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In this paper, intermediate modeling of polycrystalline plasticity is proposed for rigid viscoplatic large deformations. This approach is based on the use of a bicrystal as the elementary local element representing the polycrystal. The local homogenization is obtained by considering the bicrystal volume-averaging and the jump conditions at the assumed planar interface between the two crystals. Two interaction laws based on Taylor and Sachs type assumptions are proposed. These bicrystal-based averaging schemes are different from the classical Taylor and Sachs models since they allow for stresses and strains to vary from one single crystal to the other. We simulate uniaxial tension and compression as well as plane strain compression tests. Results in terms of stress-strain curves are shown in comparison to those of the pure Taylor and Sachs models. We also show results for texture evolution and discuss their comparison with the experimental measurements.

The growth and collapse of isolated voids in power-law viscous matrix materials are investigated. The study is restricted to axisymmetric remote stressing and to voids which are initially spheroidal with the axis of symmetry of the voids coincident with the axis of symmetry of the remote loading. Particular attention is given to the evolution of initially spherical voids, but the effect of initial void shape on subsequent void evolution is also investigated. For linearly viscous matrix materials, the voids evolve through spheroidal shapes and the work of Budiansky et al. (1982) provides the desired information about the history of void shape and volume. For nonlinear matrix materials, the void evolution is idealized as proceeding through a sequence of spheroidal shapes, and the rate of deformation for a given instant is evaluated using a Ritz procedure developed by Lee and Mear (1992). The results of the study demonstrate that the history of void volume and void shape is influenced significantly by the material nonlinearity, the remote stress state and the initial void aspect ratio.

Gurson’s constitutive theory for the plastic deformation of porous metals is specialized to small deformations of power-law solids containing a dilute concentration of voids, and the resulting incremental relations are integrated for proportional stress histories to obtain a total relation between stress and strain. The predictions of the theory are then evaluated by comparing them with accurate numerical results for spherical voids obtained by Lee and Mear (1992). The modification of Gurson’s theory proposed by Tvergaard (1982) is also discussed.