Modelling sliding wear: From dry to wet environments

Wear 261 (2006) 954–965

Modelling sliding wear: From dry to wet environments Jiaren Jiang a,∗ , M.M. Stack b a

Integrated Manufacturing Technologies Institute, National Research Council Canada, 800 Collip Circle, London, Ont., Canada N6G 4X8 b University of Strathclyde, Department of Mechanical Engineering, Glasgow G1 1XJ, UK Accepted 31 January 2006 Available online 2 May 2006

Abstract Corrosive species in various forms exist widely in the environment and can significantly affect wear behaviour of materials, usually accelerating wear. Under conditions where the environments are seemingly non-deleterious in terms of corrosivity, some species from the environment can still affect the tribological behaviour of materials. It is thus extremely important to recognise the roles of reactive species in affecting the tribological processes and to understand the processes of tribo-corrosion interactions. In this paper, the mechanisms of wear debris generation and the roles of reactive species in the generation of wear debris during sliding wear in gaseous or aqueous environments are discussed. The effect of environment on the development of wear-protective layers is described. Based on the proposed mechanisms, mathematical models for sliding wear in both dry and aqueous environments are outlined, and the validity of the models is assessed against experimental data in sliding conditions. © 2006 Elsevier B.V. All rights reserved. Keywords: Tribo-corrosion; Corrosive wear; Dry sliding wear; Wear debris; Modelling

1. Introduction Damage to materials and mechanical components due to wear has a significant impact on the economics of engineering systems both directly and indirectly in terms of material loss and associated equipment downtime for repair and replacement of worn components. In the last half-century or so, great efforts have been made in understanding the mechanisms of wear to improve the wear performance of materials. Sliding wear involves the formation of wear debris particles and their subsequent removal from the rubbing interface. Most of the existing wear theories, such as the adhesion wear theory [1,2], the delamination theory [3], the low cycle fatigue theory [4,5] and the oxidational wear theory [6,7], are mainly concerned about the generation of wear debris, ignoring the commonly observed phenomenon that wear debris particles can get involved in the wear process and significantly affect the wear of materials [8–15]. Once formed, the wear debris particle is assumed to be removed from the rubbing system to cause material loss. Meanwhile, most of the existing theories do not directly incorporate the effect of environment on the wear process, except for the oxidational wear theory. In the

∗

Corresponding author. Tel.: +1 519 430 7121; fax: +1 519 430 7064. E-mail address: [email protected] (J. Jiang).

0043-1648/$ – see front matter © 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2006.03.028

latter case, the wear loss is exclusively attributed to the cyclic formation and removal of oxide on the rubbing surfaces and is mainly applicable to the mild wear conditions [6,7]. In recent years, increasing interest has been noticed in the literature in the investigation of tribo-corrosion [16–22], which can be defined as the chemical–electrochemical–mechanical process leading to a degradation of materials in sliding or rolling contacts immersed in a corrosive environment. Such research has significant practical importance because in many engineering systems, materials forming tribological contacts are exposed to a corrosive environment in various forms and therefore are subjected to both mechanical and chemical–electrochemical solicitations. Typical examples are orthopaedic implants, chemical pumps and food processing or mining equipment. Under some other situations, the occurrence of tribo-corrosion is not always recognised in field practice, such as the accelerated corrosion of steel conveyors exposed to ambient air of high relative humidity and increased saw wear when cutting wet lumbers. Under the corrosion–wear conditions, material loss is usually accelerated as a result of synergistic interactions between the mechanical action of wear/rubbing and the corrosion reactions occurring on the wear surfaces [23–32]. Currently, the understanding on wear of metals in corrosive environments is very limited. Modelling of such complicated processes is even more challenging. Some modelling of tribo-corrosion has been carried out [33–36]; how-

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ever, it is mainly concerned with the corrosion and wear-induced corrosion aspects of the process. In order to improve the performance of materials in engineering systems, there is a constant demand to better understand the mechanisms of wear under various conditions. Modelling is one of the effective tools in helping this understanding. In this paper, the concept of low cycle fatigue as a basic mechanism for the generation of wear debris particles is presented. Based on such a concept, the roles of reactive species in the generation of wear debris during sliding wear are discussed and mathematical models for sliding wear in both gaseous and aqueous environments are outlined. The validity of the models is assessed against experimental data. 2. Low cycle fatigue as a basic mechanism for the generation of wear debris In sliding wear, the real area of contact that carries the applied load is usually a very small fraction (<10%) of the apparent area of contact. As a result, high contact pressures exist at the real area of contact. For metals, the higher asperities will almost always deform plastically even under very low apparent loading conditions. Repeated contact at these real areas leads to the generation of wear debris particles. Essentially, this process of wear debris generation fits the definition of low cycle fatigue which is a material failure mode that incorporates a cyclic plastic strain component. Wear theories based on the concept of low cycle fatigue have been presented by several groups of researchers [5,37–40]. Arnell et al. [41] set out a qualitative description of sliding wear by invoking fatigue as the dominant wear mechanism. Challen and Oxley [5] calculated the magnitude of plastic strain increments during sliding of metals and evaluated wear rates on the basis of low cycle fatigue wear theory. Experimental results and the calculations agreed well [38]. Tangena [39] also presented a low cycle fatigue wear model and experimentally verified that the low cycle fatigue wear theory produces more reasonable predictions on wear rate of metals than the classical Archard’s wear equation based on the adhesion theory. Broadly speaking, the other existing theories on the generation of wear debris can also be covered by such a low cycle fatigue wear concept. For example, in the delamination theory of wear [3,42], microcracks/voids are assumed to initiate and to propagate underneath the surface due to plastic deformation to generate wear debris. In the light of low cycle fatigue failure, a wear debris particle is generated when the fatigue life is reached under a given plastic strain amplitude. The classical adhesion wear theory can essentially be regarded an extreme situation of the low cycle fatigue model where the material at the cold weld junction reaches its fatigue life in one cycle of contact (breaks at the weak point upon each contact). Despite the apparent agreement between the wear theories based on low cycle fatigue and experimental observations, so far, no direct measurement is available to assess the material fatigue properties under sliding wear conditions. By re-analysing the data obtained by Hokkirigawa and Kato [43] from single particle scratching test, the nature of low cycle fatigue in the process of generating wear debris can be more clearly illustrated.

