Thermoplasticity theory for bidirectionally functionally graded materials

A recently developed higher order theory for the thermoelastic response of composite materials with microstructures characterized by arbitrarily nonuniform reinforcement spacing in two directions (i.e., bidirectionally functionally graded materials) is further extended to accommodate the effect of an inelastic response of the constituent phases. This theory circumvents the problematic use of the standard micromechanical approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites by explicitly coupling the local (microstructural) and global (macrostructural) responses. The theoretical framework is based on volumetric averaging of the various field quantities together with the imposition of boundary and interfacial conditions in an average sense between the subvolumes used to characterize the composite's functionally graded microstructure. Examples are presented that illustrate how the presence of plasticity and microstructure affect the free-edge interlaminar stresses in metal matrix composites and how these stresses and plastic strains can be altered and managed through functionally graded architectures. Furthermore, the results demonstrate the inability of the standard homogenization approach to capture accurately the microstructural effects in the vicinity of the free edge.