. Molecular dynamics simulations are an attractive tool for studying the fundamental mechanisms of lubricated machining processes on the atomistic scaleas it is not possible to access the small contact zone experimentally. Molecular dynamics simulations provide direct access to atomistic process properties of the contact zone of machining processes. In this work, lubricated machining processeswere investigated, consisting of a workpiece, a tool, and a cutting ﬂuid. The tool was fully immersed in the cutting ﬂuid. Both, a simple model system and real sub- stance systems were investigated. Using the simpliﬁed and generic model system,the inﬂuence of different process parameters and molecular interaction parameters were systematically studied. The real substance systems were used to represent speciﬁc real-world scenarios. The simulation results reveal that the ﬂuid inﬂu- ences mainly the starting phase of an atomistic level cutting process by reducing the coefﬁcient of friction in this phase compared to a dry case. After this startingphase of the lateral movement, the actual contact zone is mostly dry. For high pressure contacts, a triboﬁlm is formed between the workpiece and the cutting ﬂuid, i.e. a signiﬁcant amount of ﬂuid particles is imprinted into the workpiececrystal structure. The presence of a cutting ﬂuid signiﬁcantly reduces the heat impact on the workpiece. Moreover, the cutting velocity is found to practically not inﬂuence the coefﬁcient of friction, but signiﬁcantly inﬂuences the dissipationand, therefore, the temperature in the contact zone. Finally, the reproducibility of the simulation method was assessed by studying replica sets of simulations of the model system. 1 Introduction Understanding the fundamental mechanisms of lubricated tribological processes on the atomistic scale is crucial for many technical applications such as cutting and grinding in manufacturing. Cutting ﬂuids are used for two reasons: a) reduce the friction and b) reduce the heat impact and temperature of the workpiece. The fundamental mechanisms © The Author(s) 2023 J. C. Aurich et al. (Eds.): IRTG 2023, Proceedings of the 3rd Conference on Physical Modeling for Virtual Manufacturing Systems and Processes , pp. 260–280, 2023. https://doi.org/10.1007/978-3-031-35779-4 _14 Molecular Dynamics Simulation of Cutting Processes 261 in the small contact zone between a tool, a workpiece, and a lubricant behind these are today not fully understood. However, understanding these processes on the atomistic scale can be helpful for improving the macroscopic process, e.g. for modern micro- and precision machining technology. In-situ experimental investigations of the fundamentalmechanisms on the atomistic scale are not possible today. As an alternative, classical molecular dynamics (MD) simulations can be used to gain insights into lubricated tri- bological processes on the atomistic scale. Due to the strong physical basis, molecularsimulations can be applied in two general ways: a) the prediction of thermophysical properties of matter and b) modelling nanoscopic processes. In this work, the focus is on the modeling of nanoscopic cutting processes using molecular dynamics simulation. Molecular simulations are based on solving Newtons equation of motion for an atomistic many particle system – considering boundary condition imposed by the sim- ulation scenario, e.g. the movement of a tool. The interactions between the particleson the atomistic level are deﬁned by force ﬁelds. Force ﬁelds aim at representing the molecular interactions and structure of a given real substance and, hence, mostly pro- vide a reliable representation of the behavior matter. Besides using force ﬁelds for realsubstances, model systems can be favorably used in molecular simulation to study the link between molecular interaction parameters and macroscopic properties for obtaining generic information on processes [ 36,35,17,4,14,33,28]. Thereby, model systems can be used to study the fundamental mechanisms of complex processes in detail [ 8,18, 13,19,9]. The Lennard-Jones model system is the most popular and widely used model system [ 34,37]. In this work, both real substance systems and Lennard-Jones model systems were used for studying the atomistic processes of lubricated cutting. In the literature, there are several MD studies available investigating the deformation of a workpiece and material removal caused by a tool, e.g. Refs. [ 36,11,1,25,27,32, 39,38]. However, in most studies, only dry contact processes (no cutting ﬂuid) are considered, e.g. on the inﬂuence of the shape of the tool [ 2,10] and the solid material [17,11,3,42,16]. The inﬂuence of cutting ﬂuids is considered in only few studies, e.g. Refs. [ 39,45,26,30,31,6]. In this work, the inﬂuence