Analysis of cylindrical delamination cracks in multilayered functionally graded non-linear elastic circular shafts under combined loads

This paper is focused on delamination fracture analyses of a multilayered functionally graded circular shaft under two loading combinations (centric tension and torsion, and bending and torsion) assuming non-linear elastic mechanical behavior of the material. The loading combinations under consideration generate mixed-mode II/III delamination crack loading conditions (the centric tension and bending generate mode II crack loading, while the torsion is responsible for mode III crack loading). The shaft is made by concentric longitudinal layers. The number of layers is arbitrary. Besides, each layer has individual thickness and material properties. The material in each layer is functionally graded in radial direction. Hyperbolic laws are used to describe the continuous variation of material properties in radial direction. A cylindrical delamination crack (the crack front is a circle) is located arbitrary between layers. The delamination fracture is studied in terms of the strain energy release rate by analyzing the energy balance. In order to verify the solution obtained, the strain energy release rate is derived also by differentiating the complementary strain energy with respect to the delamination crack area. Parametric investigations of the behavior of the cylindrical delamination crack are carried-out. The present paper is a contribution in the fracture mechanics of multilayered functionally graded non-linear elastic circular shafts under combined loads.