Study Of The Interfacial Fracture In A Cylindrical Bi-material

With the rapid development of modern science and technology,the cylindrical bi-material structure bonded by different materials has been widely used in many high-tech fields.The bonding parts transmit the interaction between layer and layer,and in certain under external loading,the interface end tends to appear the stress concentration phenomenon.When the degree of stress concentration is too high,there will be a sharp drop in the engineering quality of the material structure,or even sudden destruction,therefore,the study of interface crack problems of cylindrical bi-material has important theoretical significance.Through means of variables separation method and the method of undetermined coefficients,the authors respectively studied the cylindrical isotropic bi-materials planar interface crack problem under the stress of the radial load and the cylindrical function gradient bi-material anti-plane interface crack problem under the action of axial shear force.As to the cylindrical isotropic bi-material interface crack problem,it was studied respectively by two kinds of methods which constructed the displacement function and tectonic stress function.Firstly,the authors converted the interface crack problem to boundary value problems of partial differential equations.By using the variable separation method,the stated containing of undetermined coefficients of displacement function and stress function was expressed by the form of infinite series.Using the method of undetermined coefficients,with the aid of boundary conditions to establish the system of equations,then the authors got the solution of undetermined coefficients,thus the authors obtained the solution to boundary value problems for partial differential equations,using displacement function or the relation between stress function and the stress and displacement,the formal expression of stress of the cylindrical isotropic bi-material near the interface crack tip and displacement under the effect of radial stress,with the form of the series,was calculated.For cylindrical functionally graded material interface crack problem,converting mechanical problems to partial differential equations boundary value problem,the authors introduce a continuous variation of shearmodulus in diameter direction,by using the variable separation method and the method of undetermined coefficients,converting the boundary value problems of partial differential equations into algebraic problems.With the aid of boundary conditions and continuity conditions,the singular integral equation is deduced,and the solution of partial differential equations is obtained.Using the relation between displacement function and stress and displacement equation,the authors calculated the expression of cylindrical function gradient bi-material near the interface crack tip stress field and displacement field under the action of axial shear stress and the expression of stress intensity factor.