Available online at www.sciencedirect.com Surface & Coatings Technology 202 (2007) 1034 – 1049 www.elsevier.com/locate/surfcoat Friction and wear of coated surfaces — scales, modelling and simulation of tribomechanisms Kenneth Holmberg a,⁎, Helena Ronkainen a , Anssi Laukkanen a , Kim Wallin b a VTT Technical Research Centre of Finland, Finland b Academy of Finland, Finland Available online 21 August 2007 Abstract Coating a surface with a thin layer changes the surface material properties and is an important tool for controlling friction and wear. The tribological mechanisms, scale effects and parameters influencing the friction and wear of coated surfaces are discussed. The basic friction and wear mechanisms can be reduced to: friction by adhesion, ploughing and hysteresis and wear by adhesion, abrasion and fatigue combined with material fracture. The tribochemical and surface physical effects and surface fatigue taking place before material fracture are treated here as pure surface material modification mechanisms. Scale effects in a tribological contact are illustrated by explaining typical surface roughness related tribological mechanisms for diamond and DLC coated surfaces. For diamond coatings asperity interlocking effects are important for rough surfaces, graphitisation is a dominating mechanism for smooth engineering surfaces and hydrogenising of dangling bonds may be crucial for physically smooth surfaces. For DLC coated surfaces, surface graphitisation is important with rougher surfaces; building up transfer layers and graphitisation is crucial for smooth engineering surfaces and hydrogenising of dangling bonds can explain superlubricity for physically smooth surfaces. An analysis of dominating surface parameters such as elastic, plastic and fracture behaviour of the top surface, the coating, the coating/ substrate interface and the substrate in addition to the coating thickness forms the basis for surface modelling. A stress intensity factor analysis of crack growth shows the importance of considering both modes I, II and III loading, crack spacing and location of crack, while crack orientation, location in crack field as well as load biaxiality have minor influences. It is shown how surface 3D FEM modelling generates stress and strain values at the nano level, within bond layers at coating/substrate interfaces and around cracks and forms the basis for better understanding the origin of wear. © 2007 Elsevier B.V. All rights reserved. Keywords: Tribology; Coatings; Modelling; Scale effects; Diamond; Diamond-like carbon (DLC) 1. Introduction Energy saving, environmental, economic and safety aspects in our society all emphasise the importance of controlling friction and wear in machinery and devices. Lubrication with oil is the most common way to control friction and wear. However, the use of liquid lubricants is often not so desirable for environmental reasons, problems with keeping it in the contact zone, ageing, circulating, storing, contamination etc. Surface engineering, where the surface properties of the moving contacts are changed ⁎ Corresponding author. VTT Technical Research Centre of Finland, P.O. Box 1000, 02044 VTT, Finland. Tel.: +358 20 7225370; fax: +358 20 7227077. E-mail address: [email protected] (K. Holmberg). 0257-8972/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.surfcoat.2007.07.105 in a favourable way by deposition or surface treatment now offers another efficient way of controlling friction and wear. The development of the vacuum deposition techniques, chemical vapour deposition (CVD) and physical vapour deposition (PVD), has been of major impact, since they make it possible to deposit a thin layer of only a few micrometers (or down to nanometer thickness) on the surfaces of most engineering materials. The geometrical change is minimal and the surface layer may have properties covering an extremely wide range, from hard diamond and ceramic coatings to very soft polymeric or lamella-structured films . In the 1980s hard ceramic TiN, TiC and Al203 coatings were commercially introduced as surface layers on tools in the production industry, and wear rates were decreased by one to two orders of magnitude or more. In the 1990s very low friction K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 diamond, diamond-like carbon (DLC) and MoS2 surface layers were investigated and some of them were introduced commercially. Their friction and wear properties were again one to two orders of magnitude lower than for earlier solutions and they were suitable for components in engines and devices requiring both low friction and low wear. In the 2000s much development work has been focussed on modifying the structures of the thin coatings in a controlled way. This includes the development of different multi-component and nanostructured coatings such as layered coatings, gradient coatings, doped coatings, nanocomposite coatings etc. This development has been reviewed recently by several authors [2–8]. These advanced surface engineering technologies make it possible to tailor the surfaces and their properties with great precision even to molecular and atomic levels (Fig. 1). However, there is one problem. It is easy to specify for some application that a certain level of low friction and low wear is needed but we have still no good generic tools to specify the surface properties that may result in the required tribological behaviour. The problem is to specify the optimal surface parameters like coating thickness, surface roughness, coating material and its structure resulting in a certain hardness, elasticity, residual stress and fracture toughness of the coating, bond layers and substrate. There is much empirically-based experience on how to choose a suitable coating for a specific purpose but still no systematic tool for this. Much of the surface engineering development work is still based on a trial and error approach. Only a few parameter interactions have been theoretically modelled, to a limited extent [1,9–17]. In this article we present our systematic approach to modelling and simulation of surface properties for tribological purposes. We first discuss the basic tribological mechanisms involved, indicate the importance of scale effects and illustrate it by a discussion on scale effects for diamond and DLC coated surfaces, discuss the parameters influencing friction and wear of coated surfaces in micro level contacts and finally show how deformations, stresses and strains can be modelled by advanced three dimensional finite element method (3D FEM) and form a 1035 basis for surface fracture analysis. The aim is to proceed in the direction of systematic surface design for tribological applications. 