Study on the crack problem of functional gradient slats type III

functional gradient materials;  cracks;  stress intensity factor;  Slats

Most of the existing literature research on the fracture problem of gradient materials assumes that the material properties are exponential functions or power functions of coordinates, and other function forms are rarely used. The author assumes that the reciprocal of the shear modulus of the functional gradient material is a linear function of the coordinates and the Poisson’s ratio is a constant, and the anti-plane crack problem of the functional gradient slats is studied. The Fourier integral transformation technology and transfer matrix method are used to solve the mixed edge value problem into a pair of singular integral equations, and the stress intensity factor of slab cracks under anti-plane loading is obtained by numerical solution of the singular integral equation, and the influence of crack relative size and material heterogeneity on the stress intensity factor is discussed.