Damage in a viscoplastic material - Part II. Overall behaviour

The overall behaviour of a damaged viscoplastic material under axisymmetric loading is addressed in this paper. A linear viscous matrix containing aligned spheroidal cavities is first considered. Its overall behaviour is estimated by means of a differential scheme. The damage-induced morphological anisotropy, due to the shape of the voids, is then analyzed. It is shown to be significant even at low volume fractions of cavities (f < 0.05), when the latter are prolate or oblate. These results are then used to predict the behaviour of a nonlinear viscous matrix containing aligned spheroidal cavities, by means of a variational principle proposed by Ponte Castaneda (1991). Two types of nonlinear matrix behaviour are considered: a power law corresponding to metal forming at moderate strain rates and a linear law with nonzero intercept suited to high strain rates. The constitutive equations of such nonlinear damaged materials have been used in a companion paper in order to study the influence of matrix compressibility on the growth of a spheroidal cavity during straining. (C) 1998 Elsevier Science Ltd. All rights reserved.