Skip to main content Accessibility help

Review of microstructure and micromechanism-based constitutive modeling of polycrystals with a low-symmetry crystal structure

  • Irene J. Beyerlein (a1) and Marko Knezevic (a2)


Predictions of the mechanical response of polycrystalline metals and underlying microstructure evolution and deformation mechanisms are critically important for the manufacturing and design of metallic components, especially those made of new advanced metals that aim to outperform those in use today. In this review article, recent advancements in modeling deformation processing-microstructure evolution and in microstructure–property relationships of polycrystalline metals are covered. While some notable examples will use standard crystal plasticity models, such as self-consistent and Taylor-type models, the emphasis is placed on more advanced full-field models such as crystal plasticity finite elements and Green’s function-based models. These models allow for nonhomogeneity in the mechanical fields leading to greater insight and predictive capability at the mesoscale. Despite the strides made, it still remains a mesoscale modeling challenge to incorporate in the same model the role of influential microstructural features and the dynamics of underlying mechanisms. The article ends with recommendations for improvements in computational speed.


Corresponding author

a)Address all correspondence to this author. e-mail:


Hide All

This paper has been selected as an Invited Feature Paper.



Hide All
1.Barrett, C.S. and Massalski, M.A.: Structure of Metals (McGraw-Hill, New York, 1966).
2.Taylor, G.I.: Plastic strain in metals. J. Inst. Met. 62, 307 (1938).
3.Asaro, R.J.: Crystal plasticity. J. Appl. Mech. 50, 921 (1983).
4.Lebensohn, R.A. and Tomé, C.N.: A self-consistent anisotropic approach for the simulation of plastic deformation and texture development of polycrystals: Application to zirconium alloys. Acta Metall. Mater. 41, 2611 (1993).
5.Lebensohn, R.A. and Tomé, C.N.: A self-consistent viscoplastic model: Prediction of rolling textures of anisotropic polycrystals. Mater. Sci. Eng., A 175, 71 (1994).
6.Lebensohn, R.A., Tomé, C.N., and Castaneda, P.P.: Self-consistent modelling of the mechanical behaviour of viscoplastic polycrystals incorporating intragranular field fluctuations. Philos. Mag. 87, 4287 (2007).
7.Molinari, A., Canova, G.R., and Ahzi, S.: A self consistent approach of the large deformation polycrystal viscoplasticity. Acta Metall. 35, 2983 (1987).
8.Molinari, A., Ahzi, S., and Kouddane, R.: On the self-consistent modeling of elastic-plastic behavior of polycrystals. Mech. Mater. 26, 43 (1997).
9.Zecevic, M., Beyerlein, I.J., and Knezevic, M.: Coupling elasto-plastic self-consistent crystal plasticity and implicit finite elements: Applications to compression, cyclic tension-compression, and bending to large strains. Int. J. Plast. 93, 187 (2017).
10.Zecevic, M. and Knezevic, M.: Modeling of sheet metal forming based on implicit embedding of the elasto-plastic self-consistent formulation in shell elements: Application to cup drawing of AA6022-T4. JOM 69, 922 (2017).
11.Zecevic, M., McCabe, R.J., and Knezevic, M.: Spectral database solutions to elasto-viscoplasticity within finite elements: Application to a cobalt-based FCC superalloy. Int. J. Plast. 70, 151 (2015).
12.Tomé, C.N., Maudlin, P.J., Lebensohn, R.A., and Kaschner, G.C.: Mechanical response of zirconium: I. Derivation of a polycrystal constitutive law and finite element analysis. Acta Mater. 49, 3085 (2001).
13.Knezevic, M., McCabe, R.J., Lebensohn, R.A., Tomé, C.N., Liu, C., Lovato, M.L., and Mihaila, B.: Integration of self-consistent polycrystal plasticity with dislocation density based hardening laws within an implicit finite element framework: Application to low-symmetry metals. J. Mech. Phys. Solid. 61, 2034 (2013).
