## Materials and Methods
### Numerical Modelling
#### 2.3.5 Calibration and Validation of the Model  
Maximum principal strain (Maxpe) with exponential traction separation law, were used as damage parameters for XFEM crack propagation. Available studies [19] show that model calibration can be successfully accomplished using either small-scale or full-scale test results. Burst test results were used to calibrate and validate the model in this study. Burst pressure of the specimen with 100 mm \(\times\) 4.3 mm crack was used for calibration. The crack length in the specimen matched the dent length perfectly. Results of the three remaining specimens (20 mm \(\times\) 4.3 mm, 60 mm \(\times\) 4.3 mm, and 200 mm \(\times\) 4.3 mm cracks) tested were used in validation. Damage parameters obtained from the calibration and validation process were fracture strain, Maxpe = 0.045, and fracture energy, G\({}_{c}\) = 2 kJ/m\({}^{2}\). High fracture strain and low fracture energy cause large plastic deformation followed by brittle crack propagation [24]. Resistance to propagation of a cohesive crack in elastic-plastic materials depends on material properties and damage parameters (cohesive strength and energy). According to [PERSON] and [PERSON] [25], the resistance is effected through plastic dissipation of energy in the material surrounding the fracture process zone and dissipation of cohesive energy inside the fracture process zone itself. Increasing cohesive strength (fracture strain) and strain hardening exponent increases the contribution of plasticity towards resistance of crack propagation but lowers contribution of cohesive energy  
Figure 4: Showing typical distribution of von Mises stress in the pipe at different loading steps followed in this study; Step 1: Apply denting pressure; Step 2: Dent the pipe; Step 3: Release the indenter from pipe surface; Step 4: Pressurize the pipe to propagate crack and burst the pipe.  
(fracture energy). Large fracture strains show that the material has a high flow stress and require large loads to plasticize. The large loads produce large traction within the fracture process zone resulting in greater resistance to fracture. Low fracture energy shows that resistance to crack propagation is fundamentally by the plastic dissipation of energy in the material around the fracture process zone. A very low amount of energy is required to separate the surfaces within the cohesive zone to form the crack. Table 1 shows burst pressures of four specimens obtained from test and predictions made using the calibrated model. The result shows that the model is generally non-conservative, and predictions were within 10% of the test results.  
Load-displacement curves [2] for the dent formation process in the experiments were used to validate the denting of the numerical model. Figure 5 shows load-displacement curves for application and release of the rigid indenter from the pipe surface. There is good agreement between test and model-derived curves for all specimens, but the maximum denting load of the model was on average 13% higher than maximum load from tests, showing the models was stiffer than the experiments. This is attributed to the firm supports achieved in modelling compared to supports used in experiments.