The Facet method: A hierarchical multilevel modelling scheme for anisotropic convex plastic potentials

International Journal of Plasticity

Volumn 25, Issue 2, 2009, Pages 332-360

  Van Houtte, Paul ^a   Yerra, Sampath Kumar ^a   Van Bael, Albert ^a,b  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b Katholieke Hogeschool Limburg   (Belgium)

Author keywords

A. Yield condition; B. Anisotropic material; B. Polycrystalline material; C. Analytic functions; Multilevel modelling

Indexed keywords

ABS RESINS; ANISOTROPY; FINITE ELEMENT METHOD; FORMING; MATHEMATICAL MODELS; METAL FORMING; PLASTICS; POLYCRYSTALLINE MATERIALS; REGRESSION ANALYSIS; SINGLE CRYSTAL SURFACES; SINGLE CRYSTALS; STRESSES;

A. YIELD CONDITION; B. ANISOTROPIC MATERIAL; B. POLYCRYSTALLINE MATERIAL; C. ANALYTIC FUNCTIONS; MULTILEVEL MODELLING;

STRAIN RATE;

EID: 55549118931     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2008.02.001     Document Type: Article

References (55)

1. Arminjon M. A regular form of the Schmid law, application to the ambiguity problem. Texture Microstruct. (1991) 1121-1128
2. Arminjon M., and Bacroix B. On plastic potentials for anisotropic metals and their derivation from the texture function. Acta Mech. 88 (1991) 219-243
3. Bacroix B., and Gilormini P. Finite element simulations of earing in polycrystalline materials using a texture-adjusted strain rate potential. Model. Simul. Mater. Sci. Eng. 3 (1995) 1-21
4. Barlat F., Brem J.C., Yoon J.W., Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi S.-H., and Chu E. Plane stress yield function for aluminium alloy sheet. Part I: Theory. Int. J. Plasticity 19 (2003) 1297-1319
5. Barlat F., Aretz H., Yoon J.W., Karabin M.E., Brem J.C., and Dick R.E. Linear transformation-based anisotropic yield functions. Int. J. Plasticity 21 (2005) 1009-1039
6. Barlat F., Yoon J.W., and Cazacu O. On linear transformations of stress tensors for the description of plastic anisotropy. Int. J. Plasticty 23 (2007) 876-896
7. Barlat F., and Chung K. Anisotropic potentials for plastically deformation metals. Modell. Simul. Mater. Sci. Eng. 1 (1993) 403-416
8. Barlat F., and Lian J. Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions. Int. J. Plasticity 5 (1989) 51-66
9. Beaudoin A.J., Mathur K.K., Dawson P.R., and Johnson G. Int. J. Plasticity 19 (1993) 833-860
10. Betten J. Applications of tensor functions to the formulation of yield criteria for anisotropic materials. Int. J. Plasticity 4 (1988) 29-46
11. Boehler J.P. Lois de comportement anisotrope des milieux continus. J. Méc. 17 (1978) 152-190
12. Bron F., and Besson J. A yield function for anisotropic materials. Application to aluminum alloys. Int. J. Plasticity 20 (2004) 937-963
13. Bunge H.J. Some applications of the Taylor theory of polycrystal plasticity. Krist. Tech. 5 (1970) 145-175
14. Bunge H.J. Texture Analysis in Materials Science (1982), Butterworth, London
15. Chung K., Lee S.Y., Barlat F., Keum Y.T., and Park J.M. Finite element simulation of sheet forming based on a planar anisotropic strain-rate potential. Int. J. Plasticity 12 (1996) 93-115
16. Darieullat M., and Piot D. A method of generating analytical yield surfaces of crystalline materials. Int. J. Plasticity 12 5 (1996) 575-610
17. Dawson P.R., Boyce D.E., Hale R., and Dukrot J.P. An isoparametric piecewise representation of the anisotropic strength of polycrystalline solids. Int. J. Plasticity 21 (2005) 251-283
18. Drucker D. Introduction to Mechanics of Deformable Solids (1967), McGraw-Hill, New York
19. Gambin W. Crystal plasticity based on yield surfaces with rounded-off corners. Z. Angew. Math. mech. 71 (1991) T265-T268
20. Habraken A.M., and Duchêne L. Anisotropic elasto-plastic finite element analysis using a stress-strain interpolation method based on a polycrystalline model. Int. J. Plasticity 20 (2004) 1525-1560
21. Hill R. A theory of the yielding and plastic flow of anisotropic metals. Proc. R. Soc. A 193 (1948) 281-297
22. Hill R. The Mathematical Theory of Plasticity (1950), Clarendon Press, Oxford, UK
23. Hill R. Constitutive dual potentials in classical plasticity. J. Mech. Phys. Solids 35 (1987) 23-33
24. Ilyushin, A.A., 1963. Plasticity. Akad. Nauk. SSSR, Moscow (in Russian).
25. Karafillis A.P., and Boyce M.C. A general anisotropic yield criterion using bounds and a transformation weighting tensor. J. Mech. Phys. Solids 41 (1993) 1859-1886
26. Kim D., Barlat F., Bouvier S., Rabahallah M., Balan T., and Chung K. Non-quadratic anisotropic potentials based on linear transformation of plastic strain rate. Int. J. Plasticity 23 (2007) 1380-1399
27. Kowalczyck K., and Gambin W. Model of plastic anisotropy evolution with texture-dependent yield surface. Int. J. Plasticity 20 (2004) 19-54
28. Lemaître J., and Chaboche J.L. Mechanics of Solid Materials (1990), Cambridge University Press
29. Lequeu P., Gilormini P., Montheillet F., Bacroix B., and Jonas J.J. Acta Metall. 33 (1984) 705-717
