The generation of mechanically mixed layers (MMLs) during sliding contact and the effects of lubricant thereon

Wear 246 (2000) 74–90

The generation of mechanically mixed layers (MMLs) during sliding contact and the effects of lubricant thereon John L. Young Jr. , Doris Kuhlmann-Wilsdorf∗ , R. Hull Department of Materials Science and Engineering, University of Virginia, Charlottesville, VA 22904-4749, USA Received 25 August 1999; accepted 30 June 2000

Abstract In unlubricated and boundary lubricated sliding, materials touch only at a restricted number (typically n ≈ 10) of isolated, typically microscopically small ‘contact spots’ that occupy but a small fraction of the macroscopic interfacial area. It is here that the load is supported by the local hardness of the softer of the two materials, and that friction and wear are generated. The intermittent local shear strains at the contact spots in the course of sliding, and eventually through their statistical movements of the entire top layers of wear tracks, are very large. This behavior has been simulated, both for dry sliding and lubrication, by means of stacked foils of pure copper and silver sheared under high superimposed pressure in a Bridgman-anvil apparatus. Strain hardening curves were obtained and the samples, now equivalent to material at wear tracks and specifically ‘mechanically mixed layers’ (MMLs), were examined microscopically by means of a variety of techniques. From the workhardening curves the coefficient of friction as well as the hardness of the MMLs was inferred. The experiment is complicated by a strong shear strain anisotropy, in fact comparable to that found at actual contact spots, namely rising from near zero strain at the anvil-sample interfaces and at the axial center of the samples to a maximum at the mid-plane and the circumference. Microscopic analysis by means of focused ion beam microscopy (FIBM) and secondary ion mass spectrometry (SIMS) revealed that in the course of sliding, MMLs are formed through the proliferation of ‘tongues’ where local folding of the material occurs. An unexpected and potentially highly important discovery was the bodily migration of volume elements of one of the metals through the other, e.g. of lumps of silver through copper and vice versa, without leaving a trace. This phenomenon was enhanced through oil lubrication. © 2000 Elsevier Science S.A. All rights reserved. Keywords: Contact spots; Mechanically mixed layers; Focused ion beam microscopy; Secondary ion mass spectrometry

1. Introduction In unlubricated or boundary-lubricated sliding, the normal force between two sides P, is almost always supported at only a restricted number of ‘contact spots’ at which the local pressure compares with the hardness of the softer side (H) and whose total area (A) is controlled by local plastic deformation so that P ∼ = AH. As the contact spots move statistically over the course of extensive sliding an interfacial zone between the two materials becomes severely sheared. Moreover, in this zone there occurs very fine mixing between the two sliding metals [1–4]. This phenomenon can be most impressively demonstrated by briskly rubbing a piece of silver on copper and thereby forming a beautifully gold-colored track on the copper surface. This color is the hallmark of thermodynamically unstable homogeneous copper–silver alloys [5,6]. ∗ Corresponding author. Tel.: +1-804-295-4920; fax: +1-804-924-4576. E-mail address: [email protected] (D. Kuhlmann-Wilsdorf).

In connection with the local shear strains, numerous studies have been performed on sliding interfaces. Dautzenberg [7] embedded an aluminum foil marker in a copper pin, at right angles to the interface. After sliding the pin on a rotating steel surface and examining the cross-section of the pin, he found that the marker had been sheared with increasing intensity from the bulk towards the surface. This was indicated by a gradual turning of the aluminum foil marker parallel to the sliding direction of the copper pin. The demonstrated shape of the aluminum marker illustrates the very large shears that commonly develop at the tribo-interfaces of ductile materials. For another example, Ives [8] found after abrading copper with sand, that some of the sand had become embedded in the copper in what he called ‘highly irregular surface deformation’. This was in fact the beginning of very common interface morphology dubbed ‘tongues’ (Fig. 1) and is a major phenomenon investigated in this paper. Next, Rigney et al. [9] found the same extremely strong shear strain gradient adjacent to tribo-interfaces. In this case, a preexisting grain boundary plays the role of Dautzenberg’s

0043-1648/00/$ – see front matter © 2000 Elsevier Science S.A. All rights reserved. PII: S 0 0 4 3 - 1 6 4 8 ( 0 0 ) 0 0 4 5 6 - 7

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Fig. 1. Schematic of the formation of MML’s at the interface between two metals. It starts with only a slightly undulating surface profile and the lamellation intensifies with progressively higher shears.

marker. Such markers indicate the enormous magnitude of the prevailing strain, namely up to hundreds or even thousands of true shear strain at the interface, decreasing to zero at a depth comparable to the size of the largest contact spots. At the same time the decreasing average dislocation cell size from the interior towards the surface can be used to assess the concurrent local workhardening. Namely, to a first approximation the inverse of the average cell size is proportional to the shear stress [10]. Commonly also present is an extremely finely mixed layer at or near the wear track that has been named the ‘mechanically mixed layer’ (MML) [11]. To summarize the results of past research and the evidence presented in this paper [12–40], these are conclusions regarding MMLs for the case of sliding between two materials of comparable hardness. • During unlubricated as well as solid and boundary lubricated sliding, MML’s originate from the statistical movements of the small asperities which from moment to moment form the load bearing ‘contact spots’. Heat transfer, electrical conduction, friction and wear arise at those contact spots. • MML’s form through the cumulatively extremely large shear strains and incidental mixing between the two sides that statistically occur at the contact spots under normal pressures comparable to the local hardness of the softer side.

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• The decisive local morphology are ‘tongues’ which are due to the tangential shearing of momentarily interlocked or at the least ‘adhering’ contact spots shown in Fig. 1. • This behavior gives rise to the widely observed Holm– Archard wear law since wear particles are tongues or parts thereof whose width and length compare to the size of the generating contact spots, and which are statistically detached after an average sliding path that is some fixed multiple of the contact spot size. • As plastic strain accumulates, the ‘tongues’ stretch out in the direction of sliding so as to overlap, thereby forming an increasingly fine lamellation. • The resulting mixing of the materials from the two sides, observed as a transfer of material across the interface when the two sides are taken apart, produces the MML. • Observation of the MML in a variety of materials reveals a refinement in the microstructure near the interface along with hardness and strain gradients normal to the interface. Building from this background, the purpose of the present research was twofold. First, to add to our knowledge of the detailed processes involved in MML formation. Second, to discover what effect, if any, a simple lubricant has on them. To this end, a Bridgman-anvil apparatus [12] was employed to simulate the extreme shearing and high local pressures at contact spots [23,24,36] and the samples were investigated by means of a new technique using focused ion beam microscopy (FIBM).

