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Nanotribology in austenite: Normal force dependence Steffen Brinckmann n, Caroline A.C. Fink, Gerhard Dehm Department Structure and Nano-/Micromechanics of Materials, Max-Planck-Institut für Eisenforschung GmbH, Düsseldorf, Germany

art ic l e i nf o

a b s t r a c t

Article history: Received 30 October 2014 Received in revised form 29 April 2015 Accepted 30 April 2015

The friction of materials has long been understood as the collective contact and interaction of microasperities. The rise of micro- and nanomechanical instruments allows the study of single microasperity contact to understand fundamentally friction and wear. This study investigates the deformation due to a single microasperity, which performs a single stroke scratch in austenite. We ﬁnd that the elastic and plastic equations for static indentation also apply for the dynamic scratching. Additionally, the friction coefﬁcient is found to be normal force dependent and we observe three domains: microstructure dominated friction, plastic plowing dominated wear and wear particle dominated tribology. & 2015 Elsevier Ltd. All rights reserved.

Keywords: Microasperity Wear Friction Hertz equation

1. Introduction Friction and material wear occur in every machinery if its components glide relative to each other. The friction results in machine efﬁciency loss and material wear leads to performance decrease. The inﬂuence of surface roughness on friction and wear is non-obvious [1,2] and contact theories for multi-asperity contact have been developed [3–5]. On the macroscale, engineers use experiments [6–8] to qualify machine components. On the smallest length-scale, atomic force microscopy (AFM) helps to fundamentally study friction forces and wear [2,9,10] for a large range of material classes [11–13]. In these experiments, the contact stresses are high and remain elastic because of the elevated nanoscale hardness [2]. The elastic solution for the stationary contact of spheres by Hertz is frequently used in dynamical and tribological applications on the nano- and microscale [14,12]. The plastic zone during scratching depends on the scratch hardness [15]. Since the hardness relates the normal force to the contact area and to the plastic depth, the similarity of wear and indentation hardness [16] leads to the hypothesis of similar plastic depth during indentation and dynamic scratching. This hypothesis is at the core of this study. The present study uses the single nanoindenter asperity to investigate the tribological behavior of austenite on a length-scale between the macroscale and the atomistic scale. We report the scratch depth and friction coefﬁcient as a function of the normal n

Corresponding author. E-mail address: [email protected] (S. Brinckmann).

load during scratching. Moreover, we relate the normal force and friction coefﬁcient to identify the underlying mechanisms.

2. Experimental procedure The as-received steel austenite (1.5 wt%C, 2.3 wt%Si, 0.3 wt% Mn, 25 wt%Cr and 19 wt%Ni) was annealed at 1200 °C for 188 h to obtain a coarse microstructure with typical grain sizes ranging from 50 μm to 1 mm. These grains were signiﬁcantly larger than the indenter contact area, and therefore allowed to investigate the individual grain response. The average geometrically necessary dislocation density determined by EBSD was ≤4.5 109 cm−2 [17] and the surface roughness was Ra = 5.8 nm . We use a Keysight G200 Nanoindenter with normal force control and a r = 5 μm spherical diamond tip. A custom experimental protocol is used which ﬁrst indents the surface, then unloads and reloads to eliminate any tangential residual force that might develop during indentation. Afterwards the sample is moved by 100 μm at either 1 μm/s or 100 μm/s. Prior and postscratching, the scratch track proﬁle is scanned with the same indenter tip, see also [18], with a normal force of 0.15 mN, which is a compromise between ensuring contact and reducing residual deformation. The ﬁrst and last 5% of data along the scratch distance are omitted because of measurement artifacts that develop. The value of 5% is a compromise between minimizing the initial artifacts and maximizing the measurement base. All measurement segments start with a 20 μm lead-in and end with an equal sized lead-out to determine the surface tilt and to ensure indenter path repeatability.

http://dx.doi.org/10.1016/j.wear.2015.04.023 0043-1648/& 2015 Elsevier Ltd. All rights reserved.

