PSI - Issue 33

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 402–415 Author name / Structural Integrity Procedia 00 (2019) 000–000

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delamination crack between layers 2 and 3 is analyzed. It can be observed in Fig. 7 that the strain energy release rate decreases with increasing of 31 q . Concerning the influence of  v , the curves in Fig. 7 show that the strain energy release rate increases with increasing of  v .

/ 3  L L   , curve 2 – at 0.5 1

2 1 / L L   ratio (curve 1 – at

Fig. 9. The strain energy release rate in non-dimensional form plotted against

/ 3  L L   and curve 3 – at 1.0 1

/ 3  L L   ). 2.0 1

The effects of 1 2 1 1 / L L E E and 1 3 1 1 / L L E E ratios are evaluated by performing calculations of the strain energy 1 2 1 1 / L L E E and 1 3 1 1 / L L E E ratios for the three-layered functionally graded cantilever beam configurations wit a delamination crack located between layers 2 and 3. The strain energy release rate in non dimensional form is plotted against 1 2 1 1 / L L E E ratio in Fig. 8 at three 1 3 1 1 / L L E E ratios. One can observe in Fig. 8 that the strain energy release rate decreases with increasing of 1 2 1 1 / L L E E ratio. The increase of 1 3 1 1 / L L E E ratio also leads to decrease of the strain energy release rate (Fig. 8). The influence of 2 1 / L L   and 1 3 / L L   ratios on the strain energy release rate is illustrated in Fig. 9 for the three-layered functionally graded beam with a delamination crack located between layers 2 and 3. The curves in Fig. 9 indicate that the strain energy release rate decreases with increasing of 2 1 / L L   and 1 3 / L L   ratios. 4. Conclusions Delamination of a multilayered functionally graded cantilever beam configuration that exhibits linear viscoelastic behaviour is analyzed in terms of the strain energy release rate. The beam under consideration is made of adhesively bonded longitudinal vertical layers. A delamination crack is located arbitrary between layers (the cross-sections of the two delamination crack arms have different widths). The material in each layer is functionally graded along the width of the layer. The visoelastic behaviour of the material is treated by using a linear viscoelastic model that consists of two springs and a dashpot. In each layer, the modulii of elasticity of the springs and the coefficient of viscosity of the dashpot are distributed continuously along the width of the layer. A time-dependent solution to the strain energy release rate is derived by considering the strain energy cumulated in the multilayered release rate at various