Microstructural modeling of adaptive nanocomposite coatings for durability and wear

Wear 266 (2009) 1003–1012 Contents lists available at ScienceDirect Wear journal homepage: www.elsevier.com/locate/wear Microstructural modeling of adaptive nanocomposite coatings for durability and wear James D. Pearson a , Mohammed A. Zikry a,∗ , Kathryn J. Wahl b a b Department of Mechanical and Aerospace Engineering, North Carolina State University, Raleigh, NC 27695-7910, United States Code 6176, U.S. Naval Research Laboratory, Washington, DC 20375-5342, United States a r t i c l e i n f o Article history: Received 22 May 2008 Received in revised form 17 December 2008 Accepted 10 February 2009 Available online 21 February 2009 Keywords: Solid lubrication Finite-element modeling Sliding wear Nanocomposite coating Thin-film Transfer film a b s t r a c t Adaptive thin-film nanocomposite coatings comprised of crystalline ductile phases of gold and molybdenum disulfide, and brittle phases of diamond like carbon (DLC) and ytrria stabilized zirconia (YSZ) have been investigated by specialized microstructurally based finite-element techniques. One of the major objectives is to determine optimal crystalline and amorphous compositions and behavior related to wear and durability over a wide range of thermo-mechanical conditions. The interrelated effects of microstructural characteristics such as grain shapes and sizes, local material behavior due to interfacial stresses and strains, varying amorphous and crystalline compositions, and transfer film adhesion on coating behavior have been studied. The computational predictions, consistent with experimental observations, indicate specific interfacial regions between DLC and ductile metal inclusions are critical regions of stress and strain accumulation that can be precursors to material failure and wear. It is shown by varying the composition, resulting in tradeoffs between lubrication, toughness, and strength, the effects of these critical stresses and strains can be controlled for desired behavior. A mechanistic model to account for experimentally observed transfer film adhesion modes was also developed, and based on these results, it was shown that transfer film bonding has a significant impact on stress and wear behavior. © 2009 Elsevier B.V. All rights reserved. 1. Introduction Computational modeling of thin-film coating wear has traditionally been based on the homogenization of coating properties to compute wear rates [1–5]. In contrast, nanocomposite thin-film (1 ␮m) coatings may comprise different material constituents, with each one being used for a desired behavior, such as lubrication, toughening, and strengthening [6]. For these advanced materials there is a need to understand how composition and microstructure [7–10], as well as velocity accommodation modes (VAMs) [11,12] affect the wear response and endurance. Hence, there is a need to (i) develop mechanical models to evaluate how coating microstructure and composition impact tribological properties as well as (ii) provide predictive capabilities to tailor multi-constituent thin-film response at the coating design stage. Recent experiments [13] and processing have identified thinfilm nanocomposite coatings with different combinations of crystalline and amorphous constituents exhibiting intrinsic lowfriction that is adaptive in real time to changes in the environment as well as possessing good wear resistance and durability. These ∗ Corresponding author. Tel.: +1 919 515 5237; fax: +1 919 515 7968. E-mail address: zikry@ncsu.edu (M.A. Zikry). 0043-1648/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2009.02.004 multicomponent coating systems provide good tribological performance over a greater operational range than a single phase coating can provide. From a design standpoint, these coatings combine the mechanical advantage of nanostructured hard phases such as nitrides and carbides with friction modifying phases. For example, the co-deposition of nanocrystalline TiN with either amorphous hydrogenated carbon (a-C:H) [14] or hydrogen free carbon (a-C) [15] results in enhanced hardness and good tribological behavior. More recently, nanocomposite coatings consisting of gold (Au), yttria stabilized zirconia (ZrO2 –Y2 O3 , YSZ), molybdenum disulfide (MoS2 ) and DLC have been developed. These systems are referred to as adaptive coatings in that low wear, environmental stability, and low-friction coefficient can be attained in dry, humid, and high temperature (500 ◦ C) operating conditions [16]. This coating performance is highly promising for a myriad of thermo-mechanical and wear applications. If the mechanisms that result in improved wear and thermomechanical response can be accurately identified, then the constituent components and coating properties can be further optimized. Hardness improvements in nanocrystalline materials are understood to be controlled by resistance to dislocation formation and movement [17]. Toughness improvements can be achieved with the addition of ductile materials. Determining optimum configurations for multicomponent mixtures with lubricating 1004 J.D. Pearson et al. / Wear 266 (2009) 1003–1012 Fig. 1. (a) Dimensions and materials involved in the nanocomposite coating finite-element models. (b) The center of the ‘active zone’ underneath the slider. The zoom shows the level of detail in meshing of the DLC borders around each inclusion. (c) The transition between the active zone and the homogenized coating region. (d) The ‘active zone’ underneath the indenter with a transfer film of 200 nm thickness. phases is challenging as optimizing hardness is not the only concern. What is not known or easily determined are what specific combinations of