Please cite this article as: S. Brinckmann, et al., Nanotribology in austenite: Normal force dependence, Wear (2015), http://dx.doi.org/ 10.1016/j.wear.2015.04.023i

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Fig. 1. (a) Tangential force as a function of the tangential displacement for three scratches with 200 mN normal force and one scratch with a 20 mN normal force. The initial slope Ktang = 4.66 mN/μm is ﬁtted for the ﬁrst 16 μm . (b) Typical curves for a nano-scratch experiment (20 mN normal force): the depth as a function of the distance during the pre-deformation scan, the scratch segment and the post-deformation scan.

The Hertz equation for the elastic displacement he of a sphere on a ﬂat surface is

⎡ 3Fn ⎤2/3 he = ⎢ ⁎ ⎥ ⎣ 4E r ⎦

(1) n

with Fn the normal force, r the radius of the indenter, E the reduced Young's modulus 1/E⁎ = (1 − ν M2 ) /EM + (1 − ν I2 ) /EI , with E and ν the elastic constants of the metal M and the indenter I. For the diamond indenter we use a Young's modulus of 1141 GPa and a Poisson's ratio of 0.07 [19]. The plastic displacement can be inferred by using the hardness deﬁnition H = Fn /A , where A is the projected contact area A = 2πrhp . These equations result in a plastic indentation depth:

hp =

Fn . 2πHr

(2)

The material hardness was determined by nine instrumented nanoindentations using a Berkovich-tip to H = 2.84 ± 0.14 GPa by averaging the results at 1 μm depth. We obtained a Young's modulus of 176 79.1 GPa by assuming a Poisson's ratio of 0.3.

3. Results As shown in Fig. 1(a), we record the tangential force1 – displacement curves for 200 mN normal force, which leads to high tangential forces and thereby reduces the determination error. The average tangential stiffness is 4.66 mN/ μm , which correlates to 16 μm tangential displacement for those measurements. For the 20 mN curve shown in Fig. 1(a), the tangential compliance displacement is roughly 2 μm . Fig. 1(b) shows the pre-deformation, scratch and post-deformation depth along the scratch for an experiment with 20 mN normal force. Each segment has an additional lead-in and the leadout, i.e. ﬁrst and last 20 μm . The pre-deformation scan reveals that the initial surface has a shallow valley at 80 μm scratch distance. At the beginning of the scratch segment, we see that the depth is increasing rapidly, as shown by the inset to Fig. 1(b) labeled with “A”. Subsequently, the depth decreases in section “B” and reaches a steady state value in section “C”. We observed the initial depth increase and subsequent decrease “A–B” in all experiments with the Keysight G200 and a Hysitron Triboindenter 950 on austenite. 1 The term “tangential” is used in this paper for the motion in the scratch direction, while the term “lateral” describes the motion on the surface perpendicular to the scratch direction.

Additionally, we conducted experiments without unloading– reloading hysteresis to verify that the initial depth increase is unrelated to the custom experimental protocol. The length of the valley in the scratch direction depends linearly on the normal load, as shown in Fig. 2(a): a normal force of 100 mN results in a maximum at 10 μm , a normal force of 50 mN results in a maximum at 5 μm . This linear behavior is less speciﬁc at lower forces. Moreover, the “A” and “B” section exhibits a much smoother curve than section “C”, e.g. the 20 mN curve is smoother up to 10 μm than exceeding 10 μm in Fig. 2(a). After the initial depth increase and subsequent decrease, i.e. starting at 15 μm , the scratch curve exhibits an almost constant depth which mimics the pre-scan surface shape, e.g. the shallow macroscale valley in the second part of the scratch segment. The macroscale depth (wavelength of tens of micrometers) during the scratch segment is superimposed with a higher frequency undulation with a period of ∼5 μm frequency, which differs between pre-scan and scratch segment. The pile-up is measured at the scratch end, i.e. at 100 μm . The post-scan measurements and the confocal measurements are similar on the macroscale (wavelength of tens of micrometers). The post-scan uses a r = 5 μm indenter tip and thereby omits smaller features that the confocal microscope captures. The indenter and confocal curves are aligned at the site of indentation and reveal that the difference at the scratch end is on the order of a few micrometers. We identify the misalignment of characteristic local features (see Fig. 1(b)) : (1) a similar valley is present in both curves at ∼55 μm ; (2) two double peaks are present in both curves at ∼75 μm and at ∼90 μm . This feature misalignment is between 1 and 2 μm . The lateral compliance leads to non-straight, i.e. curved scratches. These curved scratches are most visible at high normal loads (>20 mN). As shown in Fig. 2(b) by scanning electron microscopy (SEM), the extent of the lateral curvature is non-constant along the scratch and differs even for the same normal force. For all normal forces, the lateral motion is much smaller than the scratch width. The normal force–displacement curve, as shown in Fig. 3(a), initially has the typical indentation loading shape. After reaching the maximum load, the material is unloaded to obtain the elastic slope after indentation. Using the Oliver–Pharr method [19] and the complete area function, we obtain an average Young's modulus of 159724 GPa. We use the ﬁrst 20% of unloading data after scratching to obtain an average Young's modulus of 186 799 GPa.2 2 There are less than 10 data-points, since only 20% of the unloading is used. This low data-point count results in a large standard deviation.