of cutting ﬂuids on cutting processes were investigated on the atomistic scale. Thereby, different aspects of a cutting process were investigated such as the behavior of the ﬂuid in the lubrication gap [ 36,32], the formation of a triboﬁlm on the workpiece surface [ 32,39], the inﬂuence of the cutting speed on the process [ 27], the thermal balance of the system, and the temperature ﬁeld in the contact zone [ 36,27]. Also, the reproducibility of cutting simulations was investigated [ 38]. This chapter is organized as follows: First, the simulation scenarios, the molecular models, as well as the observables used for characterizing the system are introduced. Then, the results are presented and discussed, which includes mechanical properties, the workpiece deformation, lubrication and the formation of a triboﬁlm, thermal properties, and the evaluation of the reproducibility. 262 S. Schmitt et al. 2 Methods 2.1 Simulation Scenario The simulation scenario used in this work is depicted in Fig. 1. It consists of a workpiece, a (cutting) tool and, in the lubricated cases, of a ﬂuid. This models the contact zone of a machining process, e.g. the tip of an abrasive particle in micro grinding or an asperitycontact. In the lubricated simulations, the tool was fully submersed in the ﬂuid. In the dry cases, the tool was in a vacuum. The workpiece surface is in the x-yplane. Fig. 1. Sketch of the simulation scenario. The scenario consists of a workpiece (grey), a tool (green), and a ﬂuid or vacuum (blue). The simulation box had periodic boundary conditions in x- and y-direction. The ﬂuid was conﬁned in the box by a soft repulsive wall at the top. The workpiece was locked in position by prescribing the at least three atom layers at the bottom of the box.Dissipated heat is removed from the system by imposing the initial system temperature (speciﬁed below for the different systems) to at least four atom layers above the ﬁxed layer. In the course of the simulation, the tool carries out three consecutive movements: the indentation (negative z-direction), the cutting (positive x-direction), and the retraction (positive z-direction). Hence, the movement of the tool is predeﬁned. Three different tool shapes were used: a sphere [ 27,32], a spherical cap [ 39], and a cylinder [ 36,38]. In the latter case, a quasi-2D scenario was considered. Moreover, different cutting gaps h gapwere considered for the cutting, cf. Figure 1. The simulations contained up to 9.2 ×106particles per simulation. For the model system simulations, 5.43 ×106particles were used in the simulations: 3.65 ×106for the workpiece, 7.9 ×105for the tool, and 1.78×106for the ﬂuid. For the real substance simulations, at least 8 ×105particles were used for the workpiece, 7 ×105for the tool, and 8.68 ×105for the ﬂuid. The molecular simulation software LAMMPS [ 24] was used for the simulations. Details on the simulation scenario can be found in Refs. [ 36,27,32,39,38]. Molecular Dynamics Simulation of Cutting Processes 263 2.2 Molecular Model Simulations were carried out using a simpliﬁed model system as well as a real substance system, which are brieﬂy introduced in the following. Details on the model systemsimulations are given in Refs. [ 36,27,38]. Details on the real substance systems in Refs. [32,39]. 2.2.1 Model Systems The Lennard-Jones truncated and shifted (LJTS) model system is a generic and sim- pliﬁed system. Yet, this provides a reasonable representation of a real substances as the basis molecular interactions, i.e. repulsive and dispersive, are captured [ 35,12,44]. Hence, the simulations with the LJTS model system do not aim to model a speciﬁcreal cutting process but to investigate general mechanisms of cutting processes and the inﬂuence of molecular interaction parameters. Despite its simplicity, the LJTS system provides a physically robustness model backbone and is, at the same time, computa-tionally relatively cheap. In the presented model system, all occurring interactions were modelled by the LJTS potential (cf. Eq. 2.1). u LJ(r)=4ε/bracketleftBig/parenleftbigσ r/parenrightbig12−/parenleftbigσ r/parenrightbig6/bracketrightBig and uLJTS(r)=/braceleftbigguLJ(r)−uLJ 0r≤rc r>rcwith rc=2.5σ(2.1) In Eq. ( 2.1),uLJindicates the full Lennard-Jones potential. For the LJTS potential, interactions are truncated at rcand the potential energy uis shifted such that no discon- tinuity appears at the truncation radius. Each component (workpiece, ﬂuid, and tool) hastwo molecular interaction parameters: the energy parameter εand the size parameter σ. The size parameter σas well as the particle mass mof all components were the same in all cases. The solid-solid interactions between the workpiece and the tool were describedby the LJTS potential with a cut-off radius of r cut=21/6σsuch that they only interact repulsively. The workpiece energy parameter was chosen to represent iron [ 12] and the ﬂuid energy parameter was chosen to represent methane [ 44]. All quantities for the LJTS model systems are given in reduced units (cf. Table 1) with respect to the ﬂuid particle interaction parameters εFandσF. The solid-ﬂuid interaction energy was systematically varied in the range 0 ≤ε∗ SF≤1.7 to study its inﬂuence on the cutting process. The initial temperature was T*=0.8 and the initial pressure was p*=0.014. 