2. Experimental methods 2.1. Simulating tribological sliding via the Bridgman anvil-apparatus The study of actual contact spots is difficult not so much on account of their small area and shallow depth in the material but because they are hidden from view. When inspecting worn surfaces due to sliding contact, one cannot tell where specifically the contact spots were located from one moment to the next and even less how long they lasted or how far they moved. Because of this, sliding contact spot behavior between two ductile metals is not accurately simulated by simple pressure tests. Local conditions at contact spots, which cause mechanical alloying and the formation of MMLs, involve the already discussed extensive plastic deformation and extremely large shear stains. Therefore, as already mentioned, in recent simulation experiments [22–28,36,41–43], a Bridgman-anvil apparatus was employed. Herein, foil disk samples are placed between two pairs of anvils, one rotating and the other stationary, as shown in Fig. 2. Anvil rotation is started after a high normal pressure is applied, thereby simulating conditions at a sliding interface. During the simulation, the shear stains achievable in this device are enormous, and may exceed γ ≈ 10, 000 [23]. Thus, the Bridgman apparatus is an effective and efficient way of studying the behaviors of materials under the

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Fig. 2. Schematic of the center part of the experimental Bridgman-anvil apparatus device and, shown for comparison as the insert at the top right, Bridgman’s original sketch for his high pressure shearing device which is used to simulate the conditions in which MML’s are formed. Pressure is applied as indicated by the arrows labeled P. Two similar samples are placed symmetrically between the two B and A anvil pairs. The ‘platen’ C in the actual apparatus is a worm gear wheel rotated relative to parts B with an axis of rotation coincident with the direction of the applied pressure, P.

conditions known to prevail at contact spots specifically, and at tribo-interfaces after substantial wear, in general. Bridgman invented his anvil apparatus in the 1930s [12]. The principle of this device is represented as the insert in Fig. 2 as follows. Two disk samples are at positions A and are sheared between stationary anvils B and the rotating platen C under applied pressure p. The specific apparatus, in which all of the experiments of the present and previous cited research were done, is semi-schematically shown in Fig. 3. It is modified from the original Bridgman apparatus in order to permit continuous measurement of both sample thickness and applied torque during shearing so as to obtain the already indicated stress–strain curves. Here the average shear stress is inferred from the torque required to rotate the platen and thus to internally shear the specimens. It is measured by the load cell. The shear strain is determined from the anvil rotation in conjunction with the simultaneous thinning of the sheared samples. Their momentary thickness is measured within±2 ␮m through monitoring the distance change between the metal plate and a proximity probe, shown at the top of Fig. 3, whose output voltage is proportional to the distance of separation. However, since as shown in Fig. 3, the proximity probe is attached to the topmost anvil while the metal plate facing it is attached to the lowest anvil, this

measurement monitors the total thickness change of both specimens together, not of the specimens singly. In order to prevent slipping between anvils and samples, and thereby to ensure accurate shear stress–shear strain measure rather than slipping between samples and anvils, the applied pressure must compare to, or be greater than, the momentary hardness of the sample, i.e. for large shears must be at least equal to the ultimate shear strength of the workhardened samples. These same conditions also apply to the deformation of interlocked plastic contact spots that in actual friction and wear leads to the formation of MML’s. Because workhardening of the specimens increases their shear strength during the simulation, the desired condition of non-slip sample/anvil contact may not persist during the course of an experiment. However, the higher is the applied normal pressure, the larger the shear strain that can be imposed on the samples before slipping occurs (if any). At any rate, a minimal pressure comparable to the beginning hardness of the sample is always required to obtain any interior sample shearing at all. Further, increasing friction between samples and anvils reduces the probability of slipping. To this end the anvils are roughened through etching with 10% hydrofluoric/40% nitric acid in water. This increases the coefficient of friction µ, at the anvil–sample

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Fig. 3. Cross-section of the modified Bridgman anvil apparatus used in this research shown here at about one half of the actual size.

interface to at least µ=1 and apparently to above 2, as follows. Whether the samples slip or are internally sheared is controlled by the relative magnitudes of applied normal pressure p, sample shear strength or hardness H, and the coefficient of friction between samples and anvils µ. Namely, assuming perfectly uniform hardness in the sample, the torque required for shearing is [12] Mτ =

4π 3 R H 3

(1a)

with R the sample disk radius, while slipping occurs at Eq. (1a) with H replaced by the interfacial shear strength, i.e. by µp. As first explained in [12], shearing versus slipping depends on which requires less torque. Superficially this means that the tests require

µp > H

(1b)

Matters are complicated by the facts that (i) the pressure is not uniform over the sample area, (ii) H rises roughly linearly (but fortunately much less than proportionately) with pressure p, (iii) the shear strength H also rises with shearing and (iv) shearing is very non-uniform, in thickness as well as radial dimension. All measurements therefore necessarily yield only averages of the sample shear strength. However, by comparison among data, a great deal of information can be obtained on the dependence of the shear strength, H, on shear strain, pressure, composition, lubrication etc. Moreover, practical experience suggests that no anvil/sample slippage occurs above pav ≈ H av /2 with pav and Hav the average values of p and H, respectively, provided that the anvils are etched as indicated, as was done routinely.

