# Effect of Strain Hardening on Increase in Collapse Pressure during the Manufacture of ERW Pipe
## 3 Evaluating Collapse Pressure
### Factors That Improve the Collapse Pressure  
The factors that increase the collapse pressure were analyzed for the pipe with a \(D/t\) of 14, and those factors were heavily influenced by the sizing ratio. To evaluate the plastic behavior of the material in the circumferential direction, a finite element model with a square cross-section was constructed to simulate a compression test, as shown in Figure 12a [22]. Residual stresses and modified stress-strain curves after manufacture were applied as an initial condition to maintain continuity of the analysis. Since the pipe had seven element layers in the thickness direction, the specimen model also had seven element layers to take into account the different plastic deformation histories in the thickness direction. The mapping length of the specimen was 1.4 times the width of the cross-section. If the length of the specimen was too long, a global buckling could occur before securing sufficient deformation to derive a stress-strain curve [4]. Convergence testing confirmed that the mesh size of the mapping region was constructed as 3640 elements divided into 10 and 52 equal parts along the width and length directions, respectively. The difference between the stress-strain curves before and after manufacture was examined, as shown in Figure 12b. To evaluate the effect of the compression during the sizing process, sizing ratios of 0.1, 0.3, 0.7, and 1.0% were considered. The results showed that the slope of the strain hardening beyond the elastic region was increased following manufacture. Depending on the sizing ratio, however, there was a difference in the stress-strain curve in the vicinity of a 0.5% offset strain, which was the yield strength evaluation position suggested by _API Specification 5L: Specification for line pipe_[18]. When the sizing ratio was 0.1%, the Bauschinger effect appeared immediately after the elastic region due to the intense effect of the breakdown and to the finpass processes that caused compression and tension at the inner and outer layers, respectively. As the sizing ratio was increased, on the other hand, the Bauschinger effect disappeared, and the strain hardening showed an increased slope directly after the elastic region. Thus, the strength of the compressive yield became greater as the sizing ratio increased. This is because the yield surface was gradually moved and expanded in the compressive direction by the kinematic and isotropic hardenings with an increase in the sizing ratio. Figure 11: Range of maximum compressive strain when collapse occurs. To examine the effect of the sizing ratio in more detail for a \(D\)/t of 14, the collapse pressure with respect to the sizing ratio was compared together with the ovality and the compressive yield strength, as shown in Figure 13.  
Ovality is a widely used indicator of out-of-roundness, as follows. \[Ovality=\frac{\text{\it Outer diameter}_{max.}-\text{\it Outer diameter}_{min.}}{ \text{\it Outer diameter}_{avg.}} \tag{5}\]  
Figure 12: Compression test: (**a**) specimen model for the compression test; (**b**) compressive stress–strain curves for various sizing ratios. Up to a sizing ratio of 0.4%, the collapse pressure was increased by approximately 10%, and this tendency between the collapse pressure and the sizing ratio seemed to follow improvement of the ovality, as shown in Figure 13a. At a sizing ratio of more than 0.4%, however, the collapse pressure continued to increase, but little improvement was shown for ovality. Thus, ovality could not explain the increase in collapse pressure when the sizing ratio was greater than 0.4%. On the other hand, compressive yield strength was increased for a greater sizing ratio, as shown in Figure 13b. The correlation coefficient between the collapse pressure and the compressive yield strength was 0.67 when the sizing ratio was greater than 0.4%. The correlation coefficient between the collapse pressure and the ovality for the same range, however, was \(-0.36\), which indicated low correlation.