PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1226–1236 Author name / Structural Integrity Procedia 00 (2019) 000–000

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a notch is shown schematically in Fig. 4. It is obvious that due to the notch, the torsion moment in the external crack arm is zero.

Fig. 5. The strain energy release rate in non-dimensional form presented as a function of the torsion moment, T (curve 1 – for rod with circular notch, curve 2 – for rod without circular notch). The strain energy release rate for rod with notch is presented in non-dimensional form as a function of T in Fig. 5. In order to evaluate the influence of the notch on the longitudinal fracture behaviour, the strain energy release rate obtained for rod without notch is also presented in Fig. 5. It can be observed in Fig. 5 that the strain energy release rate for rod without notch in the external crack arm is lower in comparison to rod with notch. This finding is attributed to the fact that the torsion moment, T , is distributed on both crack arms in rod without notch. 4. Conclusions Longitudinal fracture behaviour of an inhomogeneous rod with one internal longitudinal crack is analyzed. The rod is made of non-linear-elastic material. The cross-section of the rod is a circle. The external loading consists of two torsion moments applied at the ends of the rod. The longitudinal crack presents a circular cylindrical surface. The internal and external crack arms are treated as rods of circular and ring-shaped cross-sections, respectively. The crack is located symmetrically with respect to the middle of the rod. Thus, only half of the rod is analyzed. The rod exhibits continuous material inhomogeneity in radial direction. The longitudinal fracture behaviour is studied in terms of the strain energy release rate by considering the complementary strain energy. In order to calculate the complementary strain energy, the torsion moments in the two crack arms are needed. However, due to the fact that the crack is internal, the torsion moments in the two crack arms can not be determined explicitly. Therefore, the rod is treated as a structure with one degree of internal static indeterminacy (the torsion moment in the external crack arm is taken as a redundant). The statically undetermined problem is solved by applying the theorem of Castigliano for structures which exhibit material non-linearity. The strain energy release rate is derived also by considering the balance of the energy for verification. The influence of 1 2 / R R and 0 / D B ratios and parameter, p , on the longitudinal fracture behaviour is investigated. The analysis reveals that the strain energy release rate has maximum at / 0.56 1 2  R R for the considered loading conditions and material behaviour. Also, it is found that the strain energy release rate increases with increasing of 0 / D B ratio. Increase of p leads to decrease of the strain energy release rate. The longitudinal