Elastic-plastic fracture of functionally graded circular shafts in torsion

Analytical investigations were performed of a longitudinal crack representing a cylindrical surface in circular shafts loaded in torsion with taking into account the non-linear material behavior. Both functionally graded and multilayered shafts were analyzed. It was assumed that the material is functionally graded in radial direction. The mechanical behavior of shafts was modeled by using nonlinear constitutive relations between the shear stresses and shear strains. The fracture was studied in terms of the strain energy release rate. Within the framework of small strain approach, the strain energy release rate was derived in a function of the torsion moments in the cross-sections ahead and behind the crack front. The analytical approach developed was applied to study the fracture in a clamped circular shaft. In order to verify the solution derived, the strain energy release rate was determined also by considering the shaft complimentary strain energy. The effects were evaluated of material properties, crack location and material non-linearity on the fracture behavior. The results obtained can be applied for optimization of the shafts structure with respect to the fracture performance. It was shown that the approach developed in the present paper is very useful for studying the longitudinal fracture in circular shafts in torsion with considering the material non-linearity.