Extension of the Hill (1948) yield criterion to the case of prismatic monoclinic symmetry

International Journal of Mechanical Sciences

Volumn 38, Issue 12, 1996, Pages 1273-1284

  Darrieulat, M ^a   Montheillet, F ^a  

^a CENTRE SMS   (France)

Author keywords

Orthotropic yield criterion; Prismatic monoclinic symmetry; Strain rate

Indexed keywords

CRYSTAL SYMMETRY; EQUATIONS OF MOTION; HYDROSTATIC PRESSURE; MATHEMATICAL TRANSFORMATIONS; SHEAR DEFORMATION; STRAIN RATE; TENSORS; TORSION TESTING; YIELD STRESS;

HESSIAN MATRIX; HILL ORTHOTROPIC YIELD CRITERION; ORTHOGONAL TRANSFORMATION; PRISMATIC MONOCLINIC SYMMETRY; QUADRATIC YIELD EQUATION; SHEAR STRAIN; STRESS TENSOR; STRUCTURAL TENSORS; TENSOR FUNCTION;

MECHANICS;

EID: 0030527756     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/0020-7403(96)00003-3     Document Type: Article

References (16)

1. R. Hill, A theory of the yielding and plastic flow of anisotropic metals, Proc. R. Soc. Lond. A193, 281 (1948).
2. C. S. Barrett and T. B. Massalski, Structure of Metals. Pergamon Press, Oxford (1980).
3. G. F. Smith and E. Kiral, Integrity bases for N symmetric second-order tensors: the crystal classes. Rend. Circ. Mat. Palermo II 18, 5 (1969).
4. J. F. W. Bishop and R. Hill, A theoretical derivation of the plastic properties of a polycrystalline face-centered metal. Phil. Mag. 42, 1298 (1951).
5. J.-P. Boehler, Private communication (1990).
6. M. Darrieulat, R. Fortunier and F. Montheillet, Invariant formulation of anisotropic plastic behaviour in the case of cubic symmetry. Int. J. Plast. 8, 763 (1992).
7. J.-P. Boehler, Applications of tensor functions in solid mechanics. CISM Courses and Lectures 292, International Center for Mechanical Sciences, Springer Verlag, Wien (1987).
8. J.-P. Boehler, L. El Aoufi and J. Raclin, On experimental testing methods for anisotropic materials. Res. Mech. 21, 73 (1987).
9. J.-P. Boehler, On a rational formulation of isotropic and anisotropic hardening. Proc. Int. Symp. on Current Trends and Results in Plasticity. International Center for Mechanical Sciences, Udine (1983).
10. J.-P. Boehler, Critères de rupture des matériaux composites verre/résine sous contraintes complexes. In Comportement des composites à renfort tissus. Comportement dynamique des composites, p. 229 (Edited by J.-P. Boehler, P. Hamelin and G. Verchery). Pluralis, Paris (1990).
11. F. Montheillet, M. Cohen and J. J. Jonas, Axial stresses and texture development during the torsion testing of Al, Cu and α-Fe Acta Metall. 32, 2077 (1984).
12. F. Montheillet, P. Gilormini and J. J. Jonas, Relations between axial stresses and texture development during torsion testing: a simplified theory. Acta Metall. 33, 705 (1985).
13. M. Arminjon and J.-P. Boehler, Comportement plastique et texture cristallographique des métaux anisotropes. In Colloques internationaux du CNRS, no. 319, Comportement plastique des solides anisotropes, p. 133 (Edited by J.-P. Boehler). CNRS, Paris (1985).
14. P. van Houtte, Calculation of the yield locus of textured polycrystals using the Taylor and the relaxed Taylor theories. Text. Micr. 7, 1 (1987).
15. F. Montheillet and M. Darrieulat, Relationship between Hill anisotropy parameters and texture components in rolled sheet. Proc. 6th Int. Conf. on Mechanical Behavior of Materials (ICM6), Extended Abstracts, 109, (Edited by M. Jono and T. Inoue). Pergamon Press, Kyoto (1991).
16. M. Darrieulat, Prévision du comportement plastique anisotrope des polycristaux texturés par la mécanique des milieux continus. Thèse, Ecole des Mines de Saint-Etienne, France (1993).