Crystal plasticity finite-element simulations for quasistatic deformation of polycrystals in terms of explicit dynamics

Varvara A. Romanova, Ruslan R. Balokhonov, Anzhelika Borodina, Valerii S. Shakhidzhanov, Dmitry V. Lychagin, Evgeniya S. Emelianova, Maxim Pisarev

Author details

Varvara A. Romanova
Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russian Federation
Ruslan R. Balokhonov
Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russian Federation
Anzhelika Borodina
Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russian Federation; National Research Tomsk State University, Tomsk, Russian Federation
Valerii S. Shakhidzhanov
Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russian Federation
Dmitry V. Lychagin
National Research Tomsk State University, Tomsk, Russian Federation
Evgeniya S. Emelianova
Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russian Federation
Maxim Pisarev
Institute of Strength Physics and Materials Science SB RAS, Tomsk, Russian Federation

https://doi.org/10.15593/perm.mech/2023.5.06

Crystal plasticity models combined with an explicit consideration of a polycrystalline struc- ture are an effective tool for studying the deformation phenomena throughout length scales. A numerical solution to the boundary-value problems with an explicit account for misstructural features requires extensive computational resources. The use of explicit time integration schemes effectively reduces computational costs yet providing a quasistatic solution with a high degree of accuracy. In this paper, we discuss the numerical aspects of crystal plasticity finite element simulations of quasistatic deformation phenomena in terms of explicit dynamics. The equations for plastic strain rate are formulated in a way to minimize strain rate sensitivity, which is the necessary condition for simulating quasistatic deformation at artificially high strain rates. The problems of model verification and testing at the micro, meso, and macroscales are dis- cussed using the example of aluminum single- and polycrystals.

Keywords

crystal plasticitymicromechanical modelspolycrystalsnumerical simulationplastic deformation.

ПРИМЕНЕНИЕ ПОДХОДОВ ФИЗИЧЕСКОЙ ТЕОРИИ ПЛАСТИЧНОСТИ ПРИ МОДЕЛИРОВАНИИ КВАЗИСТАТИЧЕСКОЙ ДЕФОРМАЦИИ ПОЛИКРИСТАЛЛОВ В ДИНАМИЧЕСКОЙ ПОСТАНОВКЕ

Модели физической теории пластичности кристаллов в комбинации с явным учетом зеренной структуры являются эффективным инструментом для исследования деформационных процессов в поликристаллических материалах на разных масштабных уровнях. Численное решение краевых задач с учетом морфологических особенностей микроструктуры требует значительных вычислительных ресур- сов. Переход к явным схемам интегрирования по времени позволяет эффективно минимизировать вычислительные затраты, при этом обеспечивая квазистатическое решение с высокой степенью точно- сти. В настоящей работе обсуждаются вычислительные аспекты, связанные с применением моделей физической теории пластичности при моделировании процессов квазистатического деформирования поликристаллов в динамической постановке. Приведены соотношения для описания скоростей пласти- ческих сдвигов активных систем скольжения, позволяющие эффективно исключить скоростную чувстви- тельность, что является необходимым условием моделирования при искусственно завышенных скоро- стях деформации. На примере расчетов для моно- и поликристаллов алюминия обсуждаются вопросы тестирования и верификации моделей на микро-, мезо- и макроуровнях.

Ключевые слова

физическая теория пластичности кристалловмикромеханические моделиполикристаллычисленное моделированиепластическая деформация.

