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Effects of imposed displacement and initial coating thickness on fretting behaviour of a thermally sprayed coating
Wear 271 (2011) 1080–1085
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Effects of imposed displacement and initial coating thickness on fretting behaviour of a thermally sprayed coating Kyungmok Kim a,∗ , Alexander M. Korsunsky b a b
Department of Biomechanics and Biomaterials, Ecole Nationale Supérieure des Mines de Saint-Etienne, 158 cours Fauriel, F-42023 Saint-Etienne Cedex 02, France Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
a r t i c l e
i n f o
Article history: Received 6 October 2010 Received in revised form 25 March 2011 Accepted 10 May 2011 Available online 17 May 2011 Keywords: Fretting wear Thermally sprayed coating Lubricant Displacement Thickness
a b s t r a c t This paper describes the effects of imposed displacement and initial coating thickness on fretting wear behaviour of a thermally sprayed coating. Initial coating thickness and imposed displacement between two mating components are important parameters affecting durability of a thermally sprayed coating under fretting conditions. Nevertheless, the effects of imposed displacement and coating thickness at flatand-rounded frictional contacts of aerospace dovetail connections are not sufficiently investigated. In this paper, fretting wear experiments with a double-layer thermally sprayed coating are performed under different displacement and coating thickness conditions. The effects of the parameters are then identified by directly comparing the ratio of maximum tangential force to normal force. Experimental results show that the ratio evolutions are similar on the ratio versus accumulated reciprocal sliding distance chart within the displacement range of 0.4–0.6 mm. In addition, it is demonstrated that durability of the coating is increased with increasing the initial thickness of the coating. Finally, the effect of the initial coating thickness is described with exponential evolution law of fretting damage. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Mechanical vibration or repeated external loading leads to relative displacement between two contacting components. This relative displacement could give rise to crack initiation and propagation at frictional contact, referred as fretting fatigue. It could also bring about loss of material at contact surfaces, referred as fretting wear. At the blade/disc interface in the compression section of an aero-engine, both fretting fatigue and fretting wear occur, thereby being studied for ages [1]. In-service blades are subjected to radial oscillation and centrifugal force that lead to fretting damages at the blade/disc interface. For the purpose of reducing fretting damages, a number of anti-friction coatings have been developed and proposed [2–4]. Particularly, double-layer thermally sprayed coatings have demonstrated the ability to maintain low friction coefficient [2]. A conventional double-layer thermally sprayed coating consists of a metallic interlayer (e.g., containing elements Cu, In and Ni) and a dry film lubricant (DFL). The substrate of Ti–6Al–4V alloy is coated with the metallic interlayer by plasma spraying and then DFL by a pressurised spray system.
∗ Corresponding author. Tel.: +33 477 429 313; fax: +33 477 499 694. E-mail addresses: [email protected], [email protected] (K. Kim). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.05.013
Fretting wear performance of a low friction coating is typically evaluated with Coulomb friction coefficient. The friction coefficient is expressed as the ratio of maximum tangential force to normal force in a gross slip regime, and it varies according to surface conditions such as lubrication, surface roughness, or pre-treatment. Friction coefficient evolution of a low friction coating usually consists of three distinct stages. At a primary stage, friction coefficient shortly increases or decreases due to initial surface roughness, this period is called as the initial ‘running-in’. After the primary stage, friction coefficient remains almost steady or shows small variance while coating thickness is progressively reduced (secondary stage). Once the coating thickness becomes reduced to a critical value, friction coefficient starts to increase rapidly (tertiary stage). The friction coefficient at this stage can be described by exponential evolution law of fretting damage [5]. That is, the friction coefficient growth rate is expressed with friction coefficient itself. Imposed displacement is one of important parameters affecting fretting behaviour of a low friction coating. Three distinct slip regimes appear according to imposed displacement amplitude. When displacement amplitude is zero or infinitesimally small, all parts of a contact remain adhered and no slip exists over the entire extent of the contact (full stick regime). If the displacement amplitude is sufficient to make some parts of the contact slip relative to each other, stick and slip zones appear within the contact (partial
K. Kim, A.M. Korsunsky / Wear 271 (2011) 1080–1085
slip regime). On the other hand, if the displacement amplitude is larger so that all parts of the contact slip over a counter-body, a stick zone disappears and a slip zone remains (gross slip regime). The classification into these three slip regimes according to the imposed displacement amplitude is informative for understanding the nature of the fretting fatigue and fretting wear phenomena. Fouvry et al. [6] identified the transition between fatigue-dominated (partial slip) and wear-dominated (mixed or gross slip) regimes by analyzing energy dissipation. Varenberg et al. [7] investigated the transitions among different slip regimes on uncoated systems and proposed slip index for identifying the transitions. Hager et al. [8] characterized mixed and gross slip regimes in Ti–6Al–4V interfaces by investigating the amount of wear with respect to displacement amplitude. Transition between mixed and gross slip regimes was identified on effective wear versus displacement amplitude plots. Chen and Zhou [9] investigated the transition between fretting wear and reciprocating sliding wear by measuring wear coefficient and wear volume on worn surfaces of steel. Vingosbo and Soderberg [10] investigated the effect of imposed displacement amplitude in terms of a fretting fatigue life and wear rate relationship. It was identified that there exists a coincidence of changes in wear rate and fatigue life between different slip regimes. Jin and Mall [11] investigated effects of independent pad displacement on fretting fatigue behaviour of Ti–6Al–4V alloy. Three slip regimes were identified with the evolution, not the shape, of fretting loops (tangential force–displacement). A slip regime was changed from partial slip to mixed slip and then to gross slip with increasing displacement range. Lee and Mall [12] identified the transition from mixed to gross slip on shot peened Ti–6Al–4V alloy. The transition was exhibited at a displacement of 0.05 mm regardless of the magnitude of applied bulk stress. However, these specimens used for the papers were not coated. Mohrbacher et al. [13] performed fretting tests with TiN and CVD diamond coatings under different imposed displacement conditions. The transition between partial slip and gross slip regime was identified on the tangential force versus number of cycles chart. Sabeya et al. [14] investigated the effect of imposed displacement on CuNiIn and CuNiSi coatings. The boundary between wear and seizure was established by performing fretting wear tests. The initial thickness of a coating is another critical parameter affecting durability of a coating. Zhou and Vincent [15] investigated the effect of initial coating thickness on polystyrene coatings by using ball-on-disc fretting arrangement. Friction coefficient growth rates between a thin coating and a thick one were similar to each other until about 700 fretting cycles. After the cycle, a friction coefficient value of a thin coating exceeded 1.2, since interaction between substrates occurred. Wei et al. [16] investigated the effect of thickness on fretting wear behaviour of CVD diamond coatings on steel substrates. It was found that thicker diamond coatings were worn out more smoothly. Kreines et al. [17] studied the effect of diamond film thickness on lifetime under fretting wear conditions. Fretting wear rate of the diamond film was independent of the initial film thickness. In addition, the relation between the film thickness and lifetime was non-linear, and small increase in the thickness resulted to dramatic increase in lifetime. Recently, Mohd Tobi et al. [18] investigated fretting wear behaviour of a thin, hard diamond-like coating deposited on high strength steel experimentally. In addition, computational models were developed and effects of coating thickness, coating modulus, and friction coefficient were studied. It was identified that a power–law relationship exists between wear life and number of fretting cycles. In this paper, effects of imposed displacement magnitude and initial coating thickness were investigated on thermally sprayed coated systems. Fretting wear tests with flat-and-rounded contact geometries were performed with various displacement magnitudes as well as different coating thicknesses. Friction evolution
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Fig. 1. Schematic illustrations of the fretting wear testing apparatus and samples. (a) Fretting test rig, and (b) geometries of a specimen (left) and a fretting pad (right). An initial contact size was 80 mm2 without applying normal force.
