# Effect of Strain Hardening on Increase in Collapse Pressure during the Manufacture of ERW Pipe
## Change in the Material Stress-Strain Curve during Manufactature
### Results of Simulation
Stress at the opposite side of the seam weld is the next highest. According to _API Specification 5L: Specification for line pipe_[18], the yield strength of a steel pipe should be evaluated at least 90 degrees away from the seam weld. In addition, the yield strength is generally evaluated opposite the seam weld where the influence of the welding is minimal and the deformation history is most complex [13; 15; 19]. Therefore, evaluating stress and strains at the opposite side of the seam weld could be justified. The stress-strain histories of the innermost and outermost layers were evaluated at the opposite line of the seam weld, as shown in Figure 7. During the breakdown process, the innermost and outermost  
Figure 6: Distribution of circumferential stress along the circumferential direction in squeezing and sizing processes. layers showed compressive and tensile stress, respectively. On the other hand, during the finpass and sizing processes, both the innermost and outermost layers fluctuated between tension and compression, but mostly showed compression. In the finpass process, the state of loading-unloading-loading was repeated as the compressed outermost layer was tensioned by the springback right after passing through the finpass rollers. At this time, as shown in Figure 5, the direction of the stress was opposite on the innermost and outermost layers during cyclic loading, and stress migrated to the elastic region. In other words, during the finpass process, strain hardening and the Bauschinger effect occurred alternately at the innermost and outermost layers. During the sizing process, we compared the stress-strain histories of the two sizing ratios, which amounted to the changing rate of the outer diameter of the pipe before and after the sizing process, as follows. \[\textit{Sizing ratio}=\frac{\textit{Outer diameter}_{\textit{before sizing}}- \textit{Outer diameter}_{\textit{after sizing}}}{\textit{Outer diameter}_{\textit{before sizing}}} \tag{4}\]  
When the sizing ratio was 0.1%, stresses at the innermost and outermost layers varied in the elastic region. When the sizing ratio was 1.0%, however, there was distinct compressive plastic deformation in both the innermost and outermost layers. Large amounts of compression occurred during the sizing process due to strain hardening, which resulted in the translation and expansion of the initial yield surface in the compression direction. Therefore, the compressive yield strength could be increased with sizing. The behavior was not observed for a sizing ratio of 0.1%, which suggests the effect is larger as the sizing ratio becomes greater. As shown in Figure 8, the circumferential strain history during manufacture was plotted for each layer in the thickness direction. During the breakdown process, the deformation of the center layer (i.e., layer 4) was insignificant by pure bending, but the outer layers (i.e., layers 1-3) were tensioned and the inner layers (i.e., layers 5-7) were compressed. As Figure 7 shows, during the finpass process, the compression and tension on the inner and outer layers occurred in alternating fashion. Springback occurred immediately after passing through each finpass roller, and the farther from the center layer, the greater the fluctuation of the strain due to springback. In the squeezing and sizing processes, all layers were compressed, and the magnitude of the compression at each layer was similar. Figure 7: Stress–strain curve at the outer and inner layers during manufacture. Following manufacture, we confirmed that the layers were compressed overall by the squeezing and sizing processes.