Generalized modified crack closure integral (GMCCI) and its application to interface crack problems

Abstract

It is well known that at an interface crack tip, mode mixity exists even under single mode loading situations. The modified crack closure integral (MCCI) technique together with finite element analysis has been extensively used in the past to estimate the mixed mode strain energy release rate (SERR) components at these crack tips. One of the aspects which attracted considerable attention in these problems is the convergence of SERR components as the virtual crack extension size is progressively decreased to zero. Such studies have proved to be computationally expensive as the problem has to be solved each time for various sizes of virtual crack extension. Also it was not possible to estimate the effect of preventing the crack face interpenetration on SERR estimates for large sizes of virtual crack extension greater than the contact zone size. To overcome these in this paper, a generalized modified crack closure integral (GMCCI) algorithm is proposed for four and eight-noded isoparametric quadrilateral elements, which can estimate the SERR components for several sizes of virtual crack extension through a single finite element analysis. This is achieved through a numerical integration of the crack closure integral (CCI) and for various sizes of virtual crack extension covering a large number of equal or unequal size elements ahead and behind the crack tip. The procedure developed is demonstrated with application to typical interface crack problems under remote tension and shear.