PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 103–114 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

113 11

observed in Fig. 5 that when  increases, the strain energy release rate increases too. The increase of n generates reduction of the strain energy release rate (Fig. 5). The reason for this behaviour is that the time in which the temperature is equal to its maximum value, 1 T , decreases with increasing of n . The effects of the parameters, m and  , on the strain energy release rate are evaluated too. The results obtained are shown in Fig. 6. The inspection of Fig. 6 reveals that the strain energy release rate reduces when m increases. It can also be observed in Fig. 6 that when  increases, the strain energy release rate increases too.

  E E / ratio (curve 1 – at

/      , curve 2 – at 0.5 1

/      1

1.0

Fig. 7. Variation of the strain energy release rate with

1

1

2.0 / 1 1      ).

and curve 3 – at

One can examine the influence of the material inhomogeneity on the strain energy release rate in Fig. 7. The curves in Fig. 7 show that the strain energy release rate reduces when   E E / and     1 1 / ratios increase. 4. Conclusions Longitudinal fracture in a viscoelastic inhomogeneous beam configuration subjected to both external mechanical loading and periodically varying temperature is analyzed. The beam under consideration is simply supported. A longitudinal crack is situated near the left-hand end of the beam. The mechanical loading consists of an external bending moment applied at the free end of the upper crack arm. This bending moment varies smoothly with time. The beam is continuously inhomogeneous in both longitudinal and transversal directions. Hence, the modulus of elasticity and the coefficients of viscosity of the components of the viscoelastic model vary continuously along the length and thickness of the beam. The time-dependent modulus of elasticity of the viscoelastic model is derived. For this purpose, first, the constitutive law of the model is obtained. Then the modulus is recalculated in order to take into account the effect of temperature. This modulus is used when deriving the strain energy release rate by applying the compliance method with considering the temperature and the mechanical loading. The strain energy