Finite difference based stress integration algorithm for crystal plasticity finite element method
Source abstract
Abstract
Abstract In this study, we present a Finite Difference Method (FDM)-based stress integration algorithm for Crystal Plasticity Finite Element Method (CPFEM). It addresses the complexity of computing the first derivative of resolved shear stress in the Euler backward stress integration algorithm with Newton-Raphson method. The proposed FDM-based model was verified by evaluating its accuracy, convergence and computational efficiency through single-element simulations. The developed FDM-based model can be easily applied to various constitutive models for CPFEM, overcoming the problem of deriving complex derivative regardless of constitutive models. Additionally, the proposed FDM-based model was validated with the reduced texture approach using AA 2090-T3. Specific parameters including crystallographic orientations were calibrated and the plastic anisotropy was successfully described. In addition, the earing profiles were compared using various stress integration methods. As a result, the proposed FDM-based model can be used as an alternative to the Euler backward method using analytic derivatives with the compatible accuracy, convergence, computational efficiency along with easy implementation within the CPFEM framework.
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Research context
OpenAlex topics: Metal Forming Simulation Techniques · Metallurgy and Material Forming · Numerical methods in engineering
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References (54)
Show source-provided references
1. Yoshida K, Honke T, Yamazaki Y, Hayakawa K, Nakanishi H (2022) Adjustment of crystal orientations and application to crystal plasticity simulation of cup drawing. IntJ Mater Form 15:6810.1007/s12289-022-01713-4 ↗
2. Hama T, Hirano K, Matsuura R (2022) Cylindrical cup drawing of a commercially pure titanium sheet: experiment and crystal plasticity finite-element simulation. IntJ Mater Form 15:810.1007/s12289-022-01655-x ↗
3. Zhang K, Holmedal B, Hopperstad OS, Dumoulin S, Gawad J, Van Bael A, Van Houtte P (2015) Multi-level modelling of mechanical anisotropy of commercial pure aluminium plate: crystal plasticity models, advanced yield functions and parameter identification. Int J Plast 66:3–3010.1016/j.ijplas.2014.02.003 ↗
4. Zhang K, Holmedal B, Hopperstad O, Dumoulin S (2014) Modelling the plastic anisotropy of aluminum alloy 3103 sheets by polycrystal plasticity. Modell Simul Mater Sci Eng 22:07501510.1088/0965-0393/22/7/075015 ↗
5. Saai A, Dumoulin S, Hopperstad O, Lademo O-G (2013) Simulation of yield surfaces for aluminium sheets with rolling and recrystallization textures. Comput Mater Sci 67:424–43310.1016/j.commatsci.2012.08.015 ↗
6. Liu W, Chen BK, Pang Y (2019) Numerical investigation of evolution of earing, anisotropic yield and plastic potentials in cold rolled FCC aluminium alloy based on the crystallographic texture measurements. Eur J Mech-A/Solids 75:41–5510.1016/j.euromechsol.2018.12.005 ↗
7. Roters F, Eisenlohr P, Hantcherli L, Tjahjanto DD, Bieler TR, Raabe D (2010) Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications. Acta Mater 58:1152–121110.1016/j.actamat.2009.10.058 ↗
8. Kalidindi SR, Bronkhorst CA, Anand L (1992) Crystallographic texture evolution in bulk deformation processing of FCC metals. J Mech Phys Solids 40:537–56910.1016/0022-5096(92)80003-9 ↗
9. Cuitino AM, Ortiz M (1993) Computational modelling of single crystals. Modell Simul Mater Sci Eng 1:22510.1088/0965-0393/1/3/001 ↗
10. Asaro RJ, Needleman A (1985) Overview no. 42 texture development and strain hardening in rate dependent polycrystals. Acta Metall 33:923–95310.1016/0001-6160(85)90188-9 ↗
11. Peirce D, Asaro RJ, Needleman A (1983) Material rate dependence and localized deformation in crystalline solids. Acta Metall 31:1951–197610.1016/0001-6160(83)90014-7 ↗
12. Dao M, Asaro RJ (1996) Localized deformation modes and non-Schmid effects in crystalline solids. Part I. Critical conditions of localization. Mech Mater 23:71–10210.1016/0167-6636(96)00012-9 ↗
