Investigation of a crack situated in a thin adhesive layer between two different isotropic materials

Abstract

A plane strain problem for a crack in a thin adhesive elastic-perfectly plastic layer between two different isotropic elastic materials under the action of remote mechanical loading is considered. First, the problem is solved numerically using the finite element method. The stress distributions at the crack continuations and the J-integral values are found. Further, the analytical investigation of the formulated problem is performed. It is assumed that the pre-fracture zones arise at the crack continuations and the interlayer thickness is negligibly small in comparison with the crack length. Modeling the pre-fracture zones by the crack continuations with unknown constant normal and shear cohesive stresses applied to faces of the crack, the problem of linear relationship is formulated and solved analytically. The unknown pre-fracture zone lengths and cohesive stresses are derived from the condition of stress finiteness at the new crack tips and the yielding criterion of the interlayer material. The method of definition of the normal stress co-directed with the crack faces which is used in the mentioned yielding criterion is discussed. Expressions for the crack opening displacement and for the J-integral are obtained in an analytical form as well. The values of the J-integral obtained by means of the analytical method are in a good agreement with the results of the finite element solution.