Stress intensity solutions for the bending of thin plate with a hole edge crack and a line crack

A problem of an infinite plate with a hole edge crack and a line crack subjected to remote bendings is studied in this paper, in which the crack surfaces are considered to be free from traction. By using the principle of superposition, the original problem is converted into two particular hole edge crack problems. The remote bendings is applied in the first problem. Meanwhile, in the second problem, it is assumed there is a continuous distribution of dislocations along the crack line, in which the induced tractions along the line are opposite to those obtained in the first problem. Then the solution can be formulated by a singular integral equation with the employment of the Green's function of a point dislocation of thin plate bending problem. Here the point dislocation is defined as the difference of the deflection angle of the thin plate. The closed form solution of the first problem, as well as the Green's function of the point dislocation, is obtained by means of complex stress functions approach and the rational mapping technique. Then the singular integral equation is solved numerically. We also obtain the expression of the stress intensity factors in terms of the dislocation density function. Finally, some numerical examples are calculated to investigate the interaction between the square hole edge crack and the-line crack in the infinite plate under a remote bending.