A non-linear analysis of the mode II fracture in functionally graded materials was developed by using a beam configuration with two longitudinal cracks located symmetrically with respect to the centroid. The beam mechanical behaviour was described by a non-linear stress-strain relation. The non-linear fracture was studied by the J-integral approach. An analysis of the strain energy release rate was conducted with considering the material non-linearity in order to verify the J-integral non-linear analytical solution derived. The solution obtained is very convenient for parametric studies of mode II fracture in functionally graded beams exhibiting material non-linearity. The effects of material properties and crack location along the beam height on the non-linear fracture were evaluated. The results can be used for optimization of the beam structures with respect to the fracture performance.
Numerical modelling in non linear fracture mechanics