*4.1. The Evolution Law of Induced Voltage with Working Stress*

Due to the different diameters of the specimens, the tensile force during the data analysis was converted into stress to facilitate the control variable. To compare different groups of rebars with the same stress level, the stress to yield strength ratio was taken as the abscissa and expressed by *T*p. Considering the different initial magnetization states of different specimens, their initial induced voltage peak-to-peak values after pretreatment were different. Therefore, the starting point of each group of data was excluded from the initial value, and the increment of induced voltage peak-to-peak value (Δ*Vpp*) was used as an indicator. As shown in Figure 3, Δ*Vpp* and rebar working stress are nonlinearly correlated. According to the magnetoelastic effect, the magnetization strength of the rebar changes when the stress changes. During the elastic stage, the force-induced magnetization is theoretically reversible. Therefore, during the unloading stage, the elastic strain recovery makes the reversible magnetization intensity recover. However, as shown in Figure 3, the induced voltage peaks did not fully recover when the rebar was unloaded to its starting value. This was because the plastic deformation generated by the rebar fabrication was not completely eliminated in the pretreatment stage. The magnetic domain structure was irreversibly rotated during loading, which resulted in irreversible magnetization.

**Figure 3.** The Δ*Vpp* for each stress level measured during loading and unloading: (**a**) design stress level of P50; (**b**) design stress level of P70; (**c**) design stress level of P90.

The corresponding Δ*Vpp*-*T*<sup>p</sup> curves were similar for each specimen. Therefore, the design stress range of 90% yield strength in each group of specimens was selected for further analysis. As shown in Figure 4, the relationship of the Δ*Vpp*-*σ* was similar for the same stressing process for different rebars. During the loading stage, the Δ*Vpp* decreased and then increased with the increase of working stress. During the unloading stage, the Δ*Vpp* decreased and then increased with the decrease of working stress. The corresponding Δ*Vpp*-*σ* curves in the loading and unloading stages were different. The same stress level in loading and unloading corresponded to two different Δ*Vpp*. This was due to the hysteresis of the rebar as a ferromagnetic material after loading and unloading [40].

**Figure 4.** The Δ*Vpp* corresponding to the design stress condition of P90 in the loading and unloading stages: (**a**) Group 1; (**b**) Group 2; (**c**) Group 3.

The working stress loss stage corresponded to the unloading stage. Further analysis of the unloading stage was performed. The maximum stress level was taken as the starting point for comparison purposes. The starting point of each specimen was removed from the initial value. The increment of induced voltage peak-to-peak (Δ*Vpp*) was used to characterize the working stress of the rebar, as shown in Figure 5.

There was a similar relationship between the Δ*Vpp* and working stress for rebars with different diameters. For specimens with the same diameter, due to the different composition and processing technology of different rebars, the force-induced magnetization law of rebars was different. Therefore, the reversible magnetization of each specimen was different, which made the Δ*Vpp* of different rebars different under the same working stress level. However, under different working conditions, the Δ*Vpp*-*σ* curve was similar. In the unloading stage, the Δ*Vpp* decreased first and then increased with the decrease of working stress. From the perspective of magnetic domain theory, it can be seen that the working stress had a more substantial influence on magnetization than the excitation magnetic field

at a greater working stress level. Therefore, magnetization would increase with the increase of stress at a greater stress level [41].

**Figure 5.** Comparison of the same stress level of the Δ*Vpp* under three design stress conditions for each group of specimens: (**a**) Group 1; (**b**) Group 2; (**c**) Group 3.

Comparing Figure 5a–c, it can be seen that under the same working stress level, the greater the design stress of different rebars in the same group, the lower the Δ*Vpp* corresponding to the specimen. This was because when the design stress increased, the elastic strain generated by the rebar during the prestressing process increased, reducing the rebar's effective area. In addition, the more extensive range increased the magnetization range of the rebar. Therefore, in the unloading stage, the rebar simulated the working stress loss; when the working stress was lost to the same stress level, the Δ*Vpp* measured by the specimen with high design stress was less. For each group of specimens, the turning point of the Δ*Vpp*-*σ* curve was different, but it was concentrated at 135 ± 25 MPa. For the same group, the distribution of turning points was more concentrated. For example, the turning point of Group 2 was 157.19 MPa. In the same design stress of the same group, except for D20-P90-T1 and D20-P90-T2, the turning point of the Δ*Vpp*-*σ* curve of other repetitive tests was the same stress level.

From the above analysis, it can be seen that the induced voltage peak-to-peak value was nonlinearly related to working stress. Therefore, to evaluate the working stress of prestressed rebar using the induced voltage peak-to-peak value, the mapping relationships between characteristic indicators and working stress were established by nonlinear fit and linear fit.