2.2.2 Real Substance Systems In the real substance simulations, the workpiece was modeled as a single crystal iron block, the tool was modeled as a diamond single crystal with a spherical tip shape, and the ﬂuid was either methane or decane [ 32,39]. The iron workpiece was described by an embedded atom model (EAM) [ 21]. The ﬂuid was either modelled as methane by a BZS force ﬁeld [ 44,43] or as n-decane by the TraPPE force ﬁeld [ 22], which provide an excellent description of the ﬂuid bulk phase properties [ 29]. The diamond tool was modelled by a Tersoff potential [ 41]. For methane, the initial temperature was either 100 K (for simulations with a spherical indenter) or 130 K (for simulations witha spherical cap indenter). The initial pressure was 0.1 MPa and 50 MPa, respectively. 264 S. Schmitt et al. Table 1. Deﬁnition of physical quantities in reduced units. Reduced quantities are marked by (*). The Boltzmann constant is indicated as kB. Length L∗=L/σF Temperature T∗=T/(εF/kB) Force F∗=F/(εF/σF) Time t∗=t//parenleftbig σF√mF/εF/parenrightbig V elocity v∗=v/√εF/mF Energy E∗=E/εF 2.3 Deﬁnition of Observables Different quantities were computed from the simulation trajectories, which are brieﬂy introduced in the following. The forces on the tool in tangential ( x) and normal ( y) direction, Ftand Fn, respectively, were calculated as the sum of all forces acting on the particles of the tool. The forces were calculated every 1000 timesteps. Mean values have been calculated during the cutting phase in the stationary part of the process. Thecoefﬁcient of friction is deﬁned as μ=F t/Fn. The coefﬁcient of friction was calculated by the mean values of the forces from the stationary cutting phase. The internal energy of the ﬂuid UFand the workpiece USwere calculated as the sum of the interaction energies between all respective particles. They were also sampled every 1000 timesteps. The energy dissipated by the thermostat in the substrate /Delta1Uthermo was computed as the energy difference after and before the thermostatization in each time step. The followingquantities were calculated based on the conﬁgurational data of the particles that were written out at least every 10 4timesteps. The number of ﬂuid particles in the gap between the tool and the substrate were computed as Ngap. The gap was geometrically deﬁned as depicted in Fig. 2as the volume between the tool and the workpiece surface in front of the tool center and below the undeformed surface height. The surfaces were analyzed using the alpha shape algorithm [ 7]. Based on the calculated workpiece surface, the number of ﬂuid particles below the surface that form a tribolayer were computed as Ntribo. The temperature proﬁle in the x-zplane was sampled by averaging the per-atom temperature binwise. The bins are deﬁned as depicted in Fig. 2. An estimation of the statistical uncertainty and signiﬁcance of the observations is possible by the separate reproducibility study [ 38]. Details on the deﬁnition and sampling of the observables are given in Refs. [ 36,27,32,39]. 3 Results 3.1 Mechanical Properties Figure 3. Shows the time evolution of the tangential and the normal force in cutting simulations for a dry case and a lubricated case. During the indentation, the normal force increases drastically when the tool penetrates into the workpiece and causes elastic andplastic deformation. In that phase, the tangential force ﬂuctuates around F t=0. In the Molecular Dynamics Simulation of Cutting Processes 265 y xbintop view (sphere) top view (cylinder)Δy*Δx* xside view binzΔz*Δx* gap binΔx* Fig. 2. Sketch illustrating the deﬁnition of observables. Left: Side view with the gap between the tool and the substrate and the bin to sample the temperature in x-yplane. Right: Top view with the bin to sample the temperature proﬁle in x-yplane for the case of a spherical (top) and a cylindrical tool (bottom). cutting phase, the normal force decreases and the tangential force increases until a steady state is reached. During the retraction, the both forces decay to zero. Overall, the results from the dry and lubricated case are similar. Yet, the normal force on the tool is slightly affected by the cutting ﬂuid during the indentation and