Study On Stress Intensity At Crack Tip Of Functionally Graded Materials

As a new type of composite material,functionally graded materials mainly appear in aerospace,nuclear reactors and other high-tech fields.Because the severe environment in the application process will increase the risk of material fracture,so avoiding fracture failure has become a key issue in the study of functionally graded materials.The fracture of materials is caused by cracks,and the rest and development of cracks are closely related to the stress field near the crack tip.Therefore,it is undoubtedly the most important thing in the research process to study the stress intensity factor at the crack tip,so that it is convenient to take timely measures to prevent crack propagation,which is of great significance to the study of intrinsic safety of equipment.In this paper,the functionally graded material of infinite plate under anti-plane shear load is studied.It is assumed that the physical parameters of the material change continuously in the form of negative exponential power function with arbitrary even times.On this basis,the crack tip stress performance of static crack,moving crack and dynamic crack is studied respectively.At first,the partial differential equation is transformed into a special ordinary differential equation by introducing Fourier cosine transform,Laplace cosine transform and variable substitution: the Bessel differential equation is modified,and a new displacement expression is obtained by using the general solution of Bessel differential equation,and the dual integral equations are obtained by combining stress expression with boundary conditions.Then the numerical solution results of the equations are derived by copson method,and the stress intensity factor expressions in three states are obtained.Finally,the influence of influencing parameters on stress intensity factor is analyzed by using the special solution obtained by mathematical software,which provides a theoretical basis for dealing with fracture problems later.