and durability of a thermally sprayed coating were then directly compared. 2. Experimental setup 2.1. Fretting test rig Fig. 1a shows the diagrammatic view of a fretting wear testing machine. The testing machine consists of a hydraulic ram, a 125 kN load cell, a cast iron floating chamber mounted on a machine base, two hydraulic pistons, a pair of fretting pads, a specimen, and a LVDT (linear voltage displacement transducer). One rectangularparallelepiped specimen and a pair of fretting pads with flat-and rounded geometry shown in Fig. 1b were used to perform each fretting wear test. The specimen was connected to the cross-head of the testing machine via a threaded grip with a double-wedge insert allowing pre-load to be applied to the specimen. Fretting pads were pressed against the specimen through a pair of floating hydraulic cylinders capable of moving horizontally along a line perpendicular to the specimen axis. The specimen then moved vertically within prescribed cross-head displacement range. The vertical movement of the specimen induced slip between contacting surfaces. The prescribed cross-head displacement range was sufficiently large to exceed a displacement due to a specimen elastic compliance. During a test, a normal force applied to both pads was maintained as constant and equal through the use of a hydraulic accumulator. A tangential force at each contact was measured with the load cell of the testing machine. Friction coefficient in a gross slip regime was computed as the ratio of the tangential force to the normal force induced by the hydraulic cylinders onto each pad. Relative displacement between the crosshead and the floating chamber was continuously measured with a LVDT (the nominal accuracy of about
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15000
0.7 0.6 mm
0.6
0.5 mm 0.5
0.4 mm
Qmax P 0.4
0.3 0.15 mm
0.2
Number of cycles at Qmax/P of 0.39
0.8
13000 12000 9000 6000 6000
4500
3000
0.1
0 0
0.4 0
3000
6000
9000
12000
15000
0.5 Imposed displacement (mm)
0.6
Number of cycles Fig. 3. Direct comparison of number of cycles. Fig. 2. Evolution of the ratio of the maximum tangential force (Qmax ) to normal force (P) at various imposed displacements. Qmax /P corresponds to friction coefficient in a gross slip regime. Labels denote imposed displacement magnitudes.
0.01 mm) attached to the floating chamber. Meanwhile, a closed loop control of a displacement (i.e., adjusting a displacement automatically in the course of a fretting test) was not supported in this study. 2.2. Materials and test conditions A specimen and a pad were made of Ti–6Al–4V alloy. The surface of substrate of a specimen was coated with a thermally sprayed double layer coating by plasma spraying technique. The substrate of a specimen was grit blasted and then coated with a metallic interlayer (e.g., containing elements Cu (59% in weight), Ni (36%), and In (5%)). In the atmospheric plasma spraying technique, argon and hydrogen were used as gases. Spray distance of ∼100 mm and spray rate of 5.6 × 10−4 kg/s were applied with a current of 500 A and a voltage of 70 V. Maximum particle velocity was 4.5 × 105 mm/s. A dry film lubricant (DFL) layer was then applied on the metallic interlayer in the form of epoxy matrix loaded with MoS2 particles. The dry film lubricant layer was also deposited on the surfaces of pads. The pads were shot peened prior to being coated (230R8A at 200% coverage). Shot size specification 230R corresponds to the nominal shot size (90% pass) of 0.6 mm. 8A corresponds to arc height of 0.2 mm. Initial nominal thickness of a coating on a specimen was around 0.05–0.08 mm (0.025–0.035 mm for an interlayer and 0.025–0.045 mm for a top coat). The thickness of a coating was confirmed by measurements using ultrasound, X-ray and ball cratering techniques. On the other hand, the coating on a pad had a thickness around 0.03–0.05 mm. The coated specimen was clamped between two pads that were pressed against the specimen surface with the force of approximately 10 kN (contact pressure of ∼125 MPa). These conditions simulate the geometric and loading conditions experienced in aerospace components. Displacement magnitudes of 0.15, 0.4, 0.5 and 0.6 mm were chosen for investigating the effect of imposed displacement on a coating. Each fretting test was performed at a frequency of 2.5 Hz. The ratio of the maximum tangential force to normal force was monitored in the course of the experiment as a function of the number of cycles and of the total distance slid. Experiments were terminated when the ratio exceeded about 0.5 because a coating is removed above the value.