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the shear strain due to anvil rotation, is γ nh due to thickness reduction. For this we may write

2.2. Bridgman apparatus measurements Following the preceding thesis work [42,43], during an experiment in the Bridgman apparatus the anvils are rotated at a constant angular velocity (ω), using a motor which is connected to the drive shaft at left in Fig. 3. As was stated before, workhardening during shearing strengthens the material. Therefore, increasing torque must be applied in order to continue the deformation of the sample. This torque, Mτ used to calculate the shear stress τ as Mτ =

3M 4π R 3

(2)

is measured by the output voltage VL of the load cell pictured at center right of Fig. 3. Simultaneously the average thickness h of the two samples is monitored by the proximity probe whose output voltage (Vp ) varies linearly with distance as h = Cp Vp

(3)

where CP is the proximity probe constant. Note, however, that h is an average since the sample between the area of the anvils commonly deforms into a lentil shape. The values of VL and Vp are recorded by a personal computer into an ASCII file. This file is input for a basic program that is used to calculate the number of rotations x, the average sample thickness h, in ␮m, the average shear stress in MPa τ , and the shear strain γ . In order to convert the resulting measurements into shear stress–strain curves, i.e. Hav (γ av ) curves, which give an overall picture of the sample workhardening, one still needs to determine a value for the average shear strain, γ av . On account of rotation angle, Θ, alone, the local shear strain at distance r from the rotation axis may be expressed as [36] γΘ =

rΘ h

(4)

with r the distance from the rotation axis, and the maximum shear strain at the perimeter of the sample as γmax =

RΘ h

(5)

However, both of these shear strains are only first order, perhaps zero order, estimates on account of the already noted great non-uniformity of shear, as follows: as explained, anvil etching enforces relative rest between samples and anvils for a local γ = 0 at the upper and lower specimen surfaces. This, then, generates a very strong shear strain gradient in the axial direction, with maximum shear strain along the mid-planes of the specimens. Superimposed thereon is the deliberate shearing that, nominally, vanishes at r = 0 according to Eq. (4). However, firstly, internal friction prevents this simple linear rise of shear with r and, more importantly yet, sample thinning causes an additional shear strain that is not insignificant and is distributed, again non-uniformly, throughout the sample. Hence, superimposed on the γ rΘ ,

dγnh = −M

dh h

with M ≈ 3 the Taylor factor so that   h0 γnh = M ln h

(6)

(7)

However, on account of the already mentioned evolving lentil shape of the sample, also γ nh is but a first-order average. Namely, samples undergo changes in thickness by factors of several to many, the smallest change at their center and the largest toward the perimeter. With typical initial and final sample thickness of h0 = 250 ␮m and around 20 ␮m, respectively, the shear strain due to thickness reduction alone is then γnh ≈ 3 ln(250/20) ≈ 10. Consequently, the strain minimum at the sample center, formally zero from Eq. (4), is comparable to the maximum strain attainable by most other deformation mechanisms, including rolling and wire drawing but excluding mechanical alloying (MA). Altogether, then, Eq. (5) may be, and is, used to designate some ill-defined but yet highly informative average shear strain. For determining Θ, h, τ and γ from the output voltages VL and Vp in line with the preceding explanations, as a function of time during testing, the following parameters need to be known 1. the anvil rotation speed, ω; 2. the sample radius R, i.e. that of the smaller, beveled, anvil in each anvil pair; 3. the proximity probe conversion constant, Cp ; 4. the initial sample thickness, h0 . These constants are measured or experimentally controlled in the following manner. The anvil rotation speed is varied via a speed control box and is set at a speed, namely ω ∼ 1 rpm, that avoids resonant frequencies that are inherent in the Bridgman apparatus. The exact rotation speed is measured with a stopwatch to within ± 0.05 s. The radius of the beveled anvil, which determines the effective sample radius, is chosen as 1/2(3.2 mm)≈ 1.6 mm, in fact for convenience in making TEM samples. The exact anvil radius is measured using callipers under an optical microscope with an accuracy of about ± 5 ␮m. The proximity probe constant Cp , is equal to the ratio of the thickness change (h0 –h), to the output voltage change of the proximity probe, Vp , in accordance with Eq. (3). A calibration experiment using a known thickness and measured Vp is used to determine the proportionality constant Cp . The initial sample thickness h0 , depends on the applied pressure and sample strength. Recall that the proximity probe measures changes in sample thickness, not the absolute thickness. The initial sample thickness h0 , therefore has to be determined indirectly. It is extrapolated from two values: (i) the final thickness measured with a micrometer, hf , and (ii) the total thickness change measured using the proximity probe. The aforementioned BASIC program

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calculates a temporary final thickness hT , using an assumed initial thickness of 500 ␮m. The difference between hf and hT is subtracted from 500 ␮m to obtain the correct initial thickness. 2.3. Focused ion beam microscope and scanning ion spectrometry Many of the microscopic results were obtained by means of FIBM. The focused ion beam 200 workstation, developed by the Focused Electron Ion (FEI) Company, can be used to create secondary electron images and TEM membranes. How the secondary electron images are created is described in the FIB workstations users guide and is schematically represented in Fig. 4a [44] as follows: a strong electric field is applied to the liquid metal ion source (LMIS) at the top of the column and extracts positively charged gallium ions. Two electrostatic lenses, two steering quadrupoles, and an octupole deflector in the column focus the ions into a beam (approximately 10–300 nm in diameter) and scan the beam on the specimen. As the ion beam strikes the specimen, it removes material through physical sputtering and also generates secondary electrons and ions as well as neutral particles. These secondary electrons or ions are detected and processed to form an image of the area on the specimen that is being scanned by the ion beam. The scan control system allows milling of specified patterns into the specimen thereby allowing for precise placement or creation of TEM cross-sectional membranes. Our FIB 200 workstation is also comes equipped with a Secondary Ion Mass Spectrometer and control software

Fig. 4. (a) Schematic of FIBM beam column. It produces probe sizes ranging from 10 nm with a 1 pA beam to 100 nm with a 11500 pA beam [44]. (b) Schematic of the SIMS system which provides elemental mapping of specimens [45].

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(SIMSmapIII) which offers four different ways of gathering data. These are mass spectrum acquisition, elemental mapping, depth profiling, and end point detection. In this research, the elemental mapping capability of the SIMSmapIII analysis system was utilized in particular. Here elemental mapping is generally used to confirm that materials are in the expected physical positions and to look at the distribution between different materials. The technique involves tuning the mass spectrometer to detect ions of a specific mass, and then generate an image where the brightness signal is the selected mass spectrometer output (roughly proportional to the rate of secondary ion generation for the particular species) as opposed to the total electron or ion signal.

