Longitudinal Fracture Analysis of an Inhomogeneous Stepped Rod with Two Concentric Cracks in Torsion

Abstract

Analysis of the longitudinal fracture behaviour of an inhomogeneous stepped rod with two concentric longitudinal
cracks is developed. The stepped rod has circular cross-section and exhibits continuous material inhomogeneity in radial direction.
The material has non-linear elastic mechanical behaviour. The rod is subjected to torsion. The two cracks present concentric
circular cylindrical surfaces. Thus, the fronts of the cracks are circles. The fracture is studied in terms of the strain energy release
rate by considering the complementary strain energy stored in the rod. Solutions to the strain energy release rate are derived at
different lengths of the two cracks. The balance of the energy is analyzed in order to verify the solutions. It is shown that the
solutions can be applied also when the stepped rod is inhomogeneous in both radial and length directions. The solutions are used
in order to evaluate the influences of the locations of the two concentric cracks in radial direction and the material inhomogeneity
in radial and length directions on the longitudinal fracture behaviour of the stepped rod.