Mechanics of dislocation, contact and fracture in multilayered and functionally graded materials

Abstract

Mechanical behaviors of multilayered and functionally graded materials (FGMs) with the presence of defects or under contact, are of great scientific interest and practical importance. This thesis focuses on theoretical development of mechanics of dislocation, contact and fracture in multilayered and functionally graded materials. The first part (Chapter 2 to 4) of the thesis is devoted to dislocation problems. Firstly, a new mathematical treatment of interfacial edge dislocation in multilayered medium is established. The treatment is featured by computational efficiency and accuracy regardless the total number of sublayers. It is applicable to dislocation of arbitrary shape and distribution profile. As special cases, the fundamental solution of axisymmetric ring dipole in multilayered elastic medium is also given. Then, the bi-materials solution is further derived for isolating the singularity and realizing the high precision computation of near source elastic field. It is shown that the present solutions can be analytically reduced many existing solutions of dislocation in homogenous and bi-material full space. In the second part (Chapter 5 to 7) of the thesis, three new contact problems in multilayered and functionally graded materials are examined. The first contact problem is frictionless contact between two dissimilar elastic spheres reinforced by FGM coating with both variable shear modulus and Poisson’s ratio. The contact problem is formulated and reduced to a nonlinear Fredholm integral equation of the second kind. Analytical solutions are derived for the mechanical quantities including the contact force and stress. Then, the non-linear contact force law for the spherical indention of an elastic substrate with FGM coating is explored. The nonlinear contact force law is explicitly expressed in form of extended Hertz’s solution with a correction factor. Additionally, this nonlinear contact force law for FGM coating is further incorporated into the Greenwood and Williamson model for analytically modeling of the contact of FGM coated rough surfaces. Next, an axisymmetric and frictionless contact problem of a coated elastic substrate pressed onto a rigid foundation with a rigid disc by remoted uniform compressive stress is examined. Such an incomplete contact problem is formulated as three-parts mixed boundary values problem (MBVP), which is then converted to a system of triple integral equations. Explicit analytical expressions for contact stress, resultant contact force and mode-I stress intensity factor are obtained. In the last part (Chapter 8) of the thesis, the fracture mechanics of a mode-I pressurized axisymmetric penny-shaped crack in graded interfacial zone with variable modulus and Poisson’s ratio is investigated. The crack problem is reduced to a Fredhom integral equation of the second kind. The solution procedure is also extended to address the Leonov-Panasyuk-Dugdale plastic crack. Analytical solutions in explicit form are derived for the full stress fields at the crack plane, SIF, COD, T-Stress and plastic zone for arbitrarily axisymmetric pressure in terms of the solution of the integral equations. It is shown the graded Poisson’ s ratio can have significant effects on the T-Stress and COD if the thickness of the interfacial zone is small.