the starting phase of the cutting. The peaks observed during the indentation in the dry case (causedby dislocation movement) are damped by the presence of the cutting ﬂuid molecules in the gap. During the indentation, the vast majority of ﬂuid particles is squeezed out of the gap. During the starting phase of the cutting, until a steady state is reached, the tangentialforce is slightly increased in the lubricated case compared to the dry case, which is due to an effective enlargement of the tool due to adsorbed ﬂuid particles [ 32], i.e. the tool causes more elastic and plastic deformation of the workpiece in the lubricated cases. Thecoefﬁcient of friction increases strongly in the starting phase of the cutting. In the starting phase, the lubricated simulations yield slightly lower coefﬁcients of friction compared to the dry simulations due to lubricant molecules remaining in the gap between the tool andthe substrate. In the stationary phase, the coefﬁcient of friction is very similar in the dry and the lubricated case with values between 0.4 and 0.6. Since the differences between the dry and lubricated case are small and might in general be within the scattering of the results, the reproducibility of the ﬁndings discussed here was studied (and conﬁrmed) using the model system, cf. Sect. 3.4. The inﬂuence of the solid-ﬂuid interaction energy ε ∗ SFon the cutting process was systematically investigated using the LJTS model system [ 36]. The results are shown in Fig. 4. In the starting phase of the cutting process, the coefﬁcient of friction in the lubricated cases is reduced by about 25% compared to the dry case. This is due to an increased normal force and a slightly decreased tangential force in the starting phase [36]. In the stationary phase, the coefﬁcient of friction is increased in the lubricated case compared to the dry case by approximately 15%, which is due to individually ﬂuid 266 S. Schmitt et al. Fig. 3. Normal (top) and tangential (bottom) forces on the tool as a function of time for a dry and a lubricated simulation [ 32]. The tool had a spherical shape. The temperature was T=100 K. The workpiece was an iron single crystal, the tool was a diamond, and the ﬂuid was methane. particles being imprinted into the workpiece surface. Interestingly, these ﬁndings do not dependent on the solid-ﬂuid interaction energy. The coefﬁcient of friction is reduced in the starting phase due to ﬂuid molecules remaining in the gap and effectively increasing the tool size. These ﬂuid molecules are squeezed out mostly with ongoing cutting process.The squeeze out process is discussed in detail in Sect. 3.3. Figure 5. Shows the results for the inﬂuence of the cutting speed on the coefﬁcient of friction. For both cases (dry and lubricated), no signiﬁcant inﬂuence of the cutting speed on the coefﬁcient of friction is observed in the considered velocity range. For the smallest considered cutting speed v ∗=0.66, the coefﬁcient of friction is nearly the same for the dry and the lubricated simulations with μ∗≈0.85. For the velocities 0 .1<v∗<0.3, the lubricated simulations yield smaller values for the coefﬁcient of friction compared to the dry simulations. These differences are probably within the uncertainty of the data.This is supported by the result for the highest considered velocity v ∗=0.332, which Molecular Dynamics Simulation of Cutting Processes 267 Fig. 4. Tangential force (top), normal force (middle), and coefﬁcient of friction (bottom) of the lubricated simulations related to the dry simulation as function of the solid-ﬂuid interaction ε∗ SF [36]. The tool had a cylindrical shape. The temperature was T*=0.8. The workpiece, the tool, and the ﬂuid were modeled by the LJTS potential. Mean values for the starting phase (red, 142 < t*<335) as well as the stationary phase (blue, 335 <t*<625). show the opposite trend. Using the potential parameters for methane and iron [ 12,44] for the ﬂuid and workpiece, respectively, the cutting speed range corresponds to 20 - 100 m/s in SI units, which is typical for cutting and grinding processes [ 20,5]. In the literature, relative velocities between two solid bodies up to 400 m/s were consideredusing molecular simulation (which is not representative for common manufacturing cutting processes). Nevertheless, in this high-speed regime, the coefﬁcient of friction was reported to decrease with increasing velocity [ 23,46]. Using the real substance system simulation setup, the inﬂuence of the cutting depth, i.e. the z-position of the tool with respect to the workpiece surface, was systematically investigated [ 39]. Here, also conﬁgurations with no direct contact between tool and substrate were considered, i.e. hydrodynamic lubrication (HL). In Fig. 6, the forces on the tool as well