MECHANICS OF POROUS POLYCRYSTALS: A FULLY ANISOTROPIC FLOW POTENTIAL S. Ahzi 1, * and S. E. Schoenfeld 2 1 Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-0921, U.S.A 2 U.S. Army Research Laboratory, AMSRL-WM-TD Aberdeen Proving Ground, MD 21005-5066, U.S.A. (Received in ®nal revised form 15 February 1998) AbstractÐA model for the elastic±viscoplastic behavior of a polycrystal material containing a dilute number of voids is proposed. The model couples crystal plasticity with a macroscopic description for porosity via the modi®cation of a matrix ¯ow potential to account for the presence of voids. This modi®cation is similar to those used with phenomenological models that preserve macroscopic homogeneity and account for the voids through their volume fraction only. However, unlike the Gurson-type models, our matrix ¯ow potential is fully anisotropic. It is derived by averaging the viscoplastic behavior of constituent single crystals deforming by crystallographic slip. The ¯ow potential is de®ned in an intermediate con®guration that is obtained by elastic unloading without rotation. The developed macroscopic anisotropic ¯ow potential requires numerical solutions but has the advantage of accounting for coupled texture evolution and por- osity eects. This paper presents a theoretical framework for the proposed approach. # 1998 Elsevier Science Ltd. All rights reserved Key words: B. Crystal plasticity. I. INTRODUCTION Considerable attention has been paid to the formulation of macroscopic constitutive models for porous ductile metals under isothermal conditions and relatively low tem- peratures where the matrix behavior can be modeled as rate independent. The most widely used model is that of Gurson (1977). This model has been modi®ed by various authors to account for void nucleation, slight rate sensitivity, and void coalescence leading to ductile fracture (e.g. Pan et al., 1983; Tvergaard and Needleman, 1984). Versions of this model can be found in a recent review by Tvergaard (1989). For viscoplastic materials, Duva and Hutchinson (1984) proposed a ¯ow potential for the macroscopic plastic stretching of an incompressible, isotropic power-law matrix con- taining a dilute concentration of spherical voids. Based on this work, Haghi and Anand (1992) have formulated a complete rate- and temperature-dependent macroscopic con- stitutive model for isotropic, metallic materials containing a moderate number (10±15% porosity) of voids. A generalization of the elastic-viscoplastic model of Haghi and Anand (1992) has been recently implemented by Zavaliangos and Anand (1993). In the work of International Journal of Plasticity, Vol. 14, No. 8, pp. 829±839, 1998 # 1998 Elsevier Science Ltd Pergamon Printed in Great Britain. All rights reserved PII: S0749-6419(98)00025-4 0749-6419/98 $Ðsee front matter 829 *Corresponding author.