ADIABATIC SHEAR BANDS IN FUNCTIONALLY GRADED MATERIALS

Abstract

The initiation and propagation of adiabatic shear bands (ASBs) in functionally graded materials (FGMs) deformed at high strain rates in plane-strain tension have been studied. An ASB is a narrow region, usually a few micrometers wide, of intense plastic deformation that forms after softening of the material due to its being heated up and the evolution of damage in the form of porosity has overcome its hardening due to strain and strain-rate effects. An FGM is usually composed of two or more constituents with material properties varying continuously through it; the one studied here is made of tungsten particles interspread in a NiFe matrix. Each constituent and the composite are modeled as heat-conducting, microporous, strain and strain-rate hardening, and thermally softening materials with material parameters of the composite derived from those of its constituents by the rule of mixtures. They obey the Johnson–Cook thermoviscoplastic relation, the Gurson-type flow potential, the associated flow rule, and a hyperbolic heat equation. The degradation of thermophysical parameters with the evolution of damage is accounted for with porosity representing the damage. With origin at the centroid of a square cross section, the volume fraction of each phase is assumed to vary radially until a boundary point on the square cross section is reached and then to stay constant. It is found that an ASB, aligned along the direction of the maximum shear stress, forms sooner in an FGM than in either of the two constituent materials with its location, orientation, pattern, and speed depending on the compositional profile.