Damage evaluation of interfacial materials based on <i>M</i> -integral

The paper investigates the issue of damage in interfacial materials using M -integral. It demonstrates that the integration path of M -integral can cross the material interface. The numerical calculation of M -integral is realized by using domain integral method. The accuracy of the model was verified using analytical solutions. The factors affecting the M -integral of the interfacial material are explored with the help of finite elements. The study explores the effects of elastic modulus ratio, defects, and load on the M -integral, and proposes an equivalent damage calibration method based on the M -integral. The results suggest that once the elastic modulus ratio exceeds a certain threshold, it is no longer the primary factor influencing the M -integral. The equivalent defect for elastic problems is linked to the original defect configuration and elastic modulus ratio, and is independent of the external load. This study is important for calibrating damage levels of interfacial materials, designing for damage tolerance in structures, and assessing integrity.