Fracture analysis of a viscoelastic functionally graded materials strip with a central crack

The fracture mechanical behavior of a crack in viscoelastic functionally graded materials (FGMs) is investigated. Firstly, the extensional relaxation modulus is assumed as separable form in space and time. Then, the crack problem of the viscoelastic FGMs can be turned into an elastic crack problem of FGMs by using correspondence principle. Applying Fourier transfom and boundary conditions, the elastic crack problem of FGMs is reduced to singular integral equations. The stress intensity factors (SIFs) can be obtained by solving the singular integral equations. Base on correspondence principle and Laplace transform, the SIFs of viscoelastic FGMs can be determined by inverting the transformed SIFs of correspondence elastic crack problem.