Coatings play a critical role in controlling stress concentrations, mitigating crack–defect interactions, and enhancing the durability of tribological components under frictional loading. Understanding the interactions among cracks, coatings, and defects at the microscale is therefore critical for elucidating the underlying mechanisms and ensuring the design and reliability of coated materials in friction-related applications. This study investigates the effect of coating on the interaction between a multi-branched crack and arbitrarily shaped inhomogeneities or voids. The governing equations for coatings, inhomogeneities, voids and cracks are fully coupled into a unified model. Furthermore, the stress solutions for the crack with multiple branches at any angle and length are innovatively derived in the half plane with the help of the Distributed Dislocation Technique (DDT). Based on the numerical equivalent inclusion method (NEIM) and Fast Fourier Transform (FFT) algorithms, a semi-analytical scheme with a multi-stage iterative procedure is presented to obtain the final stress solutions and the stress intensity factors (SIFs). Benchmark examples compared with finite element method (FEM) results validate the numerical implementation. The proposed semi-analytical method overcomes limitations related to crack branching, inhomogeneity shapes, and mesh complexity, offering enhanced flexibility and computational efficiency.
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