**1. Introduction**

While in applications, cutting processes are usually performed on poly-crystalline materials, from a materials-science point of view, it is also interesting to study the cutting of single crystals. In micro- and nano-cutting [1], the cutting depth may be smaller than the grain size of the material, so that crystal plasticity effects need to be taken into account.

However, also from the point of view of machining mechanics, this topic is interesting. The theory of cutting is largely based on the concept of a single shear plane responsible for the cut and the geometry of the chip formed [2,3]. For cutting polycrystalline materials, it is known that this concept is an idealization (see for instance the critical review by Astakhov [4]), and several extensions of the basic framework have been formulated [5–7]. The application of these concepts to nanocutting has been recently reviewed by Fang and Xu [1]. However, in the cutting of single crystals, plasticity will as a rule be based on the dislocation slip. If the cut system—that is, the surface orientation and the cut direction—is carefully chosen, only a single slip system will be activated, and thus, the shear plane is determined by crystallography.

Molecular dynamics (MD) simulation has been repeatedly used for studying machining processes such as nanoindentation [8,9] or the scratching of surfaces [10,11]. Furthermore, cutting has been simulated as well for fcc [12–18] as for bcc [19–22] metals and also for metallic glasses [23], ceramics [24–31], and composites [32]. MD is based on solving Newton's equations of motion for the atoms that make up the workpiece such that this simulation method allows obtaining atomistic insight into the plasticity processes relevant for machining at the nanoscale.

The analysis of MD simulations of the cutting process has often been based for the macroscopic concept of a "stagnation point" that divides the material moving upwards to form the chip from the material that moves downward into the material interior below the tool [1,33]. In this scenario, in particular the effect of tool edge curvature has been investigated [34,35]. Furthermore, a minimum cutting depth and a minimum rake angle (of the order of −65◦ to −70◦) have been postulated; for shallower cuts or blunter rakes, the material will be buried beneath the tool, and no chip is formed [1,33]. However, these ideas do not appear to have been combined up to now with a crystal plasticity analysis of the dislocation processes responsible for material separation and chip formation.

In the present paper, we will use MD simulation to study the application of machining theories to a well studied cut system, the (110)[001] cutting system of bcc Fe, since here, it was shown that indeed a single dislocation slip system is dominant in chip formation [21,22]. By varying the rake angle of the tool, we can vary the magnitude and orientation of the forces during cutting and analyze to what extent traditional machining theories describe the cutting of this system. While a few MD simulations studied the effect of the rake angle previously [33,36,37], they did not analyze the results obtained for dislocation plasticity in terms of available cutting theories. It is the objective of the present study to identify the influence of the rake angle of the cutting tool on the cutting of single crystals in terms of the dislocation plasticity.

A further motivation for studying the effect of the rake angle on metal cutting is given by the fact that in nanomachining, the geometry of the tool edge is not well characterized in the nanometer scale. On this scale, often the tool edge may be idealized by a geometry with a negative rake angle, even though the macroscopic form is sharp, possessing a positive rake angle. This issue provides a further motivation to study the influence of the rake angle on machining processes.
