Construction of macroscale yield surfaces for ductile composites based on a virtual testing strategy

Abstract

The paper describes an approach, based on computational homogenization, for constructing the macroscopic yield surface pertinent to a meso-heterogeneous ductile composite, whereby it is assumed that each constituent is elastic-plastic with (possible) hardening; however, the strategy does not depend on the particular choice of plasticity model (standard, crystal) on the mesoscale. The aim is to compute the macroscale yield properties with bounds that are defined with a priori given confidence, in terms of an “outer yield surface” and an “inner yield surface”. However, these bounds will inevitably be approximate in practice due to the difficulty to achieve guaranteed bounds for general incremental plasticity.The following ingredients are essential to the approach: (1) A “virtual testing” strategy is proposed, whereby a sufficiently large number of realizations of the presumed random meso-structure, determined by the chosen probability, are utilized as Statistical Volume Elements (SVE). (2) In order to obtain the pertinent bounds on the “directional yield stress”, SVE-computations are carried out with Dirichlet and Neumann boundary conditions. (3) A stress-driven, rather than the more traditional strain-driven, format of the SVE-problem is adopted in order to cover the macroscopic stress space in a systematic fashion.Illustrative numerical examples in 2D (particle composites) and 3D (polycrystals of Duplex Stainless Steel) conclude the paper.