conditions. Fretting wear tests at imposed displacements of 0.5 and 0.6 mm were interrupted when the ratio reached 0.47 and 0.52, respectively. Initial values of Qmax /P rapidly increased until about 0.2 (initial running-in period). The values of Qmax /P then decreased slowly, ranging from 0.1 to 0.13. Finally, the values showed strong increase after 3000 cycles. Meanwhile, a fretting test with a displacement of 0.4 mm (dark thin line) was interrupted when the ratio was 0.39. The values also decreased and strongly increased, following the initial running-in period. On the other hand, a test with a displacement of 0.15 mm was terminated after 15,000 cycles. A value of Qmax /P was not significantly changed and remained around 0.12. Fig. 3 shows direct comparison of numbers of cycles at the Qmax /P value of 0.39. It is apparent that the number of cycles at 0.39 decreases with increasing imposed displacement magnitude. When the imposed displacement was increased up to 1.5 times, the number of cycles at the value was reduced by approximately one third. Fig. 4 shows Qmax /P evolutions of the coatings with different initial coating thicknesses. Fretting tests were performed at an imposed displacement of 0.6 mm and a frequency of 2.5 Hz. The evolution labeled as 0.05–0.08 mm in Fig. 4 is equal to that of 0.6 mm shown in Fig. 2. When the initial thickness of a coating was increased two times, durability of a coating was also increased two times in terms of the number of cycles.
0.8 0.7 0.05-0.08 mm
0.6 0.5 Qmax P 0.4
0.3 0.2 0.1 0 0
3. Results and discussion Fig. 2 illustrates the evolution of the ratio of the maximum tangential force (Qmax ) to normal force (P) under various displacement
0.1-0.15 mm
3000
6000
9000 Number of cycles
12000
15000
Fig. 4. Qmax /P evolutions of thermally sprayed double layer coatings with different coating thicknesses. Labels represent the thickness variance of the coating on a specimen.
K. Kim, A.M. Korsunsky / Wear 271 (2011) 1080–1085
a
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Tangential force (Q, kN) 3 2 1
δi 0 -0.3
-0.2
-0.1
0
0.1
0.2
-1 -2
0.3 Displacement (mm)
δt
-3
b
-0.3
-0.2
Tangential force (Q, kN) 6 5 4 3 2 δi 1 0 -0.1 -1 0 0.1 0.2 -2 -3 -4 -5 δt -6
Fig. 6. Energy ratio evolutions at various imposed displacements. Labels denote imposed displacement magnitudes.
0.3 Displacement (mm)
(b) Fig. 5. Two fretting loops after (a) the initial cycle and (b) 8600 cycles. ıi denotes sliding distance and ın denotes total displacement.
During a fretting test performed at an imposed displacement of 0.5 mm, fretting loops shown in Fig. 5 were produced. The shape of a fretting loop varies according to a slip regime. Fig. 5a shows an initial fretting loop. The shape of the fretting loop is quasirectangular, maintaining a sliding distance of 0.38 mm. In a slip zone, a measured tangential force shows small change with respect to a displacement. Possible reasons may be variance of initial surface roughness between two contact sides or small difference of experimental setup between two pads. On the other hand, Fig. 5b illustrates a fretting loop after 8600 cycles, having a sliding distance of 0.03 mm. The shape of the fretting loop is similar to that of plain fatigue hysteresis loop (stress–strain). The area within a fretting loop is equal to energy dissipated to a contact surface. Dissipated energy is informative, since the ratio of dissipated energy to total energy is useful for identifying slip regimes [11]. The ratio of dissipated energy (Ed ) to total energy (Et ), so-called energy ratio, was defined as Energy ratio =
Ed Et
Energy ratio remained above 0.4 throughout the test. On the other hand, a grey thin line indicates energy ratio measured at an imposed displacement of 0.5 mm. Energy ratio came to 0.2 after 5700 cycles, indicating that a slip regime was changed from a gross slip to a partial slip. The energy ratio (a dark thin line) measured at a displacement of 0.4 mm came to 0.2 after 8400 cycles, and Qmax /P was 0.34 at the energy ratio value. It was observed that Qmax /P was continuously increased until 11,000 cycles though the test was performed in a partial slip regime. On the contrary, energy ratio values at an imposed displacement of 0.15 mm remained below 0.2 throughout the test. Fig. 7 shows worn surfaces of a specimen and a pad captured after 5600 cycles. The fretting test was conducted at a displacement of 0.6 mm and completed in a gross slip regime (at a friction coefficient of 0.52). Although some parts of a coating remained within the contact area, substrate size emerged at the contact surface was large to increase friction coefficient. It was also observed that nonuniform wear occurred on the surfaces. This non-uniformity may result from variances of initial surface roughness of a top coat and initial coating thickness. Note that the range of initial coating thickness was 0.05–0.08 mm. In the author’s earlier paper [3], remaining thickness of a thermally sprayed double layer coating was determined on worn surfaces after interrupting fretting wear tests at various friction coefficients. The relation between thickness coefficient (the ratio of the remaining coating thickness to an initial value) and friction coefficient was identified; thickness coefficient and friction coefficient were initially decreased with increasing number of cycles. Finally, the thickness coefficient on a specimen
(1)
where Et is equal to 2Qmax ın . In this study, Ed was computed by Gauss-Green formula presented in Appendix A. It is suggested that if energy ratio remains above 0.2 during whole cycles, a fretting test is carried out under a gross slip regime. In a gross slip regime, Qmax /P corresponds to friction coefficient. Fig. 6 shows energy ratio values measured at four different imposed displacements. A dark bold line denotes energy ratio of a fretting test performed at an imposed displacement of 0.6 mm.
Fig. 7. Worn surfaces of a specimen and a pad captured at Qmax /P of 0.52. The left image is a worn specimen and the right one is a worn pad.
