## 3 Parameter Optimization of the Constitutive Model
### Optimal Selection of Thermal Stress Parameters
The value \(\alpha\in(1.6\times 10^{-6},1.6\times 10^{-5})\) was estimated, and the upper and lower bounds of this range were expanded to a certain extent, taking the theoretically allowable maximum change range \((1\times 10^{-6},1\times 10^{-4})\). Since \(\alpha\) and \(\beta\) belong to the same order of magnitude, it can be considered that \(\alpha\) and \(\beta\) have the same range. 3. Determination of \(n_{2}\): It is generally believed that for most FCC metals, \(n_{2}\) is 0.5, and for individual metals, there may be a small variation around 0.5. On this basis, for S32760, we considered the maximum variation range allowed by this theory, i.e., (0,1). 4. Determination of \(p\) and \(q\): \(p\) and \(q\) are a pair of correlation constants that determine the shape of the barrier, and the intervals \(0<p\leq 1\), \(1\leq q<2\) Nemat-Nasser (1960), are generally taken for single crystals. Several typical (\(p\), \(q\)) values such as (2/3, 1), which represents a rectangular barrier; (1/2, 2), which specifies a hyperbolic barrier; and (1, 2), which denotes a sinusoidal barrier, were adopted. For most metals, (\(p\), \(q\)) could be considered as (2/3, 1), (2/3, 2), (3/4, 4/3), and (1, 1), i.e., a transition between rectangular and sinusoidal shapes. Although the values of \(p\) and \(q\) introduced above are applicable to single crystals, they could also be exploited for S32760 since the \(p\) and \(q\) parameters in the constitutive model are the mean values of the same variables in the constitutive models of the BCC and FCC structures. The range of parameters in the constitutive model determined above is the parameter range of the genetic algorithm. In this paper, a genetic algorithm was used to optimize the parameters, and a set of constitutive model parameters were calculated using the GA Optimization Toolbox. The thermal stress parameters of the S32760 constitutive model are shown in Table 3.  
Therefore, a set of initial values of the constitutive parameters of S32760 duplex stainless steel were obtained. The experimental data for the orthogonal cutting process were then used as a reference to reverse identification on the thermal stress value so that the constitutive parameters were continuously corrected until the difference between the experimental value and the simulated value was minimized. According to the constitutive parameters obtained in Table 3, the developed S32760 constitutive model is given as follows:  
Figure 8: Constitutive model parameter optimization program’s flowchart. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Undetermined Constitutive Parameters** & **The Actual Estimation Range** & **Definite Value** & **Unit** \\ \hline \(\overline{Y}\) & [1500, 3500] & 3149.06 & Mpa \\ \(n_{2}\) & (0,1) & 0.2680 & / \\ \(\phi_{sh}\) & [1000, 2000] & 1880.62 & Mpa \\ \(\alpha\) & (\(10^{-6},10^{-4}\)) & 0.00002298 & 1/K \\ \(\beta\) & (\(10^{-6},10^{-4}\)) & 0.00009213 & 1/K \\ \(q\) & [1, 2] & 1.6809 & / \\ \(p\) & (\(0,1\)) & 0.0191 & / \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Thermal stress parameters of S32760 constitutive model. \[\sigma=60+1318\epsilon^{0.07997}+ \tag{42}\] \[(3149.06\epsilon^{0.268}+1880.62)\bigg{\{}1-\left[-0.00009213T\ln( \frac{\varepsilon}{3\times 10^{9}})\right]^{\frac{1}{1.6800}}\bigg{\}}^{ \frac{1}{0.00002298T\ln(\frac{\varepsilon}{101})}}+0.00272\varepsilon\]