A modified semi-weight function method for stress intensity factor calculation of a vertical crack terminating at the interface

•A modified semi-weight function method is proposed for calculating interface-crack SIFs.•The new unified auxiliary function is independent of the crack geometry and external load.•The interface-crack SIFs depends mainly on the ratio of E2/E1 rather than the single E1 or E2.•The ratio of K2/K1 is decreased with increase of the relative crack length (a/W).•The modified semi-weight function method can be verified by other available calculation results. The interfacial crack stress intensity factor (SIF) calculation plays an important role in the safety evaluation and anti-crack design for multilayer structures. The current analytical or numerical methods have difficulty of complicated auxiliary functions or special crack-tip singular elements. In this study, a modified semi-weight function method was proposed based on the submatrix method to calculate the SIFs of the crack vertical to and terminating at the interface of bimaterial (easily appears in compressed air energy storage) and verified by two calculation examples compared with the available literature results. The effects of bimaterial parameters (Ei, υi), relative crack length (a/w2) and outer integration path (r2) on the SIFs were also analyzed. Research results show that the SIFs (K1 and K2) are related to only the ratio of E2/E1 independent of the single E1 or E2, and they are increased with increase of a/w2. The reasonable range of r2 is rs