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0.8 0.7 0.6 mm
0.6 0.5 mm 0.5 Qmax P 0.4
0.3
0.4 mm
0.2 0.1 0.15 mm
0
400
0
800 1200 1600 2000 Accumulated reciprocal sliding distance (mm)
2400
Fig. 8. Qmax /P evolution of a thermally sprayed double layer coating with respect to accumulated reciprocal sliding distance. Labels denote imposed displacement magnitudes.
was increased along with friction coefficient, since some parts of coating material on a pad were transferred to the surface of a specimen. The relation allows evaluating wear volume evolution of a thermally sprayed double layer coating tested at various displacements and coating thicknesses. Fig. 8 shows Qmax /P evolutions with respect to accumulated reciprocal sliding distance. The accumulated reciprocal sliding distance (S) is defined as S=
N
ıi
(2)
i=1
where N is the number of cycles. Within the displacement range of 0.4–0.6 mm, Qmax /P evolutions are similar each other. However, values of Qmax /P at a displacement of 0.15 mm are completely different from those measured within the displacement range of 0.4–0.6 mm. Fig. 9 shows Qmax /P evolutions of tests performed with two different initial coating thicknesses. A thick coating (0.1–0.15 mm in thickness) showed a final sliding distance of 3500 mm, maintaining longer durability than a thin coating (0.05–0.08 mm in thickness). The Qmax /P evolutions presented in Figs. 8 and 9 do not contain effects of elastic compliances of a test rig and a specimen. Thus, the plot with the
accumulated reciprocal sliding distance allows directly comparing Qmax /P evolutions of coatings performed at free displacements or with different test rigs. Exponential evolution law introduced in the author’s earlier paper [5] describes friction coefficient behaviour of a low friction coating in a gross slip regime. Friction coefficient growth rate can be expressed with friction coefficient itself in the tertiary stage (strong increase) of a friction coefficient evolution. That is, relation between friction coefficient (f) and accumulated reciprocal sliding distance (S) is a power law, i.e. df = Cf n dS
(3)
where C is the damage rate constant and n is the damage exponent. If n is unity, friction coefficient is determined as f = f 0 eC(S−S0 )
(4)
0.5
where f0 is initial friction coefficient and S0 is initial sliding distance. Fig. 10 illustrates the determination of parameters C and n in Eq. (3) on the bilogarithmic scale. It is found from the reported quality of fit (R) that the power law functions provide an adequate description. The slope of the linear fit is associated with the damage exponent n. As shown in the figure, the damage exponent values come out close to unity. But damage rate constants are different each other, since the initial thickness of a coating is different. It is identified that the damage rate constant of a thick coating (0.10–0.15 mm in thickness) is about two times higher than that of a thin one (0.05–0.08 mm in thickness).
0.4
4. Conclusions
0.8 0.7 0.05-0.08 mm
0.6
Qmax P
Fig. 10. Illustration for the determination of parameters C and n on the bilogarithmic scale. The points came from the curve fit. Markers () are experimental data of a thin coating (0.05–0.08 mm in thickness). Markers (♦) are experimental data of a thick coating (0.10–0.15 mm in thickness).
0.1-0.15 mm
0.3 0.2 0.1 0 0
400
800 1200 1600 2000 2400 2800 3200 Accumulated reciprocal sliding distance (mm)
3600
Fig. 9. Qmax /P evolutions at different initial thicknesses of a coating. Labels denote the initial thickness of a coating. Markers represent experimental data and continuous lines are curve fits (Appendix B).
This paper investigated effects of imposed displacement and initial coating thickness on a thermally sprayed coated system. Thermally sprayed coatings are usually used at the blade/disc interface in the compression section of aero-engines in order to increase fretting fatigue and wear life. In this paper, fretting wear experiments on double-layer thermally sprayed coatings were performed with an in-line test rig. One specimen and two flat-and-rounded pads were used for each fretting test. For investigating the effect of displacement magnitude on a thermally sprayed coating, four different displacement magnitudes were chosen and applied. The number of cycles at
K. Kim, A.M. Korsunsky / Wear 271 (2011) 1080–1085
Qmax /P of 0.39 decreased with increasing displacement magnitude. Direct comparison was also performed on the Qmax /P versus accumulated sliding distance chart. Experimental results show that Qmax /P evolutions with respect to sliding distance in the range of 0.4–0.6 mm are similar to each other. Energy ratio evolutions were used for identifying slip regimes during fretting tests. It was identified that fretting tests at imposed displacements of 0.4 and 0.5 mm were performed within in mixed slip regimes. For investigating the effect of initial coating thickness on a thermally sprayed coating, two different coating thicknesses were chosen. Fretting tests were performed under the same experimental conditions. It is apparent that durability of a coating increases with increasing initial coating thickness. Exponential evolution law of fretting damage was applied to friction coefficient evolutions. It is identified that the damage rate constant of a thick coating is higher than that of a thin one. In conclusion, obtained results offer fretting wear behaviour of a thermally sprayed coating used for aerospace components. In addition, proposed methods help to evaluate a low friction coating effectively. Further investigation will be focused on effects of experimental parameters such as normal force, temperature, etc. Acknowledgements The author wishes to acknowledge the support of Rolls-Royce plc and the Department of Trade and Industry (DTI) under project SMIGTE at Oxford University Technology Centre in Solid Mechanics, established in collaboration with Rolls-Royce plc. Particular thanks are due to John Schofield (Rolls-Royce plc) for his encouragement and advice. Appendix A. Calculation of dissipated energy Gauss-Green formula is useful for calculating areas within fretting loops in a gross slip regime and in a partial slip regime. The area of the fretting loop in the tangential force (Q)–displacement (d) plane is determined as 1 Area = 2
n (0.5(di+1 + di )(Qi+1 − Qi ) − 0.5(Qi+1 + Qi )(di+1 − di )) i=1
where n is the number of measured points in each fretting loop.
