## 2 Numerical Modelling  
Five different cyclic loading schemes were analyzed. All of them consist of a sinusoidal variation with time with a stress factor \(R=\sigma_{\text{min}}/\sigma_{\text{max}}=0\) (Figure 1a), as summarized in Table 1. This way, loading cycles oscillate between a null stress and a different maximum stress (\(\sigma_{\text{max}}\)) for each case of study. Thus, Load I and Load II applies a maximum load within the material elastic domain (i.e., about 75% and 90% of \(\sigma_{\text{Y}}=1300\) MPa, 0.002% offset yield strength of a typical prestressing steel used in construction [19]: 1000 and 1200 MPa, respectively). Three additional loading schemes were also considered: a load that reaches the material yield strength at maximum load (Load III), and two loading where the maximum stress overcomes the material yield strength: Load IV, 110% of yield strength (i.e., 1400 MPa) and Load V, 125% of yield strength (i.e., 1600 MPa), respectively. In all cases, a number of cycles (\(N\)) of 10 was applied in accordance to the null effect of this parameter, accounting for the results presented in previous analyses [20; 21]. Furthermore, papers [22; 23] show how the crack tip advance due to local plasticity appears during the first loading cycles. Prestressing steel wires can undergo overloading during their life in-service [24]. It is thus interesting to include this issue in the analysis. To do so, diverse overload schemes were considered in terms of the loading sequence: (i) initial overload (Figure 1b); (ii) intermediate overload (Figure 1c); and (iii) final overload (Figure 1d). In addition, the effect of the intensity of the overload was considered in terms of the overload ratio (\(\mu\)), defined as \(\mu=\sigma_{\text{overload}}/\sigma_{\text{max}}\). Thus, four different overloads ranging from 1200 MPa to 1600 MPa (Loadings Ia-Id in Table 2) were considered for the lowest in-service loading (Loading I, 1000 MPa according to Table 1). In the same way, three overloads ranging from 1300 MPa to 1600 MPa (Loadings IIa-IIc in Table 2) were considered for the highest in-service loading (Loading II, 1200 MPa according to Table 1). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Cyclic Loading Schemes** & **I** & **II** & **III** & **IV** & **V** \\ \hline \(\sigma_{\text{max}}\) (MPa) & 1000 & 1200 & 1300 & 1400 & 1600 \\ \(N\) & 10 & 10 & 10 & 10 & 10 \\ \(\lambda=\sigma_{\text{max}}/\sigma_{\text{Y}}\) & 0.75 & 0.90 & 1.00 & 1.15 & 1.25 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters (maximum stress level and number of cycles) used to define the diverse cyclic loading schemes analyzed. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Cyclic Loading Schemes** & **Ia** & **Ib** & **Ic** & **Id** & **IIa** & **IIb** & **IIc** \\ \hline \(\sigma_{\text{max}}\) (MPa) & 1000 & 1000 & 1000 & 1000 & 1200 & 1200 & 1200 \\ \(\sigma_{\text{overload}}\) (MPa) & 1200 & 1300 & 1500 & 1600 & 1300 & 1500 & 1600 \\ \(\mu=\sigma_{\text{overload}}/\sigma_{\text{max}}\) & 1.2 & 1.3 & 1.5 & 1.6 & 1.08 & 1.25 & 1.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters (maximum stress level and overload stress) used to define the diverse overloads during cyclic loading analysis. The stress state during in-service conditions can be estimated as the addition of stress generated by in-service loading (commonly variable in time; i.e., fatigue) and the residual stress state caused by manufacturing. In the case of prestressing steel wires, the conforming process of these structural components (wire drawing) applies a progressive reduction of the wire diameter in several stages (drawing steps). As a result, heavy plastic strains appear in the final wire, causing strain hardening (increasing the material strength) and non-negligible residual stress.