3. Specimen preparation In order to study how lubricants affect sliding interfaces, a system was designed for the controlled application of lubricant [43]. Herein, the 25 ␮m thick 10 cm×10 cm foils that are used for sample material, are placed one by one 5 cm below a downward facing nozzle in a stack on a moderately larger supporting cardboard square. Two separate tubes feed the nozzle, one for an oil–solvent mix and the other for a propellant. A 90 wt.% high-grade methanol and 10 wt.% lauric acid oil–solvent mixture is used rather than the undiluted oil for two reasons: to achieve a finer spray and thereby greater uniformity of distribution and, secondly, to permit better control of lubricant concentration, especially needed on account of the intended small amounts of lubricant. The propellant is high grade Argon (3 ppm O2 ). For oil application, 0.33 cc of the lubricant–solvent mix is measured into a syringe and is injected into the flowing propellant at the nozzle tip. The result is a spray of approximately 100 mm diameter droplets propelled by the Argon. This spray is uniformly distributed by sweeping the nozzle systematically and equally over all parts of the foil surface. A 250 ␮m thick stack of 10 lubricated foils in the order of 2 Cu foils followed by 2 Ag foils and so on was generated by placing a new foil pair on top of the previous one after it had been sprayed as described and the solvent had been allowed to evaporate. Each spraying was timed to leave behind a 200 Å thick layer of lauric acid. After completion of spraying and stacking, a second cardboard square, similar to that on the bottom, is placed on top of the stack. As the cardboard is rigid, the foil stack between the two pieces of cardboard can thus be handled safely. Protected by the two pieces of cardboard, the stack is next pressed in a hydraulic press at 120 MPa for 5 min. This pressing largely, though not entirely, removes air bubbles from between the individual foils. Thereafter, the cardboard is removed and the foil stack is ready as a sheet material from which Bridgman anvil shear test samples may be cut. Each shear test sample was a round 3.2 mm diameter disk that was punched out of the compacted foil stack. To this end, the compacted stack is placed on a 2 cm thick lead plate and

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a leather punch of the sample diameter is hammered through the stack into the lead plate. The lead plate is sufficiently soft to allow the leather punch to make a clean cut through the stack. After the required two samples per any one Bridgman apparatus shear test (compare Fig. 3) are cut from the pressed stack, the remainder of the stack is stored in a desiccator until more samples are needed. So as to obtain the greatest possible information from the sheared samples, the cross-section of the sample layers has to be oriented parallel to both the TEM and FIB beam direction. In order to accomplish this feat, the following novel technique for mounting cross-sectional FIBM samples was developed. The process begins by slicing the layered disk specimen into four parallel sections of similar width as shown in Fig. 5a. A 3 mm disk of silver foils is also sliced into four

equal strips. Next 500 ␮m thick Si wafer material is cleaved into 3 mm × 1.5 mm bars and the cleaved edges are (somewhat laboriously) mechanically polished. The next task is to mount a sliced foil silver section as well as an edge and middle strip of the sheared sample between the Si bars as follows: using self-closing tweezers, with tips wrapped in Teflon tape, one of the Si bars is held so that one of the polished 500 ␮m sides is face up. A thin layer of epoxy-hardener mixture is applied to that surface using a thin wire. Next an edge strip of the layered specimen (shown in Fig. 5a) is placed on the epoxy so that the edges of the layered sample section are in line with that of the Si bar. These two steps are repeated for the middle strip of the layered sample and a slice of Ag. The three layers of foils and epoxy are then sandwiched between the two Si bars (Fig. 5b, c) by means of tweezers placed on a hot plate until the epoxy has cured. At this point the FIB specimen should be approximately 2 mm ×3 mm ×0.5 mm in size. The final step is thinning the specimen and mounting it on a TEM grid. To this end, one of the 2 mm × 3 mm faces is polished flat so as to remove excess epoxy that may have wicked over the surface and to reduce it to a thickness of 1.5 mm. Now a nickel TEM sample grid is cut in half along the short direction of the oval. The sample is mounted thereon; with its previously polished edge on the dull side of the Ni TEM half grid so that the layers of foils are in the middle of the hole. Finally the specimen is thinned parallel to the plane of the TEM grid by polishing on 600grit sandpaper to a final thickness of approximately 50 ␮m. In spite of the described polishing that was done to obtain the correct specimen dimensions for use in the FIBM, the surfaces are still fairly rough as seen in Fig. 5c. Further polishing is performed using the FIBM so that the microstructure can be imaged. As was previously stated, the SIMS optics in the FIB can be used for elemental mapping of specimens. In order to optimize the conditions for data acquisition, several adjustments must be made to the FIB beam and to the sample shown in Fig. 5c. First, a platinum layer 25 ␮m × 2 ␮m is deposited on the specimen approximately 20 ␮m from the edge to protect the surface of the cross-section from ion beam damage. Next an edge of the sample must be polished at a 45◦ angle as shown in Fig. 5b. Polishing is done with a coarse beam current of 11500 pA to eliminate the surface roughness, bringing out the microstructure, and the 45◦ angling is done to orient the surface toward the SIMS optics, which increases the signal strength reaching the detector.

4. Thinning and shearing of samples in the Bridgman anvil apparatus Fig. 5. (a) Geometry of layered disk sample being cut into strips (Cu (grey), Ag (dark) lubricant (light)). (b) Drawing (not to scale) of the orientation of an FIB sample gained from the strips in (a) in reference to various beams. (c) Secondary electron image of a sample as in Fig. 5b ready for use in the FIBM.

