## 3 Results and Discussion
### Unrestrained Concentric Dent-Crack Defects
#### 3.1.2 Effect of Crack Length on Burst Pressure  
Crack length was varied from 20 to 200 mm while maintaining crack depth at 0.5t, varying dent depths from 0% to 6% OD, and denting pressures from 0 to 0.8 \(P_{\mathrm{y}}\). Increasing crack length from 20 to 200 mm in a 2% OD deep dent formed at zero pressure caused a 25% drop in the burst pressure and a 36% drop for dent depths \(\geq\)4% OD. Dent-crack defects with \(\leq\)2% OD dent depths formed at 0 pressure had the same burst pressure as plain cracks (Figure 7a). With cracks of lengths \(>\)20 mm and dent depth \(>\)2% OD, dent cracks were more severe than plain cracks, as shown in Figure 7b,c, with the disparity increasing with crack length and denting pressure.  
According to [PERSON] et al. [2; 3; 4], dent-crack defects with cracks of 0.5 t depth inside dents of 4% OD depths were unable to sustain pressure equivalent to the MAOP of the pipe if crack lengths were greater than 75 mm, regardless of the pressure at which the dents were formed. This study shows that the margin of safety is higher and varies with pressure. All dents formed at zero pressure with a 0.5 t crack would sustain the MAOP for crack lengths \(<\) 200 mm as shown in Figure 7a, while Figure 7b shows that 0.5 t deep cracks inside 4%OD deep dents formed at 0.3 \(P_{\mathrm{y}}\) denting pressure have limiting length of 100 mm. The same defect if formed at 0.5 \(P_{\mathrm{y}}\) would have a limit length less than 100 mm.  
[PERSON] et al. [2] applied the J-integral concept to decide whether the pipe had failed. Failure occurred when the J-integral value at any point in the crack reached 1.15 \(I_{\mathrm{1C}}\), the critical value of J-integral at which the material fractured. We believe, based on our analysis, that using the J-integral value at the tip of an existing crack to determine burst pressure of pipeline is conservative. Whereas crack growth in the model initiated at lower pressure, its progression beyond the immediate vicinity of the original crack tip was slowed by plasticity, enabling the pipes to sustain more pressure before bursting.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c} \hline \hline \multicolumn{2}{c}{**Crack Size (mm)**} & \multicolumn{8}{c}{**Denting Pressure (MPa)**} \\ \hline \multirow{4}{*}{**Depth**} & \multirow{4}{*}{**Length**} & \multicolumn{4}{c}{**0.0 \(P_{\mathrm{y}}\)**} & \multicolumn{4}{c}{**0.3 \(P_{\mathrm{y}}\)**} & \multicolumn{4}{c}{**0.5 \(P_{\mathrm{y}}\)**} & \multicolumn{4}{c}{**0.8 \(P_{\mathrm{y}}\)**} \\ \cline{3-14}  & & \multicolumn{4}{c}{**0.0 \(P_{\mathrm{y}}\)**} & \multicolumn{4}{c}{**0.5 \(P_{\mathrm{y}}\)**} & \multicolumn{4}{c}{**0.5 \(P_{\mathrm{y}}\)**} & \multicolumn{4}{c}{**0.8 \(P_{\mathrm{y}}\)**} \\ \cline{3-14}  & & \multicolumn{4}{c}{**Dent Depth (\%OD)**} & & \\ \cline{3-14}  & & **2\%** & **4\%** & **6\%** & **2\%** & **4\%** & **6\%** & **2\%** & **4\%** & **6\%** & **2\%** & **4\%** & **6\%** \\ \hline \multicolumn{14}{c}{**Burst Pressure (MPa)**} \\ \hline \multirow{4}{*}{0.2 t} & 20 & 15.081  & 15.12  & 15.25  & 15.52  & 15.71  & 15.83  & 14.5  & 14.8  & ** ** & ** ** & ** ** & ** ** \\ \cline{3-14}  & 20 & 15.01  & 15.19  & 15.59  & 15.64  & 15.33  & 10.8  & ** & ** & ** & ** ** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Burst pressure of pipes with unrestrained concentric dent crack defects.