Please cite this article as: S. Brinckmann, et al., Nanotribology in austenite: Normal force dependence, Wear (2015), http://dx.doi.org/ 10.1016/j.wear.2015.04.023i

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Fig. 2. (a) Depth during scratching normalized by the maximum depth as a function of the scratch distance for multiple normal loads which are given in mN. Each curve is the average of three measurements with an identical normal load and all scratch experiments were performed in the same grain. (b) Secondary electron image shows two scratches with a 100 mN normal force through the polygranular material. The dashed lines reveal the linearity of the scratches.

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Fig. 3. (a) Force–displacement curve for the 10 mN scratch made with the spherical indenter tip. The segments are labeled as follows: 1: indentation, 2: unloading, 3: reloading and 4: unloading after scratch. The depth varies at maximum load during the scratch segment, as shown by the horizontal gray line. (b) Average elastic depth during the scratch segment as a function of the normal force. The solution of the Hertz equation is given as reference.

When comparing the unloading slopes in Fig. 3(a) (curves 2 and 4), one observes that these are initially identical. After scratching, once the normal force decreases below 8 mN the unloading slope is more compliant than the unloading slope after indentation. Fig. 3(b) shows the average elastic depth as a function of the normal force together with the Hertz equation. For scratches with a normal force ≤20 mN , the average elastic depth during the scratch segment is well captured by the Hertz equation. Moreover, the scatter is small, typically about tens of nanometers. Generally, one ﬁnds that larger normal forces result in larger scattered data, although the logarithmic scale obscures this observation. The higher scratching velocity leads to less scatter in the elastic depth. For normal forces exceeding 20 mN, the average elastic displacements are signiﬁcantly larger than those given by the Hertz equation. Moreover, the data scatter is signiﬁcantly larger in this normal force regime. Comparing confocal and post-deformation indenter results of scratches exceeding 20 mN normal fore, as shown in Fig. 4(a), some short features are identical, e.g. the local maximum at ∼70 μm . On the larger length-scale large differences prevail especially ∼40 μm scratch distance, where the indenter measured a depth of roughly 0.1 μm while the confocal measurements revealed a seven times larger depth. Note that the initial depth and the pile-up height at 105 μm are almost identical in both measurements. Because there are large differences between the confocal microscopy and

post-deformation indenter measurements, we omit depth results for normal forces larger than 20 mN in the remainder of this study. The average elastic slope is shown in Fig. 4(b) and these slopes are about dhe /ds = ± 0.1 nm/μm , where he is the elastic depth and s is the tangential coordinate along the scratch. This slope magnitude equates to 10 nm for a 100 μm scratch. Low normal forces result in a slope of roughly −0.1 nm/μm and this value decreases for larger normal forces. An effect of the scratch velocity is not observed. The majority of elastic slopes are negative, i.e. the elastic depth becomes shallower along the scratch. The average plastic depth during scratching, as shown in Fig. 5(a), increases with the normal force and the measurement scatter increases similarly. All experimental results with normal forces between 2 and 10 mN have a larger plastic depth than that of Eq. (2). For smaller and larger normal forces, the plastic depth is captured by the analytical equation. The relative mean square (RMS) error for the entire curve is 22 nm. We ﬁt a power-law equation:

hp = cFnm

(3)

to both data sets (Fig. 5a). The variable c is the compliance pre-factor, which is determined as 0.0180 ± 0.0012 and 0.0207 ± 0.0015 for the 1 μm/s and 100 μm/s scratch velocity, respectively. The powerlaw exponent m is evaluated as 0.881 ± 0.025 and 0.834 ± 0.027 for

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Fig. 4. (a) Depth of a scratch with 50 mN normal force: post-scan with the 5 μm indenter tip and confocal measurements. Both measurements are aligned at 0 μm scratch distance and not scaled in the horizontal or vertical direction. (b) The average elastic slope dhe /ds during the scratch segment as a function of the normal load. Positive slopes imply that the depth is becoming deeper along the scratch.

