PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 63–74 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

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energy release rate in non-dimensional form is plotted against  at three a l / ratios for / . The curves in Fig. 4 indicate that the strain energy release rate increases with increasing of  (this behaviour is due to decrease of the beam stiffness). It can be observed also in Fig. 4 that the strain energy release rate decreases with increasing of a l / ratio (this finding is attributed to increase of the radius of the beam cross-section in which the crack front is located since the radius increases continuously from the free end towards the clamped end of the beam). The influences of 0 / Q L ratio and the location of the crack in radial direction on the longitudinal fracture behaviour of the cantilever beam are also analyzed. The crack location in radial direction is characterized by 3 1 / R R ratio. One can get an idea about the influence of 0 / Q L and 3 1 / R R ratios on the longitudinal fracture behaviour from Fig. 5 where the strain energy release rate in non-dimensional form is plotted against 0 / Q L ratio at three 3 1 / R R ratios. The curves in Fig. 5 show that the strain energy release rate decreases with increasing of 3 1 / R R ratio. Increase of 0 / Q L ratio leads to increase of the strain energy release rate (Fig. 5). Longitudinal fracture of inhomogeneous beams of continuously varying radius of the cross-section along the beam length is analyzed. Beams are loaded in tension by axial forces. A longitudinal circular cylindrical crack is located arbitrary in radial direction. The internal and external crack arms are treated as beams of circular and ring-shaped cross-section, respectively. The external radius of the cross-section of the external crack arm varies continuously along the crack length. The beams under consideration exhibit continuous (smooth) material inhomogeneity in radial direction. Besides, the material has non-linear elastic mechanical behavior. The longitudinal fracture is studied in terms of the strain energy release rate. A general approach for analyzing the strain energy release rate is developed by considering the energy balance. The approach is applicable at arbitrary law for continuous variation of the radius of the beam cross-section along the beam length. The law for describing the continuous variation of material properties in radial direction is also arbitrary. The approach is applied to analyze longitudinal fracture in an inhomogeneous cantilever beam configuration loaded in tension by two axial forces. For verification, the strain energy release rate is derived also by considering the complementary strain energy. The solution to the strain energy release rate is used to investigate the influence of the continuously varying radius of the beam cross-section, the crack length, the material inhomogeneity in radial direction, the material non-linearity and the crack location in radial direction on the longitudinal fracture. It is found that the strain energy release rate decreases with increasing 2 1 / R R ratio. The increase of the crack length leads to decrease of the strain energy release rate. The analysis reveals that the strain energy release rate increases with increasing of the material property,  . The material non-linearity leads also to increase of the strain energy release rate. Concerning the influence of the crack location in radial direction, it is found that the strain energy release rate decreases with increasing of 3 1 / R R ratio. The strain energy release rate increases with increasing of 0 / Q L ratio. The general approach for analyzing the strain energy release rate developed in the present paper can be applied in structural design of inhomogeneous beams with continuously varying radius of the cross-section along the beam length. 1.5 2 1 = R R 4. Conclusions

References

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