Fig. 6 shows the dependence of the average sample thickness on anvil rotation. As the sample thins, sample material extrudes from between the anvils [25,26]. As in earlier

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Fig. 6. Thickness vs. rotation for different samples sheared under a pressure of 2.0 GPa. The dependence of initial thickness (after pressure application but before rotation) on the sample composition, illustrates the proclivity of the layers to be squeezed out from the anvils on first pressure application. The ‘slipperiness’ of the interfaces which make possible this squeezing out at the same time permits slippage between adjacent layers, thereby partially inhibiting the interior shearing within the individual layers which is associated with thickness reduction of the sample.

research [42,43] the thickness versus rotation data have been curve-fitted using software by Jandel Scientific called Curve Table 2D with the equation  h = h0 exp −bh

r

ω 2π



√ = h0 exp(−bh x)

(8)

where x is the number of anvil rotations, h0 is the initial thickness, and bh is a numerical parameter varying between 1 and 2 depending on the material being sheared. Fig. 7 shows stress–strain curves obtained from the Bridgman-anvil apparatus. Apparent in all of them is an initially slow increase of shear stress with strain. This is ascribed to inter-layer slipping, before onset of rapid workhardening. In accordance with previous results, the workhardening data in this and all other comparable curves are successfully interpolated by Voce curves [34,42,43,45,46] using Jandel’s Curve Table 2D. Voce curves represent stage III workhardening that is followed by stage IV. That could be either another much flatter Voce curve [47,48] but is better fitted by linear hardening up to some saturation strain. If so, one finds, as expected for stage III workhardening, the Voce curve formula [45], followed in our interpolation by a linear part due to stage IV, i.e. 

−γ τ = τf − (τf − τ0 ) exp γ0

 + Dγ

(9)

where τ 0 is the shear stress at the start of rapid hardening, τ f is the final shear stress, and Dγ is the linear hardening on account of stage IV. The micrographs shown in Figs. 8–14b provide the means for more detailed interpretation of the data. They were obtained via FIBM at a beam current of 4 pA. The elemental maps (Fig. 10a and b) were imaged using the SIMS optics of the FIBM at a beam current of 1 nA. They will be seen to document the formation of ‘tongues’ (see Fig. 1), the mechanism of MML (mechanically mixed layer) formation, and the already indicated, newly discovered effect, namely the mobility of the layers among each other in the case of the lubricated samples.

5. Discussion 5.1. Thickness-rotation relationship The first characteristic of sample thickness curves, such as Fig. 6, is the decrease of the initial thickness of the specimen with increasing applied pressure [26]. In order for the material to comply with the applied pressure p (which as discussed is equivalent to the plastic zone of contact spots in tribology) some material extrudes out from between the anvils and the material strength rises as it provides the reactive force to the anvils. Fig. 6 illustrates a corollary of this

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Fig. 7. Average shear stress–strain curves for different samples sheared under a pressure of 2.0 GPa. At low strains, note the apparent strong sliding between parallel layers in lieu of distributed shearing, especially in the lubricated samples but to a minor extent also in the unlubricated samples. In their case, adsorbed moisture and trapped air will play the role of a weak lubricant.

fact by demonstrating that the initial thickness decreases, i.e. the plastic compression as load application increases, when softer materials are added to the sample under the same applied pressure, Cu being harder than Ag. What is unexpected is the extra increase in the initial compression for the lubricated samples, which is much greater than the cumulative thickness of the oil layers in them, especially in the case of Ag–Cu samples. Although there is an increase of initial thickness change with the decreased hardness of the material as discussed, most remarkably the subsequent rate at which the sample thins during anvil rotation depends on the hardness of the material in the opposite direction. Considering initial sample compression, it is clear that whatever pressure is applied, the sample material must harden accordingly since otherwise force equilibrium would not be achieved. For an initially softer material this requires a larger compression as indicated by a smaller initial thickness. Therefore, on initial loading, samples of lower strength (i.e. samples which include Ag or lubricant) squeeze out more material, resulting in a smaller initial thickness. Once equilibrium is established the rotation of the anvils squeezes out even more of the material. In the previous cited research with unlubricated samples made of very thin foils this further thinning, no matter how the momentary thickness was attained, followed the same h(t) dependence i.e. Eq. (8) [42,43]. Now, with lubricated samples, we see a previously unobserved, unexpected dependence on initial hardness of the material. Moreover, upon

further inspection it was found that during the initial application of pressure larger amounts of Ag extrude out of lubricated than unlubricated samples. This indicates that the lubricant made the interfaces between the Ag and Cu foils surprisingly ‘slippery’, allowing for patches of whole layers of material to slide past each other. Because of this, also the thinning due to the anvil rotation of the lubricated Ag–Cu (see the solid curve in Fig. 6) is much slower than that of the unlubricated Ag–Cu. Namely, in this case with anvil rotation the lubricated layer interfaces slide past each other in lieu of internal shearing within the individual layers. This in turn decreases the amount of sample thinning, since thinning is a consequence of internal shearing [25,26]. A similar, albeit smaller, effect is seen in the case of the lubricated Cu–Cu foil. However, this effect ceases altogether above ∼ = 1.5 anvil rotations as evidenced by the increased rate of sample thinning. In line with the above, gradual thinning of the sample sets in simultaneously with the onset of interior shearing, but not necessarily directly on activation of anvil rotation. Experimentally, any delay of the thinning and extrusion of material in the sample is thus due to slippage whether between the anvils and the sample surface or between layers within the samples. Whether anvil-sample slipping occurred can be ascertained by viewing the specimen surfaces under an optical microscope and noting whether the specimen surface morphology matches that of the adjacent anvil. Scoring marks on the sample show when slipping has occurred.

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causing most previously published data to be highly suspect [25,26]. The discussed inhomogeneous loading and extrusion is enhanced with the introduction of lubricants. In the case of lubricated samples, immediately on pressure application to the sample, Ag extrudes outside of the area of the anvils as already mentioned. This effect poses an additional problem to the inherent inhomogeneous strain when trying to quantify the amount of strain which the sample undergoes during shearing and will be discussed later. 5.2. Shear stress/shear strain analysis

Fig. 8. (a) FIB secondary electron image (SEI) of the microstructure of the Ag foil after being polished with the FIB at 11500 pA. (b) Same as Fig. 8a but for the copper foil. Note that the copper grain size is larger than that of the silver. This is due to recrystallization in the foils, which is evident because otherwise the grains would be strongly pancake-shaped on account of rolling down the foils. The vertical streaks seen in the image are due differential sputtering of surface grains of 11500 pA.

