Convex plastic potentials of fourth and sixth rank for anisotropic materials

International Journal of Plasticity

Volumn 20, Issue 8-9, 2004, Pages 1505-1524

  Van Houtte, P ^a   Van Bael, A ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

Author keywords

B. Anisotropic material; B. Polycrystalline material; C. Analytic functions; C. Finite elements; C. Numerical algorithms

Indexed keywords

ALGORITHMS; ANISOTROPY; APPROXIMATION THEORY; CRYSTALLOGRAPHY; FINITE ELEMENT METHOD; FUNCTIONS; POLYCRYSTALLINE MATERIALS; STRAIN; STRESS ANALYSIS; TEMPERATURE DISTRIBUTION; TEXTURES;

ANALYTIC FUNCTIONS; ANISOTROPIC MATERIALS; FINITE ELEMENTS; NUMERICAL ALGORITHMS;

ELASTOPLASTICITY;

EID: 2342544067     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2003.11.005     Document Type: Article

References (26)

1. Aernoudt E., Van Houtte P., Leffers T. Deformation and textures of metals at large strains. Mughrabi H. Plastic Deformation and Fracture of Materials [Vol. 6 of Cahn, R.W., Haasen, P. and Kramer, J., (Eds), Materials Science and Technology: A Comprehensive Treatment]. 1993;89-136 VCH, Weinheim, Federal Republic of Germany.
2. Arminjon M., Bacroix B., Imbault D., Raphanel J.L. A fourth-order plastic potential for anisotropic metals and its analytical calculation from the texture function. Acta Mech. 107:1994;33-51.
3. Barlat F., Brem J.C., Yoon J.W., Chung K., Dick R.E., Lege D.J., Pourboghrat F., Choi S.-H., Chu E. Plane stress yield function for aluminum alloy sheets - part 1. theory Int. J. Plasticity. 19(9):2003;1297-1319.
4. Bunge H.J. Texture Analysis in Materials Science. 1982;Butterworth, London.
5. Hill R. Constitutive dual potentials in classical plasticity. J. Mech. Phys. Solids. 35:1987;23-33.
6. Hill R. A theory of the yielding and plastic flow of anisotropic metals. Proc. Roy. Soc. A. 193:1948;281-297.
7. Hill R. The Mathematical Theory of Plasticity. 1950;Oxford University Press, Oxford.
8. Hiwatashi S., Van Bael A., Van Houtte P., Teodosiu C. Modelling of plastic anisotropy based on texture and disclocation structure. Computational Materials Science. 9:1997;274-284.
9. Hiwatashi S., Van Bael A., Van Houtte P., Teodosiu C. Prediction of forming limit strains under strain-path changes. application of an anisotropic model based on texture and dislocation structure Int. J. Plasticity. 14:1998;647-669.
10. Hoferlin E., Van Bael A., Van Houtte P., .Steyaert G.G., De Maré C. Biaxial tests on cruciform specimens for the validation of crystallographic yield loci. J. Mater. Proc. Tech. 80-81:1998;545-550.
11. Hu Z., Rauch E.F., Teodosiu C. Work-hardening behavior of mild steel under stress reversal at large strains. Int. J. Plasticity. 8:1992;1992. 839-856.
12. Kuwabara T., Van Bael A., Iizuka E. Measurement and analysis of yield locus and work hardening characteristics of steel sheets with different r-values. Acta Mater. 50:2002;3717-3729.
13. Lemaitre J., Chaboche J.L. Mechanics of Solid Materials. 1990;Cambridge University Press, Cambridge.
14. Li S., Hoferlin E., Van Bael A., Van Houtte P. Application of a texture-based plastic potential in earing prediction of an IF steel. Adv. Eng. Mater. 3:2001;990-994.
15. Li S., Hoferlin E., Van Bael A., Van Houtte P., Teodosiu C. Finite element modeling of plastic anisotropy induced by texture and strain path change. Int. J. Plasticity. 19:2003;647-674.
16. MacEwen S.R., Perrin R., Green D., Makinde A., Neale K. An evaluation of planar biaxial deformation in H19 can-stock sheet. Andersen S.I., et al. Modelling of Plastic Deformation and Its Engineering Applications, Proc. 13th Risø International Symposium on Materials Science. 1992;539-545 Risø National Laboratory, Roskilde, Denmark.
17. Nye J.F. Physical Properties of Crystals. 1976;Oxford University Press, Oxford.
18. Peeters P., Kalidindi S.R., Teodosiu C., Van Houtte P., 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(4):2002;783-807.
19. Teodosiu C. Materials science input to engineering models. Andersen S.I., et al. Modelling of Plastic Deformation and Its Engineering Applications, Proc. 13th Risø International Symposium on Materials Science. 1992;125-146 Risø National Laboratory, Roskilde, Denmark.
20. Van Bael, A., 1994. PhD Thesis, Dept. MTM, Katholieke Universiteit Leuven, Belgium.
21. Van Bael, A. and Van Houtte, P., 2002. A convex fourth-order plastic potential derived from crystallographic texture. In: Cescotto, S. (Ed.), Non Linear Mechanics of Anisotropic Materials, Proc. EMMC6. Dept. MSM, Univ. Liège, Belgium, pp. 51-58.
22. Van Houtte P. Fast calculation of average Taylor factors and Mandel spins for all possible strain modes. Int. J. Plasticity. 17:2001;807-818.
23. Van Houtte P. Application of plastic potentials to strain rate sensitive and insensitive anisotropic materials. Int. J. Plasticity. 10:1994;719-748.
24. Van Houtte P., Van Bael A., Winters J. The incorporation of texture-based yield loci into elasto-plastic finite element programs. Textures and Microstructures. 24:1995;255-272.
25. 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, Proc. 13th Risø International Symposium on Materials Science. Risø National Laboratory, Roskilde, Denmark, pp. 161-172.
26. Zyczkowski M. Anisotropic yield conditions. Lemaitre J. Handbook of Materials Properties, Vol. I: Deformation of Materials. 2001;155-165 Academic Press, New York.