14.Bronkhorst, C.A., Kalidindi, S.R., and Anand, L.: An experimental and analytical study of the evolution of crystallographic texturing in Fcc materials. Textures Microstruct. 14, 1031 (1991).
15.Bronkhorst, C.A., Kalidindi, S.R., and Anand, L.: Polycrystalline plasticity and the evolution of crystallographic texture in FCC metals. Philos. Trans. R. Soc. London, Ser. A 341, 443 (1992).
16.Lebensohn, R.A., Liu, Y., and Ponte Castañeda, P.: On the accuracy of the self-consistent approximation for polycrystals: Comparison with full-field numerical simulations. Acta Mater. 52, 5347 (2004).
17.Lieberman, E.J., Lebensohn, R.A., Menasche, D.B., Bronkhorst, C.A., and Rollett, A.D.: Microstructural effects on damage evolution in shocked copper polycrystals. Acta Mater. 116, 270 (2016).
18.Liu, B., Raabe, D., Roters, F., Eisenlohr, P., and Lebensohn, R.A.: Comparison of finite element and fast Fourier transform crystal plasticity solvers for texture prediction. Modell. Simul. Mater. Sci. Eng. 18, 085005 (2010).
19.Lebensohn, R.A., Rollett, A.D., and Suquet, P.: Fast fourier transform-based modeling for the determination of micromechanical fields in polycrystals. JOM 63, 13 (2011).
20.Turner, P.A. and Tomé, C.N.: A study of residual stresses in Zircaloy-2 with rod texture. Acta Metall. Mater. 42, 4143 (1994).
21.Zecevic, M., Knezevic, M., Beyerlein, I.J., and Tomé, C.N.: An elasto-plastic self-consistent model with hardening based on dislocation density, twinning and de-twinning: Application to strain path changes in HCP metals. Mater. Sci. Eng., A 638, 262 (2015).
22.Eshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proc. R. Soc. London, Ser. A 241, 376 (1957).
23.Beyerlein, I.J., Zhang, X., and Misra, A.: Growth twins and deformation twins in metals. Annu. Rev. Mater. Res. 44, 329 (2014).
24.Arul Kumar, M., Beyerlein, I.J., McCabe, R.J., and Tomé, C.N.: Grain neighbour effects on twin transmission in hexagonal close-packed materials. Nat. Commun. 7, 13826 (2016).
25.Van Houtte, P.: Simulation of the rolling and shear texture of brass by the Taylor theory adapted for mechanical twinning. Acta Metall. Mater. 26, 591 (1978).
26.Tomé, C.N., Lebensohn, R.A., and Kocks, U.F.: A model for texture development dominated by deformation twinning: Application to zirconium alloys. Acta Metall. Mater. 39, 2667 (1991).
27.Wu, X., Kalidindi, S.R., Necker, C., and Salem, A.A.: Prediction of crystallographic texture evolution and anisotropic stress-strain curves during large plastic strains in high purity a-titanium using a Taylor-type crystal plasticity model. Acta Mater. 55, 423 (2007).
28.Proust, G., Tomé, C.N., and Kaschner, G.C.: Modeling texture, twinning and hardening evolution during deformation of hexagonal materials. Acta Mater. 55, 2137 (2007).
29.Mareau, C. and Daymond, M.R.: Study of internal strain evolution in Zircaloy-2 using polycrystalline models: Comparison between a rate-dependent and a rate-independent formulation. Acta Mater. 58, 3313 (2010).
30.Proust, G., Tomé, C.N., Jain, A., and Agnew, S.R.: Modeling the effect of twinning and detwinning during strain-path changes of magnesium alloy AZ31. Int. J. Plast. 25, 861 (2009).
31.Christian, J.W. and Mahajan, S.: Deformation twinning. Prog. Mater. Sci. 39, 1 (1995).
