Analyses of the multiple cracking behaviour of brittle hollow cylinders under internal pressure

In order to elucidate the multiple cracking behaviour of brittle hollow cylinders under static internal pressure, two-dimensional dynamic finite element analyses have been performed firstly for graphite hollow cylinders with inner and outer diameter of 16 and 22 mm, respectively, under internal gas pressure. In the analyses, propagation speed of the primary crack was set to be extremely high by instantaneously releasing the nodes that defined the path of the primary crack, and internal pressure was preserved after the primary cracking. The analyses showed that the stress was enhanced due to stress waves generated by the primary cracking. The initial stress enhancement was observed at the side position of the cylinder, which was located at approximately ±90° with respect to the primary cracking site. This implied that secondary cracking could occur at the side positions. Fracture modes of the cylinders might depend on the following parameters: (1) propagation speed of the primary crack, (2) pressure drop rate after the primary cracking, (3) medium to generate internal pressure, (4) geometry of a cylinder, (5) mechanical properties of brittle materials, and (6) presence of a notch. Thus, the effect of the above parameters on the behaviour of the multiple cracking was also analysed. It was found that secondary cracking would still occur at the side positions if (i) the crack propagation speed was between 70% and 100% of the theoretical crack propagation speed, (ii) the pressure drop rate was below 10⁷ Pa/s, (iii) wall thickness of the cylinder was changed, and (iv) other brittle materials were employed. Also, it was found that multiple cracking would not be observed if liquid pressure was employed instead of gas pressure, because of fluid-structure interaction. In addition, the position of the secondary cracking would be shifted by introducing a notch on the outer surface of the cylinder. These results were in good accordance with experiments formerly reported.