DAMAGE IN A VISCOPLASTIC MATERIAL - PART II - OVERALL BEHAVIOR

The overall behaviour of a damaged viscoplastic material under axisymm etric loading is addressed in this paper. A linear viscous matrix cont aining aligned spheroidal cavities is first considered. Its overall be haviour is estimated by means of a differential scheme. The damage-ind uced morphological anisotropy, due to the shape of the voids, is then analyzed. It is shown to be significant even at low volume fractions o f cavities (f < 0.05), when the latter are prolate or oblate. These re sults are then used to predict the behaviour of a nonlinear viscous ma trix 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 fo rming at moderate strain rates and a linear law with nonzero intercept suited to high strain rates. The constitutive equations of such nonli near damaged materials have been used in a companion paper in order to study the influence of matrix compressibility on the growth of a sphe roidal cavity during straining. (C) 1998 Elsevier Science Ltd. All rig hts reserved.