Abstract
The present paper deals with longitudinal fracture analysis of an inhomogeneous non-linear elastic rod with an internal longitudinal circular cylindrical crack. The rod is loaded in torsion. The cross-section of the rod is a circle. The rod exhibits continuous material inhomogeneity in radial direction. The complementary strain energy is considered in order to derive the strain energy release rate. Since the crack is internal, the torsion moments in the crack arms which are needed to obtain the complementary strain energy can not be determined explicitly. Therefore, the rod is treated as a statically undermined structure with one internal redundant (the torsion moment in the external crack arm is taken as a redundant). The solution to the strain energy release rate, derived in the present paper, is verified by considering the balance of the energy. The longitudinal fracture behavior of the rod with internal crack is compared with that of a rod with circular notch in the external crack arm. It is found that the strain energy release rate in the rod without notch is lower than that in the rod with notch in the external crack arm.
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