An analytical model for the effect of elastic modulus mismatch on laminate threshold strength

摘要

We present an analytical model for predicting the crack tip stress intensity factor in a laminated composite material with alternating zones of residual biaxial compressive and tensile stresses. Such an arrangement of residual stress zones has been shown to be useful for enhancing the damage tolerance properties of the structure, which are manifested as a 'threshold' strength below which the material cannot fail catastrophically. This model improves upon a previous scheme for predicting crack behaviour in such a material, which assumes homogeneous material properties throughout the laminate. To make the problem tractable, this scheme models the system as a homogeneous anisotropic material when calculating the stress fields at the crack tip arising from tractions applied far away from the crack tip. A comparison of the predictions from both schemes with those from a finite element model of such a system shows that our assumptions yield an improved representation of the material's behaviour. We also present results for optimization of geometrical parameters of the system to obtain the highest possible threshold strength under the limitation of a given set of material properties. We conclude that while this scheme improves upon the homogeneous model, 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.