## 3 Results and Discussion
This tensioning was gradually reduced with the increasing temperature, as shown in Figure 9. When reaching 350 \({}^{\circ}\)C, the material probably started its recrystallization with the formation of stress-free \(\alpha\)-phase grains and ended at 500 \({}^{\circ}\)C. In this interval, there was an abrupt gap in the engineering stress and increase of elongation. In literature, for some manganese bronze alloys (UNS C67000, C67400, and C67500), the temperatures commonly used for annealing cold-worked are 425-600 \({}^{\circ}\)C, therefore the behavior found in Figure 8 is in accordance with previous research [1; 18; 19; 20; 21]. Figure 8: Effect of temperature during heat treatment (**a**) in the sample microstructures at 200, 400, and 750 \({}^{\circ}\)C, respectively, in the columns from left to right, (**b**) the mechanical properties accordingly from each applied temperature. At 700 \({}^{\circ}\)C, the sample showed a structural discontinuity between the surface and the core of the material. On the surface, the material showed \(\beta\) granular formation with the presence of a widimanstatten \(\alpha\)-phase and intermetallic microconstituents dispersed in the material structure. In the core, the material presented a solid \(\beta\) solution matrix structure and the presence of an \(\alpha\)-phase in a circular and widimanstatten pattern. The true stress-true strain curves were calculated from the engineering stress and engineering strain to represent the plastic deformation phenomenon. The true stress-strain curve is known as the flow curve and can be expressed by the power law, which was proposed by [PERSON] [30]. \[\sigma\ =K\ \varepsilon^{n} \tag{1}\]  
where \(n\) is the exponent, which represents the strain-hardening coefficient; \(\sigma\) is the true stress, MPa; \(\varepsilon\) is the true strain; and \(K\) is the strength coefficient, MPa [31]. There is an approximate linear relationship between the true stress and true strain when plotted on a log-log scale. Therefore, through linear fitting of the In\(\sigma\)-In\(\varepsilon\) curves, the strain-hardening exponent \(n\) was obtained by the fitted slopes, while the material constant InK was obtained by the fitted intercept. Figure 4:0  
Therefore, Equation (2) represents a linear system, the slope of the line gives the \(n\) value \(n=\partial\text{ln}\sigma/\partial\text{ln}\varepsilon\), and the intercept at \(\varepsilon=1\) gives the \(K\) value. Figure 10 presents graphs of the strain-hardening exponent \(n\) and strength coefficient \(K\) with respect to the annealing temperatures with the experimental data fitted with the Hollomon equation. Comparing the values that were determined in Figure 10b, when the annealing temperature was increased from 200 to 750 \({}^{\circ}\)C, the (\(n\)) values were found enhanced together with the variation from 0.2 to 0.5. The \(n\) value is related to the mechanical properties through the Hollomon equation, which describes that the value \(n\) was small, and the hardening rate was high initially with the plastic deformation; however, the hardening rate decreased rapidly with the increased strain. On the other hand, with a high \(n\), the hardening rate was smaller at the initial plastic deformation; however, the hardening rate remained low until the high strains. In other words, the higher the hardening coefficient \(n\), the more the materials will be able to deform/elongate. According to [PERSON], the strain hardening behavior described by n depends on the composition, microstructure, and dislocation population. In this case, the composition was not altered, and neither was the \(\beta\)-phase (on average 50%); therefore, the values of the strength and elongation changed according to the microstructure and dislocation, and the \(n\) values corresponded to the annealing temperature each stage, as shown in Figure 8 [32]. The effect of temperature on the Vickers hardness is shown in Figure 4:1 Each point in the figure represents an average of five readings in the perpendicular plane of the samples.