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Fig. 5. (a) Average plastic depth as a function of the normal force. The ﬁtted curve is hp = 0.019Fn0.86 (solid line) and the analytical model hp = Fn /2πHr (dashed line). (b) Average plastic slope dhp /ds as a function of the normal load. Positive slopes imply that the depth is becoming deeper along the scratch.

friction coefficient 0.4

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Fig. 6. Friction coefﬁcient as a function of the normal force. Three regimes can be identiﬁed. I: friction dominated domain, II: plastic plowing dominated domain, and III: wear particle-dominated regime.

the slow and fast scratch velocity, respectively. When using the power-law of Fig. 5(a), we compute a RMS of 10.5 nm. Concluding, the error of the ﬁtted function is half that of the analytical expression. The power-law exponents are smaller than one even when considering the uncertainty. Both exponents and compliance pre-factors are similar for the fast and slow scratch velocity. This ﬁnding is addressed in the discussion section. Fig. 5(b) shows the average plastic slope along the scratch as a function of the normal forces. These slopes and the data scatter are signiﬁcantly larger than that for the elastic slopes shown in Fig. 4(b). For normal forces less than or equal to 5 mN, the plastic slope increases monotonically, i.e. the scratch becomes deeper during scratching. For normal forces greater than 5 mN, this trend is not observed and some scratch tracks have a negative slope, i.e. the scratch becomes more shallow towards the end. Finally, we report the friction coefﬁcient as a function of the normal force, as shown in Fig. 6. The friction coefﬁcient increases with normal force, while the scatter decreases with larger normal

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forces. The friction coefﬁcient is minimal at 1 mN normal force and increases at 0.5 mN normal force. The friction coefﬁcient scatter at 0.5 mN is as large as the entire range for all normal forces.

4. Discussion In this study, we investigate the friction and wear behavior of austenite at the nano- and micrometer scale by scratching with a micrometer sized diamond sphere. The accuracy of the tangential displacement measurements is inﬂuenced by the tangential compliance. The compliance leads to a few micrometer displacements when applying a 100 mN normal force. Additionally, the x–y stage has a ±1 μm resolution. The compliance and x–y stage induced errors are small compared to the total scratch length (100 μm ). One should note that the tangential stiffness (4.66 103 N/m ) is three orders of magnitude weaker than the normal stiffness of the nanoindenter (5 106 N/m ). Surface roughness measurements by white-light confocal microscopy verify the surface proﬁle measurements of the nanoindenter for experiments with normal loads ≤20 mN. For higher normal loads, post-deformation measures by confocal microscopy and the nanoindenter show large offsets on length-scales which are comparable to the grain size, i.e. multiple tens of micrometers. These offsets arise from the formation and dragging of wear particles, which results in an almost constant offset of both measurements (Fig. 4(a)). In that speciﬁc case, the offsets are due to a wear particle which is brushed off at 65 μm and afterwards a much smaller difference occurs. Indeed, SEM images of scratch tracks with normal forces exceeding 20 mN reveal wear particles [17]. In AFM studies, the particle formation and dragging mechanism was similarly observed [2]. It should be noted that even though large differences occur on the grain size scale, shorter wavelength undulations resemble each other between the nanoindenter and confocal measurements even at high normal loads. These short wavelength similarities exist, although the white-light measurements have a ﬁner resolution than the micrometer sized indenter. The offset of these undulations between the three measurement segments, i.e. pre-scan, scratch, post-scan, are on the order of single micrometer and hence comparable to the tangential compliance determined previously. During the initial scratching section, the depth increases signiﬁcantly and decreases shortly thereafter during all experiments, see the “A–B–C” sequence in Fig. 1. This increase and decrease was observed independently whether the scratching was preceded by an indentation to the same normal load or without preceding indentation. Moreover, this increase and decrease was observed for two different indenter systems (Keysight G200, Hysitron Triboindenter 950) with a spherical tip of the same radius on similar austenite samples. In addition, this increase and decrease was veriﬁed by post-deformation confocal microscopy, see Fig. 1. Fig. 2(a) shows that the length of the depth increase and decrease depends linearly on the normal force. This observation is less obvious at low normal forces, presumable due to the low resolution of the scratch distance measurements. Because the distance of the depth increase and decrease depends on the normal load and because the curve is much smoother in this section, the “A–B” behavior is a measurement artifact and not a microstructural response. The reader is reminded that the microstructure is identical, as all scratches are performed in the same very large grain. Since this measurement artifact was observed for different nanoindenter systems, it is related to the their similarities: the initiation of the scratch motion. As the indenter tip moves with respect to the material, the indenter looses material contact in the wake of the tip and the contact area decreases suddenly. The applied force and the material hardness are constant and therefore

