NUMERICAL MODELLING OF CRACKS IN A FINITE RECTANGULAR MEDIUM

Abstract

The study of crack behaviour in infinite medium has been addressed in great detail by many researchers. Numerical formulations using complex potentials, finite element techniques and surface integral methods are described in many literature. The surface integral method using the mathematical theory of dislocations that a crack can be viewed as a continuous distribution of dislocation densities, provides a very efficient and convenient numerical formulation giving very accurate results. The problem of crack behaviour in a finite medium, which has immense practical applications in the electronic industry has not been fully explored yet. Even though simpler problems like single and multiple cracks have been studied, the problems of crack orientations, crack branching, etc. have not been addressed hitherto. In this study, a numerical model is developed to study the problems of crack orientations and crack branching in a finite medium and the solution is obtained using the surface integral method. The numerical model developed is very versatile in that the same model can be used to study infinite plate, infinite strip and finite plate problems with the same influence function for the dislocation densities. Suitable choice of the proportion of the crack length to the dimensions of the finite medium chosen and the ratio between the length and width of the finite medium would model infinite and finite mediums and infinite strip.