On the dynamic behavior of porous ductile solids containing spheroidal voids

Abstract

A new micro-mechanical model for the dynamic behavior of porous ductile materials containing oblate voids is proposed. This contribution represents an extension of the recent work of Sartori et al. (2015 Mechanics of Materials, 80, part B, 329–334) which is dedicated to the case of prolate voids. In the present work, a spheroidal representative volume element (RVE) is considered. Based on the work of Molinari and Mercier (2001 J. Mech Phys. Solids, 49, 1497–1516), the macroscopic stress is the sum of two terms: a static and a dynamic component. The static part of the macroscopic stress is described by the Gologanu et al. model (1997 CISM Courses and lectures, 377, 61–130). The dynamic macroscopic stress is evaluated using the trial velocity field of Gologanu et al. (1994 J. of Engineering materials and technology, 116, 290–297) proposed for oblate voids. As a result, a dynamic porous model is obtained for a material containing oblate voids. The model is validated by comparison with results of finite element computations. Then, the case of spherical voids is investigated as the limit of the prolate and oblate models. A proof of continuity between the two models (for oblate and prolate voids) is provided. Overall, a general model for the dynamic behavior of a porous material containing spheroidal voids is obtained. Microscale dynamic effects result in a non-associated flow theory, the flow direction being dictated by the normal to the quasistatic yield surface which is convex while the total flow stress (summation of the quasistatic yield stress with the dynamic stress) lies on a different flow surface which may be sometimes non-convex. Finally, the limit case of penny shaped cracks has been considered, showing that results can also be significantly affected by microscale inertia effects. The extension of the modeling to micro-cracked ductile material under dynamic loading opens quite interesting new perspectives.