crystalline, amorphous, brittle, and ductile materials would be optimal, and what the dominant microstructural characteristics are that affect and control this adaptive behavior. The major objective of the present study is to use microstructurally based finite-element techniques to examine how deformation and failure modes evolve in a simulated sliding contact of a multicomponent, nanostructured composite coating. In this study, detailed finite-element simulations of a linear reciprocating ballon-flat configuration are used to examine local strain and stress evolution as a function of composition and scale. Single-component coatings of each constituent (Au, YSZ, MoS2 , DLC) were modeled and used as a limiting case to determine the effects of grain morphology, interfacial regions between the constituents, and mechanical properties for coatings with different compositions. Sliding simulations were undertaken to demonstrate the influence of tangential forces on plastic deformation, fracture, and transfer film formation. Transfer film (TF) models were also developed, and the TFs were represented as both a free (unstable) or bonded (stable) third body in the contact. Based on this, third body velocity accommodation modes relating to experimentally observed wear and interfacial sliding were identified. Finally, sliding simulations were undertaken to demonstrate the influence of tangential forces on plastic deformations. In the wake of the sliding body, the stress state is analyzed for potential Mode I fracture of the brittle DLC matrix material. This paper is organized as follows: the finite-element modeling techniques are briefly outlined in Section 2. The effects of indentation stresses as a function of coating composition are presented in Section 3. Models of sliding and transfer films for adaptive multicomponent coatings are presented in Sections 4 and 5. In closure, general conclusions pertaining to optimal coating composition and the effect of transfer film bonding and sliding on the state of stress in the coating and the transfer film are presented. 2. Finite-element model and microstructural representation A two-dimensional finite-element plane-strain model was used in the indentation and sliding simulations. Based on a convergence analysis, 125,000 quadrilateral elements were used for the simulations. The coating was represented as two regions: (1) a far-field region with elements of homogenized properties and no microstructural morphologies, and (2) an active zone centered beneath the slider (Fig. 1) with relevant microstructural morphologies, constituents, and sizes. This active zone is essentially a representative volume element (RVE) that accounts for physically realistic crystalline and amorphous microstructures. This level of morphological detail cannot be represented over the entire coating, since it would be computationally prohibitive due to the mesh size requirements associated with grain and inclusion sizes and shapes. More critically, by using this two-field approach, material behavior can be investigated at appropriate physical scales within the active zone. It should also be noted that the model system has significantly different physical scales [13]: coating thicknesses on the order of microns and grain sizes on an order of nanometers, and an indenter or slider on the order of millimeters. By using this two-field approach, interrelated material and system behavior at different physical scales can be accounted for. The coatings were modeled based on the nanocomposite coating specimens prepared by Baker et al. [7] and the test geometry described by Chromik et al. [13]. The model is a representation of nanocomposite coatings on a 14 × 0.5 mm 440C steel coupon with a 0.3 ␮m thick uniform interlayer of pure titanium (for coating adhesion) between the steel substrate and the coating (Fig. 1(a) and (b)). Far-field regions away from the center of the steel substrate were assigned homogenized material properties based on reported experimental measurements [7,13]. The active microstructural zone, Fig. 1(a) and (b), is a 100-␮m wide region at the center of contact. This region directly underneath the indenter is a physical representation of the coating constituents 1005 J.D. Pearson et al. / Wear 266 (2009) 1003–1012 Au, YSZ, and MoS2 as randomly distributed and randomly sized and shaped inclusions separated by DLC regions. The model microstructure corresponds to partially crystalline phases of Au, YSZ, and MoS2 , and amorphous DLC that forms as a dispersed matrix phase. Previous studies for nanocomposite films indicated that the DLC matrix phase exhibited sp2 bonding at the inclusion interfaces and sp3 bonding away from inclusions of other constituents [16]. A specialized Voronoi tessellation algorithm was developed for these experiments to generate the random inclusion sizes and distributions in the active zone. Inclusion sizes varied from 300 to 600 nm in average diameter. Matrix phase interfacial material had an average thickness of approximately 0.1 ␮m (Fig. 1(b)–(d)) around each inclusion. Coating regions, which surround the inclusions and their interfaces, were modeled as DLC regions extending towards the free surface and downwards to the titanium interlayer for a thickness of 1 ␮m. To determine the relative volume fraction of each coating constituent, the surrounding DLC areas were not used. Rather, the total volume of the coating was taken to be the volume of the inclusions and borders. The percentages of Au, MoS2 , and YSZ phases were obtained by summing up the volumes of each separate material and dividing by the total volume of the coating. The DLC percentage was obtained by summing the volume of DLC in the interfacial regions and dividing by the total