32.Capolungo, L., Beyerlein, I.J., Kaschner, G.C., and Tomé, C.N.: On the interaction between slip dislocations and twins in HCP Zr. Mater. Sci. Eng., A 513–514, 42 (2009).
33.Proust, G., Kaschner, G.C., Beyerlein, I.J., Clausen, B., Brown, D.W., McCabe, R.J., and Tomé, C.N.: Detwinning of high-purity zirconium: In situ neutron diffraction experiments. Exp. Mech. 50, 125 (2010).
34.De Cooman, B.C., Estrin, Y., and Kim, S.K.: Twinning-induced plasticity (TWIP) steels. Acta Mater. 142, 283 (2018).
35.Beyerlein, I.J., McCabe, R.J., and Tomé, C.N.: Effect of microstructure on the nucleation of deformation twins in polycrystalline high-purity magnesium: A multi-scale modeling study. J. Mech. Phys. Solid. 59, 988 (2011).
36.Niezgoda, S.R., Kanjarla, A.K., Beyerlein, I.J., and Tomé, C.N.: Stochastic modeling of twin nucleation in polycrystals: An application in hexagonal close-packed metals. Int. J. Plast. 56, 119 (2014).
37.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. Solid. 61, 783 (2013).
38.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 II: Local behavior. J. Mech. Phys. Solid. 61, 803 (2013).
39.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).
40.Ardeljan, M., Beyerlein, I.J., McWilliams, B.A., and Knezevic, M.: Strain rate and temperature sensitive multi-level crystal plasticity model for large plastic deformation behavior: Application to AZ31 magnesium alloy. Int. J. Plast. 83, 90 (2016).
41.Ardeljan, M., Knezevic, M., Nizolek, T., Beyerlein, I.J., Mara, N.A., and Pollock, T.M.: A study of microstructure-driven strain localizations in two-phase polycrystalline HCP/BCC composites using a multi-scale model. Int. J. Plast. 74, 35 (2015).
42.Ardeljan, M., McCabe, R.J., Beyerlein, I.J., and Knezevic, M.: Explicit incorporation of deformation twins into crystal plasticity finite element models. Comput. Meth. Appl. Mech. Eng. 295, 396 (2015).
43.Cheng, J. and Ghosh, S.: A crystal plasticity FE model for deformation with twin nucleation in magnesium alloys. Int. J. Plast. 67, 148 (2015).
44.Savage, D.J., Beyerlein, I.J., and Knezevic, M.: Coupled texture and non-Schmid effects on yield surfaces of body-centered cubic polycrystals predicted by a crystal plasticity finite element approach. Int. J. Solid Struct. 109, 22 (2017).
45.Tonks, M.R., Bingert, J.F., Bronkhorst, C.A., Harstad, E.N., and Tortorelli, D.A.: Two stochastic mean-field polycrystal plasticity methods. J. Mech. Phys. Solid. 57, 1230 (2009).
46.Zhang, P., Karimpour, M., Balint, D., and Lin, J.: Three-dimensional virtual grain structure generation with grain size control. Mech. Mater. 55, 89 (2012).
47.Kalidindi, S.R.: Incorporation of deformation twinning in crystal plasticity models. J. Mech. Phys. Solid. 46, 267 (1998).
48.Bathe, K-J.: Finite Element Procedures (Prentice Hall, Englewood Cliffs, New Jersey, 1996); p. 1037.
49.Zecevic, M., McCabe, R.J., and Knezevic, M.: A new implementation of the spectral crystal plasticity framework in implicit finite elements. Mech. Mater. 84, 114 (2015).
50.Kalidindi, S.R., Bronkhorst, C.A., and Anand, L.: Crystallographic texture evolution in bulk deformation processing of FCC metals. J. Mech. Phys. Solid. 40, 537 (1992).