2. Basic friction and wear mechanisms There are a number of classifications of friction and wear mechanisms published [18–21]. Two basic friction mechanisms, adhesive friction and ploughing, are normally mentioned. The variety of classification suggestions is much larger for wear. In the early days wear was typically classified based on its appearance on the surface after the contact event. Examples of such appearance based classes are scoring, scuffing, pitting, gouging, spalling, fretting and galling. Some of these classes are more or less related to certain applications, such as gear contacts. The classifications used have recently been based more on the fundamental mechanisms of material removal due to the increased knowledge of the fundamental wear processes. The most widely used classifications are: adhesive wear, abrasive wear, fatigue wear and tribochemical wear [1,21]. We believe that the classification of basic friction and wear mechanisms can be developed even one step further and suggest the classification shown in Fig. 2. Friction is the motion resisting force at a certain moment in the process of motion between the two surfaces in contact. This may be due to: 1) adhesion, that is breaking the adhesive bonds between the two surfaces, 2) ploughing, that is resistance originating from elastic and possibly plastic deformation when a harder countersurface moves through a softer or more elastic surface and 3) hysteresis, that is resistance originating form continuous elastic deformation within one of the surfaces in motion. In the basic friction mechanisms no material removal is involved. Some debris in the contact zone would make the contact mechanisms much more complicated but still the basic mechanisms for motion resistance are those mentioned above. Fig. 1. The advanced surface coating deposition techniques offer large possibilities to modify and tailor the top surface mechanical and chemical properties that govern the friction and wear behaviour in industrial applications. 1036 K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 Fig. 2. The basic friction and wear mechanisms are related to adhesion, ploughing and hysteresis. In the case of wear these contact mechanisms result in material fracture, detachment and removal. Wear is the process of detachment of material from one surface. It is different from friction in the sense that it is not taking place at a certain moment but during a time period when the surfaces are in moving contact. The detachment of material may be due to: 1) adhesion + fracture, that is the adhesive lifting or shearing force is causing such high tension and shear stresses in the surface that they exceed the material strength and a crack is formed, resulting in crack growth and material detachment — a wear debris has been formed, 2) abrasion + fracture, that is a hard countersurface moves through a softer surface and deforms it to the extent that such high mainly shear stresses are formed that they exceed the material strength and a crack is formed, resulting in crack growth, fracture and material detachment — a wear debris has been formed, 3) fatigue + fracture, that is compressive loading of the surface deforms it to the extent that such high, mainly shear, stresses are formed that they exceed the material strength and a crack is formed, resulting in crack growth and material detachment — a wear debris has been formed. The crack growth process may take place during a number of loading cycles. By definition wear always includes material removal. Normally fracture is a term describing bulk failure of brittle materials. Here the term is understood more widely as a process starting from loss of cohesion between bond structures in the material, continuing as crack propagation and resulting in debris being liberated from the surface. The above classification of the basic wear mechanisms is focussing on how the material removal takes place. For this reason tribochemical wear is not included. The chemical processes that take place on a surface are certainly important but they are not mechanisms that cause material removal. They are chemical reactions that cause surface material modification, either improvement or degradation, and changes in, e.g., the plastic and elastic properties and fracture resistance of the top surface. The changed surface properties will either increase or decrease the strength of the material and its resistance to cracking and material removal. However, the basic mechanisms of material removal in so-called tribochemical wear are still one of the three mentioned above. Actually the fatigue wear as it is normally considered can be divided into two phases. In the first phase is only material modification taking place without any material removal. During continuous loading of the surface the close to surface material properties are slowly changed. The second phase, that is the wear or material removal phase, starts when the changed material cannot any more withstand the loading and a crack is created, it grows, material is liberated and debris is formed. It is interesting to note that the friction hysteresis mechanism is based on elastic material deformation and thus it is in a sense similar to the ploughing mechanisms, only the geometry is different. The same goes for the fatigue and fracture wear mechanism that is based on material deformation by compression and shear and is in that sense similar to the abrasion mechanism. So the next step would perhaps be to consider only two basic friction and wear mechanisms. For friction it would be adhesive friction and elastic and plastic deformation controlled friction. For wear it would be adhesive wear and plastic deformation and fracture controlled wear. The surface material modification processes, surface chemistry and fatigue, would be considered separately as non wear processes. 3. Scales in tribology It is important to understand the basic mechanisms especially when trying to model and predict friction and wear in different contact situations. At the same time it is also important to remember that very seldom do they appear in a contact situation purely as such. Normally the basic mechanisms are combined in a very complex way due to a more complicated contact geometry, involving roughness and debris, due to inhomogeneous surface materials with changing properties and due to variations in loading and sliding conditions. The main parameters influencing K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 1037 Fig. 3. The tribological contact process is determined by a number of geometry, material and energy related parameters, including changes that can be described on e.g. macro- micro- and nano-level and results in friction, wear and changed contact conditions. the tribological process are illustrated in Fig. 3. During the sliding contact some of the parameters will change, surface layers are formed, strain hardening takes place, local temperature rises causing softening, etc. and after one sliding event we may have a new set of parameters controlling the friction and wear. It is often useful