When such markings were seen, the corresponding sample was discarded. Even without lubrication, plastic deformation within the sample is non-uniform. Specifically, the softer material, i.e. Ag, begins to shear first. But most importantly, Ag and Cu slip relative to each other also in unlubricated samples. This phenomenon is represented by a disproportionately large percentage of Ag in the rings of the extruded material, Ag extending away from the area between the anvils. The uneven shearing of sample material is typically enhanced by unavoidable very slight anvil misalignments relative to the plane of rotation. Normally, the two anvils while at rest before the shearing begins, are parallel to each other but slightly tilted relative to the axis of rotation. After one half turn, as one anvil is fixed, during rotation this misalignment causes a maximum pinching effect on one side of the samples where the anvils squeeze together, while on the opposite side the pressure is at a relative minimum. Due to this slight misalignment of the anvils during rotation, all of the measured curves exhibit some apparent shear strength undulation that is periodic with the anvil rotation. Moreover, the discussed pinching after one half turn and then again after one and a half turn can cause a perforation in the samples and thereby effectively end the experiment. This effect was not recognized in previous Bridgman anvil studies

The effect of interfacial sliding during shearing is manifested in the shear stress–strain curves, shown in Fig. 7, as an unexpectedly low initial sample strength and workhardening rate. To repeat, this is caused by sliding between parallel layers due to the mobility of the interfaces between layers. Although this slipping results in a reduction in the initial shear stress and in the delay of workhardening of the specimen (very evident in Fig. 7), it ceases at higher strains. This is remarkably represented in the case of the lubricated specimens shown in Fig. 7, i.e. for lubricated Cu–Cu for which full workhardening commences at γ ≈ 40 and for lubricated Ag–Cu at γ ≈ 200. Beyond this effect, for all of the samples in the present study, i.e. all made of 25 ␮m thick foils, the workhardening rates were low in comparison to that of stacks of sub-micrometer foils [36,42,43]. We conclude that this is so because the layers in the present experiment are flatter and much more rigid and thus slide more easily past each other. It seems that such sliding between layers, even in the unlubricated state, is facilitated by adsorbed gases (especially air) and moisture which are trapped between the layers to cause a molecular lubricating effect. Correspondingly, a significant fraction of the imposed macroscopic sample shearing is accommodated not through interior deformation within the layers but, as explained, by relative sliding between them, even in the nominally unlubricated samples, thereby lowering the initial workhardening rate. This incidental air/humidity lubrication was not seen in the earlier experiments on very thin foils because they were so extremely flexible that they could not slide past each other. Ultimately, above an average shear strain of a few hundred (i.e. tens of thousands of percent strain), the curves suggest the total cessation of sliding between the layers and the operation of normal internal shearing in the course of which the samples thin. The transition between those two regimes is gradual because of the strongly inhomogeneous shear strain. As already indicated, the shear strain is greatest at the mid-plane and at the sample perimeter in axial and radial directions, respectively, with an extremely non-uniform distribution of the shear strain (Section 2.2). Therefore, internal shearing will be established at the perimeter long before the sliding between interfaces ceases near the

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rotational axis, and similarly it will continue close to the anvil faces, when it has already ceased near the mid-plane. 5.3. Microstructure analysis As discussed at the start of this paper, contact spots are the means by which materials in sliding contact become interlocked at the interface and cause the statistical strong shear sketched in Fig. 1. Initially, then, it is expected that during ordinary sliding the tangential pull between interlocked spots causes elongations in the form of easily recognizable ‘tongues’ which gradually refine and overlap into the lamellation that simulates MML’s (Fig. 1). In order to test this model we investigated the formation of the tongues and further evolving microstructure. Herein, as a first step the original microstructure of the Cu and Ag foils must be established. This is shown in Fig. 8a and b. From this, it is seen that the Ag foils tend to have a smaller grain size on average, and that Ag appears darker when imaged side by side with Cu. Figs. 9–14b document the changes in those microstructures within the layered samples sheared in the Bridgman-anvil apparatus and leading to the data in Figs. 6 and 7. In these samples recrystallization of the material is evident, characterized by more or less equiaxed grains. However, such recrystallization does not affect the physical distribution of the two materials.

Figs. 9a–b and 11a–b clarify the geometry in unlubricated Ag–Cu after the first and second anvil rotation. Specifically, Fig. 9a illustrates the creation of tongues. It is an image of the middle section of a layered sample, which has undergone one anvil rotation. Here the early stages of tongue formation are shown. Note that the direction of the shear is clearly mirrored by the direction of the tongues, as represented by the arrows at the edges of the figure. Remembering the discussed gradient of the shear strain from the middle to the edge of the specimen, the evolution of the tongues with strain can be viewed by simply comparing the microstructures between the center and edge of the same specimen as shown in Fig. 9a and b. The SEI, in Fig. 11 most impressively shows the lamellation of the tongues due to the higher strain. One would safely conclude that the mixing through this evolving lamellation is close to that of the mechanically mixed layer as illustrated in Fig. 1c. Although the distribution of the two metals can already be seen on the SEI micro-graphs due to the noticeable difference in contrast between the two metals, elemental maps from the SIMS optics are used to confirm the morphological distribution of the two components, copper and silver, for any desired area. Thus, the SIMS optics can give sub-micron information on the distribution of the two mixing materials as shown in Fig. 10a and b in comparison with Fig. 9a. Therefore, this method has been extensively

Fig. 9. (a) SEI image of the middle section of an unlubricated layer sample under 2GPa pressure and 1 anvil rotation (local shear strain γ ∼ 4.8) polished with a 150 pA ion beam current. The direction in which the tongues are elongating indicates the direction of the shear namely opposite on the two sides. (b) FIB SEI of the edge section of the same sample with an estimated local shear of γ ∼ 50. Note that the increase in shear strain from the middle section (see Fig. 9a) to the edge section (see Fig. 9b) of the sample produces more deformation between layers causing the tongues to form lamellation.

