Stress intensity factor solutions for cracks in finite-width three layer laminates with and without residual stress effects

Approximate stress intensity factor solutions for cracks in finite-width three layer laminates, with the crack located in the middle layer, were derived on the basis of force-balance between the applied stress and the modified Westergaard form of normal stress distribution ahead of the crack tip. This yielded a simple and closed form equation for the stress intensity factor that included the effects of the ratio of the moduli of the layers and the relative layer thicknesses. A comparison of the stress intensity factor values from this equation and with finite element data indicated that the difference between these two data sets was small for most of the crack lengths and the modulus ratio of the layers. The maximum difference occurred at crack lengths approaching the interface and at high moduli ratios, but was less than 10%, in general. The equations were also modified to incorporate the effects of residual stresses that arise during cooling after laminate processing, on the stress intensity factor. A comparison of the analytical data with the finite element data obtained by imposing thermal and mechanical boundary loads on the laminate specimens indicated a good agreement. The present closed form approximate solutions may be useful in fracture analyses of finite-width laminates containing cracks.