## 3 Results and Discussion
### High Temperature Properties
#### 3.2.2 Processing Map  
The model considered for the evaluation of the formability of the AMS4928 alloy in this study is a dynamic material model, which was proposed by [PERSON] and [PERSON] [21]. This is based on the energy (G) used by the material plastic deformation and the energy (J) used to generate a change in microstructures when the plastic deformation is performed according to temperatures and strain rates given to the material. In order to express this model quantitatively, the energy dispersion efficiency (\(\eta\)) is presented as shown in Equation (1). \[\eta=2m/(m+1) \tag{1}\]  
In order to increase the reliability of the strain rate sensitivity coefficient (m), it is expressed in Equation (2) as a polynomial regression equation through the polynomial fit, and accordingly, the newly defined strain rate sensitivity coefficient is shown in Equation (3). Then, the flow stress at a reduction rate of 60% is shown in Figure 6.  
\[\ln(\sigma)=\ a\ +\ \mathrm{bln}\ \dot{\epsilon}+c(\ln\ \dot{\epsilon})^{2} \tag{2}\]  
\[m\ =\ b\ +2\mathrm{ch}\dot{\epsilon} \tag{3}\]  
The strain rate sensitivity coefficient (m) obtained through this process is an indicator that this is the criterion for the stability and instability in its plastic deformation, and the contour map for the energy dispersion efficiency (\(\eta\)) is shown in Figure 7. The energy dispersion efficiency tends to increase as the strain rate is lower, and the energy dispersion efficiency (\(\eta\)) is relatively high under the strain rate of \(1\times 10^{-2}\)/s at temperatures of 800-850 \({}^{\circ}\)C and 1050-1100 \({}^{\circ}\)C, which means that microstructural changes in the material are active. The contour map through the energy dispersion efficiency may be used to derive  
Figure 5: True stress–strain curves of Ti-6 Al-4V alloy at various temperatures and strain rates; (**a**) strain rate \(1\times 10^{-2}\)/s, (**b**) strain rate \(1\times 10^{-1}\)/s, (**c**) strain rate \(1\times 10^{0}\)/s. optimal forming conditions, but it is difficult to use the contour map as a criterion for evaluating the stability during the high-temperature forming process [25]. Therefore, the methods proposed by [PERSON] [22], [PERSON] [23], and [PERSON] [24] were used to predict the possible forming defects during the high-temperature forming process. First, the criterion for plastic instability proposed by [PERSON] [22] is shown in Equation (4). \[\xi\big{(}\ \dot{\varepsilon}\big{)}=\frac{\partial\ln[\mathrm{m}/(\mathrm{m}\ +1)]}{\partial\ln\ \dot{\varepsilon}}+\ \mathrm{m}\ <0 \tag{4}\]  
where \(\xi\) is an index of flow instability and is a dimensionless value. If it represents a negative value as a function of temperature and strain rate, it is defined as an unstable region during the plastic processing. If it is defined through a polynomial regression equation, it can be expressed as Equation (5). Then, the following unstable region is shown in Figure 8. This showed a value of \(\xi(\varepsilon)<0\) under the strain rate conditions of \(1\times 10^{-2}/\mathrm{s}\)  
Figure 6: Flow stress curves at different temperatures as a function of strain rate (\(\varepsilon=0.6\)). Figure 7: Deformation contour map shown by temperature-log(strain rate) relation of Ti-6 Al-4V alloy (\(\varepsilon=0.6\)) indicating the efficiency of power dissipation. and \(1\times 10^{-1}\)/s at 800-850 \({}^{\circ}\)C and all strain rate conditions at 950 \({}^{\circ}\)C. It is expected to result in unstable plastic processing in this region. Figure 6.0  
Meanwhile, [PERSON] [23] introduced the criteria for the strain rate sensitivity coefficient (m) and temperature sensitivity coefficient (s) based on the Lyapunov function, and expressed it as a function for 1/T as shown in Equation (6) in order to interpret the relationship to the temperature sensitivity coefficient. Figure 9 shows the result of fitting, and the plastic stable region is expressed in four different conditions, as shown in Equations (7)-(10).