## 3 Results and Discussion
### Restrained Concentric Dent-Crack Defects  
Figure 10 shows the von Mises stress distribution at different stages of crack propagation through the wall of the specimen having a 60 mm \(\times\) 4.3 mm crack in a 4% OD deep restrained dent formed at 0.3 P\({}_{\rm y}\) denting pressure. The remaining ligaments experienced large stresses similar to the ligaments in the unrestrained dent-cracks prior to the start of crack propagation under pressure. Plasticization accompanied fracture but upward displacement of the internal surface of the pipe was limited by the dent restraint. There is negligible difference between the pressure required to propagate the crack and burst pressure of the pipe with restrained dent. This is in sharp contrast with the response of pipes with unrestrained dent cracks, where the crack propagated at 9 MPa internal pressure and burst at 11.14 MPa internal pressure. Unrestrained dents rebound before the cracks begin to propagate through the wall, hence releasing elastic bending stresses. The crack is then free to open and propagate when the stress intensity at its tip exceeds material strength. The rebound action is prevented in restrained dent-crack defects. Therefore, the cracks are not free and require high internal pressure to open and begin propagation. The high internal pressure also plasticizes the pipe wall around the crack tip to the extent that the pipe cannot sustain significant additional pressure once crack propagation begins. Figure 9: Variation of burst pressure with denting pressure, for pipes with 0.5 t deep cracks of varied lengths inside dents of varied depths: (**a**) Crack length = 20 mm, (**b**) Crack length = 60 mm, (**c**) Crack length =100 mm and (**d**) Crack length = 200 mm. Table 3 shows the predicted burst pressure of specimens with various sizes of restrained dent-crack defects. All specimens with cracks of depth 0.2 t inside dents sustained pressures greater than the yield pressure, P\({}_{y}\), of the pipe without fracturing. Crack length, dent depth, and denting pressures had no measurable effect on the burst pressure of the specimens, as they failed by plastic collapse. Releasing the indenter from the pipe surface with the pipe operating at MAOP did not cause crack propagation in the specimens (Table 4). With a crack of depth 0.5t, burst pressures dropped with increasing crack length, dent depth, and denting pressure similar to the pipes with unrestrained dent-crack defects. However, burst pressure of specimens with restrained dents-cracks were generally higher than burst pressures of the corresponding specimens with unrestrained dent-cracks (Table 2) and plain cracked specimens (Table 5). Restraining dents contribute in two ways to improve pipe resistance to fracture. First, compressive stresses from the restraint reduce stress triaxiality at the crack tip and secondly, they counteract hoop stresses from internal pressure. Therefore, high pressure is required to develop the fracture strain and propagate cracks in restrained dents. Restrained dent-crack defects with crack lengths \(\geq\) 100 mm inside dents of depth \(\geq\) 6% OD formed at any pressure were problematic as they displayed susceptibility to unstable crack propagation in circumferential and longitudinal directions. Denting pipes at 0.8 P\({}_{\text{y}}\) propagated cracks of length \(\geq\) 100 mm inside dents of depths \(\geq\) 4% OD. Releasing the dent restraint at MAOP did not propagate cracks of length \(<\) 60 mm. Cracks of length \(>\) 60 mm propagated but only those with lengths \(>\) 100 mm and inside dents of depth \(\geq\) 4% OD deep formed at 0.8 P\({}_{\text{y}}\) denting pressure propagated until the pipes burst when the dent restraint was released.