*3.1. Plastic Deformation*

Let us first discuss cutting for *α* = 45◦ and 0◦, which proceeded via the same plastic mechanism. Figure 2 shows the dislocations that formed during the cutting process. The dominant mechanism was the formation of edge dislocation with the Burgers vector *b* = <sup>1</sup> <sup>2</sup> [111], which moved upward in the [111] direction. Their motion transported atoms upwards at the front of the tool out of the surface and thus formed the chip. The motion could effectively be described as the shear of the material with the shear plane given by the glide plane of the dislocation system; this shear plane is conventionally denoted as the primary shear plane (PSZ). The shear angle *φ* was hence given by the angle between the Burgers vector of the dislocations and the cutting direction [001]; it amounted to *φ* = 54.7◦. We emphasize that Figure 2 demonstrates that all plasticity occurring during the cut was confined to a single shear plane; this cutting system therefore provided a textbook example of the so-called single shear plane cutting model in machining theories [2,3,5–7,50,51]. A previous analysis of this cut system for the rake angle of *α* = 15◦ gave the same conclusions on the plastic behavior during cutting [21,22].

**Figure 2.** Side view of the dislocations generated in the Fe crystal after a cutting length of 100 Å with a cutting tool of rake angle 45◦ and 0◦. On the left-hand side, an atomistic sketch shows a 2D bcc unit cell in the plotted plane that explains the slip directions. Yellow: deformed surface including unidentified defects. Color code for dislocations classified by the Burgers vector *b*: red: *b* = 100; orange: *b* = <sup>1</sup> <sup>2</sup> <sup>111</sup>; blue: *<sup>b</sup>* <sup>=</sup> <sup>1</sup> *<sup>p</sup>* 111 partial with *p* = 3, 6, or 12.

Besides the *b* = <sup>1</sup> <sup>2</sup> [111] dislocations that are immediately responsible for chip formation, Figure 2 also shows the presence of several other dislocation systems. All of them are edge dislocations with their dislocation lines oriented parallel to the tool edge. Among these are *b* = [001] edge dislocations, which move along the cutting direction, [001], to the left, parallel to the surface, as well as *b* = <sup>1</sup> <sup>2</sup> [1¯1¯1] dislocations, which move into the substrate interior. Both of these glide systems transport material away from the cut zone, but do not contribute to chip formation.

For a rake angle of *α* = −22.5◦, plasticity is illustrated in Figure 3 for various cutting lengths *L*. Here, the action of the *b* = <sup>1</sup> <sup>2</sup> [111] dislocations, close to the rake face, as barely visible, since the angle between the glide direction and the rake face was quite small, only 12.8◦, such that dislocations had only little time (and space) for moving towards the surface, before the rake surface covered them up. Due to the small activity of dislocations in the [111] direction, the upper surface started bending elastically upwards. This bending generated a large number of partial dislocations (in the following abbreviated as "partials") flowing in the [1¯1¯1] direction; they created a step on the surface at the positions where the partials were emitted (seen at a cutting length *L* = 31 Å). These partials had Burgers vectors of the form *b* = <sup>1</sup> *<sup>p</sup>* 111 with *p* = 3, 6, or 12; they formed twinning boundaries, such that the volume enclosed by these partials was by nanotwins. After this nanotwin grew to span almost the entire simulation volume (*L* = 60 Å), the process of the generation of twinning partials in the elastically bent material in front of the tool repeated itself (*L* = 100 Å).

**Figure 3.** As in Figure 2, but for a rake angle of −22.5◦ and various cutting lengths *L*.

Finally, Figure 4 shows the plastic activity when cutting with a rake angle of *α* = −45◦. Emission of *b* = <sup>1</sup> <sup>2</sup> [111] dislocations was completely suppressed as their glide direction lied within the rake tool. Now, a large amount of *b* = <sup>1</sup> *<sup>p</sup>* [1¯1¯1¯] partial dislocations were activated, which transported the material backward. These latter dislocations led to a deformation of the frontal (right-hand side) surface, where the tool entered. As a consequence, the cutting process did not lead to chip formation on the top surface, but rather to a deformation of the frontal surface.

**Figure 4.** As in Figure 2, but for a rake angle of −45◦ at the end of the cut, *L* = 100 Å.

We concluded that for *<sup>α</sup>* <sup>≥</sup> <sup>0</sup>◦, a single dislocation system—with the Burgers vector *<sup>b</sup>* <sup>=</sup> <sup>1</sup> <sup>2</sup> [111] was responsible for cutting. For a positive rake angle, hence, cutting could be well described by a single shear angle, *φ* = 54.7◦. Even for *α* = −22.5◦, this system still contributed to cutting, but was no longer dominant. For *α* = −45◦, the system was completely deactivated.
