MATHEMATICAL MODELING OF MICRO INDENTATION OF A TRANSVERSELY ISOTROPIC HALF-SPACE WITH FUNCTIONALLY GRADED COATING BY A CONICAL INDENTER

Abstract eng:
The paper considers rigid punch with conical tip which is indented into a surface of an elastic transversely-isotropic half-space with a functionally-graded transversely-isotropic coating. Elastic moduli of the coating vary independently with depth according to arbitrary positive continuously differentiable functions. Integral transformation technique is used to construct a dual integral equation of the problem. Cases of free and fixed boundaries of the contact area are considered. Fixed boundaries of the contact correspond to the case when the cylindrical punch with conical tip is indented on a depth greater than height of the punch tip. Bilateral asymptotic method is used to construct the approximated analytical expressions for the contact stresses, indentation force and radius of the contact area (in case of free boundaries). Some aspects of modeling of micro- and nano- indentation experiments are discussed. Numerical examples are provided for a case of a hard homogeneous or functionally graded transversely isotropic coating.

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