# Strain Rate of Metal Deformation in the Machining Process from a Fluid Flow Perspective
## 3 Results and Discussion
### Data Analysis and Discussion  
The strain rate distribution on each line can be calculated using Formulas (13) and (14). A single numerical value fluctuates greatly due to the influence of the front and rear grids; thus, studying the strain rate of a single grid is meaningless. The average values of each line are close to the actual distribution. The calculation results are shown in Figure 7. The average strain rates of the streamline on the rake face are \(1.53\times 105\), \(0.91\times 105\), \(0.89\times 105\) and \(0.52\times 105\) s\({}^{-1}\). The average strain rates of the shear line on the shear plane direction are \(0.54\times 105\), \(0.80\times 105\) and \(0.70\times 105\) s\({}^{-1}\), respectively. As shown in Figure 7a, the farther away from the rake face, the smaller the value will be because of the friction between the rake face and chip; the greater the friction, the greater the deformation and the higher the average strain rate will be. Figure 7b shows that the average strain rate on the second shear line is the largest because it is located at the center of the first deformation zone, and the other regions decrease in turn; this finding is similar to the calculation and simulation results [(15; 21)]. The calculated results on the rake face and shear plane were compared with the experimental results (Figure 8). The experimental results include the first streamline (Figure 5, No.1) along the rake face direction and the second shear line (Figure 6, No.2) along the shear plane direction. The actual measured values may vary considerably because of the influence of various factors (such as cutting speed, material, etc. ), but this phenomenon does not affect the study and analysis of the distribution law of the strain rate; for example, the results of the grid measurement with different cutting speeds will vary greatly, but the distribution rule of the strain rate will not change--that is, the strain rate in the center of the first deformation zone is larger than that in other regions along the shear plane direction, and the strain rate at both ends of the shear plane is the largest, with the values decreasing sequentially outward. The measurement results of the different samples may also change at the same \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Line** & & & & & **Length (\(\mu m\))** & & & \\ \hline No.1 & 31.05 & 20.2 & 19.3 & 22.43 & 24.74 & 33.58 & 25.73 & 28.43 & 22.91 & 31.16 \\ No.2 & 37.71 & 27.13 & 31.68 & 28.03 & 33.29 & 33.85 & 34.27 & 35.27 & 37.28 & 26.02 \\ No.3 & 40.09 & 37.95 & 25.33 & 31.55 & 32.42 & 37.01 & 35.59 & 37.95 & 39.18 & 28.99 \\ No.4 & 45.68 & 38.8 & 32.82 & 33.85 & 37.38 & 37.71 & 33.09 & 40.58 & 34.96 & 34.79 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Original lengths of the meshes along the rake face direction. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Line** & & & & & **Length (\(\mu m\))** & & & \\ \hline No.1 & 39.82 & 33.09 & 37.28 & 36.48 & 36.83 & 37.55 & 35.27 & 31.16 & 27.31 & 14.8 \\ No.2 & 43.32 & 38.56 & 35.88 & 41.56 & 30.93 & 40.09 & 33.04 & 35.73 & 30.74 & 19.56 \\ No.3 & 49.89 & 30.69 & 35.97 & 38.6 & 39.3 & 37.6 & 46.19 & 29.05 & 25.24 & 24.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Original lengths of the meshes along the shear plane direction. Figure 7: Average value of the strain rate (**a**) along the rake face direction and (**b**) along the shear plane direction. cutting speed, but the distribution of the strain rate still follows the same rule; so, accurate quantitative research is still not possible, but rough quantitative research can be done for specific cutting speeds. Given that the mesh is processed by femtosecond laser, the size range is small; as such, only 10 meshes were used in this experiment. As shown in Figure 8a, the trends of the curve are in good agreement; that is, they gradually decrease from the beginning of the tool tip to the stagnation point of velocity and then increase.