Bimaterial Bending Fracture Problem In The Complex Variable Method

The method of composite complex function is one of the mathematical methods for the problem composite material fracture. Many research results of composite material fracture were derived by the method of composite complex function. The analysis solutions of stress, strain, bending moment, twisting moment, composite material model I, model II; model III, under bending, under twisting, for the bending moment, torque, near the crack tip can be obtained. Recently years, the results for the problem of model I, model II and model mixed composite material interface crack fracture are obtained, the stress fields of crack tip no singularity. Sih.G.C and Chen. E.P studied the problem of isotropic bi-materials bend crack; the formulas of bending moment and twisting moment under bending were obtained.In this paper, the problem of bending of orthotropic bi-materials is studied. By using the composite complex function method of material fracture, a special deflection function is constructed; with the governing equation transformed into a class of generalized bi-harmonic equations, and on the basis of the boundary conditions two systems of homogeneous systems of linear equations with eight unknowns are obtained, from the solution of which two stress functions are derived which contain two singular exponents. The stress fields and displacement fields of semi-infinite interface crack tip orthotropic bi-materials can be obtained when the discriminations of characteristic equations are less than zero and use the coordinate transform, the calculation formulas for the bending moment, torque, stress and strains near the crack tip can be obtained. The stress fields of interface crack tip of orthotropic bi-materials no singularity. When the upper and the lower half-planes are of the same parameters, the stress field of crack of orthotropic composite materials can be obtained. The derived equation is verified with FEM analysis.Additionally, in this paper the J -integral near II interface crack tip of double dissimilar orthotropic composite materials was preliminary studied. Putting stress fields and displacement fields of crack tip into the generally formula of J -integral, the complex form of model II crack tip J -integral is derived. Because the integral relates with the path, one special computer formula of J -integral is given in the last.