volume of the coating. The mesh used for all simulations is shown in Fig. 1(b)–(d), and material distributions within this mesh were varied to create different coating compositions. Specifically, the 100 ␮m wide coating model was set to have an approximately an equal composition (25%) of all materials in the active zone, and will be referred to as the equal-composition nanocomposite. Two other nanocomposite coatings were simulated, one with 50% MoS2 , and another with 50% Au. The remaining constituent compositions were 25% DLC, 12.5% YSZ, and 12.5% Au or MoS2 . For benchmark purposes, 1 ␮m thick coatings of: (1) pure gold, (2) pure DLC, (3) pure MoS2 , and (4) pure homogenized far-field properties were also simulated. Additionally, the substrate was modeled without a coating or interlayer to delineate the mechanical response of an uncoated substrate. The elastic modulus of DLC was chosen to provide an average between the properties of sp2 and sp3 bonded carbon. For the crystalline materials (440C steel, homogenized coating, Au, MoS2 , titanium, and transfer film) in the model, a bilinear rate independent kinematic J2 plasticity formulation was used. The tangent modulus for each material was approximated as 25% of the Young’s modulus. Brittle and/or amorphous phases (YSZ, DLC, synthetic sapphire) were modeled as linear elastic. All simulations were quasi-static, and the material properties are summarized in Table 1. The evolving strength of the coating constituents was not assumed to change with inclusion and grain size. The fracture of brittle phases and the possibility for node debonding between dissimilar materials were not accounted for in the simulations. To simulate the experiments, the indenter in Fig. 1(a)–(d) was modeled as a 6.35 mm diameter deformable hemisphere with the properties of synthetic sapphire (Table 1). Contact elements were meshed along the hemispherical surface of the indenter and along the entire free surface of both the active zone and far-field regions. A constant friction coefficient of 0.05 was used for the sapphire hemisphere [13]. Friction coefficients of the four individual coating constituents given in Table 1 are representative of experimental values recorded for each individual material that was tested [19,24,25]. Sliding simulations were conducted at a velocity of 1 ␮m/s. For the sliding simulations, the indentation begins at the origin in the center of the active zone, then sliding occurs in the −x direction for 40 ␮m, then reverses toward the +x direction for 80 ␮m, and finally toward the −x direction 40 ␮m to end again at the initial location. This represents one sliding cycle, and each sliding simulation was run for two cycles total. Transfer films, which play a dominant role in the coating response and failure [13,24,26,27], were represented by including a free third body in the contact. The friction coefficient of this material was set at 0.05 for both the interface with the coating, and the interface with the indentor. This value was assumed from both the properties of the coating and the observation that the transfer film is composed almost entirely of the friction reducing constituents of the coating. The transfer film (Fig. 1(a) and (d)) was assumed to have uniform homogenized material properties based on an equal weighted average using properties of Au, MoS2 and DLC which were identified by microscopy to be the primary constituents of the transfer film [13]. The transfer film is assumed not to contain oxidation products as the components of the transfer film, with the exception of MoS2 , do not readily form oxides. The lower and upper surfaces of the transfer film were assumed to be smooth. Contact elements were placed along the upper and lower surfaces. The upper surface of the transfer film had the same curvature of the indenter, while the lower surface was flat. Therefore, the transfer film increased in thickness with increased distance from the center of contact. The thickness underneath the center of contact is approximately 200 nm, and the width of the transfer films was 1.5 mm. This results in an aspect ratio greater than unity and an increasing thickness away from the center of contact consistent with that typically observed experimentally [28]. Based on a convergence analysis, transfer films were meshed with 10,000 quadrilateral elements. For all coatings and models, the results are reported as a function of the percent nominal strain applied to the coating. The nominal strain, εNominal , is the ratio of the maximum displacement of the top surface of the coating, ıY Max Coating , to the original thickness of the coating, tCoating (1 ␮m), and is given by: εNominal (%) = ıY Max Coating tCoating × 100 (1) Experiments using the sapphire indenter previously described were typically conducted for loads ranging from 1 to 6.4 N [7,13], corresponding to nominal strains of 7% to 22% as computed from a Hertzian analysis. At these strains, the contact width varies from 50 to 95 ␮m, and is thus completely within the active zone of the finite-element model. The nominal strain induces deformations and stresses within each phase of the coating. The stresses are reported Table 1 Mechanical properties (bulk) for each constituent and typical friction coefficients for sliding at room temperature in ambient atmosphere. Material property 440C steel Gold [18] YSZ [19] DLC [15,20,21] Modulus (GPa) Yield/ultimate strength (MPa) Poisson ratio Tangent modulus (Gpa) Friction coefficient Density (kg/m3 ) 200 400 0.25 50 – 7500 78 210 250 125 600 7300 0.42 0.31 0.12 19.5 – – 0.1–0.4 0.1–0.2 < 0.1 19300 5600 2100 MoS2 [8,22,23] Titanium Sapphire (synthetic) Far-field coating [13] TF 170 190 0.13 47.5 <0.1 4500 116 500 0.32 29 – 4510 400 2100 0.31 – 0.05 3980 100 125 0.25 25 0.05 7875 166 158 0.22 41.5 0.05 8633 1006 J.D. Pearson et al. / Wear 266 (2009) 1003–1012 Table 2 Locations and magnitudes of maximum effective stress in each coating under 20% nominal strain. Subscripts indicate coating chemical composition by volume. Coating Coating  Eff, Max (MPa) Coating  Eff, Max Location (C)1.00 (Au)1.00 (MoS2 )1.00 (YSZ)0.25 Au0.25 (MoS2 )0.25 C0.25 (YSZ)0.25 Au0.25 (MoS2 )0.25 C0.25 —Elastic (YSZ)0.125 Au0.50 (MoS2 )0.125 C0.25 (YSZ)0.125 Au0.125 (MoS2 )0.50 C0.25 Steel substrate (no coating) 510 205 288 653 520 613 1060 ∼300 Surface Surface Surface Interior Interior Interior Interior Interior as the effective, or von Mises, stress defined by: vm =  (1 − 2 )2 + (2 − 3 )2 + (3 − 1 )2 2 (2) where  1 ,  2 and  3 are the principal stresses from the finiteelement simulations. 