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Fig. 1. Schematic diagram showing the cross-section geometry of the groove formed in the scratching test using a hard particle.

Using a single particle scratching test rig fitted in an SEM, Kato and co-workers [43–45] systematically studied material removal and the transitions in mechanisms of the material removal as a function of particle penetration into the specimen surface. In the rig, a round tip made of hard material was used to scratch the specimen surface to produce a groove, which has a cross-section geometry as shown in Fig. 1. In the groove, the volume of material being displaced is proportional to the area, A0 . A fraction of this displaced material, β, is removed/detached from the specimen surface to form a wear debris particle while the remaining material corresponding to the areas, A1 and A2 , is displaced to the sides of the groove to form ridges. The material removal fraction, β, is calculated by β=

A0 − A1 − A2 A0

(1)

The experimental results for SUJ 2 bearing steel (containing 0.95% C and 1.3% Cr) treated to different hardness values (250–750 HV) from ref. [43] are reproduced in Fig. 2. The heattreatment conditions included water quenching from 860 ◦ C with or without further tempering at temperatures from 200 to 750 ◦ C. The fraction of material removed, β, is determined by the “degree of penetration”, Dp , which is defined as the depth of penetration, h, divided by the half-width, a, of the groove (Fig. 1), Dp =

h a

(2)

Direct SEM observations [45] showed that the degree of penetration, Dp , also controls the modes of the material removal. Below some critical penetration value, Dp1 , the dominant wear

Fig. 2. The variation of the fraction of material removed, β, as a function of the degree of penetration, Dp , observed with heat-treated steels of various hardnesses in a single particle scratching test [43].

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test. Whether a wear debris particle is produced and how much the material is removed depends critically on the plastic strain and on the low cycle fatigue properties of the material. 3. Effect of environment on wear of materials—a physical model for the roles of reactive species in generation of wear debris particles

Fig. 3. Re-plot of data shown in Fig. 2 according to Eq. (3) showing the relationship between the fraction of the material removed, β, and the degree of penetration, Dp , in the wedge formation region for the steels with various hardnesses.

mode is ploughing and material removed in a single pass scratching is essentially zero. When the degree of penetration exceeds Dp1 , β increases rapidly with increase in the degree of penetration, Dp . The dominant wear mode transits from ploughing to wedging, where a wedge-shaped ridge is developed and eventually removed in front of the tip. With further increase in the degree of penetration above another critical value, Dp2 , the fraction of material removal reaches some steady value and cutting becomes the dominant wear mode, with most of the material in the groove being removed to cause wear loss. These critical values for Dp1 and Dp2 are material dependent. Applying a low cycle fatigue concept, Jiang and Arnell [46] re-analysed the above experimental data and obtained the following relationship between material removal fraction, β, and the degree of penetration, Dp :   Dp 1 m log β = log(k) + log (3) n n Dp2 where m is the Manson–Coffin low cycle fatigue exponent and normally takes the values of 1.4–2 [47], n and k are empirical constants. According to Eq. (3), the experimental data shown in Fig. 2 is re-plotted and is shown in Fig. 3. All the data points from the various steels with different microstructures and hardness values fall in the same straight line. This suggests that, in spite of the complicated material and loading conditions, low cycle fatigue is most probably the underlying mechanism controlling the generation of wear debris in the single particle scratching

From the above discussion, the process of generating wear debris in wear of metals has the attributes of low cycle fatigue. It is thus reasonable to assume that this involves the initiation and propagation of a microcrack. After initiation, the microcrack will propagate/grow for a certain length, each time it makes contact with an asperity from the counter surface. A wear debris particle is generated after sufficient number of cycles of contact at the same spot with the encountering surface. Obviously, the propagation rate of the microcrack, and hence the generation rate of wear debris particles, depends on the loading conditions and the low cycle fatigue properties of the material at the rubbing surface. The microcrack propagation is via the debonding at the crack tip. If some reactive species, A, are present and can react with the bonding, B, at the crack tip, then they will also affect the propagation/extension of the microcrack, usually accelerating wear. Fig. 4 shows a schematic diagram for the crack-tip debonding under the influence of a chemically activated reaction, A + B → B∗

(4)

Such reactions activate the bonding, B, at the crack tip to the activated state, B* , and weaken the bonding or reduce the surface energy (Fig. 4); consequently, the propagation of the crack is promoted [48,49]. B* is not necessarily the final/stable product of the reaction A and B and the reactions are not necessarily chemical ones in order to cause increased propagation rate of the microcrack [50]. The species, A, can be from either aqueous solutions or gaseous environments. In many cases, they can be seemingly non-deleterious. When investigating the effect of sliding speed on wear of diamond-like carbon (DLC) coatings, Jiang and Arnell [51] found a parabolic relationship between the wear rate and the sliding speed, as shown in Fig. 5. The DLC coatings were deposited using closed-field unbalanced magnetron sputtering of graphite target and contained mainly sp2 type of carbon bonding with a hardness of 17.7 GPa. The wear testing was conducted in dry air (7% relative humidity) using a ball-on-disk type rotating wear

Fig. 4. Schematic diagram showing the microcrack propagation mechanism during the generation of a wear debris particle accelerated by chemically activated reactions between reactive species, A, with the bonds, B, at the crack tip.

