# Strengthening Mechanisms in a Medium-Carbon Steel Subjected to Thermo-Mechanical Processing
## 4 Discussion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Processing** & **QT600** & **QT650** & **TF600** & **TF650** \\ \hline Grain size strengthening, \(\sigma_{\rm HP}\), MPa & 209 \(\pm\) 17 & 192 \(\pm\) 19 & 414 \(\pm\) 6 & 496 \(\pm\) 6 \\ Dispersion strengthening by (V,Nb)C carbides, MPa & 240 \(\pm\) 19 & 276 \(\pm\) 52 & 263 \(\pm\) 23 & 239 \(\pm\) 22 \\ Dispersion strengthening by M\({}_{23}\)C\({}_{6}\), MPa & 322 \(\pm\) 18 & 311 \(\pm\) 25 & 794 \(\pm\) 80 & 482 \(\pm\) 58 \\ Total dispersion strengthening, \(\sigma_{\rm P}\), MPa & 402 \(\pm\) 25 & 416 \(\pm\) 52 & 837 \(\pm\) 83 & 543 \(\pm\) 62 \\ Peierls–Nabarro or friction stress, \(\sigma_{\rm 0}^{\rm A-Fe}\), MPa & 45 & 45 & 45 & 45 \\ Solid solution strengthening, \(\sigma_{\rm SS}\), MPa & 16 & 29 & 16 & 29 \\ Dislocation strengthening attributed to free dislocations & 370 \(\pm\) 9 & 272 \(\pm\) 34 & 507 \(\pm\) 132 & 454 \(\pm\) 79 \\ \multirow{2}{*}{Dislocation strengthening attributed to dislocations with like sign (\(\rho_{\rm MX}\)), \(\sigma_{\rm d}^{2}\), MPa & 706 \(\pm\) 135 & 762 \(\pm\) 119 & 1000 \(\pm\) 100 & 909 \(\pm\) 97 \\ \multirow{2}{*}{\(\sigma_{\rm TS}\), MPa} & - & - & 1819 \(\pm\) 221 & 1567 \(\pm\) 147 \\ \multirow{2}{*}{\(\sigma_{\rm VS}\), MPa} & 1378 \(\pm\) 177 & 1444 \(\pm\) 190 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Contribution of different strengthening mechanisms to overall YS after tempering (QT) and tempforming (TF) at different temperatures. \(\rho_{\text{KAM}}\) value. The dislocation strengthening, \(\sigma_{d}^{*}\), attributed to dislocations with like sign and calculated with Equation (6) using the \(\rho_{\text{KAM}}\) value from Table 1 is presented in Table 3.  
This dislocation strengthening (\(\sigma_{d}^{*}\)) is remarkably higher than \(\sigma_{\text{d}}\) and, therefore, the contribution of intrinsic lath boundary dislocations to overall dislocation strengthening is higher than that of free interior dislocations in the tempered condition. The resulting values of YS, \(\sigma_{\text{YS}}^{*}\), for QT600 and QT650 treatments are calculated as follows:  
\[\sigma_{\text{YS}}^{*}=\sigma_{0}^{\alpha-F\epsilon}+\sigma_{SS}+\sigma_{P}+ \sigma_{HP}+\sigma_{d}^{*}, \tag{7}\]  
and presented in Table 3.  
A comparison between experimentally measured YS from Figure 4 and calculated YS from Table 3 is shown in Figure 5. It can be seen that the experimental YS match theoretical \(\sigma_{\text{YS}}^{*}\) values for the tempered steel with high accuracy, suggesting the contribution of intrinsic lath boundary dislocations to the dislocation strengthening. Theoretical \(\sigma_{\text{YS}}\) values of the steel after tempforming and experimental YSs are essentially the same if the dislocation strengthening calculated by Equation (6) using density of free dislocation, \(\rho\), is taken into account. The use of the \(\rho_{\text{KAM}}\) values for the steel in tempformed condition leads to significant overestimation of theoretical YS. Therefore, intrinsic dislocations of LABs in lamellar structure do not contribute to the dislocation strengthening due to lacking the long-range elastic stress fields. The lacking of long range elastic stress fields originating from lamellar boundaries has been found in TEM studies (Figure 3c,d). High \(\rho_{\text{KAM}}\) values (Table 1) may be calculated due to accumulative misorientation of LABs with nanoscale spacing in the lamellar structure. Subbondaries in lamellar structures do not contribute to the dislocation strengthening. Inspection of Table 3 shows that the dislocation strengthening is the major contributor to YS of the tempered steel. The dispersion strengthening and the grain size strengthening are also important for the YS of this material, while the role of the solid solution strengthening is insignificant due to almost full carbon depletion from ferrite.