Study On Interface Crack Of Functionally Graded Materials

Cylindrical functionally gradient bimaterial is a new type of composite material which is composed of two or more kinds of materials and whose composition and structure show continuous gradient change.Because the bonding part of the bimaterial transmits the interaction between layers,stress concentration will occur at the interface end under a certain load.The structural properties of materials will be affected by stress concentration,which will lead to sudden cracking of the interface.Therefore,it is of great significance to study the crack problem of cylindrical functionally gradient bi-material at the interface.The plane problem of periodic cracks at the interface of cylindrical functionally gradient bi-material subjected to radial loading is studied.The methods used are the separation of variable method,singular integral method and undetermined coefficient method.The power function model is adopted for the shear modulus of the material parameters of functionally graded materials.First the boundary crack problem is transformed into the boundary value problem of the second-order partial differential equations with displacement and the governing equations of the inner and outer layers are transformed into an infinite series expression with four undetermined coefficients cosine.Using the method of undetermined coefficients,the introduction of dislocation density function,combined with cylindrical double material the continuity of the boundary conditions,the algebraic equations is obtained by solving singular integral equations of undetermined coefficients,with the help of the relation between the displacement function and radial shear force and displacement relationship of the double cylindrical function gradient material under the effect of radial stress near the interface crack tip stress field and displacement field of the series of expressions,and through the cauchy integral method of the stress intensity factor,and the numerical analysis was carried out on the stress intensity factor.The stress intensity factor of infinite functionally graded material with antiplane dynamic crack is studied.It is assumed that the shear modulus and density of functionally gradient materials change with negative exponential power,and the functionally gradient dynamic anti-plane crack problem is transformed into the boundary value problem of partial differential equation by means of the equilibrium differential equation of the anti-plane crack problem of functionally gradient materials and the boundary condition of the dynamic anti-plane crack problem.Due to the symmetry of the cracks,Laplace inverse transform is introduced.The dual integral is solved by Copson method,and the solution of dual integral equation is integrated by parts.The local stress field at the crack tip is obtained.At last,the semi-analytical solution of stress intensity factor is obtained by Laplace inverse transform method.