3. Modeling of nanocomposite indentation behavior 3.1. Indentation to 20% strain Stresses in the equal-composition nanocomposite coating at a 20% nominal strain (the indented displacement normalized by the coating thickness) were compared to the limiting cases of single-component coatings for each constituent. For both the nanocomposite mixtures and single-component coatings, there was no significant plastic deformation in the steel substrate or titanium interlayer at 20% nominal strain. The stiffest singlecomponent coating was the DLC coating with a maximum effective stress at the free surface in contact with the indenter of 510 MPa (Table 2). The steel substrate underlying the DLC coating had a maximum effective stress of approximately 300 MPa at 10–20 ␮m below the coating interface, which is both consistent with Hertzian theory and comparable to indentation results of the steel substrate without a coating. These results indicate that the coating does not support or resist the applied loads. The maximum stress occurs at the free surface and not at the titanium interlayer. If the coating and the interlayer were to have a dominant role in load bearing, high delamination bending stresses would have occurred at the titanium/substrate interface [29]. In contrast to the single-component coatings of each material, the multicomponent nanocomposite coating exhibited localized stress gradients that were dependent on both composition and Maximum effective stress (MPa) within each material Gold MoS2 DLC – 205 – 154 119 137 141 – – – 288 238 368 235 244 – 510 – – 653 520 613 1060 – materials properties. The nanocomposite with equal composition of constituents had maximum effective stresses not at the free surface, but within the DLC–metal interfaces (Fig. 2(a)). Large gradients in stress developed across the DLC borders between separate inclusions, and these are the locations where failure and de-cohesion have been also observed experimentally [15,16,18]. However, this change in the location of maximum stress only increased the effective stress magnitude in the coating by 28% (to 653 MPa) as compared to the single-component DLC coating (Fig. 2(a), Table 2). Hence, this indicates inclusion of separate materials in a DLC coating can permit expanded tribological performance while producing a significant but manageable (28%) rise in effective stresses. When the Au content of the nanocomposite was increased to 50% Au (25% DLC, 12.5% YSZ and 12.5% MoS2 ), which may occur for coating systems whose predominant loadings occur at high temperature where DLC matrices are tribologically unstable for use in an oxidizing environment [30] and gold has been shown an effective lubricant [24], the maximum stresses in the DLC matrix decreased slightly (to 613 MPa) in comparison with the nanocomposite with equal (25% Au) composition of constituents (Fig. 2(b), Table 2). In contrast, when the equal-composition nanocomposite system was changed in composition to 50% MoS2 (25% DLC, 12.5% YSZ and 12.5% Au), as may occur for coating systems where increased solid lubrication or extraterrestrial operation is desired, the maximum stresses in the DLC matrix significantly increased, in comparison with a 25% MoS2 composition, to 1.06 GPa (Fig. 2(c), Table 2). For both nanocomposite systems with either 50% MoS2 or 50% Au, the maximum effective stress in the remaining phases YSZ and either Au or MoS2 remained essentially unchanged from the stresses developed in the nanocomposite coating with equal constituent composition. The largest changes occurred in the 50% MoS2 system with increased stresses in all phases. This indicates that while increasing the composition of MoS2 in the composite coating may be expected to reduce friction and wear, the competing effects Fig. 2. Locations and magnitudes of greatest effective stress for (a) a typical 25% equal-composition coating, (b) a 50% gold composition coating, and (c) a 50% MoS2 composition coating. Distance scale in (a) indicates microns from center of indenter for (a)–(c). J.D. Pearson et al. / Wear 266 (2009) 1003–1012 1007 Table 3 Nominal strain at the start of plastic deformation in the steel substrate with and without thin-film coatings and von Mises effective plastic strain in each ductile phase present at 56% nominal strain. of large increases in intrinsic coating stresses may induce undesired mechanical weaknesses. Modifying the nanocomposite compositions resulted in changes in the maximum effective stresses of the ductile phases, Au and MoS2 , relative to the single-component coatings of these phases (Table 2). For a pure coating of gold versus the nanocomposite coatings, the maximum effective stress in the gold coating was 205 MPa (Table 2) which was reduced to 154 MPa for the equal-composition nanocomposite (Fig. 2(a)) and 137 MPa for the 50% gold composition (Fig. 2(b)). This trend was also evident when the nanocomposite