Fracture analysis of a inhomogeneous beam with two concentric longitudinal cracks


  • Victor Rizov University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria


Inhomogeneous material, Longitudinal fracture, Two circular cylindrical cracks, Varying cross-section, Material non-linearity


The present paper is concerned with analysis of the fracture behaviour of inhomogeneous cantilever beam configuration with two concentric longitudinal cracks. The beam has a circular cross-section with linearly varying radius along the beam length. Besides, the beam exhibits continuous material inhomogeneity in radial direction. The fracture is analyzed in terms of the strain energy release rate assuming non-linear mechanical behaviour of the material. For this purpose, solutions to the strain energy release rate are derived by considering the balance of the energy. Two cantilever beam configurations with different lengths of the longitudinal cracks are analyzed. Besides, the two cracks are located arbitrary in radial direction. The longitudinal fracture behaviour of the beam is analyzed also by considering the complementary strain energy for verification. The solutions to the strain energy release rate are used to investigate the influence of the varying radius of the cross-section along the length of the beam on the longitudinal fracture behaviour. The effects of the crack lengths and the location of the two concentric cracks in radial direction on the fracture are also studied. The influences of the loading conditions of the beam and the material inhomogeneity in radial direction on the fracture behaviour are evaluated too.