PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1212–1225 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3 1 / R R ratio.

that the strain energy release rate decreases with increasing of

4. Conclusions The longitudinal fracture behaviour of a continuously inhomogeneous beam that exhibits stress relaxation behaviour is analyzed in terms of the strain energy release rate. The beam has a circular cross-section of linearly varying radius in the length direction. A longitudinal circular cylindrical crack is located arbitrary in radial direction. The beam is continuously inhomogeneous in both radial and length directions.

3 1 / R R ratio (curve 1 – obtained by using the

Fig. 8. The strain energy release rate in non-dimensional form presented in a function of

viscoelastic model shown in Fig. 2a, curve 2 - obtained by using the viscoelastic model shown in Fig. 2b).

The stress relaxation is treated by using two linear viscoelastic models under constant applied shear strain. The shear modulii and the coefficients of viscosity are distributed continuously in radial and length directions of the beam. A time-dependent solution to strain energy release rate is obtained. The solution is verified by analyzing the energy balance. The investigation reveals that the strain energy release rate decreases with the time. The analysis indicates that the strain energy release rate decreases with increasing of 2 1 / R R and 3 1 / R R ratios. The increase of a l / ratio leads to increase of the strain energy release rate. The effects of the continuous variations of the shear modulii and the coefficients of viscosity in the radial and length directions of the beam on the longitudinal fracture behaviour are studied in detail. It is found that the strain energy release rate increases with increasing of b , f , n , s , h and m (the parameters, b , f , n , s , h and m , control the continuous distribution of the shear modulii and the coefficients of viscosity in the radial and length directions of the beam). The analysis shows also that the strain energy release rate obtained by using the viscoelastic model that consists of a linear spring connected consequently to a linear dashpot is lower in comparison to that obtained by the viscoelastic model consisting of a linear spring connected consecutively to a parallel combination of a second linear spring and a linear dashpot. References Butcher, R.J., Rousseau, C.E., Tippur, H.V., 1999. A functionally graded particulate composite: Preparation, Measurements and Failure Analysis. Acta Mater. 47, 259-268. Chikh, A., 2019. Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations. Frattura ed Integrità Strutturale 14, 115-126.