## 6 Conclusions  
51 CrV4 steel, with applicability in the railway components of the crossing nose and the frog of the turnout, was analyzed in terms of its fatigue resistance under strain-controlled conditions. The material showed a cyclic softening behavior, characteristic of high-strength steels. The criterion of 50% of the total life was considered, both for determination of the fatigue resistance properties and in determination of the Ramberg-Osgood cyclic elasto-plastic hardening curve parameters, resulting in \(n^{\prime}=0.0954\) and \(K^{\prime}=1393\) MPa (values very similar to the coefficient \(K\) for monotonic loading). With respect to the resistance curves, strain-life and energy-life approaches were considered. Application of the linear-squares  
Figure 14: Comparison between the evolution of the maximum stress amplitude up to 50% of the total lifetime, obtained from the experiments and numerical outcomes. Figure 15: Comparison between the relative error in the evolution of the maximum stress amplitude up to 50% of the total life obtained from the experiments and numerical outcomes. method of the linearized power model was considered, resulting in a strain-life approach of \(\sigma_{f}^{\prime}=1601\) MPa, \(c_{f}^{\prime}=0.4780\), \(b_{f}^{\prime}=-0.093\), and \(c_{f}^{\prime}=-0.684\). Applying the same method for the total strain energy density curves resulted in a \(\kappa_{t}=257\) MJ/m\({}^{3}\), \(\alpha_{t}=-0.3917\), and a \(\Delta W_{0+}=0.490\) MJ/m\({}^{3}\), which corresponds to a fatigue limit of 447 MPa. Cyclic curve datasets were used to determine the kinematic and isotropic hardening parameters using unconstrained optimization procedures with a maximum convergence error of \(1.00\times 10^{-5}\). A kinematic hardening model with 3 non-linear plus 1 linear kinematic parameters was determined to be the best fitting model, with \(C_{1}=83.773.67\) MPa, \(\tau_{1}=582.52\), \(C_{2}=16\),778.05 MPa, \(\tau_{2}=101.71\), \(C_{3}=3013.29\) MPa, \(\gamma_{3}=15.97\), and \(C_{4}=854.52\) MPa. Regarding the isotropic hardening parameters, these were obtained separately using unconstrained optimization and considering the least squares method. The value of the saturation rate was obtained using the normalized method of the maximum stress variation in each cycle, such that \(b_{\infty}=0.8397\). The saturation value of the yield surface size was estimated using a model that takes into account its variation as a function of the applied strain amplitude, resulting in \(R_{\infty}=-260.90\) MPa. The isotropic and kinematic hardening properties of the Chaboche model were used in the material numerical modeling, to validate them in relation to the experimental results. Initially, kinematic hardening properties were assigned in a purely kinematic model, for comparison with the Ramberg-Osggod stabilized loop results. The yield stress of the kinematic Chaboche model was assumed to be the cyclic stress determined using Ramberg-Osgood, \(\sigma_{f}^{\prime}=578.49\) MPa. The results regarding the hysteresis loop were satisfactory. Afterward, numerical experiments were carried out considering the kinematic hardening model combined with the isotropic hardening model, for comparison with the experimental results. The deviation of the numerical model in relation to the behavior of the material obtained in the experiments was quantified, taking a value of 50% of the lifetime as a reference. It was found that the largest deviations occurred up to 20% of the total failure life of the material in a range of \(-10\) to 5%, approximately. As a result, the material properties determined in this investigation can be considered, not only in the analysis of crossing noses for railway infrastructure, but also in notched components, where local analyses based on elasto-plastic deformation and energy theories have more importance.