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Fig. 10. (a) Elemental Cu map of Fig. 9b, i.e. showing Cu as white. (b) As Fig. 10a but Ag map showing Ag as white.

used for positive identification of the materials, especially to reveal the intimate mixing of the metals at the original interfaces that is so clearly seen in the micrographs. As expected from Fig. 1, it sharply increases with shear strain. A stunning degree of interfacial mixing and relative movements of the two materials occurs at high strains, especially when lubricants are added (Figs. 12a–14b). Comparing 9a with 11b, a drastic refinement of the tongues is noticed due to the higher shears evidenced by fine streaks of lamellae. Additionally, the recrystallized grains in the two metals are finer. These micrographs further illustrate the axial shear strain gradient, albeit apparently irregular and masked by recrystallization refinement, as the shear strain seems to sharply increase towards the right of the sample shown in Fig. 11b. The microstructure in Fig. 11b further reveals a profound restructuring among the initial Cu–Ag–Cu–Ag–Cu layers, but more importantly yet, one may infer extensive slipping between Ag and Cu since there remains only a remnant of one of the original Ag layers. Also, Fig. 11b is indeed a fine illustration of the effect which undulations of the interface boundary have on the micro-morphology: if the foils were completely flat, the foil boundaries would all be parallel to the shear plane. Therefore, as a specimen is sheared, the foils would ideally simply slide relative to each other or else would undergo internal shearing, causing them to thin without any mixing at the interface. Instead, on account of the asperities at their surfaces, the interfaces are imperfectly aligned with the shear plane. Shearing causes the asperities to interlock and thereby to produce tongues in the manner of Fig. 1. Next the interface areal density increases strongly, causing a fine lamellation.

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That effect is still increased because the sample thins. As a result the applied shear stress rises greatly above that for sliding between Cu and Ag layers, while the strong interior straining within the layers simultaneously causes workhardening. Seen in all of the SEI’s at higher strains is a layer of particularly fine microstructure at the edges where the specimen and the anvil were in contact. This zone of fine grain size serves as a good indication that no anvil/sample slipping has occurred during the experiment. If anvil slippage had occurred it would be denoted by elongated pancake shaped grains. This proves that directly at the anvil/sample interface, the frictional yield stress between the anvil and the specimen must have been higher than the shearing yield stress within the sample. As discussed at the start of this paper, this is required so that there is no anvil/sample slipping, and as a result there is essentially no shear strain directly at the sample surfaces. Previously this effect was specifically documented for the particular case of an Al–Si composite [22]. Thus, there is a very strong shear strain gradient from γ = 0 at the anvils towards maximum shear near sample mid-plane. It was already pointed out above, that independent of the shear strain gradient through the thickness of the sample, there is the already discussed strong radial shear strain gradient in accordance with Eq. (4). Superimposed on this, however, is the shear strain due to sample thinning (see Section 2.2). The true shear stain on account of compression is estimated as   Z h h0 dh(r, ω) ∼ M ln (10) γc = −M = h(r, ω) h h0 (compare Eqs. (6) and (7)) where M ∼ = 3 is the Taylor factor for axial compression in FCC metals and h0 is the initial thickness. The previously indicated complication with using this calculation for the compression shear strain arises because, evidenced by the specimens, the structure is fixed at the anvil interface, so that the shear strain is displaced towards the mid-plane. Correspondingly, the shear strains are very inhomogeneous and for different micrographs can only be very coarsely estimated. This is especially true because particularly for our middle strips (see Fig. 5a) the distance from the rotational axis to which the micrograph pertains, cannot be ascertained. In the stress–strain curves, the average shear strain values have been used, calculated by means of Eq. (4). Unfortunately, in agreement with the present discussion, this evaluation of the shear strain is riddled with the outlined complications. They are still further compounded for our layered samples since, as discussed, not only are the shear strains moderately larger in Ag as compared to Cu but, observationally, disproportionately large amounts of Ag are extruded at the anvil periphery during shearing. In fact, whole Ag layers or parts thereof slide within the samples and are extruded at the periphery. This extraordinary mobility of the Ag layers, in addition to the gradient of the shear strain from top to bottom and edge to middle, along with the

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Fig. 11. As Fig. 9 but after 2 anvil rotations (a) near the axis of rotation with local γ ∼ 8 and (b) near the circumference with local γ ∼ 1500, respectively, polished with a 150 pA ion beam current.

already discussed inhomogeneous reduction of thickness which commonly results in a lentil-shape sample, cannot be expressed by a single value of average shear strain. The representation in the stress–strain curves (Fig. 7) based on measurements of the average thickness are thus no more than coarse guideline values. The discussed strong strain gradients allow for dramatic local changes in the shear strain observable in the micrographs. Specifically, at the rotation axis, the compression strain may but does not necessarily dominate, e.g. as computed for the initial to final sample thickness of 250 and 50 ␮m, respectively. The shear strain at the center could therefore be as low as γ c ∼ = 3 ln(250/50) = 4.8, e.g. as at the center section of the lubricated sample shown in Fig. 9a,

while it may exceed γ = Rω/ h ∼ = 2π × 3.0 mm/12 ␮m = 1570 for the edge of a dry sliding sample after 2 anvil rotations illustrated in Fig. 11b. 5.4. Effect of lubricants Although there are numerous empirical studies on the performance of lubricants on friction and wear, very little is known about why a lubricant is successful or fails and what morphological changes, if any, a lubricant causes at an interface. The results acquired from this research (shown in Figs. 12a–14b) on lubricated sliding interfaces thus make an important contribution to our knowledge. In fact they are very revealing indeed. Namely, there is conclusive evidence

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Fig. 12. (a) As Fig. 11 but for a lubricated sample, i.e. a detailed image of a lubricated layered sample sheared at 2 GPa pressure and two anvil rotations (γ ∼ 5.0) polished with a 150 pA ion beam current. Note: that there is only one distinct layer of silver present. (b) SEI image of the edge section of the sample as in (a) but with local shear of γ ∼ 630 polished with a 150 pA ion beam current. The presence of several layers of silver instead of the two original demonstrates the astonishing mobility of the Ag layers.