Bibliography

1.Crystal plasticity finite element methods: in materials science and engineering / F. Roters [et al.] – John Wiley & Sons, 2011. – 197 p. Scholar
2.Overview of constitutive laws, kinematics, homogeniza- tion and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications / D. D. Tjahjanto [et. al] // Acta Materialia. – 2009. – Vol. 58, № 4. – P. 1152-1211. Scholar
3.Trusov P. V., Volegov P. S., Kondratev N. S. Fizicheskie teorii plastichnosti. Perm, Izd-vo PNIPU, 2012, 273 p. Scholar
4.Multilevel models in physical mesomechanics of metals and alloys: results and prospects / P. V. Trusov [et al.] // Phys. Mesomech. – 2021. – V. 24. – pp. 391–417. Scholar
5.Gribov D.S., Trusov P.V. Three-level dislocation-based model for describing the deformation of polycrystals: structure, implementation algorithm, examples for studying nonproportional cyclic loading. // Phys. Mesomech. – 2022. – V. 25. – pp. 557– 567. doi: 10.1134/S102995992206008X. Scholar
6.Computational crystal plasticity: from single crystal to homogenized polycrystals / G. Cailletaud [et al.] // Technische Mechanik. – 2003. –V. 1. – pp. 130–145. Scholar
7.Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models/ M. Knezevic [et al.] // Computer Methods in Applied Mechanics and Engineering. – 2014. – V. 277. – pp. 239-259. doi: 10.1016/j.cma.2014.05.003. Scholar
8.Ostapovich K.V., Trusov P.V., Yants A.Y. Prediction of crystallographic texture formation in polycrystalline samples under severe plastic deformation based on a two-level statistical elasto- viscoplastic model. // Phys Mesomech. – 2021. – V.24. – pp.225– 236. doi: 10.1134/S1029959921030012 Scholar
9.Microstructure-based simulations of quasistatic defor- mation using an explicit dynamic approach / V. Romanova [et al.] // Facta Universitatis, series: Mechanical Engineering. – 2019. – V. 17. – pp. 243–254. Scholar
10.On the solution of quasi-static micro- and meso- mechanical problems in a dynamic formulation./ V.A. Romanova [et al.] // Phys. Mesomech. – 2019. – V. 22. – pp. 296–306. Scholar
11.Harewood F.J., McHugh P.E., Comparison of the implic- it and explicit finite element methods using crystal plasticity. // Comput Mater Sci. – 2007. – V. 39. – pp.481–494. doi: 10.1016/j.commatsci.2006.08.002. Scholar
12.Abaqus Analysis User’s Guide, Dassault Systemes, 2013 Scholar
13.Trusov P.V., Shveykin A.I., Yanz A.Y. Motion decom- position, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling.// Phys. Mesomech. – 2017. – V. 20. – pp. 357–376. doi: 10.1134/S1029959917040014 Scholar
14.Trusov P. V., Volegov P. S. Crystal plasticity theories and their applications to the description of inelastic deformations of materials. Part 3: hardening theories, gradient theories // PNRPU Mechanics Bulletin. – 2011. – Vol. 3. – pp. 146-197. Scholar
15.Busso E. P., Cailletaud G. On the selection of active slip systems in crystal plasticity. // Int. J. Plast. – 2005. – V. 21. – pp. 2212–2231. Scholar
16.Taylor G. I. Plastic strain in metals // Journal of the Insti- tute of Metals. – 1938. – Vol. 62. – pp. 307–324 Scholar
17.Bishop J. F. W., Hill R. A theoretical derivation of the plastic properties of a polycrystalline face centered metal. // Phil. Mag. – 1951. – № 42. – pp. 1298–1307. Scholar
18.Trusov P. V., Volegov P. S. Crystal plasticity theories and their applications to the description of inelastic deformations of materials. Part 1: rigid-plastic and elastoplastic theories // PNRPU Mechanics Bulletin. – 2011. – Vol. 1. – pp. 5-45. Scholar
19.Chaboche J.L. Time-independent constitutive theories for cyclic plasticity. // Int J Plast. – 1986. – V. 2. – pp. 149-188. doi.org/10.1016/0749-6419(86)90010-0. Scholar
20.Trusov P. V., Volegov P. S. Crystal plasticity: Theory and applications to the description of inelastic deformation of ma- terials. Part 2: Viscoplastic and elastoviscoplastic models// PNRPU Mechanics Bulletin. – 2011. – Vol. 2. – pp. 101-131. Scholar
21.Peirce D., Asaro R. J., Needleman A. Material rate de- pendence and localized deformation in crystalline solids. // Acta Metallurgica. – 1983. – № 31. – pp. 1951–1976. Scholar