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Appendix B. Curve fitting Fit function: f = f0 + a × Sb , f0 is initial friction coefficient, S is accumulated sliding distance Index 1 2
Coating thickness (mm) 0.05–0.08 0.10–0.15
f0
a
B
Quality of fit (R)
0.11 0.11
1.02 × 10−12 3.33 × 10−13
3.05 3.40
0.99 0.99
References [1] D.A. Hills, D. Nowell, Mechanics of Fretting Fatigue, Springer, 1994. [2] A.M. Korsunsky, K. Kim, Dissipated energy and friction coefficient evolution during fretting wear of solid lubricant coatings, Tribology International 43 (5–6) (2010) 861–867. [3] A.M. Korsunsky, A.R. Torosyan, K. Kim, Development and characterization of low friction coatings for protection against fretting wear in aerospace components, Thin Solid Films 516 (16) (2008) 5690–5699. [4] K. Kim, A.M. Korsunsky, Dissipated energy and fretting damage in CoCrAlY–MoS2 coatings, Tribology International 43 (2010) 676–684. [5] K. Kim, A.M. Korsunsky, Exponential evolution law of fretting wear damage in low friction coatings for aerospace components, Surface and Coatings Technology 202 (2008) 5838–5846. [6] S. Fouvry, P. Kapsa, L. Vincent, Analysis of sliding behaviour for fretting loadings: determination of transition criteria, Wear 185 (1995) 35–46. [7] M. Varenberg, I. Etsion, G. Halperin, Slip index: a new unified approach to fretting, Tribology Letters 17 (2004) 569–573. [8] C.H. Hager, J.H. Sanders, S. Sharma, Characterization of mixed and gross slip fretting wear regimes in Ti6Al4V interfaces at room temperature, Wear 257 (2004) 167–180. [9] G.X. Chen, Z.R. Zhou, Study on transition between fretting and reciprocating sliding wear, Wear 250 (2001) 665–672. [10] O. Vingsbo, S. Soderberg, On fretting maps, Wear 126 (1988) 131–147. [11] O. Jin, S. Mall, Effects of independent pad displacement on fretting fatigue behaviour of Ti–6Al–4V, Wear 253 (2002) 585–596. [12] H. Lee, S. Mall, Fretting behavior of shot peened Ti–6Al–4V under slip controlled mode, Wear 260 (2006) 642–651. [13] H. Mohrbacher, J.P. Celis, J.R. Roes, Laboratory testing of displacement and load induced fretting, Tribology International 18 (5) (1995) 269–278. [14] G.R. Sabeya, J.-Y. Paris, J. Denape, Fretting wear of a coated titanium alloy under free displacement, Wear 264 (2008) 166–176. [15] Z.R. Zhou, L. Vincent, Lubrication by thin polystyrene coating in fretting, Wear 231 (1999) 179–184. [16] Q. Wei, Z.M. Yu, M. Ashfold, Z. Chen, L. Wang, L. Ma, Effects of thickness and cycle parameters on fretting wear behaviour of CVD diamond coatings on steel substrates, Surface and Coatings Technology 205 (2010) 158–167. [17] L. Kreines, G. Halperin, I. Etsion, M. Varenberg, A. Hoffman, R. Akhvlediani, Fretting wear of thin diamond films deposited on steel substrates, Diamond and Related Materials 13 (2004) 1731–1739. [18] A.L. Mohd Tobi, J. Ding, S. Pearson, S.B. Leen, P.H. Shipway, The effect of gross sliding fretting wear on stress distributions in thin W-DLC coating systems, Tribology International 43 (2010) 1917–1932.
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Wear journal homepage: www.elsevier.com/locate/wear
Effects of imposed displacement and initial coating thickness on fretting behaviour of a thermally sprayed coating Kyungmok Kim a,∗ , Alexander M. Korsunsky b a b
Department of Biomechanics and Biomaterials, Ecole Nationale Supérieure des Mines de Saint-Etienne, 158 cours Fauriel, F-42023 Saint-Etienne Cedex 02, France Department of Engineering Science, University of Oxford, Parks Road, Oxford OX1 3PJ, UK
a r t i c l e
i n f o
Article history: Received 6 October 2010 Received in revised form 25 March 2011 Accepted 10 May 2011 Available online 17 May 2011 Keywords: Fretting wear Thermally sprayed coating Lubricant Displacement Thickness
a b s t r a c t This paper describes the effects of imposed displacement and initial coating thickness on fretting wear behaviour of a thermally sprayed coating. Initial coating thickness and imposed displacement between two mating components are important parameters affecting durability of a thermally sprayed coating under fretting conditions. Nevertheless, the effects of imposed displacement and coating thickness at flatand-rounded frictional contacts of aerospace dovetail connections are not sufficiently investigated. In this paper, fretting wear experiments with a double-layer thermally sprayed coating are performed under different displacement and coating thickness conditions. The effects of the parameters are then identified by directly comparing the ratio of maximum tangential force to normal force. Experimental results show that the ratio evolutions are similar on the ratio versus accumulated reciprocal sliding distance chart within the displacement range of 0.4–0.6 mm. In addition, it is demonstrated that durability of the coating is increased with increasing the initial thickness of the coating. Finally, the effect of the initial coating thickness is described with exponential evolution law of fretting damage. © 2011 Elsevier B.V. All rights reserved.
1. Introduction Mechanical vibration or repeated external loading leads to relative displacement between two contacting components. This relative displacement could give rise to crack initiation and propagation at frictional contact, referred as fretting fatigue. It could also bring about loss of material at contact surfaces, referred as fretting wear. At the blade/disc interface in the compression section of an aero-engine, both fretting fatigue and fretting wear occur, thereby being studied for ages [1]. In-service blades are subjected to radial oscillation and centrifugal force that lead to fretting damages at the blade/disc interface. For the purpose of reducing fretting damages, a number of anti-friction coatings have been developed and proposed [2–4]. Particularly, double-layer thermally sprayed coatings have demonstrated the ability to maintain low friction coefficient [2]. A conventional double-layer thermally sprayed coating consists of a metallic interlayer (e.g., containing elements Cu, In and Ni) and a dry film lubricant (DFL). The substrate of Ti–6Al–4V alloy is coated with the metallic interlayer by plasma spraying and then DFL by a pressurised spray system.
