Crack In Rectangular Planar Dual Material

In this dissertation, the problem of a rectangular planar crack in bimaterial is studied systematacially by means of the method of hypersingular integral equation in three-dimensional fracture mechanics. The effect of the boundary on the stress intensity factors is discussed in detail. The main contributions of the dissertation are as follows:(1) The elasticity point-force solutions for perfectly bonded elastic halfspaces in literatures are further studied. The compact formulae of displacements and stresses are given, which can be used as Green function in the boundary integral equation method. It contributes reference to study mechanics questions in bimaterial by means of the method of hypersingular integral equation.(2) Based on the fundamental solution, the problem of a rectangular planar crack contained in one material is investigated by means of the method of boundary integral equation. The hypersingular integral equations of a rectangular crack which is perpendicular to the interface are obtained. Then, according to the stress field near the smooth crack front, the formulae determining the stress intensity factors with the displacement discontinuities on the crack surface are proposed. And the displacement discontinuity of crack surface is approximated with the product of the fundamental density function and polynomials. Then its numerical method is presented. So the stress intensity factors can be obtained by the displacement discontinuities. Through calculating the typical questions, the effect of different interface, different distance between crack and interface and different aspect ratio of crack on the stress intensity factors is discussed in detail. Based on the method of the largest stress intensity factor computed by square root of crack's area, which was put forward by Murakami, the effect of the interface on the stress intensity factors is discussed.(3) About the problem of a rectangular planar crack vertically terminating at a bimaterial interface, the hypersingular integral equations are given. In the theoretical analysis, the stress singularities near the crack front at the interface are studied in detail. It can be derived with domain-part analysis. In the numerical method the displacement discontinuity of crack surface is approximated with the product of the fundamental density function and polynomials. So the stress intensity factors can be obtained by the displacement discontinuities. Through calculating the typical questions, the effect of different interface and different aspect ratio of crack on the stress intensity factors is discussed in detail.