as the coefﬁcients of friction are shown as function of the cutting depth h. Results are given for decane as ﬂuid. Three different lubrication regimes can be identiﬁed for different cutting depth: hydrodynamic lubrication (HL), mixed lubrication (ML), and boundary lubrication (BL). The normal and tangential force on the tool increase withincreasing cutting depth as expected. The normal forces are larger than the tangential 268 S. Schmitt et al. Fig. 5. Coefﬁcient of friction μas a function of the tool velocity v∗for a dry and lubricated cases [27]. The tool had a spherical shape. The temperature was T*=0.8. The workpiece, the tool, and the ﬂuid were modeled by the LJTS potential. forces in general. The coefﬁcient of friction behaves differently in the three regimes. In the HL regime, the coefﬁcient of friction is lowest – as expected. Here, a stable ﬂuid ﬁlm separates the two solids and leads to a good lubrication with small values of the coefﬁcient of friction. In the ML regime, the coefﬁcient of friction increases withincreasing cutting depth as the normal force strongly increases due to the direct contact between the tool and the workpiece, which is transferred via the thin lubrication ﬁlm. The coefﬁcient of friction reaches a maximum of μ≈0.21 at the border between the ML and BL regime. For larger cutting depth (BL regime), the coefﬁcient of friction decreases with increasing cutting depth. The behavior in the BL regime is mainly determined by the formation of a triboﬁlm, the squeeze-out and the resistance of the lubrication ﬁlm.Therefore, the tangential force increases more strongly compared to the normal force, which leads to a decrease of the coefﬁcient of friction. 3.2 Workpiece Deformation In the following, phenomena related to the surface of the workpiece and to the formation of dislocations in the workpiece are discussed. Figure 7shows the results for the total dislocation length as a function of the simulation time for a dry and a lubricated case. Overall, the results for the dry and the lubricated case are similar. In the indentation phase, the presence of the cutting ﬂuid leads to a slightly earlier formation of dislocationscompared to the dry simulation, which was also conﬁrmed by replica simulations of a model systems in an earlier work of our group [ 38]. This is probably due to ﬂuid adsorption layers on both the workpiece and the tool surface that effectively increasesthe size of the tool and lead to an earlier starting of elastic and plastic deformation on the workpiece. During the cutting phase, the dislocation length slightly increases in the dry case and the lubricated case. The presence of the ﬂuid has only minor effects onthe dislocation behavior – also considering the statistical uncertainties of the data [ 38]. After the retraction, an annihilation of some of the dislocations can be observed as the total dislocation length decreases. Molecular Dynamics Simulation of Cutting Processes 269 Fig. 6. Normal and tangential forces on the tool (top) and coefﬁcient of friction (bottom) as a function of the cutting depth for simulations with decane [ 39]. The tool was a spherical cap. The temperature was T=350 K. The workpiece was an iron single crystal, the tool was a diamond, and the ﬂuid was decane. Three different regimes were distinguished: boundary lubrication (BL), mixed lubrication (ML), and hydrodynamic lubrication (HL). The statistical uncertainties were estimated from the ﬂuctuation of block average values in the quasi-stationary cutting phase. Figure 8shows the deformed substrate surface at the end of the cutting process. Results are shown for two different cutting depths for both methane and decane as ﬂuid. For a cutting depth of h=− 2Å, the cutting process roughens the surface over the entire cutting length, which is mostly due to the formation of a triboﬁlm. No distinct chip formation is observed for h=− 2Å, cf. Fig. 8. A distinct chip formation is obtained for h=− 6Å, cf. Fig. 8(bottom). The chip forms primarily at the sides of the tool which is built-up by the workpiece atoms that are thrust aside of the tool. Comparing the methane results with the decane results, the chip is more pronounced and the atoms at the workpiece surface are less disordered in the methane case. This isdue to the different characteristics of the adsorption layers of methane and decane [ 39] including the particles trapped in the gap between the tool and the substrate. 