On Stress Intensity Factors of Multiple Cracks at Small Distances in 2-D Problems

Abstract

In the present work a method is proposed to predict stress intensity factors (SIFs) of strongly interacting cracks at spacings that are substantially smaller than crack lengths. The method is intended for applications where cracks are observed in stack-like/staggered arrangements as in damage patterns of some natural materials with dense lamellar microstructures. The new calculation procedure is inspired by the analytical method of Kachanov (1987) that due to its simplicity has shown to be a powerful tool for analysis of crack interactions. Although in 3-D the accuracy of Kachanov’s method remains good at quite close spacings, in 2-D problems it, however, quickly drops as the distance between cracks decreases, underestimating the effect of crack interactions, especially in ordered staggered arrangements. In this work we introduce new modeling assumptions that are suited for problems where stress fields have high gradients – a typical situation in the case of closely spaced parallel cracks. The accuracy of the method is examined on the example of two stacked cracks. The use of SIFs for estimation of material elastic compliance is also discussed.