51.Kalidindi, S.R., Duvvuru, H.K., and Knezevic, M.: Spectral calibration of crystal plasticity models. Acta Mater. 54, 1795 (2006).
52.Moulinec, H. and Suquet, P.: A numerical method for computing the overall response of nonlinear composites with complex microstructure. Comput. Meth. Appl. Mech. Eng. 157, 69 (1998).
53.Lebensohn, R.A., Kanjarla, A.K., and Eisenlohr, P.: An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int. J. Plast. 32–33, 5969 (2012).
54.Lebensohn, R.A., Liu, Y., and Castañeda, P.P.: On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations. Acta Mater. 52, 53475361 (2004).
55.Mercier, S. and Molinari, A.: Homogenization of elastic–viscoplastic heterogeneous materials: Self-consistent and Mori-Tanaka schemes. Int. J. Plast. 25, 1024 (2009).
56.Lebensohn, R.: N-site modeling of a 3D viscoplastic polycrystal using fast Fourier transform. Acta Mater. 49, 2723 (2001).
57.Lebensohn, R.A., Kanjarla, A.K., and Eisenlohr, P.: An elasto-viscoplastic formulation based on fast Fourier transforms for the prediction of micromechanical fields in polycrystalline materials. Int. J. Plast. 32–33, 59 (2012).
58.Hansen, B.L., Beyerlein, I.J., Bronkhorst, C.A., Cerreta, E.K., and Denis-Koller, D.: A dislocation-based multi-rate single crystal plasticity model. Int. J. Plast. 44, 129146 (2013).
59.Knezevic, M., Levinson, A., Harris, R., Mishra, R.K., Doherty, R.D., and Kalidindi, S.R.: Deformation twinning in AZ31: Influence on strain hardening and texture evolution. Acta Mater. 58, 6230 (2010).
60.Miehe, C., Schröder, J., and Schotte, J.: Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comput. Meth. Appl. Mech. Eng. 171, 387 (1999).
61.Beaudoin, A.J., Dawson, P.R., Mathur, K.K., Kocks, U.F., and Korzekwa, D.A.: Application of polycrystal plasticity to sheet forming. Comput. Meth. Appl. Mech. Eng. 117, 49 (1994).
62.Sarma, G.B. and Dawson, P.R.: Texture predictions using a polycrystal plasticity model incorporating neighbor interactions. Int. J. Plast. 12, 1023 (1996).
63.Ardeljan, M., Beyerlein, I.J., and Knezevic, M.: A dislocation density based crystal plasticity finite element model: Application to a two-phase polycrystalline HCP/BCC composites. J. Mech. Phys. Solid. 66, 16 (2014).
64.Sarma, G.B. and Dawson, P.R.: Effects of interactions among crystals on the inhomogeneous deformations of polycrystals. Acta Mater. 44, 1937 (1996).
65.Mika, D.P. and Dawson, P.R.: Effects of grain interaction on deformation in polycrystals. Mater. Sci. Eng., A 257, 62 (1998).
66.Delannay, L., Jacques, P.J., and Kalidindi, S.R.: Finite element modeling of crystal plasticity with grains shaped as truncated octahedrons. Int. J. Plast. 22, 1879 (2006).
67.Ritz, H. and Dawson, P.: Sensitivity to grain discretization of the simulated crystal stress distributions in FCC polycrystals. Modell. Simul. Mater. Sci. Eng. 17, 015001 (2008).
68.Zhao, Z., Ramesh, M., Raabe, D., Cuitiño, A.M., and Radovitzky, R.: Investigation of three-dimensional aspects of grain-scale plastic surface deformation of an aluminum oligocrystal. Int. J. Plast. 24, 2278 (2008).
69.Kalidindi, S.R., Bhattacharya, A., and Doherty, R.: Detailed analysis of plastic deformation in columnar polycrystalline aluminum using orientation image mapping and crystal plasticity models. Proc. R. Soc. London, Ser. A 460, 1935 (2004).
