# Analytical Modeling of Particle Scratching Process
## 3 Result and Discussion
### Force Ratio
The material constitutive model includes two parameters that yield strength \(\sigma_{y}\) and the coefficient of strain strengthening \(n\). The force ratio depends on \(\sigma_{y}\) and \(n\) when other parameters are given. The experimental setup for researching the effect of \(\sigma_{y}\) and \(n\) on force ratio is listed in Table 4, and the result is shown in Figure 10.  
Figure 8: Effect of workpiece speed on force ratio. Figure 7: Effect of grinding depth on force ratio: (**a**) the grinding condition is dry, (**b**) the grinding condition is MQL or conventional fluid. Figure 9: Effect of grit size on force ratio. As shown in Figure 10, the force ratio affected by the material constitutive model was presented. A conclusion can be drawn that \(\sigma_{y}\) does not affect the force ratio. The force ratio increases linearly with the increase in \(n\), but the increase is not obvious. The reason is that both the elastic deformation zone and the plastic deformation zone are involved in the parameter \(\sigma_{y}\), but only the plastic deformation zone is involved in the parameter \(n\). During the elastic contact phase, the smaller contact area leads to local stress concentrations that may promote material cutting rather than furrow formation, resulting in a higher plough-cut ratio (i.e., a higher percentage of cutting). Plastic deformation leads to redistribution of the contact area. It has been shown that the ratio of plastic contact area to plastic contact area decreases significantly during wear, especially when the ratio is below 0.5, and wear increases dramatically, suggesting that the material is removed in the form of flaking rather than sustained plough-cutting. In addition, the work hardening of elasto-plastic materials enhances resistance to plastic deformation, further reducing the plastic contact area and leading to a decrease in wear [25]. This dynamic change may cause the force ratio to decrease as the plastic phase progresses. The energy dissipation mainly originates from the hysteresis effect of viscoelastic materials and the deformation of the adhesion neck at the contact edge. Under elastic conditions, increased adhesion strength may lead to increased friction, but the energy release rate shows a non-monotonic trend [26]. At this time, energy accumulation is dominated by microconvex body deformation, with less material removal and potentially higher force ratios. Plastic deformation dominates energy dissipation. During friction, the subsurface maximum shear stress triggers fatigue crack initiation and extension, leading to material stripping to form abrasive debris, and energy is released through plastic deformation and thermal dissipation (frictional temperature rise). For example, frictional temperature rise can cause plastic deformation of the contact surface to expand and significantly increase wear [27]. The energy dissipation in the plastic phase is more focused on material destruction rather than furrow formation and may reduce the force ratio. \begin{table}
\begin{tabular}{c c c c c c} \hline  & \multicolumn{3}{c}{\(h_{\textit{{doc}}}\) = **30 \(\mu\)m**, \(k_{1}\) = \(k_{2}\) = 0.3, \(\mu\) = 0.5, \(r\) = 0.1 mm**} \\ \cline{2-6}  & \(\sigma_{\textbf{y1}}\) & \(\sigma_{\textbf{y2}}\) & \(\sigma_{\textbf{y3}}\) & \(\sigma_{\textbf{y4}}\) & \(\sigma_{\textbf{y5}}\) \\ \hline \(n_{1}\) & (0.2,200) & (0.2,400) & (0.2,600) & (0.2,800) & (0.2,1000) \\ \(n_{2}\) & (0.4,200) & (0.4,400) & (0.4,600) & (0.4,800) & (0.4,1000) \\ \(n_{3}\) & (0.6,200) & (0.6,400) & (0.6,600) & (0.6,800) & (0.6,1000) \\ \(n_{4}\) & (0.8,200) & (0.8,400) & (0.8,600) & (0.8,800) & (0.8,1000) \\ \(n_{5}\) & (1,200) & (1,400) & (1,600) & (1,800) & (1,1000) \\ \hline \end{tabular}
\end{table} 
Table 4: Experimental setup for studying the effect of material constitutive model. The elastic contact stresses are not uniformly distributed, with peak stresses occurring at the contact edges (e.g., the leading edge of slider motion), which tends to initiate surface/subsurface cracking in brittle materials [28,29].