A Unified Macro-and Micro-mechanics Constitutive Model And Its Applications For Fiber Reinforced Metal Matrix Composites

A unified macro- and micro-mechanics constitutive model and its applications for fiber reinforced metal matrix composites are studied to satisfy needs of analyzing mechanical behaviors of composites and structures on macroscopic and microscopic scales.Relation between macroscopic and microscopic mechanical parameters fields is analyzed. Microscopic characteristic is imposed on a point in macroscopic composite object. A unified macro- and micro-mechanics constitutive model is presented through analyzing micro-mechanics equations with weakened continuity and periodicity boundary conditions on a representative volume element which is selected based on hypothesis of periodicity in composite microstructure. The relation between macroscopic and microscopic stress and strain fields is set up in the model and the macroscopic stress-strain relation is obtained.The validity and applicability of the model are verified by the micro-mechanics finite element method and the fibrous metal matrix composites tests. Applications of the model are studied. With the model, the macroscopic elastic properties, elastoplastic stress-strain responses and yielding surfaces under multi-dimensional loads are calculated, and the influence of fiber shapes and packing arrangement on macroscopic elastoplastic properties is analyzed. A unified macro- and micro-mechanics analysis method for fibrous metal matrix composite structures is set up by integrating the model into the general finite element method program. The method can not only consider micro-structural geometry effects on macro-properties but also obtain both macroscopic and microscopic stress and strain fields, which provides sufficient quantity basis for the damage and fracture analysis of metal matrix composite structures.