to study the tribological phenomena on different size levels. Fig. 4 shows typical contact conditions that occur on a macro level when a hard sphere is sliding on a flat surface deposited with a thin coating . Even if the number of influencing parameters is large the situation is still not hopeless to control. In each contact situation there is typically a limited number of some five to ten parameters that dominate the friction and wear behaviour. If we can identify them and understand their interactions then we are well on the road to predicting and controlling both friction and wear. Dominating parameters in the contact situations shown in Fig. 4 are the coating/substrate hardness relationship (hard on soft or soft on hard), coating thickness, surface roughness and debris in the contact. These are very important parameters since in a typical PVD or CVD coated contact coating thickness, surface roughness and wear debris are all in the size range of some few micrometers and thus their interrelationship is crucial. The whole picture is becoming even more complicated since we have friction and wear related phenomena appearing on different Fig. 4. Main parameters influencing the friction in a macro-contact with thin coated surfaces are the hardness of the coating and the substrate, the coating thickness, the surface roughness and debris in the contact zone. These parameters result in several different contact conditions, each of which can be modelled by a set of dominating parameters and interaction mechanisms. 1038 K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 Fig. 5. The tribological process has been studied on machinery level, component level, contact level, asperity level and molecular level. size levels. In some cases we have shearing taking place on a nano level due to molecular or atomic interactions. In other cases we talk about cracks appearing at asperity collisions on a microlevel. Or when observing the prevention of contacts by elasto-hydrodynamic lubrication we calculate the pressure and lubricant film thickness on a macrolevel. Forces and vibrations are observed on component level while the efficiency and lifetime is estimated on machinery level. These length scales of tribology that represent different approaches to identify and understand characteristic tribology related phenomena are illustrated in Fig. 5 . Here we can talk about tribology on five different length scale levels: Nanotribology or molecular tribology includes phenomena related to the interaction between molecules and atoms, such as the effects of van der Waals forces and related interatomic phenomena, determined by the crystal and bonding structures of materials. Microtribology or asperity tribology relates to aspects typically taking place at the peaks of the surface topography. Phenomena such as adhesion between asperities, fracture, elastic and plastic deformation, debris formation, surface layer formation and topography changes are all important at this scale. Macrotribology or contact tribology relates to aspects often covering the whole contact zone, such as the longer-range stresses present within contacting bodies. Combined loading response is important particularly in highly-loaded applications like gears, bearing elements and rollers. Macro-level stresses influence observable wear mechanisms such as scuffing, scoring and pitting. Component tribology or decitribology is related to defining and measuring typical parameters originating from the interaction of components, and which define their performance, such as torque, forces, vibrations, clearance and alignment. Machinery tribology or unitribology describes the performance-related phenomena for a system of components assembled in a machine or a piece of equipment. The parameters of interest are performance, efficiency, reliability and lifetime estimation. 4. Friction and wear mechanisms of diamond and DLC coated surfaces Detailed investigations in the 1990s and 2000s carried out in many laboratories world wide have shown that extremely low friction and wear can be measured for sliding contacts with one or both surfaces covered by a thin diamond or DLC coating (Table 1). In the most favourable cases the wear has been undetectable and the friction coefficient has been even below 0.001, which is called super lubricity [24–28]. The mechanisms Table 1 Friction coefficients values and wear rates from the literature for diamond, diamond-like carbon and doped DLC coatings  Property Diamond coatings Hydrogen free Hydrogenated DLC DLC Modified/ doped DLC Structure CVD diamond a-C ta-C a-C:H ta-C:H Atomic structure Hydrogen content μ in vacuum μ in dry N2 μ in dry air 5–15% μ in humid air 15–95% RH μ in water μ in oil k in vacuum k in dry N2 k in dry air 5–15% k in humid air 15–95% k in water k in oil sp3 sp2 and sp3 sp2 and sp3 a-C:Me a-C:H:Me a-C:H:x Me = W,Ti…. x = Si,O,N,F, B… sp2 and sp3 – N1% 10–50% 0.02–1 0.03 0.08–0.1 0.3–0.8 0.6–0.7 0.6 0.007–0.05 0.001–0.15 0.025–0.22 0.03 0.007 0.03 0.03–0.15 0.05–0.23 0.02–0.5 0.03–0.4 0.002–0.08 0.07–0.1 0.03 60–400 0.01–0.7 0.06 0.01–0.06 0.0001–400 0.01–1 0.1–1 0.0001–1 – – 0.002–0.2 0.15 (0.1) 1–1000 0.1–0.2 1–5 0.0001 0.00001–0.1 0.01–0.4 The wear rate k is given in 10− 6 mm3/N·m units. K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 1039 The contact mechanism is dominated by asperity interlocking, asperity breaking and asperity ploughing. - Diamond coatings sliding in air, water or oil (Fig. 6b) with micro scale smooth topography, Ra =0.01–0.1 μm, have a friction coefficient of μ =0.001–0.1 and a wear rate k =0.0001– 0.1 · 10− 6 mm3/N m with the lowest μ and k values measured in water. A graphite film of the thickness h= 100–200 nm is formed on the contacting surfaces. The contact mechanism is shear within sp2 hybridised graphitic basal planes, formed by transformation from sp3 by sliding asperities at high local temperature and pressure. - Diamond coatings sliding in air at T b 600 °C and nonvacuum (Fig. 6c) nano scale molecularly smooth topography, Ra = 1–30 nm, have a friction coefficient that is μ = 0.03–0.15 and a wear rate of k = 0.01–5 · 10− 6 mm3/N m. The contact mechanism is shear between two flat layers of single hydrogen atoms at dangling bonds. Only weak van der Waals bonds between the atoms are present and no strong chemical bonding is involved. Corresponding contact conditions at the macro, micro and nano scales are shown in Fig. 7 for diamond-like carbon coatings. Fig. 6. Different tribological contact mechanisms determining friction and wear for diamond coated surfaces described on (a) macro scale with engineering surfaces, (b) on micro scale with smooth engineering surfaces and (c) on nanoscale with physically smooth surfaces. resulting in these conditions were first not very clear to researchers. Some mechanisms have been proposed, such as the dangling bond mechanism, surface graphitisation and