## 6 Discussion
 \tag{18}\]  
As follows from Equation (17), the \(T/\sigma\) parameter for the CT specimens used in this paper (\(a/w=0.503\)) is \(T/\sigma=5.57\), and for the CT specimens used in [18] (\(a/w=0.50\)) it is \(T/\sigma=5.50\). For the SENT specimens used in [18], the \(T/\sigma\) parameter reaches a value of \(-0.59\) after substituting the number 0.2 for \(a/w\) in Equation (18). These values are summarized in Table 3.  
Now we can plot these quantities into the diagram \(J\)--\(T/\sigma\) (Figure 11) to obtain three points for the J integral \(J_{\Delta a1}\) and three points for the J integral \(J_{\Delta a2}\). Using the least-square method, we can fit a straight line through these points to obtain the linear dependences (19) and (20):  
\[J_{\Delta a_{1}}=364.9-8.6464 xT/\sigma\text{ for }\Delta a_{1}=0.2 mm \tag{19}\]  
\[J_{\Delta a_{2}}=920.1-28.938 xT/\sigma\text{ for }\Delta a_{2}=1.0 mm \tag{20}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Source** & \(T/\sigma\) & \(J_{\Delta a1}\) **(N/mm)** & \(J_{\Delta a2}\) **(N/mm)** \\ \hline this work—CT & 5.57 & 316.2 & 785.45 \\
[18]—CT & 5.50 & 317.9 & 734.1 \\
[18]—SENT & –0.59 & 370.0 & 937.48 \\ \hline \end{tabular}
\end{table} 
Table 3: Entry quantities for further calculations as determined from the R-curves. The next step is the calculation of \(C_{2}(T/\sigma)\) according to relation (16) and expressing the course of this dependence (Figure 12) using a polynomial of the second degree (21):  
\[C_{2}(T/\sigma)=0.5748-0.0048x(T/\sigma)-0.0002x(T/\sigma)^{2} \tag{21}\]  
Similarly, we can calculate the parameter \(C_{1}\) according to relation (15):  
\[C_{1}(T/\sigma)=920.1-28.938x(T/\sigma) \tag{22}\]  
and plot it on Figure 13. It should be noted that the dependences (21) and (22) refer to the steel X65. Since the above parameters \(C_{1}\) and \(C_{2}\) are functions of the constraint parameter \(T/\sigma\), they can be used for an arbitrary cracked specimen from this steel. Figure 11: Dependences of the integrals \(J_{\Delta\alpha 1}\) and \(J_{\Delta\alpha 2}\) on the T/\(\sigma\) parameter. Figure 12: Dependence of the function \(C_{2}\) on the constraint parameter \(T/\sigma\). We are interested in the R-curve for the SENT specimens made from the X65 steel, the dimensions of the specimens being a width w = 50 mm; crack length a = 15 mm; thickness B = 8.7 mm, and length H = 500 mm. From Equation (18), we can obtain the constraint parameter T/\(\sigma\) = \(-\)0.61 for the relative crack length a/w = 15/50 = 0.3. Knowing the constraint parameter T/\(\sigma\), we can enter it into Equations (22) and (21) to obtain the R-curve parameters, namely C\({}_{1}\) = 937.75 and C\({}_{2}\) = 0.5777. The SENT R-curve, predicted by the Gurson-based method, is compared with the resulting SENT R-curve, obtained by [PERSON]'s approach, in Figure 14.  
It can be seen in Figure 14 that the SENT R-curve, determined by the GTN method, lies close to that calculated on the basis of [PERSON]'s approach which, due to accounting for the constraint, can be considered as if it were obtained experimentally. Due to the small difference between the magnitudes of the exponents in the power functions, the R-curves intersect at the point where \(\Delta a\)-1.3 mm. For \(\Delta a\) < 1.3 mm, the Gurson-based R-curve lies above that calculated on the basis of the [PERSON] approach, and for \(\Delta a\) > 1.3 mm, it lies below. The relative differences in J integrals decrease from \(\sim\)14% at \(\Delta a\) = 0.2 mm to 0% at \(\Delta a\)-1.3 mm, at which point they increase to \(\sim\)5% at \(\Delta a\) = 2.2 mm. Figure 14: Comparison of the Gurson-based SENT R-curve with that based on [PERSON]’s approach [19]. Figure 13: Dependence of the function C\({}_{1}\) on the constraint parameter _T/\(\sigma\)_.