70.Diard, O., Leclercq, S., Rousselier, G., and Cailletaud, G.: Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity: Application to crystal plasticity model identification and the study of stress and strain fields near grain boundaries. Int. J. Plast. 21, 691 (2005).
71.Shenoy, M., Tjiptowidjojo, Y., and McDowell, D.: Microstructure-sensitive modeling of polycrystalline IN 100. Int. J. Plast. 24, 1694 (2008).
72.Lim, H., Carroll, J.D., Battaile, C.C., Buchheit, T.E., Boyce, B.L., and Weinberger, C.R.: Grain-scale experimental validation of crystal plasticity finite element simulations of tantalum oligocrystals. Int. J. Plast. 60, 1 (2014).
73.Ardeljan, M., Savage, D.J., Kumar, A., Beyerlein, I.J., and Knezevic, M.: The plasticity of highly oriented nano-layered Zr/Nb composites. Acta Mater. 115, 189 (2016).
74.De Berg, M., Van Kreveld, M., Overmars, M., and Schwarzkopf, O.C.: Computational Geometry (Springer, Berlin Heidelberg, 2000).
75.Boots, B.: The arrangement of cells in “random” networks. Metallography 15, 53 (1982).
76.Aboav, D.: The arrangement of grains in a polycrystal. Metallography 3, 383 (1970).
77.DREAM.3D Version 4.2: BlueQuartz Software (Springboro, Ohio, 2013).
78.Groeber, M.A. and Jackson, M.A.: DREAM.3D: A digital representation environment for the analysis of microstructure in 3D. Int. Mater. Manu. Innov. 3, 5 (2014).
79.Knezevic, M., Drach, B., Ardeljan, M., and Beyerlein, I.J.: Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models. Comput. Meth. Appl. Mech. Eng. 277, 239 (2014).
80.Ardeljan, M. and Knezevic, M.: Explicit modeling of double twinning in AZ31 using crystal plasticity finite elements for predicting the mechanical fields for twin variant selection and fracture analyses. Acta Mater. 157, 339 (2018).
81.Barrett, T.J., Savage, D.J., Ardeljan, M., and Knezevic, M.: An automated procedure for geometry creation and finite element mesh generation: Application to explicit grain structure models and machining distortion. Comput. Mater. Sci. 141(Suppl. C), 269 (2018).
82.Tomé, C., Canova, G.R., Kocks, U.F., Christodoulou, N., and Jonas, J.J.: The relation between macroscopic and microscopic strain hardening in FCC polycrystals. Acta Metall. 32, 1637 (1984).
83.Beyerlein, I.J. and Tomé, C.N.: A dislocation-based constitutive law for pure Zr including temperature effects. Int. J. Plast. 24, 867 (2008).
84.Capolungo, L., Beyerlein, I.J., and Tomé, C.N.: Slip-assisted twin growth in hexagonal close-packed metals. Scripta Mater. 60, 32 (2009).
85.Lebensohn, R.A., Castañeda, P.P., Brenner, R., and Castelnau, O.: Full-field versus homogenization methods to predict microstructure–property relations for polycrystalline materials. In Computational Methods for Microstructure–Property Relationships, Ghosh, S. and Dimiduk, D., eds. (Springer, Boston, MA, 2011).
86.Beyerlein, I., Capolungo, L., Marshall, P., McCabe, R., and Tomé, C.: Statistical analyses of deformation twinning in magnesium. Philos. Mag. 90, 2161 (2010).
87.Capolungo, L., Marshall, P., McCabe, R., Beyerlein, I., and Tomé, C.: Nucleation and growth of twins in Zr: A statistical study. Acta Mater. 57, 6047 (2009).
88.Meyers, M.A., Andrade, U.R., and Chokshi, A.H.: The effect of grain size on the high-strain, high-strain-rate behavior of copper. Metall. Mater. Trans. A 26, 2881 (1995).
