Mechanics for the Growth of Bridged Cracks in Composite Materials: Part II. Applications

Abstract

A fracture mechanics analysis valid for long cracks is applied to three crack-bridging problems that arise in the composites area, namely, (1) matrix cracking in perfectly bonded unidirectional composites, (2) transverse cracking in perfectly bonded cross-ply laminates, and (3) matrix cracking in unidirectional composites in which frictional slip occurs at fiber matrix interfaces governed by the constant shear-stress shear-lag model of stress transfer. The fracture mechanics analysis is also applied to the three models of cracking in composites for the case in which the preexisting crack can have any length. For the first two models, which assume that there is perfect interface bonding, and which lead to linear relationships between the bridging tractions and the crack opening displacement, it is necessary to solve a linear integral equation. A unique master curve is then derived relating the cracking stress to the length of the preexisting defect. The influence of material properties and nature of the composite (that is, whether unidirectional or cross-ply laminate) is through the value of two normalizing parameters having the dimensions of stress and length, respectively. The cracking stress tends to a nonzero limit as the crack length increases. The master curve takes into account the effect of thermal residual stresses. For the third case of frictionally slipping interfaces in a unidirectional composite, the relationship between the bridging tractions and the crack opening is nonlinear. A nonlinear integral equation is formulated which can be solved for any nonlinear crack-bridging relation. Numerical solutions are obtained by iteration, and for longer crack lengths, convergence problems have led to the need to use a quasi-linearization of the nonlinear integral equation. Although the analysis is of general applicability, it is applied only to the constant shear-stress shear-lag model of stress transfer at the fiber matrix interface. A unique master curve relating the matrix cracking stress to the length of the preexisting matrix crack is determined and is shown to be identical to results derived earlier using a technique that is specific to the shear lag model. The master curve takes into account the effect of thermal residual stresses. Consistency of the new general technique with earlier work is demonstrated. Consistency of the new nonlinear technique is also demonstrated by applying it in the linear case to generate the master curve described above for the case of perfectly bonded composites. The new general technique is also shown to be applicable when fiber fracture occurs.