transfer layer formation. All three of these have been convincingly shown to work both experimentally and theoretically. However, in the literature these mechanisms are often mixed and it is not clearly understood which mechanism is dominating in which conditions. We believe that it is easier to understand the governing friction and wear mechanisms by analysing the tribological contact condition at different length scales. We call the levels macro, micro and nano scale and they are closely linked to the roughness of the surfaces in contact. On a macro scale we look at what we would call typical engineering surfaces with a surface roughness in the range of Ra = 0.1–1 μm. On a micro scale the surfaces are what we would call smooth engineering surfaces with a roughness in the range of Ra = 0.01–0.1 μm. And on nano scale the surfaces are physically smooth with a roughness in the range of Ra = 1–30 nm. In addition to the surface roughness the surrounding environment is another important parameter that we consider. - Diamond coatings sliding in air or vacuum (Fig. 6a) at a macro scale may have a very rough, sometimes pyramid shaped, topography, Ra = 0.1–1 μm; the friction coefficient is μ = 0.1–0.7 and the wear rate k = 0.1–100 · 10− 6 mm3/N m. Fig. 7. Different tribological contact mechanisms determining friction and wear for diamond-like carbon coated surfaces described on (a) macro scale, (b) micro scale and (c) nano scale. 1040 K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 The data given above originate from a number of experimental studies listed in Table I. The mechanisms referred to are summarised from the most recent literature [1–3,6,27– 29]. The parameter representing the hydrogen content in DLC coatings has not been included in the presentation above in order to more clearly illustrate the scale effect. The hydrogen effect has been analysed and discussed in detail elsewhere . tool for tribological modelling at the nano scale [30–33]. In the following we will focus on showing how FEM modelling helps us understand the interactions in a tribological contact with thin coatings on the micro scale level. Based on the analysis of the basic friction and wear mechanisms discussed above in Section 2 we will first analyse different contact situations and indicate the tribologically dominating parameters that should be the focus in a modelling study. The friction and wear is governed by the shear taking place at the top surface and in the deformed surface layer, and by the elastic, plastic and fracture behaviour both at the top surface and in the deformed surface layer. A thin coating is typically a part of this deformed surface layer. In addition surface degradation may take place due to tribochemical and fatigue processes that influence on the surface strength to withstand loaded conditions. Thus the crucial material parameters are the elastic modulus, the hardness or shear strength and the fracture toughness on the top surface, in the coating, at the coating/ substrate interface and in the substrate under the coating, as shown in Fig. 8. In this presentation hardness, H, is used as a symbol representing the resistance to plastic deformation due to its common use (even if referring to the elastic–plastic constitutive response of the material would be the correct expression). In this presentation we limit ourselves to the conditions of a sphere sliding over a flat coated surface, ideally smooth surfaces, homogenous materials and no contamination or wear debris involved. The influence of these parameters in a coated contact has been discussed elsewhere [1,6]. Adhesive friction is dominated by the shear taking place in the surface top layer or the shear in between the two interacting surfaces (see Fig. 2). Surface chemistry, reaction and transfer layers and structural parameters, like hydrogen content for DLC coatings, are important. The coefficient of friction 5. Dominating surface parameters in a coating contact la ¼ f ð s u Þ - DLC coatings sliding in air, water or oil (Fig. 7a) at a macro scale with a rough topography, Ra = 0.1–1 μm, have a friction coefficient μ = 0.01–0.6 and a wear rate k = 0.0001– 1 · 10− 6 mm3/N m. The contact mechanism is graphitisation of the top surfaces with shear within sp2 graphitic basal planes resulting in low shear resistance. In some cases the surface roughness may inhibit graphitisation resulting in high friction and wear. - DLC coatings sliding in air against a steel or ceramic countersurface (Fig. 7b) with micro scale smooth topography, Ra = 0.01–0.1 μm, have a friction coefficient μ = 0.05–0.3 and a wear rate k = 0.0001–10 · 10− 6 mm3/N m. The contact mechanism is first smoothening of the countersurface by building up a transfer layer containing typically Al, C, Cr, and Fe. The transfer layer thickness is h = 100–200 nm. Graphitisation occurs on both the DLC top surface and the countersurface transfer layer. Shear takes place within the sp2 graphitic basal planes. - DLC coatings sliding in dry nitrogen (Fig. 7c) with nano scale molecularly smooth topography, Ra = 1–30 nm, have a friction coefficient that is μ = 0.001–0.15 and a wear rate of k = 0.00001–0.1 · 10− 6 mm3/N m. The contact mechanism is shear between two flat, highly hydrogenated layers of single hydrogen atoms at dangling bonds. A positive atomic dipole charge of the hydrogen atoms out from the surface at both surfaces gives rise to repulsive forces. Complete modelling of a tribological contact is a most complex task. This is on one hand due to the large number of influencing parameters, related to contact geometry, material properties and energy input, and on the other hand, due to the number of interactions taking place simultaneously on different scales with a variation of up to ten orders of magnitude both in terms of size and time, as illustrated in Fig. 5. The picture gets even more complex when we introduce coatings on the surfaces. Still it is possible to get very useful results from tribological modelling by not trying to be too generic and instead focussing on a specific contact case and specific contact phenomena related to limited contact conditions. Advanced finite element method (FEM) techniques offer today a very good tool for tribological modelling of the mechanical behaviour, including deformations, stresses and strains, of a tribological contact both on macro and micro scales [9–17]. Molecular dynamic simulation (MDS) has developed rapidly over the last decade boosted by the increased computer power and software development. It has turned out to be a very useful ð1Þ Ploughing friction is dominated by the elastic and plastic behaviour of the coating and the substrate. Structural properties, multilayer, gradient, modified and doped structures and structural parameters, like sp2/sp3-ratio for DLC coatings, are important. The Fig. 8. Symbols used for material parameters in a coated