30. Mols K., Van Praet K., and Van Houtte P. A generalized yield locus calculation from texture data. In: Brakman C.M., Jongenburger P., and Mittemeijer E.J. (Eds). Proceedings of Seventh International Conference on Textures of Materials (ICOTOM 7) (1984), Netherlands Society for Material Science, Zwijndrecht (The Netherlands) 651-656
31. Nye J.F. Physical Properties of Crystals (1985 Edition) (1985), Clarendon Press, Oxford, UK
32. Pan J., and Rice J.R. Rate sensitivity of plastic flow and implication for yield-surface vertices. Int. J. Solids Struct. 19 (1983) 973-987
33. Peeters B., Kalidindi S.R., Teodosiu C., Van Houtte P., and Aernoudt E. A theoretical investigation of the influence of dislocation sheets on evolution of yield surfaces in single-phase b.c.c. polycrystals. J. Mech. Phys. Solids 50 (2002) 783-807
34. Ristic S., He S., Van Bael A., and Van Houtte P. Texture-based explicit finite-element analysis of sheet metal forming. Mater. Sci. Forum (2005) 495-497
35. Rockafellar R.T. Convex Analysis (Second Printing) (1972), Princeton University Press, Princeton, USA
36. Rogers, T.G., 1990. Yield criteria, flow rules, and hardening in anisotropic plasticity. In: Proceedings of the IUTAM/ICM Symposium on Yielding, Damage, and Failure of Anisotropic Solids, Villard-de-Lans, France, August 1987. Mechanical Engineering Publications Ltd., London, UK, pp. 53-79.
37. Taylor G.I. Plastic strain in metals. J. Inst. Met. 62 (1938) 307-324
38. Toth L.S., Van Houtte P., and Van Bael A. Analytical representation of polycrystal yield surfaces. In: Boehler J.P., and Khan A.S. (Eds). Anisotropy and Localization of Plastic Deformation (Proc. Plasticity'91) (1991), Elsevier Applied Science, London 183-186
39. Van Bael, A., He, S., Li S., Van Houtte, P., 2003. The simulation of cold metal deformation using convex plastic potentials calculated from texture data. In: Owen, D.R.J., Onate, E., Suarez, B. (Eds.), Computational Plasticity VII - Fundamentals and Applications (Book of Abstracts and CD-Rom Proceedings), International Center for Numerical Methods in Engineering (CIMNE), Barcelona, no continuous page numbering.
40. Van Houtte P. A comprehensive mathematical formulation of an extended Taylor-Bishop-Hill model featuring relaxed constraints, the Renouard-Wintenberger theory and a strain rate sensitivity model. Texture Microstruct. 8-9 (1988) 313-350
41. Van Houtte P. Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials. Int. J. Plasticity 10 (1994) 719-748
42. Van Houtte P. Fast calculation of average Taylor factors and Mandel spins for all possible strain modes. Int. J. Plasticity 17 (2001) 807-818
43. Van Houtte, P., 2004. The "MTM-FHM" Software System, Version 2, Manual, Department MTM, K.U.Leuven, Leuven, Belgium.
44. Van Houtte P., and Aernoudt E. Considerations on the crystal and the strain symmetry in the calculation of deformation textures with the Taylor theory. Mater. Sci. Eng. 23 (1976) 11-22
45. Van Houtte P., and Van Bael A. Convex plastic potentials of 4th and 6th rank for anisotropic materials. Int. J. Plasticity 20 (2004) 1505-1524
46. Van Houtte P., Mols K., Van Bael A., and Aernoudt E. Application of yield loci calculated from texture data. Texture Microstruct. 11 (1989) 23-39
47. Van Houtte, P., Van Bael, A., Winters, J., Aernoudt, E., Hall, F., Wang, N., Pillinger, I., Hartley, P., Sturgess, C.E.N., 1992. Modelling of complex forming processes. In: Andersen, S.I. et al. (Eds.), Modelling of Plastic Deformation and Its Engineering Applications, Proceedings of 13th Risø International Symposium on Materials Science, Risø National Laboratory, Roskilde, Denmark, pp. 161-172.
48. Van Houtte P., Van Bael A., and Winters J. The incorporation of texture-based yield loci into elastoplastic finite element programs. Texture Microstruct. 24 (1995) 255-272
49. Van Houtte P., Li S., Seefeldt M., and Delannay L. Deformation texture prediction: from the Taylor model to the Advanced Lamel model. Int. J. Plasticity 21 (2005) 589-624
50. Van Houtte P., Kanjarla A.K., Van Bael A., Seefeldt M., and Delannay L. Multiscale modelling of the plastic anisotropy and deformation texture of polycrystalline materials. Eur. J. Mech. A/Solids 25 (2006) 634-648
51. von Mises R. Mechanik der plastischen Formänderung von Kristallen. Z. Angew. Math. Mech. 8 (1928) 161-185
52. Wang C.C. A new representation theorem for isotropic functions, Part I and II. Arch. Ration. Mech. Anal. 36 (1970) 166-223
53. Ziegler H. An Introduction to Thermomechanics (1977), North Holland Publishing Company, Amsterdam
54. Życzkowski M. Anisotropic yield conditions. In: Lemaitre J. (Ed). Handbook of Materials Properties. Deformation of Materials vol. I (2001), Academic Press, New York 155-165
55. Życzkowski M., and Kurtica T. A description of distortional plastic hardening of anisotropic materials. In: Boehler J.P. (Ed). Yielding, Damage and Failure of Anisotropic Solids (1990), Mechanical Engineering Publications, London 97-111