Delamination fracture analysis of an elastic-plastic functionally graded multilayered beam

Background: A theoretical study was performed of mode II delamination in a multilayered functionally graded beam configuration with considering the material non-linearity. Methods: The fracture was analysed by the J-integral approach. Two laws (quadratic and exponential) for variation of the modulus of elasticity along the beam height were applied. The J-integral closed form non-linear analytical solutions derived were verified by performing analyses of the strain energy release rate with taking into account the material non-linearity. Parametric investigations of mode II non-linear fracture were conducted. Results: It was found that material non-linearity leads to increase of the J-integral value. Therefore, the non-linear behaviour of material has to be taken into account in fracture mechanics-based safety design of functionally graded structural members. Conclusions: The present paper contributes to the understanding of non-linear fracture in functionally graded materials. The results obtained can be used for optimization of functionally graded beam structures with respect to the fracture performance.