## 3 Numerical Results and Analysis
### Formation of Serrated Chips  
To explain the formation of serrated chips during the micro-cutting process, the distribution of stress and temperature field are used to study the changes of each stage of the detailed serrated chips. Additionally, the stress S\({}_{12}\) and temperature of the serrated formation process were sampled along the shear zone area. Stress S12 refers to the shear stress acting in the Y direction on the Y.Z. plane, which is one of the components of stress [67], allowing the determination of whether the stress in the serrated chip is uniformly distributed. Currently, several studies have emphasized the formation mechanism of serrated chips. [PERSON] et al. [68] indicated that the elastic strain is one of the dominant factors leading to the formation of shear bands, and the onset of the highly localized material softening effects. [PERSON] et al. [69] proposed the theory of periodic fracture and suggested that the serrated chips are formed by shearing and squeezing. However, [PERSON] and [PERSON] [70] indicated that a serrated chip is caused by the softness of the material due to the significant heat generated in the shear zone, and thus proposed the adiabatic shear theory. The representative theories correspond to the adiabatic shear theory. Figure 3 presents the strain of the S\({}_{12}\) rule during the formation of the serrated chips in the micro-cutting of Ti6 Al4V. Figure 4 presents the temperature field during the formation of the serrated chips in the micro-cutting of Ti6 Al4V. Figures 4a and 5a present the material deformation state of the newly serrated chip when the previous chip is formed, and the  
deformation of the workpiece due to compressive stress, respectively. Furthermore, \(S_{12}\) denotes tensile stress, and the temperature in the shear zone is approximately 100-200 \({}^{\circ}\)C. When the tool continues moving forward, the workpiece in the contact area that is continuously squeezed by the tool begins to bulge, as shown in Figures 3b and 4b. At this stage, the temperature of the shear zone increases to 500 \({}^{\circ}\)C, and the workpiece begins to soften in the shear zone. Figure 4: Temperature field distribution during chip formation at different stages. (**a**) Serrated chip initiation; (**b**) strain localization; (**c**) thermal softening localization; (**d**) serrated chip formed. Figure 5: State variable distribution along the designated path. (**a**) Variation of stress S\({}_{12}\) during chip formation; (**b**) variation of temperature during chip formation. Figure 3: Distribution of stress S\({}_{12}\) during chip formation at different stages. (**a**) Serrated chip initiation; (**b**) strain localization; (**c**) thermal softening localization; (**d**) serrated chip formed. As shown in Figures 3c and 4c, the stress concentration in the bulging area of the surface of the workpiece intensifies, thereby leading to the plastic instability of the workpiece; this phenomenon can be confirmed by [PERSON] (2017). The free surface of the serrated chip is formed, and the adiabatic shear zone becomes more pronounced. This is mainly due to the plastic deformation in the primary deformation zone, which generates a significant amount of heat. Thus, the temperature goes up to 600 \({}^{\circ}\)C and results in thermal softening of the material in the adiabatic shear zone (A.S.B. ), thereby rapidly decreasing the shear resistance. At the end of this phase, \(S_{12}\) continues to increase and is confined to a relatively narrow area. When the micro-cutting process reaches the states in Figures 3d and 4d, the expanded material continues to squeeze and narrows when the compressive stress \(S_{12}\) decreases, where the adiabatic shear zone reaches the highest temperature, which exceeds 700 \({}^{\circ}\)C. The serrated chip gradually starts to form from the back surface. Figure 5a presents the stress \(S_{12}\) sampled along the path of the shear zone (path 1, path 2, path 3, and path 4).