Partial Differential Equation Boundary Value Problem Of The Bending Fracture Of The Bimaterial

With the continuous development of science and technology, composite materials for its superior performance, are used in production widely, all areas of life. Its development situation marks a country's scientific and technological level, economic advantage and strength of society construction. Composite material is a combined material and its damage occurs from near the interface usually. Therefore, the research on mechanical properties and influence factors of the interface of composite material has importance significance for strength and reliability evaluation of combined material.Boundary element method, integral transform method and complex function method are the mathematical methods for the fracture problem of composite material. Many research results of composite material fracture were derived by the method of composite complex function. The stress fields of interface crack tip between two dissimilar orthotropic composite materials are obtained and no singularity. But the research for the fracture problem of bending of orthotropic bi-materials is seldom.In this paper, the stress fields of crack tip of interfacial cracks between dissimilar orthotropic composite materials under bending load are studied when the secular equations'discriminations are more than zero. By establishing complex functions on plane of z j, and constructing new stress function, the problem of fracture is transformed into solving boundary value problem of partial differential equation, on the basis of the boundary conditions two systems of homogeneous systems of linear equations with eight unknowns are obtained .The theoretical formulas of bending moment, torque, stress and strain, in which the stress field under pure bending, pure twisting and crinkle load crack tip of orthotropic bi-materials are obtained. Finally, the derived results are compared with FEM analysis.