surface. K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 1041 Fig. 10. Abrasive wear is characterised by a hard asperity (a) or debris (b) that deforms the countersurface in a ductile or brittle way resulting in fracture, cracking and debris generation. each location as shown in Fig. 9 b–e. Due to the depth of the debris detachment the result is - top layer fragments dominated by Ku (Fig. 9b), coating fragments dominated by Kc (Fig. 9c), coating delamination dominated by Ki (Fig. 9d) or substrate and coating debris dominated by Ks (Fig. 9c). Fig. 9. Two surfaces attach to each other by adhesion (a) and the movement of the top surface results in an adhesive force, Fa, that tries to detach material over an area, A, from one of the surfaces. The detachment may take place (b) at the top surface, (c) within the coating, (d) at the coating/substrate interface and (e) in the substrate. Abrasive wear is dominated by geometrical collision of the two moving surfaces resulting in high stresses, material shear and fracture, and debris formation. The collisions may be due to hard asperity or debris ploughing or asperity collisions, as shown in Fig. 10. The wear rate capacity of the coating/substrate system to withstand deformation is frequently called load carrying capacity. The coefficient of friction k ¼ Vabr =wd s ¼ f ðKc ; Ki ; Ks ; Hc ; Hi ; Hs ; hÞ lp ¼ f ðEc ; Hc ; Es ; Hs ; hÞ ð2Þ Hysteresis friction is mainly dominated by the elastic properties of the substrate but also to some extent by the elastic properties of the coating. The coefficient of friction lh ¼ f ðEs ; Ec ; hÞ Due to the depth of the debris detachment the result is - coating fragments dominated by Kc, - coating delamination dominated by Ki or - substrate and coating debris dominated by Ks. ð3Þ Adhesive wear is dominated by the fracture behaviour in the surface top layer, in the coating, at the coating/substrate interface and in the substrate. With fracture we understand here the property of the material to resist cracking, intrinsic detachment and breaking to parts. The adhesive force, Fa, from the counterface tries to tear off part of the surface material over the contact area A (Fig. 9a). When surface roughness is included A will decrease and the adhesive wear typically decrease. The wear rate k ¼ Vadh =wd s ¼ f ðKu ; Kc ; Ki ; Ks Þ ð5Þ Fatigue wear is a result of material degradation where the strength of the material decreases to a level so that it cannot any more withstand the repeated loading. The result is fracture, cracking, and debris formation (Fig. 11). It is dominated by the ð4Þ where Vadh is the volume of adhesive wear, w is the load and s is the sliding distance. The breaking of the material may take place at different locations in the surface depending on the material strength at Fig. 11. Fatigue wear is characterised by repeated loading of the coated surface resulting in cracking at the surface in the coating, at the interface or in the substrate, followed by fracture, material detachment and debris generation. 1042 K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 elastic and fracture properties of the coating, the coating/substrate interface and the substrate. The loading may be rolling or sliding. The wear rate k ¼ Vfat =wd s ¼ f ðKu ; Kc ; Ki ; Ks ; Ec ; Ei ; Es ; hÞ ð6Þ Due to the depth of the debris detachment the result is - top layer fragments dominated by Ku, coating fragments dominated by Kc, coating delamination dominated by Ki or substrate and coating debris dominated by Ks. Surface modification is here considered separately from the pure wear mechanisms since it alone will not result in material liberation. Still it is very important to consider in a wear process since it often precedes the wear event and may be the reason for wear to start. Typical surface modification mechanisms are chemical reactions taking place at the surface and material fatigue from repeated loading. Chemical reactions and sometimes even physical structural modifications, such as oxidation of metallic coatings, graphitisation of DLC and crystallographic re-orientation of MoS2 coatings, take place mainly at the top surface and influence the shear, τu, and fracture, Ku, properties and thus the adhesive friction and adhesive wear. Sometimes also the whole coating structure and the coating/substrate interface may be affected. Fatigue is a result of repeated compressional loading on the material that weakens the molecular structure by including cumulative damage to a level that it cannot take the loading any more. The maximum compressional stress peaks are normally under the coating in the substrate because the coating layer is very thin. Thus the substrate elastic properties, Es, and fracture toughness, Ks, are crucial. If the stress peaks are high also closer to the surface, the elastic and fracture properties of both the coating and the coating/substrate interface, Ec, Kc, Ei and Ki, may also be important. 6. Modelling the surface loading conditions, stresses and strains 6.1. The contact geometry In our work the tribosystem of a sphere sliding on a coated flat surface with increasing normal load was chosen for the study. This corresponds to the contact of the diamond tip sliding against the coating in a scratch tester and thus there is much empirical information available to compare with. The method is widely used today by the coating industry and coating development laboratories, as well as in research for evaluating the tribological properties of coatings. The scratch test is generally accepted as a good and efficient method for the quality assessment of a coated surface . In the scratch test procedure the diamond stylus has a Rockwell C geometry with a 120° cone and a 200 μm radius spherical tip. The scratch test procedure is described in the European Standard prEN 1071-3 . 6.2. Contact mechanisms, deformations and stress generation The material loading and response conditions in a scratch tester have been divided into three phases by Holmberg  to illustrate the contact and deformation mechanisms involved. Phase one represents the ploughing of a stylus in the substrate material. The substrate material is deformed by elastic and plastic deformation and a groove is formed. Phase two represents the bending and drawing of the coating like a sheet on top of the substrate surface. The upper surface of the coating rubs against the stylus front surface and the force required for pulling the coating is equal to the frictional force on the coating against the stylus front surface. The bending movements cause stresses and stress release in the coating. Phase three represents pulling the coating from one point on the surface when fixed over the substrate. The increasing pulling force results in cracks at the place of maximum tensile stress. The sliding spherical diamond tip deforms the surface both plastically and elastically as schematically shown in Fig. 12. At the initial stage a small spherical indent is formed and the plastic material flow pushes up the material around the indent in a torus formed shape. As the tip moves forward a groove with increasing depth is formed. Under the tip there is both plastic and elastic deformation while in the surface behind the tip only the plastic part prevails. Another torus shape is formed in front of the tip. The stress field in the coated surface is formed as a result of the following four effects: 1) Friction force. The friction force between the sliding tip and the surface results in compressional stresses from the pushing force in front of the tip and tensional stresses from the pulling force behind the tip. 2) Geometry changes. The elastic and plastic deformations are spherical indent, groove and torus shaped. They result in bending of the coating as shown in Fig. 12. The stresses are both compressional and tensional. 