PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1237–1248 Author name / Structural Integrity Procedia 00 (2019) 000–000

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The fracture of the cantilever is analyzed also when the loading consists of an axial force, 10  F N, applied at the free end the external crack arm. In this loading case the variation of the non-dimensional strain energy release rate with the 1 2 / R R ratio is demonstrated in Fig. 5.

1 2 / R R . The loading consists of an axial force applied at the free end

Fig. 5. The non-dimensional strain energy release rate versus the ratio,

of the external crack arm.

As can be seen in Fig. 5, the strain energy release rate increases with increasing of 1 2 / R R ratio (this is due to the decrease of the wall thickness of the external crack arm). 4. Conclusions Longitudinal cylindrical cracks in non-linear elastic round bars loaded in tension are investigated. The longitudinal cracks under consideration are cylindrical surfaces. Thus, the crack front is a circle. It is assumed that the bars exhibit smooth material inhomogeneity in radial direction. Besides, the material exhibits non-linear mechanical behaviour that is treated by the Rambeg-Osgood constitutive law assuming that the modulus of elasticity varies continuously in radial direction. A general solution procedure to the strain energy release rate is derived for a crack located arbitrary in radial direction. The procedure is applied for studying the longitudinal fracture behaviour of a cantilever. The fracture in the cantilever is studied also by analyzing the energy balance in order to verify the solution to the strain energy release rate. A parametric analysis is conducted to examine how the material inhomogeneity in radial direction, material non-linearity, crack location in radial direction and the loading conditions affect the longitudinal fracture behaviour of the cantilever. The analysis reveals that the strain energy release rate gradually decreases with increasing of t p (it should be noted that t p is a parameter that regulates the material inhomogeneity in radial direction). It is found also that the non-linear mechanical behaviour of the inhomogeneous material induces