Failure stability of a cracked layer between dissimilar materials

Abstract

A composite is designed to fail locally such that energy can be dissipated more uniformly. Cracking of the matrix in a fiber-reinforced composite is not necessarily undesirable provided that the failure can be localized. Such a condition is investigated by depicting a cracked matrix layer between two orthotropic media whose elastic properties are those equivalent to the fiber and matrix depending on the volume fraction. An index of failure stability “ l” is determined from the local and global relative minima of the strain energy density function, denoted by [( dW/ dV) min ] L , and [( dW/ dV) min ] G , respectively. The former refers to the local coordinate systems at each point while the latter refers to the global coordinate system for the entire system. Depending on the load, geometry and material inhomogeneity, l being the distance between [( dW/ dV) min max ] L and [( dW/ dV) min max ] G serves as a measure of the degree of failure stability. The failure of the cracked layer system is found to become more stable as the crack matrix layer thickness is reduced. Influence of load type is also analyzed in combination with changes in material properties and fiber volume fraction.