3.3 Lubrication and Formation of Triboﬁlm The number of ﬂuid particles trapped in the gap between the tool and the workpiece (cf. Fig. 2) were computed at the end of the indentation phase. These results are shown as a function of the solid-ﬂuid interaction in Fig. 9. For the case of no attractive interactions between the solid and the ﬂuid particles, the number of particles in the gap N gapat the 270 S. Schmitt et al. Fig. 7. Dislocation length in the workpiece as a function of time for a dry and a lubricated simulation [ 32]. The tool had a spherical shape. The temperature was T=100 K. The workpiece was an iron single crystal, the tool was a diamond with a spherical tip shape, and the ﬂuid wasmethane. The dislocation analysis was carried out with the DXA algorithm [ 40]. Fig. 8. Top view on the workpiece surface at the end of the cutting phase for the cutting depths h=− 2,−6Å (top to bottom) [ 39]. Results are shown for simulations with methane (left) and decane (right) as ﬂuids. The tool was a spherical cap. The workpiece was an iron single crystal and the tool was a diamond. The visualizations were created using Paraview [ 15]. end of the indentation is lowest and close to zero. With increasing solid-ﬂuid interac- tion energy, more particles remain trapped in the gap until a steady plateau is reached for approximately ε∗ SF≈0.75. For larger values, Ngapstays approximately constant. Interestingly, this behavior is in line with the contact angle behavior of the studied LJTS Molecular Dynamics Simulation of Cutting Processes 271 system [ 4], i.e. total wetting is reached at approximately ε∗ SF≈0.75. This means the number of particles increases with decreasing contact angle until total wetting is reached. Fig. 9. Number of ﬂuid particles in the gap between the tool and the workpiece N∗gap(cf. Fig. 2) as function of the solid-ﬂuid interaction energy ε∗ SF[36]. The tool had a cylindrical shape. The tem- perature was T*=0.8. The workpiece, the tool, and the ﬂuid were modeled by the LJTS potential. The dashed line is an empirical correlation of the form N∗gap=126.5−101.7e−ε∗ SF/0.422. The properties of the surface are strongly inﬂuenced by single ﬂuid molecules that are imprinted into the workpiece surface. This is observed for both the methane as wellas the decane case. Yet, both systems show different characteristics due to the different molecular shape of the ﬂuid molecules. A screenshot of each system is shown in Fig. 10. The imprinted ﬂuid molecules can be interpreted as a triboﬁlm that forms in the upperpart of the workpiece near the surface due to the extreme load. In the case of methane, the triboﬁlm is mainly build-up by methane atoms occupying regular lattice sites of the iron crystal. The overall lattice structure of the workpiece remains undamaged in thiscase. Due to decane being a long linear chain molecule, the workpiece lattice structure is signiﬁcantly broken up in the decane case. Decane molecules are also imprinted into the substrate surface, but the imprinted molecules destroy the regular lattice and causean unstructured formation of the upper atom layers of the workpiece. The formation of a triboﬁlm is further analyzed in Fig. 11, which shows the number of ﬂuid particles imprinted in the substrate surface N tribo as a function of the z-coordinate for three different cutting depths. The formation of the triboﬁlm is mainly observed at large cutting depth as the number of imprinted ﬂuid particles is signiﬁcantly lower. For both studied ﬂuids, the number ofﬂuid particles is largest for z≈− 2Å and the number decreases with decreasing z.F o r methane, the imprinted sites reach depths of up to z=− 12Å. The decane sites only reach depths of up to z=− 9Å. The different characteristics observed in the screenshots (cf. Fig. 10) can be conﬁrmed by the histograms shown in Fig. 11. The methane particles are accumulated at speciﬁc depths, i.e. distinct peaks forming in the histogram. This isdue to the methane particles occupying regular lattice sites of the workpiece lattice. 272 S. Schmitt et al. Fig. 10. Screenshots of the rear side of the contact zone (tool moves to the right) at cutting depth h=− 6Å [ 39]. The tool was a spherical cap. The workpiece was an iron single crystal, the tool was a diamond, and the ﬂuid was methane (left) or decane (right). Green particles indicate toolparticles, grey particles the workpiece particles, dark blue CH 4(left) or CH 3(right) sites (end group of decane), and light blue CH 2sites (middle group of decane). Fig. 11. Histograms of ﬂuid particles imprinted in the workpiece surface Ntribo as a function of the z-coordinate [ 39]. Results for h=4,−2,−6Å. The tool was a spherical cap. The workpiece was an iron single crystal, the tool was a diamond, and the ﬂuid was methane (left) or decane (right). For the decane simulations, these peaks cannot be observed which is in line with the unstructured triboﬁlm observed in Fig. 10. 