Micromechanical models based on hypersingular integro-differential equations for analyzing weak interfaces between dissimilar orthotropic materials
Date of Issue2015
School of Mechanical and Aerospace Engineering
This thesis is concerned with the development and formulation of micromechanical models for estimating the effective stiffness coefficients of a microscopically damaged interface between dissimilar orthotropic materials under antiplane and inplane deformations. The effective stiffness coefficients are important parameters in the macro-level spring-like model for a weak interface. The microscopically damaged interface is modeled as containing a periodic array of micro-cracks. Three different micromechanical models are proposed for the micro-cracked interface. The first model is the so called three-phase model which highly simplifies a period interval of the interface into three parts: (i) a representative micro-crack, (ii) perfectly bonded parts and (iii) effective regions with an unknown stiffness. The only details of the original micro-cracked interface captured in the three-phase models are the density of the micro-cracks and the average micro-crack length which is the length of the representative micro-crack. In the second model, all the micro-cracks are of the same length and are evenly distributed throughout the interface. Like the three-phase model, this model is a highly simplified one having only the density and the average length of the micro-cracks as micro-details of the micro-cracked interface. As may be expected, the values of the effective stiffness coefficients calculated using the second model are close to the ones predicted by the three-phase model. The third model is a more realistic one in which a period interval of the interface contains a large number of randomly generated micro-cracks. It is used to analyze statistically the effective stiffness coefficients of the micro-cracked interface. In addition to the density and average length of the micro-cracks, the statistical variations in the micro-crack length and the random positions of the micro-cracks are captured in such a micromechanical-statistical approach. The interfacial conditions in all the three micromechanical models are formulated in terms of hypersingular integro-differential equations. The displacement jumps across the damaged parts of the interface, which appear directly as unknown functions in the hypersingular integro-differential equations, are needed to estimate the effective stiffness coefficients of the micro-cracked interface. The micromechanical models above are used to estimate the effective stiffness coefficients of micro-cracked interfaces for each of the following problems: (i) an interface between two dissimilar half-spaces, (ii) an interface between a thin elastic layer and an elastic half-space, and (iii) a pair of parallel interfaces in an elastic trimaterial. Each of the problems under consideration is formulated in terms of hypersingular integro-differential equations. Numerical procedures for solving these hypersingular integro-differential equations and estimating the effective stiffness coefficients are outlined. The numerical results obtained from the micromechanical models demonstrate that the effective stiffness coefficients are influenced by the densities of the micro-cracks on the interfaces, the elastic moduli and the geometries of the materials. Numerical values of the effective stiffness coefficients are obtained for parametric studies for specific cases of the problems under consideration. The effects of various parameters, such as the micro-crack density and the variations in the micro-crack length, on the effective stiffness coefficients are examined in detail.
DRNTU::Engineering::Mechanical engineering::Mechanics and dynamics