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with the increase of sliding speed. As a result, wear rate starts to increase with further increase in sliding speed at the higher speeds (v > 15 m min−1 , Fig. 5). A semi-quantitative expression was derived for the relationship between the specific wear rate and sliding speed based on the mechanism presented here (Fig. 4 and reaction (4)), i.e., assuming that the control step in the generation of wear debris particles is chemically activated interactions between some reactive species from the environment and bonds at the crack tip. Fairly good agreement between the analysis and the experimental results was obtained [51]. 4. General considerations on the dry sliding wear processes Fig. 5. The variation of specific wear rate of a diamond-like carbon (DLC) coating as a function of sliding speed and sliding distance, s [51].

rig against steel balls (6.35 mm diameter) under a normal load of 25 N and contacting frequencies of 5–35 Hz. Detailed analysis showed that the significant effect of sliding speed on wear of the DLC could not be explained according to the frictional heating effect. Based on the mechanism shown in Fig. 4, this phenomenon was reasonably explained. Thus, at the low sliding speeds (below approximately 15 m min−1 ), the time interval between two consecutive contacts between asperities at/near a given microcrack for the reactive species to migrate to the tip of the crack decreases with increase in sliding speed. As a result, the size and generation rate of wear debris particles are significantly reduced and the wear rate decreases (Fig. 5). With further increase in sliding speed over 15 m min−1 , the sliding induced surface temperature rise increases and can have a significant effect on the transportation and reaction rate of reactive species at the crack tip, promoting the generation of wear debris particles and increasing the wear rate. Since temperature usually enters thermally activated processes in an exponential term (in the Arrhenius equation form), the acceleration effect of temperature on wear due to the increased reaction rate soon outweighs the deceleration effect of decreasing reaction time

From experimental observations, the dry sliding wear process can be described as schematically illustrated in Fig. 6. Wear debris particles are generated by the relative motion of the rubbing surfaces under load. Some of these are removed from the wear tracks to form loose wear particles, resulting in wear loss. The others are retained within the wear tracks where they are comminuted by repeated plastic deformation and fracture while freely moving between the rubbing surfaces. Once fragmented to a small enough size, the particles are agglomerated at certain locations on the contacting wear surfaces, due to the adhesion forces arising from surface energy [52], and establish relatively stable compact layers. The development of such layers reduces material loss since newly formed wear debris particles are re-cycled into the layers; also, as the wear debris particles have been heavily deformed and oxidized, these layers are hard and wear-protective. On further sliding, two competitive processes occur in the compact layers, namely breakdown of the layers, which causes wear, and sintering/cold-welding between particles within the layers, which leads to consolidation of the layers. Sintering of very fine wear debris particles can occur at temperatures only slightly above 20 ◦ C [53], but occurs more rapidly as the temperature (operating and/or surface temperature) is increased. The oxidational environment also facilitates the consolidation of these layers due to the chemical sintering

Fig. 6. Diagram showing the processes of dry sliding wear of metals.

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effect between particles. If the surfaces of the layers become solid before the layers are broken down, ‘glaze’ layers may develop on top of the compact particle layers, leading to reduced friction and wear. The critical temperature for ‘glaze’ layers to form is the transition temperature under a given set of conditions above which wear decreases significantly. 4.1. Mathematical model for the dry sliding wear process From the above description of the wear process, it is possible to develop a model for the wear process [13]. The model considers the involvement of wear debris particles in the development of wear-protective layers. The wear rate of these layers is assumed to be negligible compared to that of other areas uncovered by such wear-protective layers and, hence, wear debris particles are generated only in those other areas. In other words, if the fraction of the total apparent area of contact, Aa (t), at time, t, covered by wear-protective layers is equal to Ce (t), then the area generating wear debris particles will be equal to Aa (t)[1 − Ce (t)]. Suppose N(t) wear debris particles are generated per unit time on a unit area of the wear surface at time, t, and the size distribution of the newly generated wear debris particles is represented by a function, f(D), where a fraction of f(D) dD of the total particles have the size of D to D + dD. The probability of a wear debris particle being removed from the wear track is equal to Pr (D) which is a function of the particle size, D, and the contact conditions (geometry, load, separation of the rubbing surfaces, etc.). Thus, the wear volume of the specimen after sliding time, t, is given by   π t Aa (t) N(t)[1 − Ce (t)] V (t) = 6 0   ∞ × D3 f (D)Pr (D) dD dt (5) 0

Similarly, the volume of wear debris particles retained within the rubbing surfaces at time, t, is given by   π t Vret (t) = Aa (t) N(t)[1 − Ce (t)] 6 0   ∞ × D3 f (D)[1 − Pr (D)] dD dt (6) 0

If it is assumed that all the retained particles are compacted eventually to form wear-protective layers, of average thickness, δ, which is typically 2–15 ␮m [54], then the coverage of the wear surface by such layers is given by Cc =

Vret (t) Aa δ

(7)

Wear-protective layers are particularly effective if ‘glaze’ oxide of a critical thickness, δc , can develop on their surfaces. If the oxidation kinetics of the wear debris are expressed in terms of the scale thickness, y, as y = g(t)

(8)

then the critical time, tcg , for a ‘glaze’ of critical thickness, δc , to develop on the compacted layer is given by tcg = g−1 (δc )

(9)

where g(t) is a generic expression describing the oxidation kinetics for the given system (e.g., parabolic, linear or logarithmic) and g−1 (δc ) is the inverse function of g(t) at time tcg . If an area of compact particle layer, dAc (τ), is developed at time, τ, then this will develop into a ‘glaze’ layer after a period of tcg , i.e., at time (τ + tcg ). Thus, the total coverage of the apparent area of contact by the ‘glaze’ layers, Cg (t), at time, t, is given by  t−tcg dAc (τ) Cg (t) = (10) Aa (t) 0 Areas of compacted debris particle layers and ‘glaze’ layers may co-exist on wear surfaces and both are wear-protective, although the latter are more effective. When both types of layers are present, the concept of an equivalent protective coverage of the wear surface, Ce , can be introduced, defined as Ce =