composition was changed from 25% gold to 50% MoS2 where the gold inclusions had a maximum stress of 141 MPa (Fig. 2(c)). This further substantiates that increasing the percentage of MoS2 increases the coating stress. This underscores Au is the most ductile and weak material in the coating, and any compositional changes do not markedly affect the gold phase’s stress state. A coating of pure MoS2 is similar in its behavior to gold when compared to the equal-composition coating. The maximum effective stress in a pure MoS2 coating was 288 MPa (Table 2) and decreased to 238 MPa (Fig. 2(a)) for the equal-composition coating. This trend was similar when the composition was changed from 25 to 50% gold where the maximum effective stress in the MoS2 inclusions was 235 MPa (Fig. 2(b)). Furthermore, when the composition was changed again to 50% MoS2 , the maximum effective stress increased to 244 MPa (Fig. 2(c)). In general, increasing the percentage of MoS2 in the nanocomposites correlated with increased maximum effective stress in the coatings. For the equal-composition nanocomposite, both ductile materials have maximum effective stress greater than the yield stresses. For the gold and MoS2 inclusions, the stresses were 1.3 times higher than the respective yield stress. For the pure coatings of gold and MoS2 , the stresses were 1.6 times higher than the respective yield stress. 3.2. Indentation to 56% strain For the equal-composition nanocomposite and the pure coatings, indentations were undertaken to a depth of 56% nominal strain to further understand the coatings response under increased loadings, which could correspond to high local stresses and strains associated with frictional spiking and transfer film removal. When an uncoated steel substrate is indented, plastic strains develop quickly and attain a maximum of approximately 0.5% at 56% nominal strain (Table 3). When a micron thick coating and a titanium interlayer are also included, the nominal strain to induce plastic deformations in the substrate almost triples and the maximum plastic strains are slightly less than an order of magnitude lower in comparison with a pure steel substrate. It should be noted this trend applies for the hard brittle coatings of pure DLC and the soft ductile coatings of pure gold. This effect is due to the increased uniform diffusion of the load over the contact area when applied through a thin combination of coating and a titanium interlayer, which would not resist the load because they are generally more compliant than the substrate. The maximum normal stresses and maximum equivalent plastic strains for the equal-composition nanocomposite coating and a pure DLC coating are shown in Fig. 3 for nominal strains ranging from 1 to 56%. For the equal-composition coating, the final equivalent plastic strains reached in the ductile phases (gold and MoS2 ) at 56% nominal strain were much lower than for a pure coating of either gold or MoS2 (Table 3). However, this tradeoff between the lubrication of the MoS2 and toughening of the gold occurred with increases of approximately 77% in the maximum normal stress in the DLC phase for the equal-composition nanocomposite in comparison with a pure DLC coating (Fig. 3). A large increase is seen in the maximum DLC normal stress for the equal-composition coating in comparison with a pure DLC coating. Stresses in the titanium interlayer are largely unchanged between the two coatings, as seen in Fig. 3. In both cases, the rate of stress increase in the DLC phase is largest when plastic deformation develops in the substrate (Fig. 3). In comparison with the pure DLC case, the rate of increase in the normal stress for the remaining equal-composition coating constituents (gold, MoS2 and YSZ) remains largely unchanged with the start of substrate plastic deformation (Fig. 3(a)). The rate of accumulation of plastic strains in these phases however increases slightly and temporarily before returning to values from before plastic deformation in the substrate (Fig. 3). Hence, loads for coatings, which introduce plasticity in the substrate, should be avoided in design and result in increases in plastic strain accumulation in the ductile phases. This is likely to increase the probability of coating failure by increasing the interfacial stresses at DLC borders where failure is known to initiate [15,16,18]. 4. Sliding behavior The tangential forces and shear stresses from sliding originate from the friction coefficient, and result in stresses in addition to those induced by the normal load in both the wake and zone preceding the center of contact of the slider. The additional mechanical energy, E* , introduced into the coating’s contact zone by sliding a sapphire indenter can be expressed as a function of the friction coefficient as [30]: E∗ =  tf PVf (t) dt (3) 0 where P is the applied load, V the sliding velocity, f(t) the coefficient of friction as a function of time and tf the final time at the end of sliding. This energy is dissipated in many forms, most notably as wear, heat generation, fracture, and in plastic deformations. Results from the finite-element simulations of sliding are used to analyze the energy dissipation modes of fracture and plastic work. Sliding simulations were conducted with the equal-composition nanocomposite at 20% nominal strain as described in Section 2. Plastic deformations account for a portion of the energy dissipated by the coating, and this is shown in Fig. 4. Plastic strains develop 1008 J.D. Pearson et al. / Wear 266 (2009) 1003–1012 Fig. 4. (a) Total energy dissipated (J) through plastic work in the ductile coating phases (Au and MoS2 ) versus total slid distance of the indenter. Note that gold is measured against the rightmost ordinate