2.3.2. Constitutive Law

The constitutive law of the material describes the relationship between the flow stress of the material and the plastic deformation, the strain rate, and the temperature, which can be summarized by the functional equation:

$$
\sigma = f(\dot{\varepsilon}, T) \tag{12}
$$

where <sup>σ</sup> is the rheological stress in the plastic deformation process of material; . ε is the strain rate; and T is the deformation temperature. Rheological stress can be calculated by the Zener–Hollomon formula. The specific expression is:

$$\sigma(T,\dot{\varepsilon}) = \sigma\_{\mathcal{P}} \sin h^{-1} \left[ \left( \frac{Z}{A} \right)^{\frac{1}{n}} \right] \tag{13}$$

where, *A*, σ*p*, and n are the material parameters, and Z is the Zener–Hollomon parameter. The specific expression is:

$$Z = \dot{\varepsilon} \exp\left(\frac{\dot{Q}}{RT}\right) \tag{14}$$

where *Q* is the activation energy independent of temperature and *R* is the gas constant. The specific parameters are shown in Table 2.

**Table 2.** 2024 aluminum alloy material parameters [36].

