A modified semi-weight function method for SIF calculation of arbitrary inclined interface crack with both single complex-root and double real-root singularities

Abstract

An arbitrary inclined crack terminated at the interface usually has singularity of single complex-root or double real-root at crack tip. Currently, most methods of the stress intensity factor (SIF) calculation (e.g., Mellin transformation method, enrichment strategy method) only consider the single complex-root singularity, with difficulty in solving auxiliary functions. Although the scaled boundary method takes the double real-root singularity into account, it needs to set special finite elements at crack tip. In this study, based on the sub-matrix method and the reciprocal theorem of work, a modified semi-weight function method is proposed to calculate SIF of the arbitrary interface crack with consideration of both single complex-root and double real-root singularity, and also analyze the effect of bimaterial parameters (Gi), crack inclination angle (w) and relative length (a/L) on the SIFs. This modified method has the advantages of uniform auxiliary function (independent of crack size and external load) and simple finite element calculation (without special singularity element). Moreover, its validity is verified by good agreement of our calculation results with the available literature results and finite element results. The research results can provide a theoretical basis for anti-crack design of multi-layer caverns of the compressed air energy storage (CAES).