13. Yoon JW, Barlat F, Gracio JJ, Rauch E (2005) Anisotropic strain hardening behavior in simple shear for cube textured aluminum alloy sheets. Int J Plast 21:2426–244710.1016/j.ijplas.2005.03.014 ↗
14. Marin E, Dawson P (1998) On modelling the elasto-viscoplastic response of metals using polycrystal plasticity. Comput Methods Appl Mech Eng 165:1–2110.1016/S0045-7825(98)00034-6 ↗
15. Marin E, Dawson P (1998) Elastoplastic finite element analyses of metal deformations using polycrystal constitutive models. Comput Methods Appl Mech Eng 165:23–4110.1016/S0045-7825(98)00033-4 ↗
16. Kim J-B, Yoon JW (2015) Necking behavior of AA 6022–T4 based on the crystal plasticity and damage models. Int J Plast 73:3–2310.1016/j.ijplas.2015.06.013 ↗
17. Choi S-H, Kim D, Seong B, Rollett A (2011) 3-D simulation of spatial stress distribution in an AZ31 Mg alloy sheet under in-plane compression. Int J Plast 27:1702–172010.1016/j.ijplas.2011.05.014 ↗
18. Choi S-H, Kim E-Y, Woo W, Han S, Kwak J (2013) The effect of crystallographic orientation on the micromechanical deformation and failure behaviors of DP980 steel during uniaxial tension. Int J Plast 45:85–10210.1016/j.ijplas.2012.11.013 ↗
19. Steinmann P, Stein E (1996) On the numerical treatment and analysis of finite deformation ductile single crystal plasticity. Comput Methods Appl Mech Eng 129:235–25410.1016/0045-7825(95)00913-2 ↗
20. Mellbin Y, Hallberg H, Ristinmaa M (2014) Accelerating crystal plasticity simulations using GPU multiprocessors. Int J Numer Meth Eng 100:111–13510.1002/nme.4724 ↗
21. Miehe C (1996) Exponential map algorithm for stress updates in anisotropic multiplicative elastoplasticity for single crystals. Int J Numer Meth Eng 39:3367–339010.1002/(SICI)1097-0207(19961015)39:19<3367::AID-NME4>3.0.CO;2-7 ↗
22. de Souza Neto E (2001) The exact derivative of the exponential of an unsymmetric tensor. Comput Methods Appl Mech Eng 190:2377–238310.1016/S0045-7825(00)00241-3 ↗
23. Raabe D, Roters F (2004) Using texture components in crystal plasticity finite element simulations. Int J Plast 20:339–36110.1016/S0749-6419(03)00092-5 ↗
24. Raabe D, Wang Y, Roters F (2005) Crystal plasticity simulation study on the influence of texture on earing in steel. Comput Mater Sci 34:221–23410.1016/j.commatsci.2004.12.072 ↗
25. Böhlke T, Risy G, Bertram A (2005) A texture component model for anisotropic polycrystal plasticity. Comput Mater Sci 32:284–29310.1016/j.commatsci.2004.09.040 ↗
26. Böhlke T, Risy G, Bertram A (2006) Finite element simulation of metal forming operations with texture based material models. Modell Simul Mater Sci Eng 14:36510.1088/0965-0393/14/3/003 ↗
27. Rousselier G, Barlat F, Yoon JW (2009) A novel approach for anisotropic hardening modeling. Part I: Theory and its application to finite element analysis of deep drawing. Int J Plast 25:2383–240910.1016/j.ijplas.2009.04.002 ↗
28. Rousselier G, Barlat F, Yoon JW (2010) A novel approach for anisotropic hardening modeling. Part II: Anisotropic hardening in proportional and non-proportional loadings, application to initially isotropic material. Int J Plast 26:1029–104910.1016/j.ijplas.2010.01.001 ↗
29. Rousselier G, Luo M, Mohr D (2012) Macroscopic plasticity modeling of anisotropic aluminum extrusions using a reduced texture methodology. Int J Plast 30:144–16510.1016/j.ijplas.2011.10.004 ↗
30. Luo M, Rousselier G (2014) Modeling of large strain multi-axial deformation of anisotropic metal sheets with strength-differential effect using a reduced texture methodology. Int J Plast 53:66–8910.1016/j.ijplas.2013.07.006 ↗
31. Rousselier G, Luo M (2014) A fully coupled void damage and Mohr-Coulomb based ductile fracture model in the framework of a reduced texture methodology. Int J Plast 55:1–2410.1016/j.ijplas.2013.09.002 ↗
32. Kim E-Y, Choi S-H, Shin E-J, Yoon J (2012) Simulation of earing behaviors in bake hardening steel exhibiting a strong off-γ-fiber component. Int J Solids Struct 49:3573–358110.1016/j.ijsolstr.2012.02.027 ↗