3.4 Thermal Properties Thermal properties of a cutting process such as the temperature in the contact zone and the heat ﬂux absorbed by the workpiece, are crucial for the product quality and the man-ufacturing process. The MD simulations carried out in this work were evaluated in detail Molecular Dynamics Simulation of Cutting Processes 273 regarding the thermal properties. Figure 12shows the spatial temperature distribution in the x∗−y∗plane by snapshots at a cutting length of L∗=77. Fig. 12. Temperature proﬁle in the x∗−y∗plane at the cutting length L∗=77 for dry (left) and lubricated (right) simulations [ 27]. Results shown for two different velocities, v∗=0.066 (top) and v∗=0.332 (bottom). The tool had a spherical shape. The bulk temperature was T*=0.8. The workpiece, the tool, and the ﬂuid were modeled by the LJTS potential. The evaluation procedure is depicted in Fig. 2. Simulation results for two different cutting speeds, v∗=0.066 and v∗=0.332, are shown. Results from a dry case are compared to the results from a lubricated case. The temperature increases for both cases with increasing tool velocity. In the dry simulation, the temperature increases mainly in the chip, i.e. the energy dissipates in the direct vicinity of the contact zone – as expected.From the chip, the heat is transported to the bulk of the substrate in the dry case. In the simulation scenario, the tool is thermostatted which is why the temperature in the tool keeps constant. If a ﬂuid is present, the increase of the temperature in the contact zoneis reduced as the heat is also transported into the ﬂuid. Therefore, the temperature of the cutting ﬂuid near the contact zone is increased compared to the bulk ﬂuid temperature. Hence, the ﬂuid has important cooling capabilities. In Fig. 13, the results for the energy balance of the system are shown. The energy balance includes all sources and sinks of the system. Energy is added to the system by the work done by the tool. Energy is removed from the system by a thermostat inthe workpiece (cf. Fig. 13). In the cutting simulations, the thermostat acts as a heat sink and removes dissipated energy from the system such that a quasi-stationary state is established. The energy which is not removed by the thermostat heats up the substrate and(if present) the ﬂuid, i.e. their internal energy increases. The change of the internal energy of the workpiece U Wand the ﬂuid UF, energy removed by the thermostat /Delta1Uthermo , and the work done by the tool WTare shown in Fig. 13as a function of time. Therein, UW and UFindicate the changes of the total energy (kinetic and potential) of the workpiece and ﬂuid particles, respectively. The energy removed from the system /Delta1Uthermo was computed from the rescaled kinetic energy imposed by the thermostat. The work done 274 S. Schmitt et al. by the tool WTwas computed from the integral of the total force (in moving direction) during the process. The ﬂuid strongly inﬂuences the energy balance of the process. Fig. 13. Energy balance of the system including internal energy changes of the workpiece UW and the ﬂuid UF, energy removed by the thermostat /Delta1Uthermo , and the work done by the tool WT [36]. The shaded areas include all lubricated simulation cases with different solid-ﬂuid interactions energies. The solid lines represent the dry simulation case. The tool had a cylindrical shape. The initial temperature was T*=0.8. The workpiece, the tool, and the ﬂuid were modeled by the LJTS potential. The heat removed by the thermostat as well as the change of the internal energy of the substrate is reduced up to 20% by the presence of a ﬂuid. This cooling effectdepends on the solid-ﬂuid interaction energy [ 36]. The ﬂuid reduces the friction during the cutting phase, and part of the dissipated energy in the contact zone heats up the ﬂuid, which directly cools the contact zone. Nevertheless, the main part of the energy added to the system by the cutting process is dissipated. The energy dissipated is signiﬁcantly larger than energy required for the defect generation and plastic deformation. 3.5 Reproducibility The statistical uncertainties and the reproducibility of the simulation method was assessed using a set of eight replicas. The single simulations of the set only differ in their initial velocities that are assigned before the equilibration of the simulation box. Basedon the eight replica simulations, the standard deviation σwas calculated for several observables. In Fig. 14, the results for the normal force are shown. The time evolution of the normal force agrees in general with the results given in Fig. 3. The higher normal force in the case with a ﬂuid compared to the dry case is conﬁrmed by these results. The standard deviation of the normal force among the replica simulations is relatively smallin the indentation phase. Molecular Dynamics Simulation of Cutting Processes 275 Fig. 14. Normal force on the tool as a