# Assessment of Fatigue Life and Failure Criteria in Ultrasonic Testing Through Thermal Analyses
## 4 Results  
### T-N Curves  
The graphs and thermographic images obtained using the thermography method are shown in Figures 5-9. These images illustrate the thermal gradients measured at the center of the specimen, where the maximum stress is concentrated. Figures 5-8 display the T-N curves corresponding to identical stress levels under varying intermittent loading conditions. \begin{table}
\begin{tabular}{c c c} \hline
**Pulse–Pause (ms)** & \(f_{\text{eff}}\) **(Hz)** & \(\sigma_{\text{a}}\) **(MPa)** \\ \hline \hline \multirow{6}{*}{300–500} & 360 \\  & 420 \\  & 440 \\  & 450 \\  & 460 \\
300–500 & 7521.63 & 470 \\  & 480 \\  & 500 \\  & 520 \\  & 540 \\  & 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Experimental conditions to obtain the S-N curve. \begin{table}
\begin{tabular}{c c c} \hline
**Pulse–Pause (ms)** & \(f_{\text{eff}}\) **(Hz)** & \(\sigma_{\text{a}}\) **(MPa)** \\ \hline \hline \multirow{6}{*}{300–200} & 270 \\  & 11,600.93 & 315 \\  & 360 \\  & 405 \\ \hline \multirow{6}{*}{200–200} & 270 \\  & 9680.54 & 315 \\  & 405 \\ \hline \multirow{6}{*}{200–300} & 270 \\  & 7598.78 & 360 \\  & 405 \\ \hline \multirow{6}{*}{300–500} & 450 \\  & 480 \\  & 500 \\  & 520 \\  & 540 \\  & 600 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experimental conditions with IR camera. These graphs highlight the significance of the pulse-pause technique in facilitating cooling during the tests. The influence of intermittent loading on each \(\sigma_{\text{a}}\) is evident. Longer pulse-pause durations result in higher temperatures at the center of the specimens. Tests with a pulse-pause interval of 300-200 ms produced the highest temperatures across all stress levels, as anticipated. Specimens subjected to 45% and 40% of \(\sigma_{\text{u}}\), equivalent to 405 MPa and 360 MPa, respectively, failed under these conditions, with temperatures exceeding 300 \({}^{\circ}\)C.  
Figure 5: Thermal gradients of pulse–pause with 300–200 ms.  
Figure 6: Thermal gradients of pulse–pause with 200–200 ms. Figure 8 depicts the thermal gradients for a pulse-pause interval of 300-500 ms. This intermittent loading scheme was selected based on the initial results shown in Figures 5-7. The test began at a stress level of 450 MPa, corresponding to 50% of \(\sigma_{\rm u}\). The thermal gradients indicated that the specimen maintained temperatures below 25 \({}^{\circ}\)C. Consequently, subsequent tests were conducted at higher stress levels, revealing that under this condition, even at 66% of \(\sigma_{\rm u}\), the specimens did not exhibit elevated temperatures. All tests maintained temperatures below 40 \({}^{\circ}\)C.  
Figure 8: Thermal gradients of pulse–pause with 300–500 ms.  
Figure 7: Thermal gradients of pulse–pause with 200–300 ms. The thermal gradients shown in Figure 9 illustrate the effect of the cooling system during VHCF tests. Specimens without cooling did not reach a steady-state temperature until after 10\({}^{6}\) cycles. In contrast, cooled specimens achieved steady-state temperature before completing 100,000 cycles. Cooling reduced the maximum temperature by approximately 45 \({}^{\circ}\)C at a stress amplitude of 360 MPa. At a stress level corresponding to 30% of the ultimate tensile strength (\(\sigma_{\mathrm{u}}\)), air cooling reduced the temperature by 15 \({}^{\circ}\)C.  
In comparison with previous results with higher f\({}_{\mathrm{eff}}\), the specimens experienced significant temperature effects that compromised the material's fatigue performance. In contrast, the 300-500 ms pulse-pause interval minimized temperature-related impacts, preserving the material's fatigue capability. Figure 10 highlights the influence of intermittent loading and stress levels on temperature rise. It is evident that higher stress amplitudes (\(\sigma_{\mathrm{a}}\)) and increased loading frequencies result in a more pronounced initial temperature gradient (R\({}_{\mathrm{0}}\)).