PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1212–1225 Author name / Structural Integrity Procedia 00 (2019) 000–000

1222

11

D D 1 / 

N t tG 

. The curves in Fig. 3 indicate that the strain energy release rate decreases with the time. The strain 0  t in Fig. 3 is due to the instantaneous stress that is modelled by the spring in the viscoelastic 2 1 / R R ratio characterizes the continuous variation of the cross section along the beam length. One can observe in Fig. 3 that the strain energy release rate decreases with increasing of 2 1 / R R ratio. energy release rate at model depicted in Fig. 2a. It should be noted that

Fig. 5. The strain energy release rate in non-dimensional form presented in a function of the non-dimensional time according to the viscoelastic model shown in Fig. 2b (curve 1 – at / 0.4  a l , curve 2 – at / 0.6  a l and curve 3 – at / 0.8  a l ). The influence of the continuous variation of the coefficient of viscosity, 1  , in radial and length directions of the beam on the longitudinal fracture behaviour is evaluated by using the viscoelastic model shown in Fig. 2a. For this purpose, the strain energy release rate in non-dimensional form is presented in a function of b in Fig. 4 at three values of f . One can observe in Fig. 4 that the strain energy release rate increases with increasing of values of b and f . The variation of the strain energy release rate with the time caused by the stress relaxation is studied also by applying the linear viscoelastic model depicted in Fig. 2b. The influence of the crack length on the strain energy release rate is analyzed too (the crack length is characterized by a l / ratio). The strain energy release rate in non dimensional form is presented in a function of non-dimensional time in Fig. 5 at three a l / ratios. It is evident from Fig. 5 that the strain energy release rate decreases with time. It can also be observed in Fig. 5 that the strain energy release rate increases with increasing of a l / ratio. The effect of the continuous variation of the coefficient of viscosity, 2  , along the radius and length of the beam on the longitudinal fracture behaviour is investigated by using the viscoelastic model shown in Fig. 2b. For this purpose, the strain energy release rate in non-dimensional form is presented in a function of n in Fig. 6 at three values of s . The curves in Fig. 6 show that the strain energy release rate increases with increasing of n and s . The influence of the continuous variation of the shear modulus, 02 G , in radial and length directions of the beam on the longitudinal fracture behaviour is evaluated. The viscoelastic model shown in Fig. 2b is used. In order to evaluate this influence, the strain energy release rate in non-dimensional form is presented in a function of h in Fig. 7 at three values of m . It can be observed in Fig. 7 that the strain energy release rate increases with increasing of h and m .