Contact stress analysis of layered solids with complex crack patterns

Hard protective coatings are widely used in modern tribology. However, coating performance under severe contact conditions is limited by their ability to withstand high-magnitude contact stresses. Fracture mechanics analyses of layered solids are important for gaining insight into the mechanisms of coating strength and endurance, and are crucial for understanding the effect of coating microstructure on its performance. A new approach to the numerical analysis of cracks in layered elastic solids is proposed here. It combines three-dimensional (3D) FFT with the theory of periodic eigenstrain and the conjugate gradient method. The new method is best suited for analyzing complex 3D crack patterns, such as those produced in protective coatings by roughness-induced contact stresses. Numerical examples illustrating the advantages as well as limitations of the new approach are presented. The method is then used to study the potential effect of coating layer structure on 3D crack propagation through the coating thickness.