89.Beyerlein, I.J. and Tomé, C.N.: A probabilistic twin nucleation model for HCP polycrystalline metals. Proc. R. Soc. A 466, 2517 (2010).
90.Beyerlein, I.J., McCabe, R.J., and Tome, C.N.: Stochastic processes of 1012 deformation twinning in hexagonal close-packed polycrystalline zirconium and magnesium. Int. J. Multiscale Comput. Eng. 9, 459 (2011).
91.Lentz, M., Risse, M., Schaefer, N., Reimers, W., and Beyerlein, I.: Strength and ductility with$\left\{ {10\bar{1}1} \right\}$$\left\{ {10\bar{1}2} \right\}$ double twinning in a magnesium alloy. Nat. Commun. 7, 1 (2016).
92.Rollett, A., Lebensohn, R., Groeber, M., Choi, Y., Li, J., and Rohrer, G.: Stress hot spots in viscoplastic deformation of polycrystals. Modell. Simul. Mater. Sci. Eng. 18, 074005 (2010).
93.Kocks, U.F., Tomé, C.N., and Wenk, H-R.: Texture and Anisotropy (Cambridge University Press, Cambridge, U.K., 1998).
94.Zecevic, M., Knezevic, M., Beyerlein, I.J., and McCabe, R.J.: Origin of texture development in orthorhombic uranium. Mater. Sci. Eng., A 665, 108 (2016).
95.Knezevic, M., Crapps, J., Beyerlein, I.J., Coughlin, D.R., Clarke, K.D., and McCabe, R.J.: Anisotropic modeling of structural components using embedded crystal plasticity constructive laws within finite elements. Int. J. Mech. Sci. 105, 227 (2016).
96.Yoo, M.H.: Slip modes of alpha uranium. J. Nucl. Mater. 26, 307 (1968).
97.Daniel, J.S., Lesage, B., and Lacombe, P.: The influence of temperature on slip and twinning in uranium. Acta Metall. 19, 163 (1971).
98.Cahn, R.W.: Twinning and slip in a-uranium. Acta Crystallogr. 4, 470 (1951).
99.Cahn, R.W.: Plastic deformation of alpha-uranium; twinning and slip. Acta Metall. 1, 49 (1953).
100.Anderson, R.G. and Bishop, J.W.: The effect of neutron irradiation and thermal cycling on permanent deformations in uranium under load. In Symposium on Uranium and Graphite (1962); p. 17.
101.Fisher, E.S. and McSkimin, H.J.: Adiabatic elastic moduli of single crystal alpha uranium. J. Appl. Phys. 29, 1473 (1958).
102.Rollett, A.D.: Comparison of experimental and theoretical texture development in alpha-uranium. In Symposium on Modeling the Deformation of Crystalline Solids, TMS, Lowe, T.C., Rollett, A.D., Follansbee, P.S., and Daehn, G.S., eds. (1991); p. 361.
103.McCabe, R.J., Capolungo, L., Marshall, P.E., Cady, C.M., and Tomé, C.N.: Deformation of wrought uranium: Experiments and modeling. Acta Mater. 58, 5447 (2010).
104.Brown, D.W., Bourke, M.A.M., Clausen, B., Korzekwa, D.R., Korzekwa, R.C., McCabe, R.J., Sisneros, T.A., and Teter, D.F.: Temperature and direction dependence of internal strain and texture evolution during deformation of uranium. Mater. Sci. Eng., A 512, 67 (2009).
105.Choi, C.S. and Staker, M.: Neutron diffraction texture study of deformed uranium plates. J. Mater. Sci. 31, 3397 (1996).
106.Wu, K., Chang, H., Maawad, E., Gan, W.M., Brokmeier, H.G., and Zheng, M.Y.: Microstructure and mechanical properties of the Mg/Al laminated composite fabricated by accumulative roll bonding (ARB). Mater. Sci. Eng., A 527, 3073 (2010).