∗ Corresponding author. Tel.: +33 477 429 313; fax: +33 477 499 694. E-mail addresses: [email protected], [email protected] (K. Kim). 0043-1648/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2011.05.013
Fretting wear performance of a low friction coating is typically evaluated with Coulomb friction coefficient. The friction coefficient is expressed as the ratio of maximum tangential force to normal force in a gross slip regime, and it varies according to surface conditions such as lubrication, surface roughness, or pre-treatment. Friction coefficient evolution of a low friction coating usually consists of three distinct stages. At a primary stage, friction coefficient shortly increases or decreases due to initial surface roughness, this period is called as the initial ‘running-in’. After the primary stage, friction coefficient remains almost steady or shows small variance while coating thickness is progressively reduced (secondary stage). Once the coating thickness becomes reduced to a critical value, friction coefficient starts to increase rapidly (tertiary stage). The friction coefficient at this stage can be described by exponential evolution law of fretting damage [5]. That is, the friction coefficient growth rate is expressed with friction coefficient itself. Imposed displacement is one of important parameters affecting fretting behaviour of a low friction coating. Three distinct slip regimes appear according to imposed displacement amplitude. When displacement amplitude is zero or infinitesimally small, all parts of a contact remain adhered and no slip exists over the entire extent of the contact (full stick regime). If the displacement amplitude is sufficient to make some parts of the contact slip relative to each other, stick and slip zones appear within the contact (partial
K. Kim, A.M. Korsunsky / Wear 271 (2011) 1080–1085
slip regime). On the other hand, if the displacement amplitude is larger so that all parts of the contact slip over a counter-body, a stick zone disappears and a slip zone remains (gross slip regime). The classification into these three slip regimes according to the imposed displacement amplitude is informative for understanding the nature of the fretting fatigue and fretting wear phenomena. Fouvry et al. [6] identified the transition between fatigue-dominated (partial slip) and wear-dominated (mixed or gross slip) regimes by analyzing energy dissipation. Varenberg et al. [7] investigated the transitions among different slip regimes on uncoated systems and proposed slip index for identifying the transitions. Hager et al. [8] characterized mixed and gross slip regimes in Ti–6Al–4V interfaces by investigating the amount of wear with respect to displacement amplitude. Transition between mixed and gross slip regimes was identified on effective wear versus displacement amplitude plots. Chen and Zhou [9] investigated the transition between fretting wear and reciprocating sliding wear by measuring wear coefficient and wear volume on worn surfaces of steel. Vingosbo and Soderberg [10] investigated the effect of imposed displacement amplitude in terms of a fretting fatigue life and wear rate relationship. It was identified that there exists a coincidence of changes in wear rate and fatigue life between different slip regimes. Jin and Mall [11] investigated effects of independent pad displacement on fretting fatigue behaviour of Ti–6Al–4V alloy. Three slip regimes were identified with the evolution, not the shape, of fretting loops (tangential force–displacement). A slip regime was changed from partial slip to mixed slip and then to gross slip with increasing displacement range. Lee and Mall [12] identified the transition from mixed to gross slip on shot peened Ti–6Al–4V alloy. The transition was exhibited at a displacement of 0.05 mm regardless of the magnitude of applied bulk stress. However, these specimens used for the papers were not coated. Mohrbacher et al. [13] performed fretting tests with TiN and CVD diamond coatings under different imposed displacement conditions. The transition between partial slip and gross slip regime was identified on the tangential force versus number of cycles chart. Sabeya et al. [14] investigated the effect of imposed displacement on CuNiIn and CuNiSi coatings. The boundary between wear and seizure was established by performing fretting wear tests. The initial thickness of a coating is another critical parameter affecting durability of a coating. Zhou and Vincent [15] investigated the effect of initial coating thickness on polystyrene coatings by using ball-on-disc fretting arrangement. Friction coefficient growth rates between a thin coating and a thick one were similar to each other until about 700 fretting cycles. After the cycle, a friction coefficient value of a thin coating exceeded 1.2, since interaction between substrates occurred. Wei et al. [16] investigated the effect of thickness on fretting wear behaviour of CVD diamond coatings on steel substrates. It was found that thicker diamond coatings were worn out more smoothly. Kreines et al. [17] studied the effect of diamond film thickness on lifetime under fretting wear conditions. Fretting wear rate of the diamond film was independent of the initial film thickness. In addition, the relation between the film thickness and lifetime was non-linear, and small increase in the thickness resulted to dramatic increase in lifetime. Recently, Mohd Tobi et al. [18] investigated fretting wear behaviour of a thin, hard diamond-like coating deposited on high strength steel experimentally. In addition, computational models were developed and effects of coating thickness, coating modulus, and friction coefficient were studied. It was identified that a power–law relationship exists between wear life and number of fretting cycles. In this paper, effects of imposed displacement magnitude and initial coating thickness were investigated on thermally sprayed coated systems. Fretting wear tests with flat-and-rounded contact geometries were performed with various displacement magnitudes as well as different coating thicknesses. Friction evolution
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Fig. 1. Schematic illustrations of the fretting wear testing apparatus and samples. (a) Fretting test rig, and (b) geometries of a specimen (left) and a fretting pad (right). An initial contact size was 80 mm2 without applying normal force.
and durability of a thermally sprayed coating were then directly compared. 2. Experimental setup 2.1. Fretting test rig Fig. 1a shows the diagrammatic view of a fretting wear testing machine. The testing machine consists of a hydraulic ram, a 125 kN load cell, a cast iron floating chamber mounted on a machine base, two hydraulic pistons, a pair of fretting pads, a specimen, and a LVDT (linear voltage displacement transducer). One rectangularparallelepiped specimen and a pair of fretting pads with flat-and rounded geometry shown in Fig. 1b were used to perform each fretting wear test. The specimen was connected to the cross-head of the testing machine via a threaded grip with a double-wedge insert allowing pre-load to be applied to the specimen. Fretting pads were pressed against the specimen through a pair of floating hydraulic cylinders capable of moving horizontally along a line perpendicular to the specimen axis. The specimen then moved vertically within prescribed cross-head displacement range. The vertical movement of the specimen induced slip between contacting surfaces. The prescribed cross-head displacement range was sufficiently large to exceed a displacement due to a specimen elastic compliance. During a test, a normal force applied to both pads was maintained as constant and equal through the use of a hydraulic accumulator. A tangential force at each contact was measured with the load cell of the testing machine. Friction coefficient in a gross slip regime was computed as the ratio of the tangential force to the normal force induced by the hydraulic cylinders onto each pad. Relative displacement between the crosshead and the floating chamber was continuously measured with a LVDT (the nominal accuracy of about
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15000
0.7 0.6 mm
0.6
0.5 mm 0.5
0.4 mm
Qmax P 0.4
0.3 0.15 mm
0.2
Number of cycles at Qmax/P of 0.39
0.8
13000 12000 9000 6000 6000
4500
3000
0.1
0 0
0.4 0
3000
6000
9000
12000
15000
0.5 Imposed displacement (mm)
0.6
Number of cycles Fig. 3. Direct comparison of number of cycles. Fig. 2. Evolution of the ratio of the maximum tangential force (Qmax ) to normal force (P) at various imposed displacements. Qmax /P corresponds to friction coefficient in a gross slip regime. Labels denote imposed displacement magnitudes.