Cg Cc + Cc limit Cg limit

(11)

Cc limit and Cg limit are the critical coverage by compact and ‘glaze’ layers, respectively, above which the wear surfaces become completely protected and the transition from severe to mild wear occurs. For the nickel-base alloy, N80A, Cc limit ≈ 0.4 – 0.6 and Cg limit ≈ 0.2 [13]. 4.2. The effect of oxygen partial pressure on sliding wear The activity of oxygen and/or other reactive species in the environment can affect the wear process in several ways. Reactive species such as oxygen can affect the size of wear debris particles, DL , by affecting the surface energy, γ, of the material according to the following expression, which has shown good agreement with experimental observations [55]: DL ≥

12γ E(νεmax )2

(12)

where E is the elastic modulus of the contact surfaces, εmax the maximum vertical strain in the wear surface due to the frictional action which is approximately equal to the strain limit of the material at the formation of the wear debris and ν is the Poisson’s ratio. The surface energy, γ, is related to the partial pressure of the reactive species, pA , by the Gibbs’ adsorption isotherm and the classical Langmuir gas adsorption isotherm,   RT γ(pA ) = γ0 − ln(1 + bpA ) (13) NA σ 0 where γ 0 is the surface energy of a solid in vacuum, σ 0 the area of an adsorption site, R the gas constant, T the absolute temperature, NA the number of bonds per unit area along the crack-plane and b is the constant in Langmuir isotherm representing the ratio between the rate constants for adsorption and desorption of a gas on a solid. Normally, the presence of gaseous species in the environment reduces the size of loose wear debris particles [56].

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The presence of reactive species, A, such as oxygen may also affect the propagation of microcrack according to the mechanism discussed in Section 3, i.e., by reaction (4). Such reactions reduce the time, tc , for the microcrack to propagate a length of DL to generate a wear debris particle. Thus, the generation rate of wear debris particles, N, which is inversely proportional to tc , is increased [14,57]. Under certain conditions, the presence of reactive species such as oxygen may also modify the mechanisms of wear. For example, at sufficient reaction rate of the reactive species with the rubbing surfaces and under mild loading conditions, wear debris may generate only from the reaction products such as oxide layers and mild wear regime may develop, such as in the case of oxidational wear. Eqs. (5)–(11) constitute a generic and complete set of equations that can be applied to calculate wear in dry sliding systems where the severe to mild wear transition is a result of development of compact wear debris particle layers. No specific assumptions have been made on the mechanisms of generation of wear debris, the number and size distributions of the debris particles, as well as their removal/retaining probabilities. Although the model has been presented based on the generation of wear debris particles as a result of sliding wear, it can also be applied to sliding systems where the particles are introduced externally. The various parameters in Eqs. (5)–(11) for reciprocating pin-on-disk sliding wear of nickel-base alloys have been determined [13,14], including the effect of partial pressure of oxygen on size and generation rate of wear debris particles [14,57]. Substituting these parameters into these equations, the wear process has been simulated. Fig. 7 shows an example for the simulated variation of wear volume as a function of sliding time and its comparison with experiments for a nickel-base alloy, N80A, using a pin-on-disk reciprocating sliding wear rig at a sliding speed of 83 mm s−1 , reciprocating frequency of 8.3 Hz and a normal load of 15 N at 20 ◦ C. The general shape of the simulated curve agreed well with the experimental results, although

5. Modelling of sliding wear of metals in aqueous environments

Fig. 7. Variation of wear volume of a nickel-base alloy, Nimonic N80A, as a function of sliding time at 20 ◦ C—a comparison between experiments (box marks and the dotted line) and simulation (the solid line). (Sliding conditions: reciprocating pin-on-disk sliding, like-on-like, 12.5 mm radius domed pin end, speed of 83 mm s−1 , 8.3 Hz contact frequency, 15 N normal load, in dry air.)

There are several unique features for wear of metals in an aqueous environment as compared with dry sliding wear, which need to be considered when modelling such wear processes. In the first place, corrosion usually takes place at a considerably higher rate than in dry sliding wear conditions and this can cause significant direct material loss. Secondly, synergy between corrosion and wear is widely observed during sliding wear in various aqueous environments [23–32]; i.e., corrosion is accelerated by the mechanical action of wear and wear loss is enhanced by the presence of the corrosion conditions. Thirdly, loose wear debris particles can be easily washed away from the rubbing interface by the aqueous solution; therefore, it becomes difficult to develop wear-protective layers from the compaction of wear debris particles on the wear surface. This is clearly demonstrated by the following example. Fig. 9 compares the results for sliding wear of Stellite 12 alloy against 316 stainless steel under dry and wet sliding conditions. The wear tests were conducted on a thrust washer test rig in which the end of a rotating cup specimen slides against a station-

Fig. 8. A comparison of the simulated and the experimentally measured wear volumes as a function of temperature (Nimonic N80A alloy, same sliding conditions as those given in the caption of Fig. 7).

the predicted wear volume was nearly twice that of the experimental measurement under the same conditions. Fig. 8 shows a comparison between the simulation and experimental results for the variation of wear as a function of temperature under the same sliding conditions. The model seems to overestimate the wear at the low temperature range and underestimate the wear at the higher temperatures. However, the agreement in the general trend is fairly good. When the effect of oxygen partial pressure was taken into account, a much better agreement between the simulation results (the solid line in Fig. 8) and the experimental data is obtained than when this effect was ignored (the dotted line in Fig. 8). This seems to support the concepts that the generation of wear debris involves the microcrack initiation and propagation process similar to a fatigue process (Section 2) and that the presence of reactive species in the environment can lead to chemically activated microcrack propagation (Fig. 4 and reaction (4)).

