FINITE ELEMENT METHOD FOR CRACK PROBLEMS IN VISCOELASTIC FUNCTIONALLY GRADED MATERIALS

A finite element approach is developed to analyze the crack problems in viscoelastic functionally materials with arbitrary volume fraction distribution of constituents. By Laplace transform, the boundary problems are solved in phase domain based on graded element considering the heterogeneous of material and singular element describing the singularity of stresses near crack tips. The virtual crack closure technique modified by Rybicki et al. is applied to evaluate strain energy release rate, and the stress intensity factor is determined by means of nodal stress and strain energy release rate, respectively. The relationships of fracture parameters in time domain and phase domain are formulated, and the corresponding solutions in time domain are obtained by numerical Laplace inversion. The crack problem in viscoelastic functionally graded plate with edge crack parallel to graded direction is investigated. Two cases are involved in the analysis. The first one is for special functionally graded material with relaxation modulus expressed by the product of spatial variable function and time function. The second one is for general functionally graded materials of arbitrary volume fraction distribution of constituents. The validity of the finite element method proposed in the paper is verified in the first case on the basis of the elastic-viscoelastic correspondence principle. For the second case, Mori-Tanaka method is used to predict the effective relaxation modulus of functionally graded materials in phase domain. The results in creep loading condition show that the strain energy release rate increases with time elapsed, and the variation range depends on the volume content of viscoelastic constituent. The stress intensity factor may change over time due to the stress redistribution around crack tip originating from the heterogeneous viscoelasic property of graded material, and the time-dependent variation is influenced by the distribution pattern of volume fraction.