22.Arsenlis A., Parks D. M. Modeling the evolution of crys- tallographic dislocation density in crystal plasticity. // J. Mech. Phys. Solids. – 2002. – V. 50, № 9. – pp. 1979–2009. Scholar
23.Ma A., Roters F. A constitutive model for fcc single crystals based on dislocation densities and its application to uniax- ial compression of aluminium single crystals. // Acta Materialia. – 2004. – V. 52, № 12. – pp. 3603–3612. Scholar
24.Ma A., Roters F., Raabe D. A dislocation density based con- stitutive model for crystal plasticity FEM including geometrically neces- sary dislocations. // Acta Mater. – 2006. -V. 54. – pp. 2169–2179. Scholar
25.Evers L.P., Brekelmans W.A.M., Geers M.G.D. Non-local crystal plasticity model with intrinsic SSD and GND effects // J. Mech. Phys. Solids. – 2004. – V. 52, № 10. – pp. 2379–2401. Scholar
26.Hollenstein M., · Jabareen M., · Rubin M.B., Modeling a smooth elastic–inelastic transition with a strongly objective numer- ical integrator needing no iteration. // Comput Mech. – 2013. – V.52. – pp.649–667. doi: 10.1007/s00466-013-0838-7. Scholar
27.Forest S., Rubin M.B., A rate-independent crystal plas- ticity model with a smooth elastic–plastic transition and no slip indeterminacy. // European J. Mech. – A Solids. – 2016. –V.55. pp. 278-288, doi: 10.1016/j.euromechsol.2015.08.012. Scholar
28.Crystal plasticity modeling of the cyclic behavior of pol- ycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses. /Farooq H [et al.] // Int J Plast. –2020. – V.126. – 102619. doi: 10.1016/j.ijplas.2019.10.007. Scholar
29.Romanova V.A., Balokhonov R.R., Karpenko N.I. Simula- tion of the mechanical behavior of materials with regard to the 3D internal structure // Phys. Mesomech. – 2004. – Vol. 7. – pp. 71-79. Scholar
30.Romanova V., Balokhonov R. A Method of step-by-step packing and its application in generating 3D microstructures of polycrystalline and composite materials. // Engineering with Com- puters. – 2021. – V. 37. – pp. 241–250. Scholar
31.Mecking H., Kocks U.F., Kinetics of flow and strain- hardening. // Acta Metallurgica. – 1981. – V.29. – pp.1865-1875. doi: 10.1016/0001-6160(81)90112-7. Scholar
32.Armstrong R.W. Dislocation and grain size roles in physical mesomechanics. // Phys. Mesomech. – 2021. – V. 24. – pp. 418–425. doi:10.1134/S1029959921040068. Scholar
33.Teplyakova L.A., Lychagin D.V., Bespalova I.V. Mech- anisms of deformation macrolocalization in aluminium single crys- tals with loading axis orientation [110] // Phys. Mesomech. – 2004. – Vol. 7, is. 6. – pp. 63-78. Scholar
34.Mechanical aspects of nonhomogeneous deformation of aluminum single crystals under compression along [100] and [110] directions. / V. Romanova [et al.] // Metals. – 2022. – 12. doi: 10.3390/met12030397. Scholar
35.Poverhnostnye sloi i vnutrennie granicy razdela v geterogennyh materialah pod red. V.E.Panina. Novosibirsk: Izd-vo SO RAN, 2006. Scholar
36.Evolution of mesoscopic deformation-induced surface roughness and local strains in tensile polycrystalline aluminum / Romanova V. A. [et al.] // Phys. Mesomech. – 2021. – V. 24. – pp. 570-577. doi.org/10.1134/S1029959921050088 Scholar
37.Early prediction of macroscale plastic strain localization in titanium from observation of mesoscale surface roughening / V. Ro- manova [et al.] // Int J Mech Sci. – 2019. – V. 161–162. – 105047. Scholar
38.Balokhonov R., Emelianova E., Pisarev M., Zinovieva O., Shakhidjanov V., On the definition of RVE size in simulations of mesoscale deformation-induced surface roughening in poly- crystals. / V. Romanova [et. al] // Procedia Structural Integrity. – 2021. doi: 10.1016/j.prostr.2021.03.010 Scholar
39.Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity. Application to crystal plas- ticity model identification and the study of stress and strain fields near grain boundaries / O. Diard [et al.] // Int J Plast. – 2005. – V. 21. – pp. 691–722. Scholar
40.Intergranular and intragranular behavior of polycrystal- line aggregates. Part 1: F.E. model / F. Barbe [et al.] // Int J Plast. – 2001. – V. 17. – pp. 513–536. Scholar
41.Peirce D., Asaro R. J., Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals. // Acta Metallurgica. – 1982. – № 30. – pp. 1087–1119. Scholar