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of wear debris and the corrosion products. On the other hand, abrasive wear due to entrapped loose wear debris particles can be expected to be minimal under most wet sliding conditions as the wear track is normally very shallow, far below the order of 0.5 mm as observed in the above example (Fig. 9). In a general term, the total material loss, Vwc , under corrosion–wear conditions is a combination of material losses due to wear, Vw , and due to corrosion, Vc , Vwc = Vw + Vc

Fig. 9. Variation of wear of Stellite 12 cup sliding (rotating) against 316 stainless steel disk as a function of sliding distance under dry and wet (water) sliding conditions.

ary disk, making an annular wear track. In this case, the contact frequency between the two rubbing surfaces is nominally infinite, although the real contact frequency between asperities at a given location on the surface will have limited values depending on the material properties and loading conditions. The cup was made of Stellite 12 alloy and the disk was made of 316 stainless steel. For the wet sliding test, the specimens were immersed in a de-ionised water bath during the sliding. The sliding speed was 0.15 m s−1 and the normal contact pressure was 0.53 MPa. It was observed that under the dry sliding conditions, a large amount of wear debris particles was embedded and compacted on the soft (316 stainless steel) disk surface, forming wear resistant layers and protecting the disk from further wear. Wear of the stainless steel disk was negligible below a sliding distance of 2500 m and this was barely detectable after a total sliding distance over 4000 m, although wear of the Stellite cup increased continuously with sliding distance. However, when the sliding was carried out in water, wear debris particles were easily removed from the rubbing interface to the water bath and no compaction/embedding of wear debris particles on the stainless steel disk surface was observed. The wear of the disk was very severe (notice the different scales for wear of the disk and the cup in Fig. 9), while the wear of the cup specimen was considerably lower than that of the disk. Cup wear was also much lower than during dry sliding wear at sliding distances below 1500 m. After sliding for over 1500 m, a deep wear track (∼0.55 mm) was formed on the disk and loose wear debris particles were accumulated in the wear track. As the hard wear debris particles could not compact to form wear-protective layers, they acted as abrasives and considerably accelerated the wear of the Stellite cup specimen. As a result, wear of the cup increased rapidly after prolonged sliding (Fig. 9). The above results suggest that the involvement of wear debris particles in the development of wear-protective layers during wet sliding wear can be neglected under most sliding conditions (except in conditions where chemical depositions are significant). This assumption will be used in the following discussion. However, it must be pointed out that this should not be taken as a general rule. Under certain conditions, it may still be possible to develop wear-protective layers from the accumulation and compaction of corrosion/reaction products or from a mixture

(14)

As has been mentioned earlier, this total material loss, Vwc , under corrosion–wear conditions is usually higher than the sum of material loss due to wear, Vwo , measured in the absence of corrosion and the material loss due to corrosion only, Vco , without the influence of wear. The difference is the synergistic effect and can be attributed to the sum of the corrosion-induced wear,

Vw , and wear-induced corrosion, Vc , which represent the increase of wear due to corrosion and increase of corrosion due to wear, respectively [17,26,58], Vwc = Vw + Vc = Vwo + Vco + Vw + Vc

(15)

Eq. (15) provides a phenomenological description of the corrosion–wear phenomenon. Obviously, there is a strong need for better mechanistic understanding and modelling of the synergistic effect in tribo-corrosion. 5.1. Corrosion in the presence of wear, Vc Most engineering metallic materials used in tribological applications develop a thin (typically 2–3 nm on stainless steels) surface oxide film in liquid corrosive environments almost spontaneously under oxidising conditions. Such a film passivates the metal surface and protects the metal from further rapid dissolution/corrosion. Wear actions (either hard particle intruding or sliding) can activate the metal surface and increase the corrosion rate by (a) removing [35,59–62] or damaging [62] the protective passive films on the surface and (b) increasing internal energy of the metal surface due to the plastic, normally very severe, deformation. Material loss due to corrosion, Vc , during sliding in a corrosive environment is related to the anodic corrosion current under the influence of wear, Ia,w , by Faraday’s law:  t  Aatom Vc = Vco + Vc = Ia,w dt (16) ze Fρ 0 where Aatom is the atomic weight of the dissolving metal during electrochemical corrosion, F the Faraday’s electrochemical equivalent, ze the average discharge valence of the metal for anodic reactions during corrosion and ρ is the density of the metal. The corrosion current, Ia,w , can be experimentally determined. For metals that can passivate in the corrosion environment, Ia,w is composed of two components: (a) the repassivation anodic current with a density of ia passing through the area, Ar , where the passive film has been removed/damaged by the mechanical wear action and (b) the passive current with a den-

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sity of ip passing through the rest of the apparent area of contact, Aa − Ar , where the passive film have been fully developed. Aa is equal to the apparent area of contact, assuming that the areas surrounding the wear track are insulated from electrochemical reactions. For non-passive metals, ir = ip . If it is assumed that a depassivation–repassivation event occurs in between two successive contact events during corrosion–wear sliding tests, then, the depassivation frequency is equal to the contact frequency, f, and the anodic current, Ia,w , can be expressed by  1/f  1/f Ia,w = fAr ir (t) dt + f (Aa − Ar ) ip (t) dt (17) 0

