The initiation and propagation of adiabatic shear bands (ASBs) in functionally graded materials 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 of the material due to the temperature rise and the evolution of damage in the form of porosity overcomes the hardening due to strain- and strain-rate effects. A FGM is usually comprised of two or more constituents with material properties varying continuously through the body; here, the FGM is comprised of tungsten particles in a nickel-iron 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 being derived from those of its constituents by the rule of mixtures. They obey the Johnson-Cook thermoviscoplastic relation, 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 it remains constant. It is found that an ASB, aligned along the direction of the maximum shear stress, forms sooner in a FGM than in either of the two constituent materials with its location, orientation, pattern and speed depending upon the compositional profile.
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