Modeling surface pressure, interfacial stresses and stress intensity factors for layered materials containing multiple cracks and inhomogeneous inclusions under contact loading

• Model for cracks and inclusions in layered materials under contact loading.
• Interactions among solid contact bodies, coating layer and structural defects.
• Solution for stress intensity factors at crack tips.
• Solution of surface pressure and interfacial stress field.

This work develops a semi-analytic solution for multiple cracks and inhomogeneous inclusions in a two-dimensional multi-layered material subject to contact loading. The solution not only considers the interactions among all the inclusions and cracks but also the surface deformation of the layered material caused by both the surface loading and subsurface inclusions and cracks. The solution strategy is to treat each material layer as an inhomogeneous inclusion with respect to the substrate and then utilize Eshelby's equivalent inclusion method to model each inhomogeneous inclusion as a homogenous inclusion with initial eigenstrain plus unknown equivalent eigenstrain, while using the distributed dislocation technique to model each crack of mixed modes I and II as a distribution of climb and glide dislocations with unknown densities. As a result, the original inhomogeneous or heterogeneous material problem is converted into a new homogenous material problem. The new problem is further decomposed into two sub-problems: a homogenous half-space contact sub-problem in which the unknown surface contact area and normal pressure and tangential traction within it are determined as an inhomogeneous crack and inclusion sub-problem in which the unknown equivalent eigenstrains and dislocation densities are determined. As the two sub-problems are correlated, an algorithm is developed to integrate them and all the unknowns are solved by means of iteration using the conjugate gradient method. The stress intensity factors of cracks are also obtained by the dislocation densities at the crack tips. An accurate description of the surface pressure, the subsurface elastic field of the layered heterogeneous materials and the stress intensity factors of subsurface cracks allows their fracture and delamination analyses to be conducted.