0

Mischler and co-workers [35,63] assumed that the removal of passive films during sliding corrosion–wear occurs on the real area of contact, Ar , which depends on the mechanical properties of the material and the contact surface topographies. Landolt et al. [63] analysed three possible situations for the contact topography. For sliding between two ductile rough bodies or a hard rough body sliding on a smooth ductile body, the following expression applies:  1/2 W Ar = Kw l (18) H where Kw is a constant, l the width of the wear track, W the normal load and H is the hardness of the metal. For sliding of a smooth hard body over a rough ductile body, the dependency of Ar on (W/H) is linear. As ideal “smooth” surfaces are rarely encountered in the micro-scale for most sliding systems, especially after the very initial sliding stage, the actual power is expected to vary between 1/2 and 1. In the following discussion, Eq. (18) will be used. However, the obtained results can be easily extended to account for the actual situations. Based on the argument that a critical load is required to delaminate a passive film [62] and that a stress distribution exists in every contact point under elastic loading conditions [64], Garc´ıa et al. [34] introduced a concept of active wear track area for the calculation of the active corrosion surface area, Ar , which was defined as the surface area that looses its passive film due to a mechanical loading. This is different from the real area of contact that carries the applied load. It was shown that the active wear track area, Ar , depended on load and contact frequency. For the sliding of a rotating 316 stainless steel disk on a corundum ball in 0.5 M H2 SO4 solution (f = 0.83–2.5 Hz), the wear surface was not activated by the wear action at loads below 2 N, i.e., Ar = 0. No wear-induced corrosion occurs under such conditions. At loads between 2 and 12 N, the active wear track area was proportional to contact frequency, f, and followed a parabolic relationship with the applied load. The controlling mechanism of wear in this intermediate load range is a passivation–scraping–repassivation process. At loads over 12 N, wear debris particles will include both the passive films and the underneath bulk material. Under such conditions, fresh metal surfaces will be created by both the removal of the passive films and the generation of wear debris. It can be expected that, unless the loading conditions are so severe that the passive films on the whole rubbing surface are removed after each cycle of contact,

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i.e., the real area of contact reaches the apparent area, the active wear track area should still follow a parabolic relationship with the normal load. Thus, Eq. (18) can be assumed to hold under most sliding conditions above the critical load for delaminating the passive films. For more accurate estimations, the load in Eq. (18) should be subtracted by the amount of the critical load. In Eq. (17), the passive current density, ip , corresponds to the current density at the polarised potential in the passive region. It can be measured using conventional polarisation techniques. The repassivation current density, ir , usually decays very rapidly after depassivation due to re-growth of the passive film [33,34,65] and can be approximated by an exponential function:   −τ ir = (i0 − ip ) exp + ip (19) τ0 where τ 0 is a characteristic passivation time. The lower the value of τ 0 , the faster the metal passivates. Applying Eqs. (17)–(19) to Eq. (16), the material loss due to corrosion under the influence of wear, Vc , is obtained as   Aatom t Vc = Vco + Vc = ze Fρ   

 1/2 −1 W × Aa ip +Kw l (i0 −ip )fτ0 1 − exp H fτ0 (20) The amount of material loss, Vco , which would occur under ‘pure’ corrosion conditions without wear is equal to   Aatom Vco = (20a) A a ip t ze Fρ while the wear-induced corrosion is given by     1/2  −1 Aatom t W (i0 − ip )fτ0 1 − exp Kw l

Vc = ze Fρ H fτ0 

(20b) 5.2. Wear in the presence of corrosion, Vw As has been mentioned above, wear debris particles including both the passive films and the underneath bulk material will be generated at high load levels and contact frequencies. In fact, although Garc´ıa et al. [34] have suggested that removal and regeneration of the passive films, i.e., corrosion, dominates the material loss at the intermediate load levels, it is apparent that there are always spots/asperities on the rubbing surfaces where the local contact load is high enough to cause mechanical damages to the underneath metal bulk. During sliding in aqueous environments, if it is assumed that the accumulation and compaction of wear debris particles on the wear surfaces can be neglected, i.e., Pr (D) = 1 and Ce = 0 in Eq. (5), which is often the case, particularly in strongly acid media where hydroxides and many oxides are soluble, then, according

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to Eq. (5), the wear volume can be expressed by     ∞ π t πDa3 Aa (t)N(t) NAa t V (t) = D3 f (D) dD dt = 6 0 6 0 (21) where Da is the average diameter of wear debris particle. Apparently, the effect of corrosion on sliding wear of metals can be analysed according to its effect on the two factors, Da and N. According to the concept of micro-fatigue crack propagation, a critical time, tc , is required for an existing microcrack nucleus to propagate a length, D, of the diameter of a wear debris particle and is related to the microcrack growth rate, da/dn, by  tc  tc da da dτ = f dτ (22) D= 0 dτ 0 dn If Nc active microcrack sites are present on a unit area of the wear surface, then the generation rate, N, of wear debris particles can be calculated by N=

Nc tc

(23)

From Eqs. (22) and (23), a corrosive solution can affect wear in several ways. Firstly, corrosion can increase the number of potential microcrack initiation sites, Nc . During a wear process, the wear surface is, on a microscopic scale, always unevenly loaded and deformed. Damage to any surface films that may exist will also be non-uniform. Thus, localised corrosion attack of the wear surface will occur when a corrosive solution is present. This is similar to situations in corrosion fatigue and in stress corrosion cracking where such localised attack can promote the initiation of short cracks. As a result, the density of active crack initiation sites, Nc , will be different from, and is usually higher than, that in a reference environment where corrosion is prohibited. Secondly, reactive or corrosive species at the crack tip can promote the propagation of the crack (increasing da/dn) [48,49], increasing the generation rate of wear debris particles by reducing tc (Eq. (23)). Thirdly, the corrosive environment may also affect the average wear debris particle size, Da , although it is very difficult to predict if and how this factor will vary with the corrosion conditions. Finally, it is possible under certain conditions that wear is reduced as a result of crack-tip blunting or the formation of some wear-protective load-bearing areas from the corrosion products. In the following analysis, only the corrosion-enhanced microcrack propagation will be considered. According to studies on corrosion fatigue [66–68], the rate of crack growth, (da/dn)e , under a given amplitude of stress intensity in a deleterious environment comprises three components:         da da da da = + + (24) dn e dn r dn cf dn s where (da/dn)r is the rate of crack growth in a reference environment where the ‘pure’ mechanical fatigue occurs, (da/dn)cf represents the crack growth rate due to the interaction of cyclic mechanical loading (fatigue) and attack of environment and (da/dn)s is the contribution by sustained-load crack growth (that is, by ‘stress corrosion cracking’) at stress intensity levels above KISCC [69].

