Theoretical and numerical analysis of stress and stress intensity factor in bi-material

Abstract

PurposeThe purpose of this paper is to evaluate theoretically and numerically the stress and stress intensity factor (SIF) at the time of propagation of the crack in bi-material. The problem is formulated using two thin materials which are bound by a cracked adhesive at the tip and having a micro-crack in one of these two materials.Design/methodology/approachThe plane stresses and the SIF will be determined as a function of two parameters (Poisson’s ratio and Shear modulus). The numerical analysis is carried out on a flat element, having a main crack in one of these ends, and a micro-crack varies in the vicinity of this main crack. The problem is analyzed by the finite element method and processed by computational software (ABAQUS).FindingsThe numerical and theoretical analysis allowed the author to determine and compare the values of plane stresses and SIF in each area of the material.Originality/valueThe theoretical analysis of SIF is based mainly on a mathematical calculation of equations of plane stresses; these equations are determined by development of complex analytical functions of bi-materials given by other researchers. Using the numerical method, several models are modeled by changing the micro-crack position relative to the main crack to determine the plane stresses and SIF for each position.