33. Knezevic M, Landry NW (2015) Procedures for reducing large datasets of crystal orientations using generalized spherical harmonics. Mech Mater 88:73–8610.1016/j.mechmat.2015.04.014 ↗
34. Eghtesad A, Barrett TJ, Knezevic M (2018) 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 155:418–43210.1016/j.actamat.2018.06.017 ↗
35. Peirce D, Asaro R, Needleman A (1982) An analysis of nonuniform and localized deformation in ductile single crystals. Acta Metall 30:1087–111910.1016/0001-6160(82)90005-0 ↗
36. Belytschko T, Liu WK, Moran B, Elkhodary K (2014) Nonlinear finite elements for continua and structures. John Wiley & Sons
37. de Souza Neto EA, Peric D, Owen DR (2011) Computational methods for plasticity: theory and applications. John Wiley & Sons
38. Choi H, Yoon JW (2019) Stress integration-based on finite difference method and its application for anisotropic plasticity and distortional hardening under associated and non-associated flow rules. Comput Methods Appl Mech Eng 345:123–16010.1016/j.cma.2018.10.031 ↗
39. Yoon S-Y, Lee S-Y, Barlat F (2020) Numerical integration algorithm of updated homogeneous anisotropic hardening model through finite element framework. Comput Methods Appl Mech Eng 372:11344910.1016/j.cma.2020.113449 ↗
40. Jamal M, Asadabadi SJ, Ahmad I, Aliabad HR (2014) Elastic constants of cubic crystals. Comput Mater Sci 95:592–59910.1016/j.commatsci.2014.08.027 ↗
41. Nolan D, Lally C, McGarry J (2022) Understanding the deformation gradient in Abaqus and key guidelines for anisotropic hyperelastic user material subroutines (UMATs). J Mech Behav Biomed Mater 126:10494010.1016/j.jmbbm.2021.104940 ↗
42. Bassani JL, Wu T-Y (1991) Latent hardening in single crystals. II. Analytical characterization and predictions, Proceedings of the Royal Society of London. Ser A: Math Phys Sci 435:21–4110.1098/rspa.1991.0128 ↗
43. Ma A, Roters F, Raabe D (2006) A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations. Acta Mater 54:2169–217910.1016/j.actamat.2006.01.005 ↗
44. Dunne F, Rugg D, Walker A (2007) Lengthscale-dependent, elastically anisotropic, physically-based hcp crystal plasticity: Application to cold-dwell fatigue in Ti alloys. Int J Plast 23:1061–108310.1016/j.ijplas.2006.10.013 ↗
45. Shanthraj P, Zikry M (2011) Dislocation density evolution and interactions in crystalline materials. Acta Mater 59:7695–770210.1016/j.actamat.2011.08.041 ↗
46. Austin RA, McDowell DL (2011) A dislocation-based constitutive model for viscoplastic deformation of fcc metals at very high strain rates. Int J Plast 27:1–2410.1016/j.ijplas.2010.03.002 ↗
47. Jeong J, Voyiadjis GZ (2022) A physics-based crystal plasticity model for the prediction of the dislocation densities in micropillar compression. J Mech Phys Solids 167:10500610.1016/j.jmps.2022.105006 ↗
48. Asaro RJ (1983) Crystal plasticity. J Appl Mech 50(4b):921–93410.1115/1.3167205 ↗
49. Inal K, Wu P, Neale K (2002) Finite element analysis of localization in FCC polycrystalline sheets under plane stress tension. Int J Solids Struct 39:3469–348610.1016/S0020-7683(02)00162-2 ↗
50. Ali U, Muhammad W, Brahme A, Skiba O, Inal K (2019) Application of artificial neural networks in micromechanics for polycrystalline metals. Int J Plast 120:205–21910.1016/j.ijplas.2019.05.001 ↗
51. Barlat F, Brem J, Yoon JW, Chung K, Dick R, Lege D, Pourboghrat F, Choi S-H, Chu E (2003) Plane stress yield function for aluminum alloy sheets—part 1: theory. Int J Plast 19:1297–131910.1016/S0749-6419(02)00019-0 ↗
52. Yoon JW, Barlat F, Dick R, Karabin M (2006) Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function. Int J Plast 22:174–19310.1016/j.ijplas.2005.03.013 ↗
53. Barrett TJ, Knezevic M (2019) Deep drawing simulations using the finite element method embedding a multi-level crystal plasticity constitutive law: experimental verification and sensitivity analysis. Comput Methods Appl Mech Eng 354:245–27010.1016/j.cma.2019.05.035 ↗
54. Yoon JW, Dick R, Barlat F (2011) A new analytical theory for earing generated from anisotropic plasticity. Int J Plast 27:1165–118410.1016/j.ijplas.2011.01.002 ↗