Under corrosion–wear conditions, (da/dn)s essentially represents a steady microcrack growth due to residual stresses at the crack tip when the region is not in contact with the opposite rubbing surface; it is therefore dependent of time and surface deformation/load. It is also temperature-dependent [69] as corrosion reactions are involved in the process. Wei and Shim [68] derived an expression for corrosion fatigue, (da/dn)cf , of steels in water by assuming that the chemical reaction step of water molecules with the steel surface to generate hydrogen was the control step in promoting embrittlement at the crack tip: 

da dn

 cf

   −1 = gcfs 1 − exp fτi

(25)

The term gcfs ≡ (da/dn)cfs denotes a maximum attainable crack growth rate under given conditions and is independent of temperature and frequency. τ i is a characteristic reaction time for the chemical reaction controlling the corrosion fatigue process. Although the above equation was derived by assuming a particular reaction step, it can be expected that in other environments and for other metals, some other controlling step of chemical or electrochemical reactions causing weakening of materials at the crack tip will occur and τ i will be the characteristic time for the corresponding reaction step. The same concept can be applied to the case of corrosion–wear. By applying Eq. (25) and substituting Eq. (24) into Eq. (22), the time, tc , to generate a wear debris particle with a diameter D can be obtained:    −1 −1 tc = D gr + gcfs 1 − exp + gs f −1 fτi 

(26)

where gr ≡ (da/dn)r and gs ≡ (da/dn)s . Substitute Eq. (26) into Eq. (23), the generation rate of wear debris particles, N, during corrosion–wear is obtained N = Nc fD

−1



    −1 gr + gcfs 1 − exp + gs fτi

(27)

The material loss, Vw , due to wear in the presence of corrosion is thus obtained by substituting Eq. (27) into Eq. (21): Vw =

πD2 Nc Aa ft 6

    −1 + gs (28) gr + gcfs 1 − exp fτi



In Eq. (28), the ‘pure’ wear component, Vwo , that would occur in a reference environment without corrosion is equal to Vwo =

πD2 Nc Aa ft gr 6

(28a)

while the corrosion-induced wear is represented by πD2 Nc Aa ft

Vw = 6

    −1 + gs gcfs 1 − exp fτi



(28b)

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6. Discussion on the modelling results of wear in aqueous corrosion environments: construction of wear map for sliding in aqueous conditions Expressions for the contributions of corrosion and wear to the overall material loss during corrosion–wear have been obtained in Eqs. (20) and (28), respectively. However, data for several of the parameters in these equations are not available either from the literature or from experimental estimations. It is therefore difficult at this stage to make a generalised quantitative assessment of the model. Nevertheless, the model covers some of the important issues involved in corrosion–wear and provides a useful basis for further discussion and development. In order to assess the relative importance of corrosioninduced wear, Vw , and wear-induced corrosion, Vc , in causing the combined effect of corrosion and wear, the ratio,

Vw / Vc , can be used as a criterion. If this ratio is less than some critical value, then the corrosion–wear can be described as wear-induced corrosion dominated. Otherwise, the process is dominated by corrosion-induced wear. The expression for Vw in Eq. (28b) is complicated and contains parameters for crack growth rates which are closely related to the load conditions and to mechanical properties of the material but which cannot be explicitly expressed. If it is assumed that Vw is proportional to load, W, and is inversely proportional to the material hardness, H, as has been observed in many of the corrosion–wear studies [24,27,28,70,71], then

Vw W/H ∝

Vc [Aatom t/(ze Fρ)]Kw l(W/H)1/2 (i0 − ip )fτ0 × [1 − exp(−1/fτ0 )] or   2    −1 W α = fτ0 1 − exp H fτ0

(29)

where α is a constant. Taking an arbitrary value of α = 25 (to make the values of W/H fall in the reasonable range for normal experimental conditions), Eq. (29) is plotted in Fig. 10 for the transition boundary between the corrosion-induced wear dominated regime and the wearinduced corrosion dominated regime. According to this simple map, the corrosion–wear tends to be dominated by wear-induced corrosion at low loads and at high frequencies of interactions between the rubbing surfaces. On the other hand, at high loads and low sliding frequencies and for metals with high passivation capabilities (low τ 0 ), the wear regime tends to be dominated by corrosion-induced wear. The concept developed in the current model can be applied to interpret some of the experimental observations reported in the literature. For example, Iwabuchi et al. found that the enhancement of mass loss for sliding wear of stainless steel [72,73] and SKD61 die steel [74] against an alumina ball in sea water and in Na2 SO4 solution was mainly due to wear-induced corrosion. However, Li and co-workers [24–28] have observed that corrosion-induced wear for stainless steels in various aqueous solutions was more dominant. The major difference in experimental conditions in these cases was that Iwabuchi et al. [72–74]

Fig. 10. Wear–corrosion map developed from the mathematical model for sliding in aqueous conditions, showing the dominant regime transitions between corrosion-induced wear and wear-induced corrosion. The ratio, W/H, between load, W, and material hardness, H, in the vertical coordinate axis represents the relative loading intensity, while the dimensionless number, 1/(fτ 0 ), for the horizontal coordinate axis represents the relative time for the corrosion-assisted crack propagation; f is the contact frequency between the opposing rubbing surfaces and τ 0 is a characteristic time for the corrosion passivation reaction of the metal. Domains of experimental conditions by various research groups are shown in the shaded regions and by the star.

