PSI - Issue 33

Victor Rizov et al. / Procedia Structural Integrity 33 (2021) 428–442 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

441

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continuously along the thickness of the beam. A time-dependent solution to the strain energy release rate that accounts for the stress relaxation is derived. For this purpose, the balance of the energy is considered. The curvatures and the coordinates of the neutral axes which are involved in the solution are determined by using the equations for equilibrium of the lower crack arm and the un-cracked beam portion. A time-dependent solution to the strain energy release rate is obtained also by applying the compliance method for verification. The solution to the strain energy release rate is used to investigate the evolution of the strain energy release rate with the time. The analysis reveals that the strain energy release rate decreases with the time (this behaviour is due to the stress relaxation). The influence of the crack location along the thickness of the beam on the strain energy release rate is evaluated. It is found that the strain energy release rate decreases with increasing of h h / 1 ratio (this ratio characterizes the crack location along the thickness of the beam). The influence of the material gradient on the strain energy release rate is also studied. The calculations indicate that the strain energy release rate increases with increasing of UP LW E E / and UP LW   / ratios. A time-dependent solution to the strain energy release rate is derived also for the case of material with different viscoelastic behaviour in tension and compression. The investigation shows that the strain energy release rate for material with different viscoelastic behaviour in tension and compression is higher than that for material with identical viscoelastic behaviour in tension and compression. The analyses developed in the present paper can be applied in design of functionally graded members and components which are subjected to stress relaxation. 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