1.Crystal plasticity finite element methods: in materials sci- ence and engineering / F. Roters [et al.]. – John Wiley & Sons, 2011. – 197 p. Scholar
2.Overview of constitutive laws, kinematics, homogeniza- tion and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications / D.D. Tjahjanto [et. al] // Acta Materialia. – 2009. – Vol. 58, № 4. – P. 1152–1211. Scholar
3.Трусов П.В., Волегов П.С., Кондратьев Н.С. Физиче- ские теории пластичности. – Пермь: Изд-во ПНИПУ, 2012. – 273 с. Scholar
4.Multilevel models in physical mesomechanics of metals and alloys: results and prospects / P.V. Trusov [et al.] // Phys. Mesomech. – 2021. – Vol. 24. – P. 391–417. Scholar
5.Gribov D.S., Trusov P.V. Three-level dislocation-based model for describing the deformation of polycrystals: structure, implementation algorithm, examples for studying nonproportional cyclic loading // Phys. Mesomech. – 2022. – Vol. 25. – P. 557– 567. DOI: 10.1134/S102995992206008X Scholar
6.Computational crystal plasticity: from single crystal to homogenized polycrystals / G. Cailletaud [et al.] // Technische Mechanik. – 2003. – Vol. 1. – P. 130–145. Scholar
7.Three dimensional predictions of grain scale plasticity and grain boundaries using crystal plasticity finite element models / M. Knezevic [et al.] // Computer Methods in Applied Mechanics and Engineering. – 2014. – Vol. 277. – P. 239–259. DOI: 10.1016/j.cma.2014.05.003 Scholar
8.Ostapovich K.V., Trusov P.V., Yants A.Y. Prediction of crystallographic texture formation in polycrystalline samples under severe plastic deformation based on a two-level statistical elasto- viscoplastic model // Phys Mesomech. – 2021. – Vol. 24. – P. 225– 236. DOI: 10.1134/S1029959921030012 Scholar
9.Microstructure-based simulations of quasistatic defor- mation using an explicit dynamic approach / V. Romanova [et al.] // Facta Universitatis, series: Mechanical Engineering. – 2019. – Vol. 17. – P. 243–254. Scholar
10.On the Solution of Quasi-Static Micro- and Meso- mechanical Problems in a Dynamic Formulation / V.A. Romanova [et al.] // Phys. Mesomech. – 2019. – Vol. 22. – P. 296–306. Scholar
11.Harewood F.J., McHugh P.E., Comparison of the implic- it and explicit finite element methods using crystal plasticity // Comput Mater Sci. – 2007. – Vol. 39. – P. 481–494. DOI: 10.1016/j.commatsci.2006.08.002 Scholar
12.Abaqus Analysis User’s Guide. – Dassault Systemes, 2013. Scholar
13.Trusov P.V., Shveykin A.I., Yanz A.Y. Motion decom- position, frame-indifferent derivatives, and constitutive relations at large displacement gradients from the viewpoint of multilevel modeling // Phys. Mesomech. – 2017. – Vol. 20. – P. 357–376. DOI: 10.1134/S1029959917040014 Scholar
14.Трусов П.В., Волегов П.С. Физические теории пла- стичности: теория и приложения к описанию неупругого де- формирования материалов. Ч. 3: теории упрочнения, гради- ентные теории // Вестник ПНИПУ. Механика. – 2011. – Т. 3. – C. 146–197. Scholar
15.Busso E.P., Cailletaud G. On the selection of active slip systems in crystal plasticity // Int. J. Plast. – 2005. – Vol. 21. – P. 2212–2231. Scholar
16.Taylor G.I. Plastic strain in metals // Journal of the Insti- tute of Metals. – 1938. – Vol. 62. – P. 307–324. Scholar
17.Bishop J.F.W., Hill R. A theoretical derivation of the plastic properties of a polycrystalline face centered metal // Phil. Mag. – 1951. – № 42. – P. 1298–1307. Scholar
18.Трусов П.В., Волегов П.С. Физические теории пла- стичности: теория и приложения к описанию неупругого де- формирования материалов. Ч. 1: жесткопластические и упру- гопластические модели // Вестник ПНИПУ. Механика. – 2011. – Т. 1. – С. 5–45. Scholar
19.Chaboche J.L. Time-independent constitutive theories for cyclic plasticity // Int J Plast. – 1986. – Vol. 2. – P. 149–188. DOI: 10.1016/0749-6419(86)90010-0 Scholar
20.Трусов П.В., Волегов П.С. Физические теории пла- стичности: теория и приложения к описанию неупругого де- формирования материалов. Ч. 2: вязкопластические и упруго- вязкопластические модели // Вестник ПНИПУ. Механика. – 2011. – Т. 2. – С. 101–131. Scholar
21.Peirce D., Asaro R.J., Needleman A. Material rate de- pendence and localized deformation in crystalline solids // Acta Metallurgica. – 1983. – No. 31. – P. 1951–1976. Scholar
