Issue 39

M. Shariati et alii, Frattura ed Integrità Strutturale, 39 (2017) 166-180; DOI: 10.3221/IGF-ESIS.39.17 177 von Mises stress (Pa) longitudinal stress (Pa) Longitudinal displacement (m) Figure 10 : Stress and displacement contours for the axisymmetric cross sections of a cylinder with a circumferential crack of length a = 0.05m at rotational speed of 1800 rpm. For investigating the effect of the inner radius of the cylinder on the SIF, hollow cylinders with three different circumferential crack lengths under static uniform tensile load of 1 V MPa are analyzed. In this analysis, the values of the height and thickness of the cylinders are chosen to 0.2 m and 0.1 m, respectively. In addition, the material gradient parameter is considered to be 0.2. The results are presented in Fig. 11. It is observed that K I increases with increasing the inner radius of hollow cylinder. For small crack sizes, the curve rises gradually. These behaviors have been reported in reference [12]. [ 5 L P . , 3D P a =0.01 a =0.03 a =0.05 Figure 11 : Plots of SIF vs. inner radius of hollow cylinder under uniform axial tension for P 0.2 . FG hollow cylinder with internal circumferential crack under dynamic loading According to the previous section, an epoxy/glass functionally graded hollow cylinder with an inner circumferential crack (Fig. 7) under impulsive tensile load is analyzed. The values of the height, inner and outer radius of the cylinder are chosen to H 0.2 m, i R 0.1¬m and o R 0.2¬m, respectively. In addition, the material gradient parameter is chosen to P 0.2 for this example. A uniform impulsive tension 1 V MPa at time t 1¬Ƭs is applied to the upper and lower surfaces of cylinder and the stress intensity factors are obtained at specified time steps ( t s 1¬ P ' ). The SIF vs. time curves for different crack sizes are plotted in Fig.12. The stress wave arrival time to the circumferential crack tip decreases with increasing crack radius similar to a penny- shaped crack. Fig. 12 shows that the maximum value of SIF in dynamic loading condition is so much larger than its value