Double control parameters of viscoelastic fracture for polymer graded materials

The time dependent characteristics of stress intensity factors (SIFs) and strain energy release rate for mode Ⅰ cracks in polymeric graded materials with arbitrary distribution of volume content of constituent materials under creep loading were investigated. The effective relaxation modulus was predicted based on Mori-Tanaka approach. In Laplace transform domain, the fracture parameters were determined by applying graded finite element method and virture crack closure technique, and their correspondent quantities in physical space were obtained with numerical Laplace inversion. The polymeric graded plate strips with edge crack parallel to graded direction were analyzed, and both far field homogeneous tension and three-point bending were considered respectively. The numerical results show that the strain energy release rate increases with time elapsed and its variation range is dependent on the volume fraction of viscoelastic constituent, and the intensity of stress field near crack tip varies with time due to stress redistribution originating from heterogeneous viscoelasic behaviour of graded materials. The SIFs increase with time when crack is located on the side with less volume content of viscoelastic constituent, and decrease on the contrary. The time-dependent variation range of SIFs is influenced by both the distribution of volume fraction of constituents and loading mode, and reaches the maximum value for the linear distribution of volume fraction. The increase or decrease of SIFs will speed or abate the damage in the process zone near crack tip. These results suggest that it is necessary to adopt both SIFs and strain energy release rate to control the time delayed fracture in polymeric graded materials.