function of time for the dry and the lubricated case (top) and the corresponding instantaneous standard deviation (bottom) [ 38]. The shaded area includes the entire range of the results of all eight replica simulations. The tool had a cylindrical shape. The temperature was T*=0.8. The workpiece, the tool, and the ﬂuid were modeled by the LJTS potential. The standard deviation increases with progressing indentation. In the starting phase of the cutting (cf. Sect. 3.1), the lubricated simulations show signiﬁcantly higher statistical uncertainties. At the beginning of the stationary phase ( t∗≈300), the normal forces in the dry and the lubricated simulations agree within the scattering of the replica sets. Thestandard deviation is slightly higher in the dry simulations in the starting phase of the cutting compared to the lubricated simulations. In Fig. 15, the coefﬁcient of friction calculated from the eight replicas is shown with its corresponding standard deviation. In the starting phase ( t ∗<300), the coefﬁcient of friction of the dry simulations is signiﬁcantly larger compared to the simulations with a ﬂuid. The difference exceeds the scattering of the replica sets, which indicates that thedifferences between a lubricated and a dry case in the starting phase are signiﬁcant. The coefﬁcient of friction is reduced in the lubricated case in the starting phase of the cutting due to ﬂuid particles trapped in the gap between tool and the workpiece (cf. Sect. 3.3). Until the ﬂuids are squeezed out of the gap, the tool experiences a larger normal force, which decreases the coefﬁcient of friction in a lubricated case compared to a dry case. Inthe stationary phase of the cutting process, the coefﬁcient of friction is slightly increased in the lubricated case, which is due to individual ﬂuid particles being imprinted into the workpiece surface, which requires additional work done by the tool in the lubricatedcase. In general, no systematic differences in the reproducibility of dry and lubricated simulations were found. Moreover, the time dependency of the standard deviation for 276 S. Schmitt et al. the normal force and the coefﬁcient of friction indicate that no differences between the simulations of a replica build up with ongoing process. Fig. 15. Coefﬁcient of friction as a function of time for the dry and the lubricated case (top) and the corresponding instantaneous standard deviation (bottom) [ 38]. The shaded area includes the entire range of the results of all eight replica simulations. The tool had a cylindrical shape. Thetemperature was T *=0.8. The workpiece, the tool, and the ﬂuid were modeled by the LJTS potential. 4 Conclusions In this work, the inﬂuence of lubrication on the contact zone of cutting processes was studied on the atomistic scale using classical MD simulation. Thereby, new insightswere obtained on the fundamental mechanisms of lubrication and cooling provided by the presence of cutting ﬂuids. Different simulations scenarios were used including model systems as well as real substance systems. The mechanical properties of the contact werestudied in means of the normal and tangential force as well as the coefﬁcient of friction. It was found that the presence of a ﬂuid has an important inﬂuence in the starting phase of the atomistic cutting process, i.e. decreases the coefﬁcient of friction, which is due to ﬂuidmolecules trapped in the gap between the workpiece and the tool. The inﬂuence of the cutting depth on the cutting process was investigated using two different ﬂuids: methane and decane. Based on the results, three different lubrication regimes were identiﬁed for different cutting depths: the hydrodynamic lubrication regime for very small cutting depths, the mixed lubrication regime for cutting depths that correspond approximatelyto the size of ﬂuid molecules, and the boundary lubrication regime cutting for cutting Molecular Dynamics Simulation of Cutting Processes 277 depths that yield signiﬁcant elastic and plastic deformation of the workpiece. Within these different regimes, the coefﬁcient of friction shows different characteristics. The presence of a ﬂuid has important thermal effects on the atomistic cutting process, i.e. it is found to reduce the maximum temperature in the contact zone and reduce theheat impact of the workpiece. The heat absorbed by the workpiece is reduced by up to 20% by the presence of a ﬂuid lubricant. For future for, the simulation scenario should be reﬁned, e.g. considering a rough surface topography, such that the reality of tribologicalcontact processes is captured in more detail. Acknowledgement. The authors gratefully acknowledge access to the ELWE supercomputer at Regional University Computing Center Kaiserslautern (RHRK) under the grant TUKL-MTD.