# Fracture Assessment of Weld Joints of High-Strength Steel in Pre-Strained Condition
## 3 Pre-Strain Effect on Fracture Toughness
### Estimate of Critical CTOD in Pre-strained ETCP  
The equivalent CTOD ratio \(\beta_{\text{2a}}\) for the ETCP with crack length \(2a\) was determined using Equation (1) [13]. \[\beta_{2a(ETCP)}=\beta_{0(ETCP)}\cdot(2a/11)^{k_{ETCP}(m,\ YR)},\ k_{ETCP}(m,\ YR)=\frac{-0.57+3.1 YR-1.45 YR^{2}}{ \exp\{-0.35(m-10)\}+1} \tag{1}\]  
According to ISO 15635 [25], the yield strength used in the calculation of the CTOD--when located in (or is partially in) the transformed HAZ--is higher than the yield strength of the base metal and weld metal (WM) strength applied, as it is difficult to evaluate the strength of the actual HAZ. When under-matched, weld-joint, pre-strain is applied, most of the deformation occurs in the base material, and the strength of the base metal becomes almost similar to that of the WM. Therefore, the yield strength of the base material was used in the CTOD calculation in this study and  
Figure 4: Monographs of equivalent CTOD ratio \(\beta_{0}\) for double-edged, through-thickness crack panel (ETCP) with a reference crack length of 2a = 11 mm. \begin{table}
\begin{tabular}{c c c} \hline
**Temperature** & \multicolumn{2}{c}{**Critical CTOD (3 PB)**} \\ \hline
**T** (\({}^{\circ}\)**C**) & \(\delta_{\text{cr}}\) **(mm)** & \(\delta_{\text{cr}}\) **ave. (mm)** \\ \hline \(-20\) & 0.012 & \\ \hline \(-20\) & 0.049 & 0.079 \\ \hline \(-20\) & 0.177 & \\ \hline \(0\) & 0.047 & \\ \hline \(0\) & 0.108 & 0.1 \\ \hline \(0\) & 0.145 & \\ \hline \end{tabular}
\end{table} 
Table 5: Critical crack tip opening displacement (CTOD) data of 3.0% pre-strained HAZ obtained by the three-point bend test. was estimated from the stress-strain curves of base steel, without the pre-strain, as shown in Figure 5. The yield stress of the pre-strained HAZ \(\sigma_{\text{Y}}\)pre can be obtained using Equation (2) [18]. \[\sigma_{Y}^{pre}=S_{Y}\big{(}\varepsilon_{pre}\big{)} \tag{2}\]  
where \(S_{Y}(\varepsilon_{\text{pre}})\) is the true stress of the original HAZ at the true pre-strain \(\varepsilon_{\text{pre}}\). The tensile strength of the pre-strained HAZ \(\sigma_{\text{T}}\)pre can be determined by Equation (3) [18];  
\[\sigma_{T}^{pre}=\sigma_{Y}\frac{1+\varepsilon_{T}}{1+(\varepsilon_{T}- \varepsilon_{pre})} \tag{3}\]  
where \(\sigma_{\text{T}}\) and \(\varepsilon_{\text{T}}\) are the tensile strength and uniform elongation of the original HAZ, respectively. The estimated YR of the 3.0% pre-strained steel was 0.90, where \(\sigma_{\text{Y}}\)pre and \(\sigma_{\text{T}}\)pre are 684 MPa and 759 MPa, respectively. The equivalent CTOD ratio \(\beta_{0}\) for the ETCP with YR = 0.90 was 0.08 for m = 20 (Figure 4). The equivalent CTOD ratios \(\beta_{2\text{a}}\) for the 3.0% pre-strained ETCP, with different crack lengths \(2a\), were calculated using Equation (1); the results are listed in Table 6.  
The critical CTOD \(\delta_{\text{cr,ETCP}}\) of the 3.0% pre-strained ETCP with the double-edged crack in the HAZ was estimated from the critical CTOD \(\delta_{\text{cr,3 PB}}\) for the 3.0% pre-strained 3 PB specimen, given in Table 5, in the form of \(\delta_{\text{cr,ETCP}}=\delta_{\text{cr,3 PB}}/\beta_{2\text{a}}\). In this estimation, the median of \(\delta_{\text{cr,3 PB}}\) at each temperature was used. Figure 6 presents the estimated critical CTOD for the 3.0% pre-strained ETCP, as a function of the crack length \(2a\), at the temperatures \(0\ ^{\circ}\text{C}\) and \(-20\ ^{\circ}\text{C}\). The critical CTOD \(\delta_{\text{cr,ETCP}}\) decreased with the increasing crack length \(2a\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**2a** & \(\beta_{0}\)(ETCP) & \(\beta_{2\text{a}}\)(ETCP) \\ \hline
10 & 0.08 & 0.07 \\
20 & 0.08 & 0.15 \\
30 & 0.08 & 0.22 \\
40 & 0.08 & 0.30 \\
50 & 0.08 & 0.37 \\
60 & 0.08 & 0.45 \\
70 & 0.08 & 0.52 \\
80 & 0.08 & 0.60 \\
90 & 0.08 & 0.68 \\
100 & 0.08 & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Equivalent CTOD ratio \(\beta\) for 3.0% pre-strained ETCP (\(YR\) = 0.9, \(m\) = 20), as a function of crack length \(2a\).