On modelling the growth and the orientation changes of ellipsoidal voids in a rigid plastic matrix

Abstract

A phenomenological ductile damage model is developed to take into account the growth and the changes of orientation of defects in a undamaged material matrix under large plastic straining. This constitutive model is based on a skew-symmetric tensor-valued function, originally presented by Wang C C (1970 New theorem for isotropic function part 1 and part 2 Arch. Rational Mech. Anal. 36 166–223) and modified for anisotropic functions by Boehler J P (1978 Lois de comportement anisotrope des milieux continus J. Mécanique 17 153–90). A finite element model of a three-dimensional unit cell containing a tilted ellipsoidal void is used to identify the constitutive parameters of the proposed model. Then, this law of orientation change is compared with the two-dimensional model of Bilby B A and Kolbuszewski M L (1977 The finite deformation of an inhomogeneity in two-dimensionnal slow viscous incompressible flow Proc. R. Soc. A 355 335–53) deduced from the original work of Eshelby J D (1957 The determination of the elastic field of an ellipsoidal innclusion and related problem Proc. R. Soc. A 241 376–96). In the proposed ductile damage model, the radius changes of the void are based on the modified version of the Rice and Tracey void growth law presented by Thomason and adapted for the transformation of an ellipsoidal void of any orientation in the sound matrix. The new proposals are checked with different non-linear finite element analyses.