A novel interaction integral method for extracting key fracture parameters of interfacial cracks in composite materials containing inhomogeneous initial thermal strain

Interfacial fracture in advanced heterogeneous structures subjected to localized thermal processes represents a critical challenge in structural integrity analysis, particularly when spatial temperature gradients induce complex, inhomogeneous initial thermal strain fields that significantly alter crack-tip singularities. A novel interaction integral framework is derived to extract the stress intensity factors at interface crack tips under inhomogeneous initial thermal strain. The formulation explicitly incorporates the contributions of spatially varying thermal strain and material inhomogeneity, ensuring strict domain independence for both continuous and discontinuous strain fields across multi-material interfaces. Following rigorous verification of result accuracy and integral conservation against benchmark problems, the methodology is applied to investigate the synergistic effects of strain gradients and material architecture on fracture response. Analysis of diverse initial strain distributions reveals a significant reversal phenomenon, wherein higher strain concentrations transition from promoting crack opening in short-crack regimes to inducing a shielding effect in long cracks as ligament constraints attenuate. The study further extends to multi-layered composite systems, quantifying the synergistic regulation of material mismatch and functional gradients on crack-tip parameters while identifying the decisive role of local thermal hotspot positioning in governing fracture driving forces. This interaction integral framework provides a robust computational tool for structures with complex inhomogeneous initial fields, facilitating advanced fracture assessment and crack-resistant design of composites.