## 5 Results and Discussion
### Cyclic Curve  
The fatigue strength parameters in the low-cycle regime and the properties of cyclic hardening of the 51 CrV4 were the aims of the present study. A criterion of 50% of the total fatigue life was considered for the determination of the fatigue curve under straining. Datasets obtained from the experiments were used to build a stabilized cyclic curve of Ramberg-Osgood. Figure 5 depicts the fatigue tests performed for different strain ranges. The material presented a cyclic softening behavior for all applied strain amplitude levels. Regarding the sample tested for a strain amplitude of 0.9%, an inferior monotonic yield strength to the other samples was observed. Compared with the other datasets, it was possible to verify that the mechanical characteristics of this specimen were biased in relation to the observed average behavior. Consideration of this dataset allowed providing a more statistical behavior of the cyclic mechanical properties of the material. Figure 4: Monotonic behavior under tensile loading of chromium-vanadium alloyed steel. \begin{table}
\begin{tabular}{c c c c c c c} \hline \(E\) (GPa) & \(\sigma_{\textbf{02}}\) (MPa) & \(\sigma_{uts}\) (MPa) & \(\varepsilon_{uts}\) (\%) & \(\varepsilon_{f}\) (\%) & \(R_{A_{f}}\) (\%) & \(H_{RC}\) \\ \hline
203.8 & 1042 & 1277.33 & 5.90 & 22.71 & 77.29 & 38 \\ \(\pm\)1.2 & \(\pm\)13.85 & \(\pm\)5.03 & \(\pm\)0.09 & \(\pm\)0.68 & \(\pm\)26.23 & - \\ \hline \end{tabular}
\end{table} 
Table 3: Mechanical properties obtained from monotonic tensile tests for steel 51 CrV4. Stabilised hysteresis loops were determined for each strain amplitude. In order to use a consensual criterion for consideration of the stress amplitude value, the criterion of half-life was assumed, because this criterion has been used in several investigations. Figure 6 depicts the hysteresis loops for each applied strain amplitude. There was a certain coherence in the growth of the maximum stress in each hysteresis loop and the applied strain amplitude, except for the test with a strain amplitude of 0.9%. The deviation in the behavior for this result goes back to what was verified in Figure 5.  
The stabilized cyclic curve using [PERSON]'s model (Equation (13)) was considered. The elasto-plastic parameters for the cyclic behavior were obtained using linear regression, according to the least-squares method. The plastic strain amplitude was assessed as the width of the hysteresis loop measured over the axis \(\sigma=0\). The elastic strain amplitude was evaluated from the decomposition of the total strain into elastic and plastic strain components, as described in Equation (1). Table 4 presents a summary of the elasto-plastic parameters for monotonic and cyclic loading conditions. Figure 5: 51 CrV4 steel behavior under cyclic straining conditions until failure. Figure 6: Representation of the stable hysteresis loops obtained from the cyclic tests. Comparison of the elasto-plastic hardening model obtained from cyclic conditions with the monotonic elasto-plastic curve. The regression model for determining the constants of \(K^{\prime}\) and \(n^{\prime}\) presented a coefficient of determination, \(R^{2}\), inferior to 0.67. Additionally, the tested strain levels encompassed the initial zone with a greater hardening material. For superior strain levels around 0.5%, the hardening presented from the monotonic curve was not so pronounced, and the error associated with the extrapolation of the cyclic curve was also inferior. The results of the cyclic and monotonic parameters with the increase in the hardening exponent were 0.0513 to 0.0954, revealing a reduction in the gradient of the cyclic hardening capacity of the material (around 14.04%). On the other hand, the hardening coefficient remained practically constant, \(K^{\prime}\) = 1393 MPa. With respect to the yield strength, \(\sigma^{\prime}_{02}\) had the same meaning as \(\sigma_{02}\), however applied in cyclic conditions. Thus, considering a value 0.2% of residual plastic strain, \(\sigma^{\prime}_{02}\) results in 769.96 MPa.