and MoS2 against the leftmost ordinate. (b) Ratio of total energy dissipated via plastic work to the energy input during sliding (in %). Fig. 3. (a) Coating maximum normal stress,  YY (leftmost ordinate) in each material and effective von Mises plastic strain (rightmost ordinate, materials marked in italics) developed in the MoS2 , gold, and steel phases (no plastic deformation in other remaining materials) for the 25% equal-composition nanocomposite. (b) Coating maximum normal stress (leftmost ordinate) in each material and effective von Mises plastic strain (rightmost ordinate, material marked in italics) developed in the steel phase (no plastic deformation in other remaining materials) for a pure DLC coating and titanium interlayer. during the first sliding trip of the indenter, and these strains accumulate rapidly in the MoS2 phase and slower in the gold (Fig. 4(a)). Residual plastic strains remaining in the wake of the slider cause permanent residual stresses up to 100 MPa. As seen in Fig. 4(b), plastic deformations account for up to 15% of the total energy input during the initial pass. Fig. 4(a) shows the total energy dissipated by plastic work for both the gold and MoS2 phases. As seen, the MoS2 dissipates two orders of magni- tude more work than the gold phase during the first sliding trip of the indenter (160 ␮m total slid distance). The MoS2 equilibrates quickly after the first pass, and the second pass dissipates only 3.6% of the energy dissipated during the first pass. The gold behaves similarly, except during the second pass, the rate of energy dissipation is 38.9% that of the first pass. This type of successively decreasing plastic strain accumulation in the ductile phases has been verified experimentally [31]. In the wake of the indenter, the shear stresses fall quickly to zero, while underneath the indenter the shear stresses reach a maximum of around 100–200 MPa. The highest stresses are confined to the DLC borders. In the leading edge of the contact, the shear stresses are higher in the coating in comparison with the trailing edge of the contact (Fig. 5(a) and (b)). It is not clear whether the shear stress increase is more heavily dominated by sliding velocity or the friction coefficient, although it has been previously shown that friction shifts the location of maximum shear stress toward the edge of the contact, and that sliding velocity has a larger effect on temperature in the contact than on stress distribution [30]. Sliding over the same area, but in an opposite direction, induces different maximum stresses in the DLC matrix borders depending on the orientation of the border with respect to the sliding. The coating could be optimized for sliding direction in some cases. Fig. 6(a) and (b) illustrates this effect for DLC borders around MoS2 inclusions, and Fig. 6(c) and (d) illustrate the effect to a lesser extent for the gold inclusions. As can be seen from these images, borders which are slanted perpendicular to the direction of sliding have higher stresses than borders of opposite orientation for each pass of the slider. In the wake of the indenter during the sliding simulations, tensile stresses develop in the coating material which can lead to the opening of Mode I surface cracks. Fig. 7(a)–(c) shows cross sectional views of the in-plane tensile stress distribution at the trailing edge of the indenter 21 and 60 ␮m after the first sliding pass as well as an idealized surface flaw which can develop with coating wear. 1009 J.D. Pearson et al. / Wear 266 (2009) 1003–1012 Fig. 5. Shear stress developed under the slider within the same region of coating in (a) the leading edge of the contact and (b) the trailing edge of the contact. Stresses are measured in MPa and distances measure distance from center of coating in microns. These flaws can be of any shape subjected to an opening mode of stress. In the present analysis, we assume semi-elliptical surfaceflaws (Fig. 7(c)) to show how increases in the stress-intensity factor can lead to unstable crack growth in the coating. Since the DLC is brittle, has the highest stress and strength, and is the matrix material where cracking is experimentally observed, we only use the stresses in the DLC regions (which is also elastic) to calculate the stress-intensity factor. The mechanics governing crack opening involve a combination of crack geometry, applied stress, and material properties. For an idealized, semi-elliptical surface flaw, the stress-intensity factor, KI , is given by: KI = 1.12  a Q (4) where a is the maximum crack depth of penetration into the coating,  is the applied Mode I tensile stress field and Q is dependent upon the material’s yield stress and an elliptic integral of the second kind as: Q (=)  0 /2  1−  c 2 − a2 c2  sin2  1/2 2 d  − 0.212  ys 2 (5) where c is the cracks half-width in the plane of the coating and  ys is the material’s yield strength. The maximum tensile stresses in the plane of the coating reach a maximum depth of 10% of the coating’s thickness (Fig. 7(a)). This corresponds to a maximum stress field of  = 100 MPa at an assumed maximum crack depth a = 0.1 ␮m. The crack’s width in the plane of the coating can be estimated from SEM images taken of a TiC coating system as reported on by Voevodin and Zabinski [15]. In this work, SEM images reveal surface cracks range from <1 ␮m to ≈10 ␮m in length, giving a range for c from 0.5 to 5 ␮m. With these assumptions, the range for Q, assuming cracking in the DLC matrix material at the surface, is 1.10 with c = 0.5 ␮m and 1 for c = 5 ␮m. Assuming Q = 1 for the worst case scenario, the calculated fracture toughness for the DLC matrix to avoid a self propagating crack Fig. 6. Maximum effective stress (MPa) in the DLC matrix material when between (a) and (b) MoS2 and (c) and (d) gold inclusions. Slider position in (a) and (b) is at +11 ␮m from center of coating. Slider position in (c) and (d) is at −5 ␮m from center of coating. Slider direction of travel is indicated by the arrow in the distance scale for each image. Distance scale indicates position in microns from center of coating. Arrows on figures indicate regions of coating where maximum stresses are dependant upon orientation of border with sliding direction. 