3) Bulk plasticity concentration. The spherical indentation pattern causes the substrate to deform plastically, reaching its peak value at an angle of about 45° from the plane of symmetry in the plane of the coating. This can be identified with local tensile stress minima and maxima of deformation between the tensile stress peaks around the indenter (at locations of 0 and 90°, respectively). 4) Residual stresses. It is very common especially for thin ceramic coatings that they, due to the deposition process, contain even very considerable compressional residual stresses. These are typically of the order of 0.5–3 GPa but values even as high as 10 GPa may appear [1,37,38]. When the diamond stylus is drawn over the surface with an increasing normal load, a very complex and dynamic stress field is formed with stress concentrations at changing locations. For e.g. a TiN or DLC coated steel surface it typically results in a coating fracture and spalling pattern. The formation of cracks in the groove of a scratch tester has been shown by several authors [35,39–43]. They can typically be described as a) angular K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 1043 Fig. 12. The stress field in a coated surface resulting from a sliding sphere is a result of four loading effects: friction force, geometrical deformations, bulk plasticity concentration and residual stresses. Illustration (a) shows the loading effects with exaggerated dimensions and deformations and (b) with correct dimension interrelationships. cracks, b) parallel cracks, c) transverse semi-circular cracks, d) coating chipping, e) coating spalling, and f) coating breakthrough. Methods for the determination of mechanical properties of coatings and contact stresses have been reported [44,45]. 6.3. Modelling the contact by three dimensional finite element method A three dimensional finite element model has earlier been reported and was now further developed for calculating the stresses and strains in the coated surface and for identifying the stress concentrations where the first cracks of the coated surface are expected to occur [9–11,17]. The scratch test experiment was discretised using the inherent symmetry of the geometry and introducing a finite element mesh where mesh sizing is of the order of the coating thickness (Fig. 13). After analysing the convergence behaviour of the boundary value problem and assessing whether suitable accuracy of contact-related field variables can be attained, a suitable mesh density around the contact area was found to be 25 nm–8 μm. Bilinear hybrid elements were used in Abaqus 6.6-3, 6.2-1 and Warp3D 15.3 finite element software. The volume of the finite element slit taken to describe the scratch test configuration was 12 × 4 × 2 mm 3 (length, width, thickness). The substrate deformation behaviour was characterised as elastic–plastic with isotropic hardening, while the coating was modelled to behave in a linear–elastic manner. The sliding spherical diamond tip was modelled as completely rigid. The kinetic formulation was presented applying a finite strain deformation description. The contact event was modelled by describing two contact zones, commonly referred to as the master and slave surfaces, where the master surface is the one having greater rigidity. During the progress of the experiment the relative positions of the master and slave surfaces define the contact event. The contact formulation was of the finite sliding type due to large local deformations and the distance the tip travels during the experiment. The contact was presented as a ‘hard contact’ between smooth surfaces, i.e. tractions are transferred at the instant of contact but not before. Computational initial oscillations were treated with viscous damping. A velocityindependent Coulombian friction model was used to characterise related surface interactions, and the surfacehardening effect due to plastic deformation of the substrate Fig. 13. Schematic illustration of the three dimensional finite element mesh. The mesh sizing is in the range of 0.025–100 μm and the number of mesh degrees of freedom is about 500.000. 1044 K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 included in the model. The basic model is in detail described in . The results are inferred and analysed primarily with respect to the first principal stress. Generally, studies in the current field apply the von Mises equivalent stress to characterise deformation and failure events. However, the von Mises stress has its greatest potential in understanding and modelling deformation-related events, such as the plasticity of metals, and is not usually associated with the brittle type of failure. It can be argued, and has often been presented  that local unstable cracking is more dependent on the prevailing tensile stress state than the practically nonexistent state of deformation, and that deformation-related parameters and invariants do not comply with the physical appearance of fracture. Most local approach models for such failure micromechanisms rely on the first principal stress. Since the current work is related to cracking of a brittle layer incapable of exhibiting much more than elastic deformation all the way to final rupture, it can be expected that the use of the first principal stress as a fundamental stress component to explain the physical fracture patterns will bring about the most success. Compared to real scratch tester contact conditions, the following limitations have been set for the sake of simplicity: - Compressive residual stresses normally occurring in ceramic thin coatings are not included in the simulation cases reported here. They have been introduced into the model and results with residual stresses have been reported separately [17,47]. - The stress relaxation effect of previously generated cracks on the stress distribution is not included in the present simulations. - The surfaces in the model are ideally smooth, which means that surface roughness effects are not considered. - The materials are considered to be fully homogenous and free from contaminants, pinholes and such defects often occurring in thin ceramic coatings. 