PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 88–100

99

Author name / Structural Integrity Procedia 00 (2019) 00 – 00

12

1 3 / p p E E ratios. It can be observed in Fig. 10 that the strain energy release rate decreases with

Fig. 10 at three

1 3 / p p E E ratios.

1 3 / p p   and

increasing of

Finally, the influence of the viscoelastic material behaviour on the delamination fracture is evaluated by using the rheological model shown in Fig. 1d. The three-layered cantilever beam with a delamination crack located between layers 2 and 3 is studied. The time-dependent delamination fracture behaviour is examined in Fig. 11 where the strain energy release rate in non-dimensional form is plotted against the non-dimensional time at three 3 1 /   ratios. The curves in Fig. 11 indicate that the strain energy release rate increases with the time. Here again the strain energy release rate at 0  t is induced by the instantaneous elastic strain simulated by the spring j E . The increase of 3 1 /   ratio leads to decease of the strain energy release rate (Fig. 11). The delamination fracture behaviour obtained by using the four rheological models (Fig. 1) for a given time is compared in Fig. 12 where the strain energy release rate in non-dimensional form is plotted against the bending moment, M . The three-layered cantilever beam configuration with a delamination crack located between layers 2 and 3 is considered. It is evident from Fig. 12 that the highest strain energy release rate is obtained by using the viscoelastic model shown in Fig. 1d. One can observe in Fig. 12 that the lowest strain energy release rate is found when the viscoelastic model shown in Fig. 1b is used. It can also be observed in Fig. 12 that the strain energy release rates obtained by using the viscoelastic models shown in Fig. 1a and Fig. 1c take interstitial positions. 4. Conclusions The influence of the viscoelastic material behaviour on the delamination fracture in multilayered beam configurations which are subjected to creep is analyzed. The fracture behaviour is studied in terms of the strain energy release rate. An approach for deriving of the strain energy release rate is developed by considering the balance of the energy. The viscoelastic behaviour of the material is treated by applying four linear viscoelastic models for a constant applied stress. These models are constructed from different combinations of linear springs and dashpots. The approach is used to analyze the delamination fracture in a multilayered cantilever beam configuration subjected to creep. For verification, the strain energy release rate in the multilayered cantilever is obtained also by differentiating the strain energy with respect to the delamination crack area. The analysis reveals that due to the creep the strain energy release rate increases with the time. It is found also that the strain energy release rate decreases with increasing of 2 1 /   , 3 1 /   , 1 2 / p p   , 1 3 / p p   , 2 1 / E E , 1 2 / p p E E and 1 3 / p p E E ratios. The investigation indicates that for a given time the strain energy release rate obtained by using the viscoelastic model constructed through consequently connection of a linear dashpot, a linear spring and a parallel combination of a second linear spring and a second linear dashpot is higher than the strain energy release rates obtained by the other three viscoelastic models considered in the present paper. The lowest strain energy release rate is found when the viscoelastic material behaviour is treated by applying a model consisting of a linear spring that is mounted parallel to a linear dashpot. Acknowledgements The present study was carried-out with the financial support of the Research and Design Centre (CNIP) of the University of Architecture, Civil Engineering and Geodesy (UACEG), Sofia (Contract BN – 217/2019).

References

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