| Summary: | Material surfaces in contact are often subjected to damages such as wear, contact fatigue and plastic deformation. Such surface damages not only affect surface performance but also lead to material failure. It is critical to predict these damages for the design of advanced functional materials. On the one hand, micro-defects such as inclusions, voids and cracks, which are formed at or beneath the surface during the material manufacturing process, can induce and increase surface damages. On the other hand, surface coatings are extensively employed to a variety of mechanical components, cutting tools and instruments to provide heat-, oxidation- and wear-resistance. Thus, this PhD research is proposed to investigate damages to contact surfaces of materials with internal defects. Firstly, the semi-analytic solution for the stress field of multiple cracks and inhomogeneous inclusions of arbitrary shape beneath a half-space surface subjected to prescribed loading has been developed. The interactions among all the inclusions and cracks are fully taken into account by a newly developed methodology that combines the equivalent inclusion method (EIM) and the distributed dislocation technique (DDT). Using the EIM, the inhomogeneous inclusions are modeled as homogeneous inclusions with unknown equivalent eigenstrains. Using the DDT, the cracks are modeled as a distribution of edge dislocations with unknown densities. Coupled governing equations with unknown equivalent eigenstrains and dislocation densities are established to satisfy the stress and strain conditions of inclusions and free surface traction conditions of cracks. A modified conjugate gradient method is developed to solve the governing equations and a fast Fourier transform algorithm is utilized to improve computational efficiency. Secondly, the semi-analytic solution for multiple cracks and inhomogeneous inclusions beneath a half-space surface subjected to contact loading has been developed. The solution takes into account not only the interactions among all the cracks and inclusions but also the interactions between them and the surface loading body. The original problem of an inhomogeneous half-space under contact loading is first converted into the new problem of a homogeneous half-space with unknown dislocation densities and equivalent eigenstrains using the DDT and EIM under contact loading. The new problem is then decomposed into the sub-problem of a homogeneous half-space with unknown dislocation densities and equivalent eigenstrains and the sub-problem of a homogeneous half-space under a contact loading with unknown surface contact area and pressure. Afterwards, an algorithm is developed to integrate the two sub-problems to determine the unknown dislocation densities and surface contact area and pressure. Thirdly, the semi-analytic solution for the inhomogeneous half-space contact problem has been extended to account for the crack propagation that is driven by surface cyclic contact loading and affected by the presence of subsurface inclusions. The maximum hoop stress criterion is incorporated for the prediction of crack propagation direction and the Paris law is applied to determine the crack propagation rate. Meanwhile, a zigzag crack path consisting of many small vertical and horizontal cracks is applied to model the arbitrary crack propagation path. This PhD research provides a framework for investigating inhomogeneous materials with internal defects under contact loading. It has potential applications to provide guidance for various engineering problems concerning material dissimilarity, surface damage and internal failure.
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