7. Simulation of surface stresses and strains 7.1. Simulated contact conditions The above described contact conditions and sliding process have been simulated by the computer model. The following parameters were used in the calculations of the stress and strain distributions: Scratch test parameters: sliding distance 10 mm, load increases linearly from 5 N pre-load and 0.5 μm indentation depth before sliding starts to 50 N and 3 μm indentation depth at 10 mm sliding distance, and the sliding velocity is not included in the model, i.e. the model is time independent. Sliding stylus (Rockwell C): radius of the spherical tip 200 μm, the material is diamond, Young's modulus 1140 GPa, hardness 80 GPa, Poisson's ratio 0.07, and the roughness is ideally smooth. Coating: thickness 2 μm, the material is titanium nitride (TiN) deposited by PVD, Young's modulus 300 GPa, hardness 25 GPa, Poisson's ratio 0.22, and the roughness is ideally smooth. Bond layer: thickness 500 nm, hard ceramic layer with a Young's modulus of 500 GPa and Poisson's ratio 0.22. Substrate: the geometry is an ideally smooth plate, the material is High Speed Steel, Young's modulus 200 GPa, hardness 7.5 GPa, Poisson's ratio 0.29, the yield strength is estimated from ultimate bending strength to 4100 MPa, and the strain hardening coefficient is 20. Friction: The values for the coefficient of friction were measured from samples corresponding to the above material combination. In the simulations a constant value 0.08 was used for the coefficient of friction due to friction from interfacial shear which excludes the ploughing component of friction. 7.2. First principal stresses of a TiN coated steel surface with hard bond layer One typical simulated stress distribution is shown in Fig. 14. The figure is a topographical stress-field map where each colour corresponds to a certain stress level range at the surface and at the intersection shown in the figure. The observation direction is similar to that in Fig. 12 but the spherical tip is invisible in order to display the stresses. The border of the corresponding contact area of the coated plate and the sphere is close to the green to yellow colour transition half circle where the stresses are close to zero. The smoothly changing stress field shows a considerable compressional stress under the diamond tip, indicated by green and blue colours, and the variations in the tensile stresses around the contact zone, indicated by the orange and red colours. The maximum compressional stresses under the tip are about 5200 MPa and the compressional stresses ranges about 40 μm down below the surface. It can also well be seen that there is a thin range of high tensile stresses within the bond layer right under the loaded tip. These tensile stresses are about 3000 MPa just under the tip. A circular region of high tensile stresses is seen as a red belt around the contact zone. It has its maximum value at some distance behind the back of the contact zone at the location of the formed groove edge. Here it reaches a level of about 3300 MPa. This is the place where the first cracks normally occur in scratch test experiments with similar coated surfaces. Behind the contact zone there is a tail of high residual tensile stresses on the surface in the groove area having values of about 2500 MPa. Fig. 15 shows a close up of the part of Fig. 14 just at the back end of the contact zone by the symmetry plane. It shows both the distribution of the rapid stress change in this region and the very high tensile stresses in the bond layer just behind the contact zone, being as high as 5150 MPa. 7.3. Strain in a TiN coated steel surface with hard bond layer The strain distribution for the same contact conditions as in Fig. 14 is shown in Fig. 16. The dark red region directly under K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 1045 Fig. 14. Topographical stress-field maps showing first principal stresses on the coating and at the symmetry plane intersection of the steel sample coated with a 2 μm thick TiN coating (E = 300 GPa), a 500 nm hard interface layer (E = 500 GPa) and loaded by a sliding spherical diamond tip. Sliding direction is from left to right. The values on the colour scale are given as MPa. The stress field at 15 N load and 2.1 mm of sliding is shown. the loading tip shows large strain due to both elastic and plastic deformation and it reaches about 40 μm down under the surface. The red tail behind the contact region shows the residual plastic strain just under the groove and it reaches about 20 μm down under the groove surface. 7.4. First principal stresses of a TiN coated steel surface with interface crack Cracks at the surface will have a considerable influence on the formed stress fields. The lateral cracks generated at the interface Fig. 15. Close up of the region just behind the back of the contact zone at the interface plane in Fig. 14. 1046 K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 Fig. 16. Topographical strain-field maps showing equivalent strain on the coating and at the symmetry plane intersection of the steel sample coated with a 2 μm thick TiN coating (E = 300 GPa), a 500 nm hard interface layer (E = 500 GPa) and loaded by a sliding spherical diamond tip. Sliding direction is from left to right. The values on the colour scale represent the equivalent strain at 15 N load and 2.1 mm of sliding. between the coating and the substrate are of special interest since they indicate the break down of the coating/substrate adhesion. The growth of these lateral cracks result in the formation of larger detached coating flakes and coating delamination from the surface. Fig. 17 shows the stress pattern and the high stresses formed by the ends of one short lateral crack at the interface. Fig. 17. Topographical stress-field maps showing first principal stresses at the symmetry plane intersection of the steel sample coated with a 2 μm thick TiN coating (E = 300 GPa), having a 1 μm long lateral crack at the coating/substrate interface and loaded by a sliding spherical diamond tip. Sliding direction is from left to right. The values on the colour scale represent relative stress at 10 N load and 1.2 mm sliding. K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 1047 Fig. 18. Crack growth parameters studied and used terminology. 