A new semi-analytic method for calculating the thermal-mechanical coupling stress intensity factor of interfacial crack

The interfacial crack thermal-mechanical coupling stress intensity factor (SIF) calculation plays an important role in anti-cracking design and safety assessment of compressed air energy storage (CAES) multi-layer cavern. In current SIF calculation method, there is no consideration of thermal-mechanical coupling effect caused by the difference between the singularity of stress field (lambda) and temperature field (lambda T). In this study, a new semi-analytic method for calculating the thermal-mechanical coupling SIF of interfacial crack is established based on a new thermal-mechanical coupling Williams expansion for the cases of both insulated and constant temperature. The singularity index of temperature field at the crack-tip is dependent on the material parameters (heat conduction coefficient ki) for the crack perpendicular to and terminated at the interface, but independent on the material parameters (ki) for the crack located at the interface. The larger the difference of bi-material's heat conduction coefficient (ki), the larger the value of stress field when the crack is located on the side of larger Young's modulus (Ei) or on the side of lower ki. The semi-analytic method is degenerately verified by available literature results (without thermal-mechanical coupling term) and completely verified by finite element results (with thermal --mechanical coupling term), which can provide a theoretical basis for anti-cracking optimal design of CAES multi-layer caverns under thermal-mechanical loading condition.