An Analytical Model for the Effect of Elastic Modulus Mismatch on Laminate Threshold Strength

Abstract

ABSTRACTA scheme for calculating the stress intensity factor at the crack tip in a two-dimensional bimaterial laminate composite has been developed to model the damage tolerance obtained in brittle ceramics by using this geometry. One limitation of the model is its assumption of homogenous elastic properties throughout the composite, limiting the accuracy of predictions it can make about real material systems. Finite element simulations of the same architecture that allow for elastic modulus mismatch give results that are moderately different from those obtained from the homogeneous model. We present an analytical expression for the stress intensity factor around a crack tip in a laminated composite that can take into account the elastic modulus mismatch. To make the problem tractable, the model is based on the assumption that the system behaves as a homogeneous anisotropic material when the stress field at the crack tip arises out of far field tractions applied away from the crack tip. The model improves upon the homogeneous model, giving results that are closer to those from the finite element simulations. We, however, conclude that more work is required to predict the stresses at the tip as the crack approaches a material interface before a complete analytical model can be obtained.