Nonlinear Fracture of Functionally Graded Beams Under Mode II Loading Conditions

A theoretical study of Mode II fracture in functionally graded beams was carried out. A beam configuration with two symmetric longitudinal cracks was suggested in order to generate Mode II loading conditions. The beam mechanical behavior was described by nonlinear stress-strain relation. The fracture behavior was analyzed by applying the J-integral approach. Closed form analytical solutions were derived of the J-integral for two laws for variation of the modulus of elasticity along the beam height. Nonlinear analyses of the strain energy release rate were performed by considering the energy balance in order to verify the J-integral solutions. The results obtained can be applied to optimize the functionally graded beam structure with respect to the Mode II fracture performance. Also, the analytical solutions derived are very convenient for parametric studies of nonlinear fracture behavior of functionally graded beams. The present paper contributes towards the development of nonlinear fracture mechanics of functionally graded materials.