PSI - Issue 28

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

1246 10

crack location on the longitudinal fracture behaviour of the cantilever shown in Fig. 2. Formula (1) is applied to calculate the strain energy release rates which then are written in non-dimensional form as 0 2 / G G E R N  . It is assumed that 10  F N and 0.003 2  R m. The material inhomogeneity in radial direction is characterized by t p . In the calculations, 1 2 / R R ratio is introduced in order to characterize the crack location in radial direction. The influence of material inhomogeneity in radial direction on the longitudinal fracture behaviour is illustrated in Fig. 3 where the variation of the non-dimensional strain energy release rate with t p for / 0.3 1 2  R R , / 0.5 0  H E and 0.7  n is shown. Figure 3 demonstrates that the strain energy release rate decreases gradually with increasing of t p (the explanation of this phenomenon is found in the fact that the shaft stiffness increases with increasing of t p ).

Fig. 4. The non-dimensional strain energy release rate versus the external force magnitude, F . Curve 1 - at /

0.3 1 2  R R , curve 2 - at

/ 0.5 1 2  R R and curve 3 - at / 0.7 1 2  R R . Figure 3 presents also the variation of the non-dimensional strain energy release rate, calculated assuming linear elastic behaviour of the inhomogeneous shaft, with t p . It should be noted that the linear-elastic behaviour of the inhomogeneous material is modelled by substituting of  H in the general solution procedure for the strain energy release rate developed in section 2 of the present paper (this approach is based on the fact that at  H the Ramberg-Osgood constitutive law transforms in the Hooke’s law). Figure 3 indicates that the material non-linearity induces a significant increase of the strain energy release rate. In order to evaluate the influence of the loading on the fracture behaviour of the cantilever (Fig. 2), the variation of the non-dimensional strain energy release rate with the magnitude of the external force, F , at three 1 2 / R R ratios is shown in Fig. 4. It becomes obvious that the strain energy release rate decreases with increasing of 1 2 / R R ratio (Fig. 4). This behaviour is explained by the fact that the stiffness of the internal crack arm increases. Figure 4 demonstrates the quick increase of the strain energy release rate with the increase of the axial force magnitude.