THERMOPLASTICITY THEORY FOR BIDIRECTIONALLY FUNCTIONALLY GRADED MATERIALS

A recently developed higher order theory for the thermoelastic respons e of composite materials with microstructures characterized by arbitra rily nonuniform reinforcement spacing in two directions (i.e., bidirec tionally functionally graded materials) is further extended to accommo date the effect of an inelastic response of the constituent phases. Th is theory circumvents the problematic use of the standard micromechani cal approach, based on the concept of a representative volume element, commonly employed in the analysis of functionally graded composites b y explicitly coupling the local (microstructural) and global (macrostr uctural) responses. The theoretical framework is based on volumetric a veraging 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 m icrostructure. Examples are presented that illustrate how the presence of plasticity and microstructure affect the free-edge interlaminar st resses in metal matrix composites and how these stresses and plastic s trains can be altered and managed through functionally graded architec tures. Furthermore, the results demonstrate the inability of the stand ard homogenization approach to capture accurately the microstructural effects in the vicinity of the free edge.