5

the indentation depth has to increase in order to prevent the reduction of contact area. Section “B” is due to the tilting of the indenter load-cell, which is in essence a cantilever. It should be noted that the initial “A–B” sequence was excluded when calculating the average depth for Figs. 3–5. The effect of the lateral compliance becomes more pronounced for larger normal forces, i.e. scratches with high normal forces become non-straight (Fig. 2b). For these forces, the friction forces increase and the microstructure reactions become more pronounced. If the microstructure is softer in one lateral direction, the indenter tip moves in this direction and an increased amount of plasticity develops on this side. The microstructure inﬂuenced lateral motion is evident from Fig. 3(a): two neighboring scratches with the same normal force show a different behavior because the grain orientation under the scratches differs, as veriﬁed by electron backscatter diffraction (EBSD). Using instrumented Berkovich indentation, we determined Young's modulus of 176 79 GPa. Using the unloading slopes of the spherical tip after the initial indentation (159 724 GPa) and after scratching (186799 GPa), a similar Young's modulus was determined when accounting for the data scatter. Concluding, unloading from indentation is similar to unloading after scratching. However, the data scatter is signiﬁcantly larger when evaluating Young's modulus after scratching. After scratching, once the normal force decreases below roughly 80% of the maximal force, the unloading slope becomes more compliant than during initial unloading, as shown in Fig. 3 (a) curve 4 lower section. This behavior is due to the only partially embedded tip during scratching compared to a fully embedded tip during nanoindentation. Although the indenter is plowing through the material, the elastic depth is identical to Hertz equation, which was developed for small indentation depths and for stationary indenters and which has no ﬁtting parameters. Additionally, the elastic depth contribution has only a shallow slope along the scratch length: the elastic strain distribution does not change during scratching. The plastic scratch depth is predicted by an analytical equation for spherical indentation using the material hardness (see Eq. (2)) for low and for high normal forces. This relation is based on static indentation and its agreement to scratching shows the similarities between both methods. This ﬁnding is in agreement with Tabor's study [16] that revealed that the indentation hardness is similar to the scratch hardness. After verifying that Eqs. (1) and (2) are applicable during microscale scratching, we combine both equations to obtain the plastic depth as a function of the elastic depth:

hp =

2 E ⁎ he2/3 . 3π H r

(4)

The plastic depth is a measure of the wear rate: a higher plastic depth results in a higher wear rate, which is typically measured as loss volume. The wear rate scales inversely with the hardness during microscale scratching. Tabor [16] observed that the wear rate drops as the macroscale indenter scratches harder phases. Using the radionuclide-technique on macroscale sliding bearings, Scherge et al. [7] observed the inverse proportionality of wear and hardness. The ﬁtted plastic depth power-law, see Eq. (3), has no velocity dependence because the error-bars overlap. Moreover, neither elastic depth nor friction coefﬁcient show a dependence on the scratch velocity in the velocity range 1–100 μ /s. Previous studies [2] have found that the velocity dependence on the friction behavior is small because the localized heat energy diffuses fast in the body, which is signiﬁcantly larger than the contact volume. For macroscale contact, the velocity dependence of the friction

