Interface stress analysis of two bonded isotropic materials by finite difference method

Abstract

Bilayer composites, such as metal-metal, steel-polymer, concrete-steel etc., having different mechanical properties layer by layer are widely used for modern structures This thesis deals with the stress analysis of two dimensional bilayer composite materials. Materials under consideration are assumed to be perfectly bonded together. Finite difference method is used for the solution of two dimensional elastic problems. A numerical model for rectangular geometry based on displacement potential function has been developed to investigate the problem. In each layer of the composite the mechanical properties are isotropic. Finite difference scheme has been developed for the management of boundary conditions so that all possible mixed boundary conditions can be applied in any boundary points as well as at the interface of isotropic layers. Special numerical formulations yield to new formula structures are employed at the interface as well as adjacent boundary points of the interface. An effective programming code has been developed in FORTRAN language to solve the problems of bilayer composites.In order to compare the results by the present finite difference method, another numerical technique namely finite element method is used. Validation of the results is performed by using commercially available FEM package software. It is observed that the results agree well within the acceptable limit, which also confirms to the reliability of the finite difference method. At the interface, there is a single value for each displacement component but two different values for each stress component of the bilayer composite having different mechanical properties in each layer. Like as usual critical zone of a bilayer composite under mechanical loading, the interfacial zone is also a zone of critical stresses. Changing in Poisson’s ratio in any layer has significant effects on the results of all layers of the bilayer composite. Due to the mathematical expressions of stresses and displacements for two dimensional elastic problems, the study of the effects of Poisson’s ratio is intricate rather the study of the effects of Modulus of elasticity is straightforward. In general, the material having higher modulus of elasticity experiences higher stresses.