Shear–band development in polycrystalline metal with strength–differential effect and plastic volume expansion

Abstract

Experimental studies have shown that the flow stress of some metals is clearly influenced by superimposed hydrostatic pressure. Flow stress increases with the hydrostatic pressure, and consequently it is often observed that the flow stress is clearly larger in a uniaxial compression test than in a uniaxial tension test. This phenomenon is known as the strength–differential effect (SDE). In addition, metals undergoing uniaxial tension and compression show a permanent volume expansion (dilatancy) which is insensitive to the sign of the hydrostatic pressure. In this paper, shear–band development in polycrystalline metal with the SDE and dilatancy is studied, using a rate–dependent crystal–plasticity model with a full three–dimensional, body–centred–cubic, slip–system structure. It is postulated that the appearances of the SDE and dilatancy are consequences of non–Schmid effects existing in each slip system. In the finite–element analyses performed here, each Gaussian integration point in a finite element represents a polycrystal consisting of many of crystal grains having different orientations. As a boundary–value problem, a rectangular specimen subjected to plane–strain tension is considered. Although the finite–element geometry is chosen to be two dimensional, the constitutive model incorporates the full three–dimensional slip–system structure. As a polycrystal model to be embedded in each integration point, an extended Taylor model is employed. Thus, macroscopic manifestations of non–Schmid effects are studied. The influences of hydrostatic stress, internal friction, plastic volume expansion and strain–rate sensitivity on macroscopic shear–band formation in polycrystals are investigated. Results are directly compared with predictions from a classical Schmid–law–based crystal–plasticity theory.