1010 J.D. Pearson et al. / Wear 266 (2009) 1003–1012 Fig. 7. In plane tensile stresses (MPa) developed 21 ␮m behind indenter (a) in the coating material after first sliding pass. In plane tensile stresses developed +60 ␮m behind indenter (b) after first sliding pass showing the decay and uniformity of the far-field tensile stresses. Typical semi-elliptical surface-flaw dimensions. Distance scales in (a) and (b) indicate distance in microns from center of coating. under the tensile stresses in the indenter’s wake, is shown in Table 4. Experimental reports of the fracture toughness of DLC coatings [32–34] (Table 4) have shown that the fracture toughness of DLC alone is orders of magnitude below that required to support the tensile stresses in the presence of a pre-existing surface flaw at the free surface without crack growth and failure. However, the fracture toughness of a material is a function of the surface energy. The difference in surface energy of each of the coating constituents determines the relative interfacial bonding strengths of the nanocrystalline regions. The fracture toughness, KIC , in a homogeneous material is given [32] as: KIC = 2 E (6) where E is the materials modulus and is the surface energy. Table 4 lists surface energies [30,32] of the coatings constituents and the calculated theoretical fracture toughness of each material. Note that zirconium oxide is substituted for YSZ and pure molybdenum is substituted for MoS2 in the table. As the table indicates, the stress-intensity factor is generally greater than the critical fracture toughness. The coating is able to support these cracks because of the toughening provided by the ductile elements and the observation that the tensile stresses decay through the thickness of the coating to approximately 25 MPa at the titanium interlayer junction (Fig. 7(b)). At this depth and stress, the calculated KIC value to prevent crack propagation is approximately 25% of the value determined at the surface. Table 4 √ Fracture toughness, KIC , of DLC matrix material in MPa mm. Surface energy, , of −2 coating constituents in mJ m . Measurement Fracture toughness Surface flaw, Q = 1, Eq. (3) Nastasi et al. [32] Hou and Gao [33] Li and Bhushan [34] 1.98 3.19 × 10−4 3.1 × 10−5 − 7.1 × 10−5 8.9 × 10−2 − 3.7 × 10−1 Irwin formula: Pure • DLC ( = 5400) • Mo ( = 2300) • Au ( = 1100) • ZrO2 ( = 530) 1.64 8.84 × 10−1 4.14 × 10−1 4.72 × 10−1 5. Transfer film (TF): effects and nanocomposite behavior It has been observed that wear increases during friction spikes; this may be due to changes in transfer film adhesion and debris accumulation [13]. Hence, it is essential to include the effects of these free materials found within the contact. In this analysis, a homogenized third body was included in the 1 ␮m thick equal-composition nanocomposite coating model (Fig. 1(c)) to simulate a uniform transfer film and the coating was then indented to 1.4% nominal strain by the sapphire slider pressing upon the TF. Transfer films are dynamic during wear tests and change in thickness at the transition between low wear and high wear [13]. The mechanism for adherence of the film to the counterface is also dynamic, and it is not well characterized or understood [35]. For these reasons, the transfer film was modeled as a free third body in the contact in two ways: (1) Completely free from adhesion to the indenter (frictional sliding between counterface and TF and between the TF and the coating) simulating an unstable TF; and (2) Rigidly bonded to the indenter upon initial contact with frictional sliding between the TF and the coating only, simulating a stable, bonded, TF. Both methods represent the interfacial sliding VAM, which is the most often identified accommodation mode for these coatings [11]. The unstable TF model represents the start of the change from interfacial sliding to the interfacial shearing VAM and extrusion of debris. It should be noted that stability here does not refer to the transfer film remaining stable over long sliding distances in the contact region, but rather to the simulated bonding between the TF and the counterface. Both transfer film models were indented to 1.4% nominal coating strain, and the results were compared to determine the effects of bonding on the transfer film and the coating. Results indicate that the stable transfer film has higher stresses for both the coating and the transfer film in comparison with an unstable film (Fig. 8(a)). In general, maximum effective stresses in each material are significantly higher in the stable film with the largest increases occurring in the DLC and the transfer film. J.D. Pearson et al. / Wear 266 (2009) 1003–1012 1011 are destructive to both the thin-film coating and the transfer film. These high stresses arising from rigid bonding serve to damage the transfer film and the coating. However, when the transfer film is modeled as a free third body (unstable film) as may happen with a stable transfer film when the stresses grow larger than the adhesion strength of the transfer film to the indenter, the stresses in the film and coating decrease. Assuming the transfer film constituents (gold, MoS2 , DLC) have higher affinities for adhesion (see Table 4 surface energies) to each