A viscoelastic fracture mechanics model for a functionally graded materials strip with general mechanical properties

In this paper, a viscoelastic fracture mechanics model is developed to investigate crack problem in viscoelastic functionally graded materials (FGMs) with general mechanical properties. Firstly, for the viscoelastic FGMs, the extensional relaxation functions and the relaxation functions of Poisson's ratio are assumed to take the form separable in space and time. Then, according to the correspondence principle, the crack problem of the viscoelastic FGMs is turned into a corresponding elastic crack problem of FGMs with general mechanical properties. In general, for actual FGMs with general mechanical properties, it is difficult to obtain analytical solutions of the governing differential equations. In order to circumvent this problem, a multi-layered model for the FGMs is developed. In the multi-layered model, the mechanical properties of each layer are described by exponential functions. Then, the corresponding elastic crack problem of the FGMs is turned into a group of singular integral equations which can be solved numerically. Based on the correspondence principle and Laplace transform, the stress intensity factors (SIFs) of viscoelastic FGMs can be determined by inverting the transformed SIFs. Some numerical examples are given to study influences of the various material, geometric parameters and loading conditions on the SIFs.