Differential Hardening in Sheet Metal Under Biaxial Loading: A Theoretical Framework

Abstract

A simple constitutive framework is proposed to take account of progressive changes in a stress-based criterion of yielding as plastic deformation accumulates. The analysis is relevant to a sheet of isotropic or orthotropic material which is subsequently loaded in its plane by biaxial tensions (σ1, σ2) in arbitrary fixed ratio. Under these circumstances there is evidence that texture development causes significant changes in the shapes of successive yield loci in (σ1, σ2) space. Here such departures from geometric similarity are explicitly linked to a presumed dependence on σ1/σ2 of the exponent m in a standard power-law representation of the stress-strain characteristic under each constant value of σ1/σ2. The linkage is formulated in detail for several types of representation, and it is shown how a family of yield loci associated with any conjectural dependence m(σ1/σ2) can be generated readily by computer graphics. Some typical examples are given, in particular when m (σ1/σ2) reflects the distinctive trends reported for certain kinds of brass and aluminum sheet (e.g., Wagoner, 1980; Stout and Hecker 1983).