0.01 mm) attached to the floating chamber. Meanwhile, a closed loop control of a displacement (i.e., adjusting a displacement automatically in the course of a fretting test) was not supported in this study. 2.2. Materials and test conditions A specimen and a pad were made of Ti–6Al–4V alloy. The surface of substrate of a specimen was coated with a thermally sprayed double layer coating by plasma spraying technique. The substrate of a specimen was grit blasted and then coated with a metallic interlayer (e.g., containing elements Cu (59% in weight), Ni (36%), and In (5%)). In the atmospheric plasma spraying technique, argon and hydrogen were used as gases. Spray distance of ∼100 mm and spray rate of 5.6 × 10−4 kg/s were applied with a current of 500 A and a voltage of 70 V. Maximum particle velocity was 4.5 × 105 mm/s. A dry film lubricant (DFL) layer was then applied on the metallic interlayer in the form of epoxy matrix loaded with MoS2 particles. The dry film lubricant layer was also deposited on the surfaces of pads. The pads were shot peened prior to being coated (230R8A at 200% coverage). Shot size specification 230R corresponds to the nominal shot size (90% pass) of 0.6 mm. 8A corresponds to arc height of 0.2 mm. Initial nominal thickness of a coating on a specimen was around 0.05–0.08 mm (0.025–0.035 mm for an interlayer and 0.025–0.045 mm for a top coat). The thickness of a coating was confirmed by measurements using ultrasound, X-ray and ball cratering techniques. On the other hand, the coating on a pad had a thickness around 0.03–0.05 mm. The coated specimen was clamped between two pads that were pressed against the specimen surface with the force of approximately 10 kN (contact pressure of ∼125 MPa). These conditions simulate the geometric and loading conditions experienced in aerospace components. Displacement magnitudes of 0.15, 0.4, 0.5 and 0.6 mm were chosen for investigating the effect of imposed displacement on a coating. Each fretting test was performed at a frequency of 2.5 Hz. The ratio of the maximum tangential force to normal force was monitored in the course of the experiment as a function of the number of cycles and of the total distance slid. Experiments were terminated when the ratio exceeded about 0.5 because a coating is removed above the value.
conditions. Fretting wear tests at imposed displacements of 0.5 and 0.6 mm were interrupted when the ratio reached 0.47 and 0.52, respectively. Initial values of Qmax /P rapidly increased until about 0.2 (initial running-in period). The values of Qmax /P then decreased slowly, ranging from 0.1 to 0.13. Finally, the values showed strong increase after 3000 cycles. Meanwhile, a fretting test with a displacement of 0.4 mm (dark thin line) was interrupted when the ratio was 0.39. The values also decreased and strongly increased, following the initial running-in period. On the other hand, a test with a displacement of 0.15 mm was terminated after 15,000 cycles. A value of Qmax /P was not significantly changed and remained around 0.12. Fig. 3 shows direct comparison of numbers of cycles at the Qmax /P value of 0.39. It is apparent that the number of cycles at 0.39 decreases with increasing imposed displacement magnitude. When the imposed displacement was increased up to 1.5 times, the number of cycles at the value was reduced by approximately one third. Fig. 4 shows Qmax /P evolutions of the coatings with different initial coating thicknesses. Fretting tests were performed at an imposed displacement of 0.6 mm and a frequency of 2.5 Hz. The evolution labeled as 0.05–0.08 mm in Fig. 4 is equal to that of 0.6 mm shown in Fig. 2. When the initial thickness of a coating was increased two times, durability of a coating was also increased two times in terms of the number of cycles.
0.8 0.7 0.05-0.08 mm
0.6 0.5 Qmax P 0.4
0.3 0.2 0.1 0 0
3. Results and discussion Fig. 2 illustrates the evolution of the ratio of the maximum tangential force (Qmax ) to normal force (P) under various displacement
0.1-0.15 mm
3000
6000
9000 Number of cycles
12000
15000
Fig. 4. Qmax /P evolutions of thermally sprayed double layer coatings with different coating thicknesses. Labels represent the thickness variance of the coating on a specimen.
K. Kim, A.M. Korsunsky / Wear 271 (2011) 1080–1085
a
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Tangential force (Q, kN) 3 2 1
δi 0 -0.3
-0.2
-0.1
0
0.1
0.2
-1 -2
0.3 Displacement (mm)
δt
-3
b
-0.3
-0.2
Tangential force (Q, kN) 6 5 4 3 2 δi 1 0 -0.1 -1 0 0.1 0.2 -2 -3 -4 -5 δt -6
Fig. 6. Energy ratio evolutions at various imposed displacements. Labels denote imposed displacement magnitudes.
0.3 Displacement (mm)
(b) Fig. 5. Two fretting loops after (a) the initial cycle and (b) 8600 cycles. ıi denotes sliding distance and ın denotes total displacement.