used a ball-on-disk reciprocating wear rig (6.4 mm alumina ball, 10–50 N, 1.5 mm amplitude reciprocating at 8.3 Hz) while Li and co-workers [24–28] used a pin-on-ring continuous sliding wear machine (6 mm alumina ball, 38 mm diameter ring, 0.025–0.19 m s−1 , 5–95 N). The time interval between two successive contact between the ball and the given point on the specimen surface was 60.2 ms in Iwabuchi et al.’s experiments which is much shorter than the repassivation time, τ 0 , of the alloys (typically approximately 200 ms [74]), while this time interval for Li and co-workers rig was 628–4773 ms which is far beyond the typical repassivation time of typical 200 ms for most of the materials studied. Thus, the metal surface was always at the active dissolution state during sliding in Iwabuchi et al.’s tests, leading to a large contribution of corrosion to the total corrosion–wear loss. On the other hand, the active dissolution and repassivation process in the pin-on-ring rig used by Li and co-workers took only a small fraction of the total sliding time; processes damaging the near- and sub-surface layer of the material such as corrosion, stress corrosion, corrosion fatigue, hydrogen embrittlement and other processes had enough time to take place. These processes can greatly accelerate the initiation and propagation of microcracks in the generation of wear debris, significantly increasing the synergistic effect due to corrosion-induced wear. Assuming that the characteristic repassivation time, τ 0 , of the alloys is equal to 200 ms and taking a value of Hv2500 MPa for the hardness of the stainless steels, the experimental conditions of the two groups appear in the wear-induced corrosion dominated region and the corrosion-induced wear dominated region, respectively, on the wear map in Fig. 10. Yahagi and Mizutani [75] investigated the effect of off-time (the time interval at which the load was not applied) during a cyclic loading (for 60 s)—unloading test on corrosion–wear

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of grey cast iron in sulphuric acid (65% H2 SO4 ) on a pinon-disk (continuous sliding) wear rig. It was found that the corrosion–wear rate of the iron initially increased considerably with increase in the unloading time (off-time) and, after reaching a maximum wear rate at an off-time of approximately 10 s, decreased with further increase in the off-time. Above 100 s, the wear rate reduced to a level similar to the rate in a continuous sliding test. Their experimental conditions most probably fall within the corrosion-induced wear dominated region on the wear map, as indicated by the star in Fig. 10, with the following parameters (assuming τ 0 = 200 ms): (fτ 0 )−1 = 4.1, W/H = 0.0065. Indeed, it was determined that the corrosion only contributed less than 3.5% to the total material loss even in the prolonged off-time immersion. According to the present model, during the unloading period (the off-time), some activation process promoting the initiation and propagation of microcracks within the highly strained wear surface might have taken place, which would greatly facilitate the generation of more and larger wear debris particles in the following sliding action, enhancing the wear loss. On the other hand, during the prolonged off-time immersion in the electrolyte, dissolution of the wear surface was able to blunt the tips of microcracks and reduce the number of active microcracks within the wear surface, decreasing corrosion-induced wear damage during the following sliding. Eventually, after long enough off-time, the status of the wear surface became similar to that in the continuous sliding, leading to a similar total wear loss to the continuous sliding as material loss due to corrosion is negligible (<3.5%). Garc´ıa et al. [7] investigated the sliding wear of TiN coatings sliding against corundum balls under various sliding speeds and contact frequencies. It was found that wear rate of the coating was inversely proportional to the contact frequency. Including the contact frequency as an independent factor considerably reduces scattering/spread of wear rate data as compared with using speed and load only. Although the mechanisms are different under the oxidational wear conditions described by Garc´ıa et al. [7] and in the more severe situations considered in the current paper, both involve some chemical or physico-chemical reactions/interactions between the environment of the wear surface where the activation step(s) can be potentially rate control. Therefore, the results by Garc´ıa et al. and the analysis results obtained in this paper strongly suggest that contact frequency should be taken as an independent parameter in describing or characterising the wear behaviour of materials. This model outlines the major factors affecting corrosion– wear of metals. However, many parameters are unknown. It can only be regarded as a descriptive one. Much more effort is required to justify the concepts presented here, to refine the model and to extend the application of the model to specific corrosion–wear systems. 7. Conclusions Low cycle fatigue is an important mechanism for the generation of wear debris particles during sliding wear of metals. The generation of wear debris particles can be described as a process of microcrack initiation and propagation similar to that

occurring in low cycle fatigue. The presence of reactive species in the environment can affect the generation of wear debris during sliding wear due to chemically activated reaction(s) at the crack tip that weaken(s) the bonding of atoms at the tip, increasing the rate of generation of wear debris particles. Through applying such a concept, many experimental observations can be successfully discussed and explained. Mathematical models for sliding wear in both gaseous and aqueous environments have been presented. For dry sliding wear, the compaction of wear debris particles on rubbing surfaces plays an important role in promoting the transitions in wear from low to high rates by forming wear-protective compact particle layers. In addition, a wear–corrosion map has been constructed from the mathematical model for sliding wear in aqueous conditions. Experimental data from various research groups are included in the map. It gives a qualitatively reasonable presentation. The ratio between the contact frequency, f, between the opposite rubbing surfaces, and the corrosion passivation rate, 1/τ 0 , i.e., fτ 0 , is found to be a very important factor in determining the dominant material loss regime for a given tribo-system. At low fτ 0 values, corrosion/wear-induced corrosion tends to be more significant in causing the overall material loss. However, corrosion-induced wear tends to be the dominant regime for material loss at high fτ 0 values. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]

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