7.5. Crack propagation in a TiN coated steel surface II and III (in-plane and out-of-plane shear). The results are presented using the equivalent SIF concept, i.e. The crack propagation has been studied by Boundary Element Method (BEM) by  based on analysis of the simulated stresses in the coated surface. The parameters influencing on crack propagation studied can be summarised as (Fig. 18): qﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ 2 KE ¼ KI2 þ KII2 þ ð1 þ mÞKIII 1) 2) 3) 4) loading modes, (I, II, III). orientation of the crack, (θ = 0, 20°, 45°) density of the crack field, crack spacing (ρ =5, 10, 30 μm and ∞) location of the crack in the crack field, (centrecrack, centrecrack + 1 etc., edgecrack) 5) location of the crack on the scratch groove (middle cracks, side cracks) 6) tensile load biaxiality in loading mode I, (β = 0, 0.5, 1) Observe that the crack spacing ρ = ∞ = infinite corresponds to one single crack and ρ = 0 to an infinite number of cracks approaching each other. The results of the BEM analysis are summarised in Fig. 19. BEM analysis results for single crack cases with different crack angles are presented for uniaxial tension and for loading modes ð7Þ The crack angle is defined such that cracks oriented at an angle of 0 degrees are perpendicular to the applied uniaxial tension. All results were presented over a normalized crack front parameter, s, and given normalized with the value of stress intensity factor (SIF) at the deepest point of the single crack case under uniaxial tension. It was shown that crack oriented from the perpendicular plane towards tension exhibit a somewhat smaller equivalent crack driving force, the differences being of the order of 15% for crack tilted 20° and 30% for crack tilted 45°. Different loading mode effects to crack driving force are indicated, mode II component is being somewhat pronounced over the mode III. The effects of biaxial loading are of the order ∞ ∞ of 5–10% with biaxiality ratios (β) of 1 and 0.5, β = σ22 /σ11 , where the stress components are applied at model boundary. The effects of crack field density on straight cracks with uniaxial tension are depicted. A single uniaxial tension crack Fig. 19. The effect of different crack growth parameters on normalized stress intensity factor (SIF). 1048 K. Holmberg et al. / Surface & Coatings Technology 202 (2007) 1034–1049 case is provided for reference. Two effects are noted, first how crack density introduces a differing driving force to variable density crack fields and second, how center and edge cracks exhibit a somewhat different driving force dependant on crack density. For crack fields with a lower density the crack driving force is higher in comparison to dense crack cases and separate cracks are relatively independent of each other, i.e. different cracks have nearly identical crack driving forces. It was noted, that the crack density is an extremely important parameter in evaluating the SIF values, the effects being more than meaningful. Crack location, i.e. whether edge or center cracks are concerned, has similar effects as with straight cracks under unidirectional tension. Loading biaxiality had no remarkable effect on straight scratch bottom cracks, but the differences become noticeable when angular cracks are concerned. The differences for the ρ = 5 μm crack field are at their maximum of the order of 35%, the biaxiality effects affect edge and center crack field cracks much in the same fashion and of the same order of magnitude. Biaxial loading is seen to have a similar effect as with the middle crack fields, the overall difference between the single transversal middle crack being of the order of 40–60%. Different density crack fields are seen to produce relatively field density insensitive results, whilst differing quite a bit from the single crack solution, the difference being of the order of 80%. 8. Conclusions The article discusses the basic friction and wear mechanisms, scale effects and parameters influencing the friction and wear of surfaces coated with thin films. This forms the basis for surface optimisation by modelling, stress simulation and surface fracture calculations. It is shown that the basic friction and wear mechanisms can be reduced to friction by adhesion, ploughing and hysteresis and wear by adhesion, abrasion and fatigue combined with material fracture. The tribochemical and surface physical effects and surface fatigue taking place before material fracture are treated as pure surface material modification mechanisms. The scale effects in a tribological contact are illustrated by explaining typical surface roughness related tribological mechanisms for diamond and DLC coated surfaces. For diamond coatings asperity interlocking effects are important for rough surfaces, graphitisation dominates for smooth engineering surfaces and hydrogenisation of dangling bonds may be crucial for physically smooth surfaces. For DLC coated surfaces surface graphitisation is important with rougher surfaces, building up transfer layers and graphitisation is crucial for smooth engineering surfaces and hydrogenising of dangling bonds can explain superlubricity for physically smooth surfaces. An analysis of dominating surface parameters such as elastic, plastic and fracture behaviour of the top surface, the coating, the coating/substrate interface and the substrate in addition to the coating thickness forms the basis for surface modelling. The dominating parameters depending on the governing basic wear mechanisms have been identified. Stress simulations locate high tensile stresses on the top surface behind a sliding spherical tip and high residual tensile stresses in the coating covering the deformed groove. Hard interlayers between the coating and substrate generate extremely high tensile stresses and the formation of stress concentrations at crack ends for cracks at the coating/substrate interface are shown. A stress intensity factor analysis of crack growth shows the importance of considering all modes I, II and III stresses, crack spacing and location of crack in the scratch groove, while crack orientation, location in crack field as well as load biaxiality have minor influences. The study shows how surface 3D FEM modelling generates stress and strain values at nano level, at coating/substrate interfaces and around cracks and forms a basis for understanding the origin of wear. Micro and nano scale modelling, simulation and fracture calculations are very useful tools for a systematic approach to finding optimal surface and coating parameters and for successful surface design for a specific application. Acknowledgements The authors want to acknowledge the following colleagues for the interesting and valuable discussions in relation to the work: Allan Matthews, Sheffield University, UK; Philippe Kapsa, Ecole Central de Lyon, France; Henry Haefke and Imad Ahmed, CSEM, Switzerland; Ali Erdemir, Argonne National Laboratory, USA; Koij Kato, Tohoku University, Japan; and Kaj Pischow and Rosa Aimo, Savcor Coatings. The financial support of TEKES the Finnish Technology Agency; Taiho Kogyo Tribology Research Foundation, Japan; Savcor Coatings, Finland; and the VTT Technical Research Centre of Finland is gratefully acknowledged. References  K. Holmberg, A. 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