**Appendix A. The (100)[011] Cut System: Twinning**

For general cut surfaces and cut directions, more than one dislocation slip system—and hence shear plane—contributes to chip formation [22], and the analysis provided here for the (110)[001] system will not hold. We illustrate the complexities arising with the example of the (100)[011] system.

In this system, the slip direction responsible for chip formation, [111], made an angle of *φ* = 35.3◦ to the surface. Figure A1 illustrates the deformation occurring under cutting for three rake angles, *<sup>α</sup>* <sup>=</sup> <sup>45</sup>◦, 0◦, and <sup>−</sup>45◦. Perfect dislocations with the Burgers vector *<sup>b</sup>* <sup>=</sup> <sup>1</sup> <sup>2</sup> 111 were activated, which glided to the top surface. In addition, and more pronouncedly, twinning partials *b* = <sup>1</sup> *<sup>p</sup>* 111 showed up. The generation of a twinning boundary is most clearly seen in the figure for the rake angle of 0◦, where it is marked by a dense net of partial *b* = <sup>1</sup> <sup>6</sup> [111] dislocations. The slip direction [1¯11] was only activated for *α* = −45◦.

The twinning partials led to the generation of twin boundaries, which are highlighted in Figure A2. The largest twin was generated for *α* = −0◦. Twinned surfaces were recognizable by their smooth surfaces, while the *b* = <sup>1</sup> <sup>2</sup> 111 dislocations arriving at the surface led to surface roughening. Note that for this cutting system, even the *α* = −45◦ tool led to chip formation, since now the shear angle *φ* = 35.3◦ was smaller, enabling dislocation glide to the surface even for strongly negative rake angles.

The twinning occurring in front of the tool was equivalent to several shear planes being active temporarily during the cutting process and thus complicated any simple analysis in terms of the single shear plane model.

**Figure A1.** Side view of the dislocations generated in the Fe (100)[011] cutting system at cutting length 100 Å with a cutting tool of rake angles 45◦, 0◦, and −45◦. Dislocations and slip directions are denoted as in Figure 2.

**Figure A2.** Same cutting systems as in Figure A1, but highlighting twinning boundaries (pink). Vacancies are shown in blue, while surfaces and dislocations are colored gray.
