In Proceeding AD '11 Proceedings of the EDBT/ICDT 2011 Workshop on Array Databases, Uppsala, Sweden – March 25, 2011, pp. 36–47.CrossRefGoogle Scholar
106. Jackson, M., Simmons, J.P., and De Graef, M.: MXA: A customizable HDF5-based data format for multi-dimensional data sets. Model. Simul. Mater. Sci. Eng. 18, 065008 (2010).CrossRefGoogle Scholar
107. Jackson, M.A., Groeber, M.A., Uchic, M.D., Rowenhorst, D.J., and Graef, M.: H5EBSD: An archival data format for electron back-scatter diffraction data sets. Integr. Mater. Manuf. Innov. 3, 4 (2014).CrossRefGoogle Scholar
108. Schmitz, G.J.: Microstructure modeling in integrated computational materials engineering (ICME) settings: Can HDF5 provide the basis for an emerging standard for describing microstructures? JOM 68, 77 (2016).CrossRefGoogle Scholar
109. Diehl, M., Eisenlohr, P., Zhang, C., Nastola, J., Shanthraj, P., and Roters, F.: A flexible and efficient output file format for grain-scale multiphysics simulations. Integr. Mater. Manuf. Innov. 6, 83 (2017).CrossRefGoogle Scholar
110. Huang, Y.: A user-material subroutine incorporating single crystal plasticity in the ABAQUS finite element program. Technical Report. Cambridge (1991).Google Scholar
111. Roters, F., Eisenlohr, P., Kords, C., Tjahjanto, D.D., Diehl, M., and Raabe, D.: DAMASK: The Düsseldorf advanced material simulation kit for studying crystal plasticity using an FE based or a spectral numerical solver. In Procedia IUTAM: IUTAM Symposium on Linking Scales in Computation: From Microstructure to Macroscale Properties, edited by Cazacu, O. (Elsevier, Amsterdam, 3, 2012), p. 3.Google Scholar
112. Guyer, J.E., Wheeler, D., and Warren, J.A.: Fipy: Partial differential equations with python. Comput. Sci. Eng. 11, 6 (2009).CrossRefGoogle Scholar
113. Gaston, D., Newman, C., Hansen, G., and Lebrun-Grandié, D.: MOOSE: A parallel computational framework for coupled systems of nonlinear equations. Nucl. Eng. Des. 239, 1768 (2009).CrossRefGoogle Scholar
114. Alnæs, M., Blechta, J., Hake, J., Johansson, A., Kehlet, B., Logg, A., Richardson, C., Ring, J., Rognes, M., and Wells, G.: The FEniCS project version 1.5. Arch. Numer. Soft. 3, (2015).Google Scholar
115. Arndt, D., Bangerth, W., Davydov, D., Heister, T., Heltai, L., Kronbichler, M., Maier, M., Pelteret, J.-P., Turcksin, B., and Wells, D.: The deal.II library, version 8.5. J. Numer. Math. (2017).CrossRefGoogle Scholar
116. Meier, F., Schwarz, C., and Werner, E.: Crystal-plasticity based thermo-mechanical modeling of Al-components in integrated circuits. Comput. Mater. Sci. 94, 122 (2014).CrossRefGoogle Scholar
117. Grilli, N., Janssens, K.G.F., and Van Swygenhoven, H.: Crystal plasticity finite element modelling of low cycle fatigue in fcc metals. J. Mech. Phys. Solids 84, 424 (2015).CrossRefGoogle Scholar
118. Ebrahimi, A. and Hochrainer, T.: Three-dimensional continuum dislocation dynamics simulations of dislocation structure evolution in bending of a micro-beam. MRS Adv. 1, 1791 (2016).CrossRefGoogle Scholar