# An Advanced DEM-FEM Method for Herringbone Gear in Shot Peening
## 2 Experimental Process and Materials  
### Mechanical Behavior of 10 CrNi2 Mo3 Cu2V Steel  
The material of herringbone gear is 10 CrNi2 Mo3 Cu2V, and its chemical composition is shown in Table 1. Before conducting the shot peening simulation model, it is necessary to determine the mechanical behavior of the 10 CrNi2 Mo3 Cu2V material. The mechanical behavior is studied through the Hopkinson pressure bar experiment to provide mechanical behavior parameters for the finite element simulation process. In this study, the ALT1000 Split Hopkinson Pressure Bar (SHPB) testing system (Instron, Norwood, MA, USA) was used to determine the mechanical behavior of the material, as shown in Figure 1. The selected strain rates in the experimental process are 1000 s\({}^{-1}\), 3000 s\({}^{-1}\), and 5000 s\({}^{-1}\). The strain, strain rate, and stress of the specimen can be calculated according to Equation (1) [38], obtaining the stress-strain relationship curve of the specimen:  
\[\left\{ \begin{array}{l}\varepsilon(t)=-\dfrac{2C_{0}}{L}\varepsilon_{R}(t)\\ \sigma(t)=\dfrac{E_{0}A_{0}}{A}\varepsilon_{T}(t)\end{array} \right. \tag{1}\]  
where \(C_{0}\) represents the velocity of the elastic wave in the bar, \(L\) is the length of the specimen, \(\varepsilon_{R}\) is the waveform signal recorded by the incident bar, \(E_{0}\) denotes the elastic modulus of the pressure bar, \(A_{0}\) is the cross-sectional area of the bar, \(A\) is the cross-sectional area of the specimen, and \(\varepsilon_{T}\) is the waveform signal recorded on the transmission bar. During the shot peening process, the introduction of plastic deformation leads to the modification of the material. Therefore, only the stress-strain relationship in the plastic stage is presented in the experimental results of this paper. After obtaining the mechanical behavior of the material, it is necessary to establish an appropriate constitutive model to reflect the material's mechanical behavior during the shot peening process. The Johnson-Cook (J-C) constitutive model has been proven to describe the mechanical behavior during the shot peening process [38]. Therefore, this paper establishes the J-C constitutive model \begin{table}
\begin{tabular}{c c c c c c c c} \hline
**Cr** & **Ni** & **Mo** & **Cu** & **V** & **C** & **Mn** & **Si** & **Fe** \\ \hline
1.0 & 2.0 & 3.25 & 2.0 & 0.1 & 0.11 & 0.4 & 0.9 & the rest \\ \hline \end{tabular}
\end{table} 
Table 1: Chemical composition of 10 CrNi2 Mo3 Cu2V. Figure 1: Tensile test process. based on the experimental test results, providing a foundation for subsequent shot peening finite element models. The specific form of the J-C constitutive model is:  
\[\sigma=(A+B\epsilon_{eq}^{n})\bigg{(}1+C\ln\frac{\dot{\epsilon}}{\dot{\epsilon}_ {0}}\bigg{)}\bigg{(}1-\bigg{(}\frac{T-T_{r}}{T_{m}-T_{r}}\bigg{)}\bigg{)}^{m} \tag{2}\]  
Here, \(\sigma\) is the flow stress, \(\epsilon_{eq}\) is the equivalent plastic strain, \(\dot{\epsilon}\) is the equivalent plastic strain rate, \(\dot{\epsilon}_{0}\) is the reference strain rate, \(T\) is the test temperature, \(T_{m}\) is the material's melting temperature, and \(T_{r}\) is the room temperature. The parameters A, B, n, C and m are coefficients to be determined. A is the yield strength at the reference strain rate; B is the strain hardening coefficient; n is the strain hardening exponent; C is the strain rate sensitivity coefficient; and m is the thermal softening coefficient. The equation's right-hand side is composed of three parts, representing the influence of strain on stress, the influence of strain rate on stress, and the influence of temperature on stress, respectively. Since shot peening is a cold working process, in Equation (2), \(T=T_{r}\). The experimental test results and the established J-C constitutive model are shown in Figure 2. It can be observed that the test results at a strain rate of 1000 s\({}^{-1}\) are the closest to the calculated results obtained using the J-C constitutive model.