A Theory for the mechanical properties of metal-matrix composites at ultimate loading

Abstract

A theory describing the strain, ultimate strength, and work during uniform strain to ultimate loading of metal-matrix composites deformed in tension parallel to the reinforcement is presented. These quantities may be calculated for composites of arbitrary volume fraction using only the component stress-strain curves. The theory is based on the systematic application of a macroscopic principle commonly used to predict the ultimate strength of ductile monolithic materials—namely, that necking occurs when the load borne by the material is maximized. For brittle reinforcing elements, the results are identical to those of previous workers. For ductile reinforcing elements, necking strains intermediate between those of the components and ultimate strengths increasing smoothly with volume fraction from that of the matrix to that of the reinforcement are predicted. The theory can be used to predict the variation of composite ultimate properties with any parameter of interest. In this paper the variation with volume fraction and yield strength of the matrix are studied, with both exact solutions and useful approximations being derived.