Stress Intensity Factor Of Crack Tip Of Functionally Graded Material Plate

Gradient functional materials are produced as new materials developed to meet the requirements of practical production.It is assisted by ordinary materials,using composite technology to constantly change the composition elements,so that its composition and structure from one direction to the other direction of continuous change,and then get the function with the composition elements slowly change the material.it has applications in many fields,so it is essential to consider the safety of functional gradient materials.Therefore,it is particularly important to study the fracture behavior of this material.In this paper,we first consider the mechanical properties of the crack tip of infinite plate under the anti-plane load with static crack and moving crack,and then consider the mechanical properties of the infinite long crack tip under the anti-plane load with dynamic crack.the shear modulus is expressed by any negative exponential power function.By introducing cosine transform,the governing equation is transformed into a standard Bessel integral equation,and then the dual integral equation is obtained by substitution method.By means of Copson-Sih method,the numerical solution of dual integral equation is given.The crack tip of infinite plate and infinite strip gradient functional material is numerically analyzed Stress intensity factor.these results contribute to the study of crack fracture behavior in the material boundary.Finally,the influence of non-uniform coefficient,crack length,crack velocity and gradient corresponding to force intensity factors are mainly considered.