for bodily motion of Ag through Cu and to a minor extent vice versa. Remembering the geometry of the layered foil samples (Fig. 5a) a whole Ag layer is missing, for example, in the middle section of the lubricated layered sample shown in Fig. 12a. The only evidence that the second layer existed is a ‘chunk’ of Ag, which has been left behind. The story is told in Figs. 12a–14b: instead of just one Ag layer as in Fig. 12a, we find multiple Ag layers at the edge of the same specimen in Fig. 12b. Initially doubting that the indicated bodily motion is an actual phenomenon rather than some odd artifact, the experiment was repeated numerous times, but the results were strikingly similar, as represented in Figs. 13a–14b. Specifically, in Fig. 13a the Ag layers vanished and only a part of them has coagulated and migrated toward the anvil surface. Conversely, at the edge of the same

sample (Fig. 13b), four Ag layers are found. We conclude that (i) the two Ag layers initially in the middle have slipped out from between the adjoining Cu layers without leaving a trace and (ii) have forced their way bodily through the Cu to lodge within parts of the same layers that the four Ag layers at the edge could be due to the separation of the initial two 25 ␮m Ag double layers. However, if so, there must have been a similar bodily migration of copper layers between them. Interestingly, the seemingly undisturbed recrystallized structure of the surrounding Cu proves that after, or concurrent with, the migration of Ag through Cu, there is a self-healing process. At any rate, there is no trace of the intermediate positions of the Ag layers, and this notwithstanding the fact that the actual relative sliding between

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Fig. 13. (a) SEI of the middle strip of a lubricated layered sample under 2 GPa pressure after two anvil rotations with local γ ∼ 10. Note that apparently the initial pressure application expelled all silver from the sample center except for a small chunk and that the copper has completely healed after the passage of the silver, meaning also that the lubricant adhered to the silver and was expelled with it. (b) As Fig. 13a but for the edge strip with local shear γ ∼ 1500. Note in contrast to Fig. 13a there is little if any silver depletion. However, the two layers missing from the center are evident here as additional layers. At the same time, tongue lamellation is minor, i.e. the bulk of the anvil rotation was accommodated through Ag–Cu interfacial slipping.

silver and copper will have been accommodated within the oil or incidental adsorbed material between them. A possible explanation for this phenomenon is seen in Fig. 14a and b. This SEI shows a segregation of the finely mixed Cu and Ag layers from the surrounding copper which, no doubt, acts to decrease the interfacial energy. This segregation effect is even more apparent in the lubricated samples (e.g. Fig. 14a and b). In this case when the specimen was sheared under high pressure, the oil layer segregated, as seen by the wicking of epoxy into the void left by the oil, and there is a coarsening of the interfaces as like metals tend to attract each other in order to lower their energy. The segregation of the oil layers can enclose entire areas, which allows bodily sliding of one metal past the other. Any interfacial contamination, whether deliberate or otherwise, also acts as an inhibitor against recrystallization of the interface. As a result contaminants are evidently able to freeze the interface in a higher energy state. In Fig. 14a of

Fig. 14. (a) SEI of an edge section with γ ∼ 1500. Where due to the oil intermixing with the interface recrystallization has been reduced. (b) SEI middle section with γ ∼ 10. Due to the segregated oil layer the intermixed material was able to bodily migrate to the surface of the sample. The epoxy in (a) wicked into as pace that had been filled with segregated oil.

the lubricated sample, this is shown by the abrupt end of the recrystallized Cu adjoining the fine lamellar structure of the mixed metals and similarly in Fig. 11a of the unlubricated sample. Comparing all of the data, thickness versus anvil rotation curves, shear stress–stain curves, and micrographs, one can safely conclude that they all show the same behavior: When the load is applied to the layer samples in the Bridgman-anvil apparatus, slipping between the layers, which is enhanced by lubricant, occurs and material is extruded out at the perimeter. This is shown by the dependence of initial thickness and of the subsequent thickness-anvil rotation curves on sample composition, as well as the depletion of the silver layers in the middle of the lubricated sample and their enrichment at the edges documented in the micrographs. After the possible initial expulsion of the silver from the center of the lubricated samples on pressure application, at the onset of shearing via anvil rotation, the

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slipping between layers continues until asperities at the interface interlock. This causes the formation of tongues and lamellation which forces internal shearing and results in the rise of the shear stress. Oil seems to bond more strongly to the silver. Therefore, when the silver is extruded out of the sample, the lubricant extrudes with it, both, so to speak, worming their way through the copper to the perimeter of the sample. The surprising observation that the Cu can heal behind the pathway of a chunk of silver without leaving a trace (see Fig. 12a) means that all of the lubricant moves along with the silver. The inference from Fig. 12a and 13a, and the results presented in this research, is that all of the discussed phenomena can similarly take place at ordinary tribo-interfaces.

bology Program, Division of Civil and Mechanical Systems, under the guidance of Dr. Jorn Larsen-Basse is gratefully acknowledged. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

6. Summary [10]

The simulation of adhesive wear through shearing under high pressures has been expanded through new techniques developed to obtain microstructure information at all scales from nanometers to millimeters. From this research, the following conclusions emerge: (1) At least some types of adhesive wear result from shearing at tribo-interfaces which, beginning with interlocked contact spots, causes geometric elongations dubbed ‘tongues.’ (2) Through a simple geometric distortion of surface waviness, continued shearing leads to fine lamellation of these tongues. (3) This results in nano-scale mixing at the interface i.e. MML’s. (4) Bodily motion of volume elements of the two metals, in our case. Ag through Cu and vice versa, can take place, which leaves no trace due to the dynamic recrystallization of the metals. (5) The addition of lubricants enhances the bodily motion of one metal through the other. (6) Additionally, segregation of oil can occur. From the evidence presented in this research several questions emerge which need further investigation. Specifically, is the described coarsening and bodily motion of one lubricated metal through another during severe deformation restricted to only metals of similar hardness? Under what conditions does the segregation of oil and the self-healing proceed? Can this phenomenon be used as a viable means for lowering wear rates in mechanical systems? Would more complex lubricants have similar or enhanced effects under severe plastic deformation? In order to gain answers to these questions future research needs to be done using different lubricants, possibly ones with additives, performed with the same Cu–Cu and Ag–Cu systems along with replacing Ag with a more commercially viable material such as a pearlitic 440C steel.

Acknowledgements The financial support of this research through the National Science Foundation, Surface Engineering and Tri-

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