The elastic-plastic contact problem of a ceramic coating on a half-space indented by an elastic sphere is solved by the use of the finite element method under a variety of conditions. An elastic-plastic material behavior with isotropic strain hardening was employed. Results for stresses, during loading and after unloading, on the surface and along the axis of symmetry are presented and formation of cracks is discussed in detail, emphasizing the influence of the thickness of coating. It is shown that the circumferential stress on the surface of the coating is highly tensile so that radial cracks are induced for a sharp indenter. But, for a blunt indenter, the radial stress is tensile and is always larger than the circumferential stress, leading to the formation of circumferential cracks. It is also shown that, in the case of a sharp indenter, radial cracks can be induced during unloading.

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