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coefﬁcient in lubricated bearings is termed Stribeck-effect and has been known for more than a century. Using rate-equations for the dissipated power, the velocity dependence of the friction coefﬁcient was studied for lubricated steel [20]. For dry friction at the macroscale, a velocity dependence is observed for a large number of materials [21,22]. The plastic slope scatters signiﬁcantly for medium and high normal forces. Both data-points of Fig. 5(b) (20 mN, −2 nm/μm ) are discussed in more detail to investigate the scatter origin: both scratches start in a grain with [5 3 29] normal orientation, which is close to [0 0 1] and which results in a large plastic depth. Both scratches continue across grains which are less favorably oriented as the plastic depth decreases [13 1 16] ∼ [1 0 1]. Therefore, the plastic slope is negative along the scratch. The other scratches do not start in such a favorable oriented grain that maximizes the plastic depth and, hence, do not exhibit a similar negative slope. Concluding, the magnitude of plasticity depends on the local grain orientation. Since the slopes are on the order of nm/μm and close to the initial surface roughness, the slopes are insigniﬁcant to draw general material scientiﬁc conclusions. The friction coefﬁcient was found to increase with increasing normal force. Bhushan et al. [11,2] observe a similar trend for lower normal forces and argue that the friction coefﬁcient is low in nano-contacts and that the friction coefﬁcient approaches the macroscopic value at large normal forces. Based on the present study using a 5 μm spherical tip, the friction coefﬁcient can be divided into three domains:

In the high normal force domain (Fn > 20 mN) plastic wear occurs

and wear particles develop [17], which lead to additional elastic compliance (Fig. 3). It is common to observe the adhesion of these particles on the counter-body and abrasion of the counter body at the macroscale [14]. Moreover, the post-deformation measurements of the nanoindenter and confocal microscopy differ signiﬁcantly in this domain. Concluding, the term “wear” coefﬁcient should be used in this domain. In the medium normal force domain (2 mN ≲ Fn < 20 mN) the friction coefﬁcient scatter is small and plastic plowing is the dominant deformation mechanism, which results in small scatter in plastic and elastic depth (Figs. 3 and 5(a)). Hence, the friction coefﬁcient is referred to as ‘‘plowing’’ coefﬁcient. In this domain, the crystal orientation of the deforming grains result in characteristic slip patterns [17]. At low normal forces (Fn ≲ 2 mN ), the friction coefﬁcient is determined by the microstructural elements and the plastic depth is small (hp < 50 nm , see Fig. 5(a)). As plasticity is negligible, the term friction coefﬁcient applies in this normal force domain. The large scatter in the friction coefﬁcient at low normal forces manifests the observation that in this load regime the friction coefﬁcient is inﬂuenced by the microstructural behavior (crystal structure, secondary phases, anisotropy, and Young's modulus).

One contribution to the friction coefﬁcient at low normal forces are water molecules that could be absorbed at the surface of the austenite and nanoindenter tip. These water molecules could signiﬁcantly inﬂuence the results at low scratch depth htotal < 10 nm . However, all scratches of this study have total displacements that are larger than 10 nm .

5. Conclusions The following conclusions are drawn based on the present study which investigated single stroke scratch deformation of austenite steel by a diamond microasperity.

The scratch displacement can be separated into elastic and

plastic contributions. Across two orders of magnitude of normal forces, the elastic depth follows the Hertz equation, which was developed for a stationary indentation without plasticity. The plastic deformation follows loosely an analytical equation based on the material hardness during stationary indentation. The friction coefﬁcient decreases with decreasing normal force and the coefﬁcient is rather independent of deformation velocity. Friction and wear can be divided into three domains at the microscale. In the high normal force domain, a signiﬁcant amount of material is piled-up and extruded on the scratch ﬂanks as wear particle forms. In the medium normal force domain, plastic plowing occurs without wear particles. In the low normal force regime, microstructural elements inﬂuence the friction coefﬁcient.

Acknowledgment The authors thank Holger Pfaff for his support in executing the scratch experiments at his facility at Keysight GmbH. The authors thank Maxwell Frost for his proofreading of the paper.

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Please cite this article as: S. Brinckmann, et al., Nanotribology in austenite: Normal force dependence, Wear (2015), http://dx.doi.org/ 10.1016/j.wear.2015.04.023i

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