The strength of composite materials loaded in uniaxial tension under pressure

Abstract

This paper presents a method for the evaluation of the tensile strength of composite materials made of a soft matrix with hard inclusions. The tensile strength is calculated as the force per unit area required for the onset of plastic flow in the material. In addition to the tensile strength, the severity of the core deformation and the rate of void formation are also estimated. The results are based on an upper-bound analysis with a two parameter family of velocity fields which accounts for both non-homogeneity of deformation and void formation. The model of the composite and the family of the velocity field used here have already appeared in published articles. Moreover, the application of the present method to estimate the tensile strength in cases when ductile deformation prevails (i.e. when there is no void formation) would lead to the same results as in the previous studies based on the same model and velocity fields. New here is the completeness of the analysis. All possible flow patterns, including for the first time void forming flows, were considered. This made it possible to show that the conditions required to ensure that one or another flow pattern prevails (i.e. those conditions found here and in other articles based on the same model) are not only necessary but also sufficient, at least from a theoretical point of view. The results of this paper have not yet been confirmed experimentally. Although the general trends are in the expected direction, so far no attempt has been made to find the degree of correlation between the theory and the behavior of real materials.