Elastic Contacting Mechanics With Different Types Of Interface Between Composites

The problems of contacting interface between two solids are related to many fields of mechanical transmissions,such as bearing supports,gear transmissions,frictional transmissions,etc.Research on bi-materials concerning inclusion and additive problems and layer-substrate systems are of fundamental importance in contact micromechanics.On one hand,analytical solutions to the elastic fields induced by eigenstrains,such as plastic strains,in materials subjected to different types of joints are important for developing numerical simulations of advanced materials.On the other hand,optimal designs of the layered materials require the understanding of their mechanical behaviors based on deformation and stress analyses.This research conducted analytical investigations and numerical analyses,based on the theories of micromechanics and the semi-analytical modeling(SAM),on the elastic fields of bi-materials due to inclusions or addites inside and/or contact loads outside.Several typical interfacial contact models and corresponding numerical algorithms have been developed in this work.Taking the application of some practical bi-materials into consideration,it is believed that the present solutions can provide a theoretical basis for the design of advanced materials and for the prediciton of their performance improvement.This thesis includes two portions.First,this thesis reports the derivation of a set of explicit integral kernels for the eigenstrain-induced elastic fields in two perfectly bonded or frictionlessly joined halfspace solids or bi-materials.The elastic responses caused by arbitrary inclusions inside one of the two joined half-spaces are solved for the cases of known Galerkin vectors for the inclusion in the half-space solid.Explicit closed-form solutions for a cuboidal inclusion with uniform eigenstrains are derived as the basic solutions,i.e.,the influence coefficients.By discretizing the arbitrarily shaped single or multiple inclusions into a number of small elementary cuboids,the entire elastic response to the inclusions can be obtained through summation of the contributions from all elements with the assistance of the fast Fourier transform algorithms for convolution or correlation involved in the solutions.Cases for the elastic fields subjected to a cuboidal or a spherical inclusion,and multiple cuboidal inclusions,are analyzed.These two sets of the formulas complete the series of analytical solutions for eigenstrain fields in half-spaces,and the results reveal that the joined half-space problems based on the Galerkin vectors under two types of boundary conditions,frictionless or perfectly bonded,are actually extensions of the halfspace problem.Secondly,the contact and stress studies of layer-substrate systems are essentials for understanding the mechanisms of layer delamination from its substrate and further interface fatigue due to relative slip.The present work aims to solve the contact problems involving a half-space material and an imperfectly joined elastic layer.The derivation work has obtained the analytical frequency-response funciton(FRF)expressions for the elastic fields of a layered half-space with four types of imperfect interface solid subjected to combined normal and sliding tractions,which enable the incorporation of the DC-FFT algorithm and the CGM for efficient numerical solutions to the elastic responses.More attentions are paid to the effects of the material Young's modulus mismatch,the layer thickness change,and friction coefficient variation on the elastic fields under different interfacial conditions.The maximum von Mises stresses and their locations are analyzed for different material and interfacial coefficient cases.The effects of interface properties on the contact behaviors of the material system are further investigated.