PSI - Issue 33

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 416–427 Author name / Structural Int grity Procedia 00 (2019) 000–000

426

11

8  N t

1 E

rate at

is due to instantaneous recovery of part of the strain in the spring .

1 E

The influences of the crack length and the continuous change of along the beam thickness on the longitudinal fracture behaviour are investigated. For this purpose, calculations of the strain energy release rate are performed at various values of and ratios. The results obtained are illustrated in Fig. 4 where the strain energy release rate in non-dimensional form is plotted against at three ratios. The curve in Fig. 4 indicate that the strain energy release rate decreases with increasing of . It can also be observed in Fig. 4 that the strain energy release rate increases with increasing of ratio. The influences of crack location along the beam thickness and the continuous change of along the beam length are investigated too. One can get an idea about these influences from Fig. 5 where the strain energy release rate in non-dimensional form is plotted against at three values of ratio. One can observe in Fig. 5 that the strain energy release rate decreases with increasing of and ratio. The influences of continuous change of in the thickness direction of the beam is shown in Fig. 6 where the strain energy release rate in non-dimensional form is plotted against at three values of . It is evident from Fig. 6 that the strain energy release rate decreases with increasing of and . The effect of continuous change of along the thickness of the beam is also studied. The results of the study are shown in Fig. 7. One can observe in Fig. 7 that the strain energy release rate decreases with increasing of and . 4. Conclusions The influence of strain recovery upon unloading on longitudinal fracture of a continuously inhomogeneous viscoelastic beam is analyzed. The creep behaviour of the beam is treated by using a linear viscoelastic model. The modulii of elasticity and the coefficient of viscosity of the model are distributed continuously along the thickness and the length of the beam. A longitudinal crack is located symmetrically with respect to the mid-span. The time dependent longitudinal fracture of the beam is analyzed in terms of the strain energy release rate. For this purpose, time-dependent solutions to the strain energy release rate for both loading and unloading phases are derived by using the strain energy cumulated in the beam. Time-dependent solutions to the strain energy release rate are obtained also by considering the beam compliance for verification. Solutions are applied to study the variation of the strain energy release rate with time in both loading and loading phases. The study reveals that the strain energy release rate increases with time (this behaviour is due to the creep). Upon partial unloading of the beam the strain energy release rate decreases instantaneously. This finding is attributed to instantaneous recovery of part of the strain in the spring, . A parametric investigation of the time-dependent longitudinal fracture is carried-out. First, the effects of crack length and crack location along the beam thickness are investigated. It is found that the strain energy release rate increases with increasing of ratio (this ratio characterizes the crack length). The increase of ratio leads to decrease of the strain energy release rate (the ratio characterizes the location of the crack along the beam thickness). The effects of material inhomogeneity on the longitudinal fracture are investigated too. For this purpose, calculations of the strain energy release rate are carried-out at various values of material properties, , , , , and (these properties characterize the material inhomogeneity in thickness and length directions of the beam). The investigation reveals that the strain energy release rate decreases with increasing of , , , , and .  a l /  a l /  a l / UP E 1 F  h h / 1 F  h h / 1 2 E  F   F    F  1 E a l / h h / 1 h h / 1    F  F  F     F 

F 

F 