107.Yang, D., Cizek, P., Hodgson, P., and Wen, C.e.: Ultrafine equiaxed-grain Ti/Al composite produced by accumulative roll bonding. Scr. Mater. 62, 321 (2010).
108.Bronkhorst, C.A., Mayeur, J.R., Beyerlein, I.J., Mourad, H.M., Hansen, B.L., Mara, N.A., Carpenter, J.S., McCabe, R.J., and Sintay, S.D.: Meso-scale modeling the orientation and interface stability of Cu/Nb-layered composites by rolling. JOM 65, 431 (TMS Warrendale, PA, 2013).
109.Hansen, B.L., Carpenter, J.S., Sintay, S.D., Bronkhorst, C.A., McCabe, R.J., Mayeur, J.R., Mourad, H.M., Beyerlein, I.J., Mara, N.A., Chen, S.R., and Gray, G.T. III: Modeling the texture evolution of Cu/Nb layered composites during rolling. Int. J. Plast. 49, 71 (2013).
110.Mayeur, J., Beyerlein, I., Bronkhorst, C., and Mourad, H.: The influence of grain interactions on the plastic stability of heterophase interfaces. Mater 7, 302 (2014).
111.Mayeur, J.R., Beyerlein, I.J., Bronkhorst, C.A., and Mourad, H.M.: Incorporating interface affected zones into crystal plasticity. Int. J. Plast. 65, 206 (2015).
112.Mayeur, J.R., Beyerlein, I.J., Bronkhorst, C.A., Mourad, H.M., and Hansen, B.L.: A crystal plasticity study of heterophase interface character stability of Cu/Nb bicrystals. Int. J. Plast. 48, 72 (2013).
113.Jia, N., Eisenlohr, P., Roters, F., Raabe, D., and Zhao, X.: Orientation dependence of shear banding in face-centered-cubic single crystals. Acta Mater. 60, 3415 (2012).
114.Carpenter, J., Nizolek, T., McCabe, R., Zheng, S., Scott, J., Vogel, S., Mara, N., Pollock, T., and Beyerlein, I.: The suppression of instabilities via biphase interfaces during bulk fabrication of nanograined Zr. Mater. Res. Lett. 3, 50 (2015).
115.Carpenter, J.S., Nizolek, T., McCabe, R.J., Knezevic, M., Zheng, S.J., Eftink, B.P., Scott, J.E., Vogel, S.C., Pollock, T.M., Mara, N.A., and Beyerlein, I.J.: Bulk texture evolution of nanolamellar Zr–Nb composites processed via accumulative roll bonding. Acta Mater. 92, 97 (2015).
116.Wang, C. and Li, R.: Effect of double aging treatment on structure in Inconel 718 alloy. J. Mater. Sci. 39, 2593 (2004).
117.Kuo, C.M., Yang, Y.T., Bor, H.Y., Wei, C.N., and Tai, C.C.: Aging effects on the microstructure and creep behavior of Inconel 718 superalloy. Mater. Sci. Eng., A 510–511, 289 (2009).
118.Ghorbanpour, S., Zecevic, M., Kumar, A., Jahedi, M., Bicknell, J., Jorgensen, L., Beyerlein, I.J., and Knezevic, M.: A crystal plasticity model incorporating the effects of precipitates in superalloys: Application to tensile, compressive, and cyclic deformation of Inconel 718. Int. J. Plast. 99(Suppl. C), 162 (2017).
119.Li, D.S., Garmestani, H., and Schoenfeld, S.: Evolution of crystal orientation distribution coefficients during plastic deformation. Scripta Mater. 49, 867 (2003).
120.Knezevic, M. and Kalidindi, S.R.: Fast computation of first-order elastic-plastic closures for polycrystalline cubic-orthorhombic microstructures. Comput. Mater. Sci. 39, 643 (2007).