22.Arsenlis A., Parks D.M. Modeling the evolution of crys- tallographic dislocation density in crystal plasticity // J. Mech. Phys. Solids. – 2002. – Vol. 50, no. 9. – P. 1979–2009. Scholar
23.Ma A., Roters F. A constitutive model for fcc single crystals based on dislocation densities and its application to uniax- ial compression of aluminium single crystals // Acta Materialia. – 2004. – Vol. 52, no. 12. – P. 3603–3612. Scholar
24.Ma A., Roters F., Raabe D. A dislocation density based con- stitutive model for crystal plasticity FEM including geometrically neces- sary dislocations // Acta Mater. – 2006. – Vol. 54. – P. 2169–2179. Scholar
25.Evers L.P., Brekelmans W.A.M., Geers M.G.D. Non-local crystal plasticity model with intrinsic SSD and GND effects // J. Mech. Phys. Solids. – 2004. – Vol. 52, no. 10. – P. 2379–2401. Scholar
26.Hollenstein M., Jabareen M., Rubin M.B. Modeling a smooth elastic–inelastic transition with a strongly objective numer- ical integrator needing no iteration // Comput. Mech. – 2013. – Vol. 52. – P. 649–667. DOI: 10.1007/s00466-013-0838-7 Scholar
27.Forest S., Rubin M.B. A rate-independent crystal plastic- ity model with a smooth elastic–plastic transition and no slip inde- terminacy // European J. Mech. – A Solids. – 2016. – Vol. 55. – P. 278–288. DOI: 10.1016/j.euromechol.2015.08.012 Scholar
28.Crystal plasticity modeling of the cyclic behavior of pol- ycrystalline aggregates under non-symmetric uniaxial loading: Global and local analyses / H. Farooq [et al.] // Int J Plast. – 2020. – Vol. 126. – P. 102619. DOI: 10.1016/j.ijplas.2019.10.007 Scholar
29.Романова В.А., Балохонов Р.Р., Карпенко Н.И. Мо- делирование механического поведения материалов с учетом трехмерной внутренней структуры // Физ. мезомех. – 2004. – Т. 7. – С. 71–79. Scholar
30.Romanova V., Balokhonov R. A method of step-by-step packing and its application in generating 3D microstructures of polycrystalline and composite materials // Engineering with Com- puters. – 2021. – Vol. 37. – P. 241–250. Scholar
31.Mecking H., Kocks U.F. Kinetics of flow and strain- hardening // Acta Metallurgica. – 1981. – Vol. 29. – P. 1865–1875. DOI: 10.1016/0001-6160(81)90112-7 Scholar
32.Armstrong R.W. Dislocation and Grain Size Roles in Physical Mesomechanics. // Phys. Mesomech. – 2021. – Vol. 24. – P. 418–425. DOI: 10.1134/S1029959921040068 Scholar
33.Теплякова Л.А., Лычагин Д.В., Беспалова И.В. Зако- номерности макролокализации деформации в монокристаллах алюминия с ориентацией оси сжатия [110] // Физ. мезомех. – 2004. – Т. 7, № 6. – С. 63–78. Scholar
34.Mechanical Aspects of Nonhomogeneous Deformation of Aluminum Single Crystals under Compression along [100] and [110] Directions / V. Romanova [et al.] // Metals. – 2022. – Vol. 12. DOI: 10.3390/met12030397 Scholar
35.Поверхностные слои и внутренние границы раздела в гетерогенных материалах под ред. В.Е. Панина. – Ново- сибирск: Изд-во СО РАН, 2006. Scholar
36.Evolution of Mesoscopic Deformation-Induced Surface Roughness and Local Strains in Tensile Polycrystalline Aluminum / V.A. Romanova [et al.] // Phys. Mesomech. – 2021. – Vol. 24. – P. 570–577. DOI: 10.1134/S1029959921050088 Scholar
37.Early Prediction of Macroscale Plastic Strain Localiza- tion in Titanium from Observation of Mesoscale Surface Roughen- ing / V. Romanova [et al.] // Int J Mech Sci. – 2019. – Vol. 161– 162. – P. 105047. Scholar
38.On the definition of RVE size in simulations of mesoscale deformation-induced surface roughening in polycrystals / R. Balokhonov, E. Emelianova, M. Pisarev, O. Zinovieva, V. Sha- khidjanov // Procedia Structural Integrity. – 2021. DOI: 10.1016/j.prost.2021.03.010 Scholar
39.Evaluation of finite element based analysis of 3D multicrystalline aggregates plasticity. Application to crystal plas- ticity model identification and the study of stress and strain fields near grain boundaries / O. Diard [et al.] // Int J Plast. – 2005. – Vol. 21. – P. 691–722. Scholar
40.Intergranular and intragranular behavior of polycrystal- line aggregates. Part 1: F.E. model / F. Barbe [et al.] // Int J Plast. – 2001. – Vol. 17. – P. 513–536. Scholar
41.Peirce D., Asaro R.J., Needleman A. An analysis of nonuniform and localized deformation in ductile single crystals // Acta Metallurgica. – 1982. – No. 30. – P. 1087–1119. Scholar

Article information

Published: 4 December 2023
Issue date: 4 December 2023
Issue: No. 5 (2023)