PSI - Issue 28

Victor Rizov et al. / Procedia Structural Integrity 28 (2020) 1226–1236 Author name / Structural Integrity Procedia 00 (2019) 000–000

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3. Numerical results In the present section of the paper, numerical results are reported in order to evaluate the influences of material inhomogeneity, crack location in radial direction and material non-linearity on the longitudinal fracture behaviour of the rod with internal crack. For this purpose, calculations of the strain energy release rate are carried-out by applying the solution to the strain energy release rate (27). The strain energy release rate is presented in non-dimensional form by using the formula   0 2 / G G B R N  . It is assumed that 0.004 0  R m and 10  T Nm. The crack location in radial direction is characterized by 1 2 / R R ratio. The material inhomogeneity is characterized by the parameter, p .

Fig.4. Geometry and loading of inhomogeneous rod with notch in the external crack arm.

The influence of material inhomogeneity on the longitudinal fracture behaviour of the rod is illustrated in Fig. 2 where the strain energy release rate in non-dimensional form is presented as a function p at / 0.8 0  D B and 0.7  n . The curves in Fig. 2 show that the strain energy release rate decreases with increasing of p . This finding is attributed to the fact that the stiffness of rod increases with increasing of p . In order to evaluate the influence of the material non-linearity on the longitudinal fracture, the strain energy release rate obtained assuming linear-elastic behaviour of the inhomogeneous rod is presented also in Fig. 2 for comparison with the non-linear solution. It should be noted that the linear-elastic solution to the strain energy release rate is derived by substituting of 0  D in the non-linear solution (27) since at 0  D the stress-strain relation (7) transforms into the Hooke’s law assuming that B is the shear modulus. One can observe in Fig. 2 that the strain energy release rate increases when the rod exhibits material non-linearity. The influences of crack location in radial direction and 0 / D B ratio on the longitudinal fracture of the rod are also evaluated. For this purpose, the strain energy release rate in non-dimensional form is presented as a function of 1 2 / R R ratio in Fig. 3 at three 0 / D B ratios. The curves in Fig. 3 indicate that the strain energy release rate has maximum at / 0.56 1 2  R R for the considered loading conditions and material behaviour. It can also be observed in Fig. 3 that the strain energy release rate increases with increasing of 0 / D B ratio. The longitudinal fracture of the inhomogeneous non-linear elastic rod loaded in torsion is analyzed also assuming that a circular notch of depth, 1 2 R R  , is introduced in the external crack arm in the middle of the rod. The notch divides the external crack arm in two symmetric parts of length, a , each. The geometry and loading of the rod with