121.Knezevic, M. and Landry, N.W.: Procedures for reducing large datasets of crystal orientations using generalized spherical harmonics. Mech. Mater. 88, 73 (2015).
122.Jahedi, M., Paydar, M.H., Zheng, S., Beyerlein, I.J., and Knezevic, M.: Texture evolution and enhanced grain refinement under high-pressure-double-torsion. Mater. Sci. Eng., A 611, 29 (2014).
123.Eghtesad, A., Barrett, T.J., and Knezevic, M.: Compact reconstruction of orientation distributions using generalized spherical harmonics to advance large-scale crystal plasticity modeling: Verification using cubic, hexagonal, and orthorhombic polycrystals. Acta Mater. 155, 418 (2018).
124.Knezevic, M., Al-Harbi, H.F., and Kalidindi, S.R.: Crystal plasticity simulations using discrete Fourier transforms. Acta Mater. 57, 1777 (2009).
125.Al-Harbi, H.F., Knezevic, M., and Kalidindi, S.R.: Spectral approaches for the fast computation of yield surfaces and first-order plastic property closures for polycrystalline materials with cubic-triclinic textures. Comput. Mater. Continua 15, 153 (2010).
126.Knezevic, M., Kalidindi, S.R., and Fullwood, D.: Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals. Int. J. Plast. 24, 1264 (2008).
127.Kalidindi, S.R., Knezevic, M., Niezgoda, S., and Shaffer, J.: Representation of the orientation distribution function and computation of first-order elastic properties closures using discrete Fourier transforms. Acta Mater. 57, 3916 (2009).
128.Landry, N. and Knezevic, M.: Delineation of first-order elastic property closures for hexagonal metals using fast Fourier transforms. Materials 8, 6326 (2015).
129.Barton, N.R., Knap, J., Arsenlis, A., Becker, R., Hornung, R.D., and Jefferson, D.R.: Embedded polycrystal plasticity and adaptive sampling. Int. J. Plast. 24, 242 (2008).
130.Barton, N.R., Bernier, J.V., Lebensohn, R.A., and Boyce, D.E.: The use of discrete harmonics in direct multi-scale embedding of polycrystal plasticity. Comput. Meth. Appl. Mech. Eng. 283, 224 (2015).
131.Bunge, H-J.: Texture Analysis in Materials Science: Mathematical Methods (Cuvillier Verlag, London, 1993).
132.Van Houtte, P.: Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials. Int. J. Plast. 10, 719 (1994).
133.Mihaila, B., Knezevic, M., and Cardenas, A.: Three orders of magnitude improved efficiency with high—Performance spectral crystal plasticity on GPU platforms. Int. J. Numer. Meth. Eng. 97, 785 (2014).
134.Savage, D.J. and Knezevic, M.: Computer implementations of iterative and non-iterative crystal plasticity solvers on high performance graphics hardware. Comput. Mech. 56, 677 (2015).
135.Mellbin, Y., Hallberg, H., and Ristinmaa, M.: Accelerating crystal plasticity simulations using GPU multiprocessors. Int. J. Numer. Meth. Eng. 100, 111 (2014).
136.Knezevic, M. and Savage, D.J.: A high-performance computational framework for fast crystal plasticity simulations. Comput. Mater. Sci. 83, 101 (2014).
137.Alharbi, H.F. and Kalidindi, S.R.: Crystal plasticity finite element simulations using a database of discrete Fourier transforms. Int. J. Plast. 66, 71 (2015).
138.Beyerlein, I., Li, S., Necker, C., Alexander, D., and Tomé, C.: Non-uniform microstructure and texture evolution during equal channel angular extrusion. Philos. Mag. 85, 1359 (2005).
139.Knezevic, M., Daymond, M.R., and Beyerlein, I.J.: Modeling discrete twin lamellae in a microstructural framework. Scripta Mater. 121, 84 (2016).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed