PSI - Issue 47

Victor Rizov / Procedia Structural Integrity 47 (2023) 3–12 Author name / Structural Integrity Procedia 00 (2019) 000–000 9 energy release rate in non-dimensional form is plotted against q by using solutions (24), (29) and (30). It can be observed in Fig. 2 that the strain energy release rate decreases with increasing of q . 11

Fig. 5. The strain energy release rate in non-dimensional form plotted against M F / ratio (curve 1 – at

1.2  p , curve 2 - at

1.4  p

and curve 3 - at 1.6  p ). The curves in Fig. 2 indicate that the strain energy release rate derived assuming increase of crack 1 and crack 3 is higher and lower, respectively. The strain energy release rate derived assuming increase of crack 2 has intermediate value. In order to evaluate the effect of the location of crack 1 in radial direction on the fracture, the strain energy release rate in non-dimensional form is plotted against 1 4 / R R ratio in Fig. 3 by using the solution derived at increase of crack 1. One can observe in Fig. 3 that the strain energy release rate decreases with increasing of 1 4 / R R ratio. The strain energy release rate obtained assuming linear viscoelastic behaviour is also plotted in Fig. 3 (the linear viscoelastic solution is obtained by substituting of 1  H and 1  p in the non-linear solution since at 1  H and 1  p the term,     p H B / 1 1    , in non-linear relation (1) transforms into the Hooke’s law). The curves in Fig. 3 show that the non-linear viscoelastic behaviour leads to increase of the strain energy release rate. The strain energy release rate in non-dimensional form is plotted against H in Fig. 4 at three values of 4 R . It can be observed in Fig. 4 that strain energy release rate decreases with increasing of H . Increase of 4 R leads also to decrease of that strain energy release rate (Fig. 4). The influence of material property, p , on the fracture is analyzed too. For this purpose, the strain energy release rate in non-dimensional form is plotted against M F / ratio in Fig. 5 at three values of p . One can observe in Fig. 5 that the strain energy release rate increases with increasing of p . 4. Conclusions An inhomogeneous beam with three longitudinal circular cylindrical cracks is analyzed. The cross-section of the beam is a circle. The beam exhibits continuous material inhomogeneity in radial direction. Besides, the material has non-linear viscoelastic behaviour. The loading consists of an axial force and a bending moment. Solutions to the strain energy release rate are derived by analyzing the balance of the energy. The solutions are controlled by