other than the counterface material (sapphire), these results indicate the following: wear rates are greatest when the transfer film is absent or being removed. In this case, debris from the coating is generated, and from this debris a transfer film begins to form from debris bonding to the indenter. As the current results indicate, this bonding represents the stable TF, which causes high stresses in the coating and the TF. Hence, the TF film, which formed on the counterface from debris, is able to increase in size and not be removed due to the rigid bonding, but fails by debonding as a film from the slider due to both high stresses (from bonding) and the greater affinity between TF constituents over the sapphire indenter. This transfer film mode now represents the unstable transfer film model, which results in a reduced state of stress. While this mode reduces the stress and is beneficial to the TF and coating, without bonding between the indenter and transfer film, the TF will eventually be transported and worn away from the contact zone. Thus, the wear cycle is initiated with the generation of new debris. In summary: (1) Tribo-chemical bonding due to energy (mechanical pressure, heat and friction) in the contact forms rigid bonds between wear debris and slider, thus developing a TF with stable bonding. (2) Rigid bonding, however, induces higher stresses in the TF and leads to eventual debonding of the TF (unstable). This leads to a competing period of beneficial low wear balanced with gradual loss of the TF due to the coupling between lack of bonding with the slider and the mechanical extruding action of the contact. (3) The debonded film is eventually worn away (leading to high wear and friction spiking periods) and replaced by new worn debris material from the contact and coating. 6. Conclusions Fig. 8. (a) Coating and transfer film maximum effective stress in each material for the 25% equal-composition nanocomposite. Stable transfer film results in solid black lines and regular text from highest stress to lowest, Unstable transfer film in bold lines with markers and italicized text from highest stress to lowest. Transfer film effective stress in the central most loaded region under 1.4% nominal coating strain for (b) Stable and (c) Unstable models. Note that above the TF film in (b) and (c) is the indenter and below is the nanocomposite coating. For the unstable transfer film, the free third body experiences the highest stress in the model, whereas for the stable film, the highest stress is experienced by the DLC surpassing that of even the transfer film. The stable transfer film has a maximum effective stress 7.6 times greater than the yield stress, and 3.4 times greater than the yield stress for the unstable film. Both films have the highest stresses at the free surface in contact with the coating, but the stable film has a larger region of high stress on the surface. This region also extends at the periphery upward toward the indenter contact surface (Fig. 8(b) and (c)). Plastic strains are not notable in the steel and MoS2 at these low loads, and plastic strains accumulate significantly faster in the transfer film than in the coating ductile phases. These results all indicate that stable, or rigidly bonded, transfer films, where the VAM is by definition interfacial sliding, induce stress states that Finite-element simulations and microstructural models of adaptive nanocomposite coatings were investigated to understand how different ductile and brittle material mechanisms, coating constituents, and toughening and strengthening behavior are affected by indentation and sliding. Critical regions, which are associated with an accumulation of stresses and strains, generally occurred at interfaces between the ductile constituents and the DLC matrix. The computational results indicate that increasing the relative percentage of MoS2 results in higher stresses in the coating compared with increasing the relative percentage of gold. These results underscore a competition between the effects of superior tribological properties associated with MoS2 and maintaining manageable stress levels that would not exceed the coating strength. In sliding simulations, the computational analyses indicate that the presence of MoS2 and Au resulted in approximately 15% of the initial energy dissipation through plastic work. This rate decreased by an order of magnitude as the number of sliding trips increased. For the Au phases, the plastic work was lower in comparison with the MoS2 , but these ductile phases essentially dissipate the applied energy associated with sliding, and also toughen the nanocomposite coating. The highest stresses are located in the interior of the coating, and do not occur at the surface where the predominant wear occurs. It is believed the subsurface plastic deformations from the high 1012 J.D. Pearson et al. / Wear 266 (2009) 1003–1012 stresses weaken the coating and increase its susceptibility to wear and fracture at the surface. Transfer film bonding to the indenter was found to dominate the stress distribution within both the coating and the transfer film. Stable adhered films resulted in higher stresses than those for debonded films. Based on these results, the motion in the contact forms this type of film, and tribo-chemical reactions occur which promote bonding to loose debris associated with wear. These reactions continue until the stresses are too high and the film must delaminate from the slider. This leads to competing periods of beneficial low wear balanced with gradual loss of the TF due to the coupling between lack of bonding with the slider and the mechanical extruding action of the contact. 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