Crack and contact problems in graded materials.

摘要

Graded materials, also known as functionally graded materials (FGMs) are generally multi-phase composites with continuously varying thermomechanical properties. They are primarily used as coatings and interfacial zones and they tend to reduce residual stresses and provide protection against severe thermal and mechanical environments. In recent years, functionally graded materials are proposed to be used as coatings or bulk materials to enhance the resistance of structural components to tribological damage. Failure in tribological applications results from high stresses at the contact surfaces and can occur in the form of cracking in brittle materials and plastic deformation in ductile materials. The main cracking patterns in brittle surfaces subjected to contact stresses are observed to be Hertzian cracking in spherical indentation and surface cracking due to frictional sliding contact.; The main objective in this study is to examine the surface crack problem in a graded medium subjected to frictional sliding contact by a rigid stamp of arbitrary profile. First, the problem of surface cracking in a homogeneous medium due to sliding contact is examined. Using the equations of elasticity for a homogeneous semi infinite medium the fracture and contact problems are formulated in coupled form and solved numerically to compute the mixed mode stress intensity factors and contact stresses. The exact elasticity formulation developed to formulate the crack/contact problem in a homogeneous medium is then extended to formulate crack and contact problems in a graded medium. First a surface crack problem in a graded material with known crack surface tractions is solved. This problem is reduced to two uncoupled singular integral equations which are solved numerically. Finally, the crack problem in a graded medium due to sliding contact is examined. This problem is reduced to a system of three singular integral equations which is solved using a collocation method. The results obtained consist of mainly, the effect of the material nonhomogeneity parameter and friction coefficient on the mixed mode stress intensity factors at the crack tip, contact stresses and required contact force.