During a fretting test performed at an imposed displacement of 0.5 mm, fretting loops shown in Fig. 5 were produced. The shape of a fretting loop varies according to a slip regime. Fig. 5a shows an initial fretting loop. The shape of the fretting loop is quasirectangular, maintaining a sliding distance of 0.38 mm. In a slip zone, a measured tangential force shows small change with respect to a displacement. Possible reasons may be variance of initial surface roughness between two contact sides or small difference of experimental setup between two pads. On the other hand, Fig. 5b illustrates a fretting loop after 8600 cycles, having a sliding distance of 0.03 mm. The shape of the fretting loop is similar to that of plain fatigue hysteresis loop (stress–strain). The area within a fretting loop is equal to energy dissipated to a contact surface. Dissipated energy is informative, since the ratio of dissipated energy to total energy is useful for identifying slip regimes [11]. The ratio of dissipated energy (Ed ) to total energy (Et ), so-called energy ratio, was defined as Energy ratio =
Ed Et
Energy ratio remained above 0.4 throughout the test. On the other hand, a grey thin line indicates energy ratio measured at an imposed displacement of 0.5 mm. Energy ratio came to 0.2 after 5700 cycles, indicating that a slip regime was changed from a gross slip to a partial slip. The energy ratio (a dark thin line) measured at a displacement of 0.4 mm came to 0.2 after 8400 cycles, and Qmax /P was 0.34 at the energy ratio value. It was observed that Qmax /P was continuously increased until 11,000 cycles though the test was performed in a partial slip regime. On the contrary, energy ratio values at an imposed displacement of 0.15 mm remained below 0.2 throughout the test. Fig. 7 shows worn surfaces of a specimen and a pad captured after 5600 cycles. The fretting test was conducted at a displacement of 0.6 mm and completed in a gross slip regime (at a friction coefficient of 0.52). Although some parts of a coating remained within the contact area, substrate size emerged at the contact surface was large to increase friction coefficient. It was also observed that nonuniform wear occurred on the surfaces. This non-uniformity may result from variances of initial surface roughness of a top coat and initial coating thickness. Note that the range of initial coating thickness was 0.05–0.08 mm. In the author’s earlier paper [3], remaining thickness of a thermally sprayed double layer coating was determined on worn surfaces after interrupting fretting wear tests at various friction coefficients. The relation between thickness coefficient (the ratio of the remaining coating thickness to an initial value) and friction coefficient was identified; thickness coefficient and friction coefficient were initially decreased with increasing number of cycles. Finally, the thickness coefficient on a specimen
(1)
where Et is equal to 2Qmax ın . In this study, Ed was computed by Gauss-Green formula presented in Appendix A. It is suggested that if energy ratio remains above 0.2 during whole cycles, a fretting test is carried out under a gross slip regime. In a gross slip regime, Qmax /P corresponds to friction coefficient. Fig. 6 shows energy ratio values measured at four different imposed displacements. A dark bold line denotes energy ratio of a fretting test performed at an imposed displacement of 0.6 mm.
Fig. 7. Worn surfaces of a specimen and a pad captured at Qmax /P of 0.52. The left image is a worn specimen and the right one is a worn pad.
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0.8 0.7 0.6 mm
0.6 0.5 mm 0.5 Qmax P 0.4
0.3
0.4 mm
0.2 0.1 0.15 mm
0
400
0
800 1200 1600 2000 Accumulated reciprocal sliding distance (mm)
2400
Fig. 8. Qmax /P evolution of a thermally sprayed double layer coating with respect to accumulated reciprocal sliding distance. Labels denote imposed displacement magnitudes.
was increased along with friction coefficient, since some parts of coating material on a pad were transferred to the surface of a specimen. The relation allows evaluating wear volume evolution of a thermally sprayed double layer coating tested at various displacements and coating thicknesses. Fig. 8 shows Qmax /P evolutions with respect to accumulated reciprocal sliding distance. The accumulated reciprocal sliding distance (S) is defined as S=
N
ıi
(2)
i=1
where N is the number of cycles. Within the displacement range of 0.4–0.6 mm, Qmax /P evolutions are similar each other. However, values of Qmax /P at a displacement of 0.15 mm are completely different from those measured within the displacement range of 0.4–0.6 mm. Fig. 9 shows Qmax /P evolutions of tests performed with two different initial coating thicknesses. A thick coating (0.1–0.15 mm in thickness) showed a final sliding distance of 3500 mm, maintaining longer durability than a thin coating (0.05–0.08 mm in thickness). The Qmax /P evolutions presented in Figs. 8 and 9 do not contain effects of elastic compliances of a test rig and a specimen. Thus, the plot with the
accumulated reciprocal sliding distance allows directly comparing Qmax /P evolutions of coatings performed at free displacements or with different test rigs. Exponential evolution law introduced in the author’s earlier paper [5] describes friction coefficient behaviour of a low friction coating in a gross slip regime. Friction coefficient growth rate can be expressed with friction coefficient itself in the tertiary stage (strong increase) of a friction coefficient evolution. That is, relation between friction coefficient (f) and accumulated reciprocal sliding distance (S) is a power law, i.e. df = Cf n dS
(3)
where C is the damage rate constant and n is the damage exponent. If n is unity, friction coefficient is determined as f = f 0 eC(S−S0 )
(4)
0.5
where f0 is initial friction coefficient and S0 is initial sliding distance. Fig. 10 illustrates the determination of parameters C and n in Eq. (3) on the bilogarithmic scale. It is found from the reported quality of fit (R) that the power law functions provide an adequate description. The slope of the linear fit is associated with the damage exponent n. As shown in the figure, the damage exponent values come out close to unity. But damage rate constants are different each other, since the initial thickness of a coating is different. It is identified that the damage rate constant of a thick coating (0.10–0.15 mm in thickness) is about two times higher than that of a thin one (0.05–0.08 mm in thickness).
0.4
4. Conclusions
0.8 0.7 0.05-0.08 mm
0.6
Qmax P
Fig. 10. Illustration for the determination of parameters C and n on the bilogarithmic scale. The points came from the curve fit. Markers () are experimental data of a thin coating (0.05–0.08 mm in thickness). Markers (♦) are experimental data of a thick coating (0.10–0.15 mm in thickness).
0.1-0.15 mm
0.3 0.2 0.1 0 0
400
800 1200 1600 2000 2400 2800 3200 Accumulated reciprocal sliding distance (mm)
3600
Fig. 9. Qmax /P evolutions at different initial thicknesses of a coating. Labels denote the initial thickness of a coating. Markers represent experimental data and continuous lines are curve fits (Appendix B).
This paper investigated effects of imposed displacement and initial coating thickness on a thermally sprayed coated system. Thermally sprayed coatings are usually used at the blade/disc interface in the compression section of aero-engines in order to increase fretting fatigue and wear life. In this paper, fretting wear experiments on double-layer thermally sprayed coatings were performed with an in-line test rig. One specimen and two flat-and-rounded pads were used for each fretting test. For investigating the effect of displacement magnitude on a thermally sprayed coating, four different displacement magnitudes were chosen and applied. The number of cycles at
K. Kim, A.M. Korsunsky / Wear 271 (2011) 1080–1085
Qmax /P of 0.39 decreased with increasing displacement magnitude. Direct comparison was also performed on the Qmax /P versus accumulated sliding distance chart. Experimental results show that Qmax /P evolutions with respect to sliding distance in the range of 0.4–0.6 mm are similar to each other. Energy ratio evolutions were used for identifying slip regimes during fretting tests. It was identified that fretting tests at imposed displacements of 0.4 and 0.5 mm were performed within in mixed slip regimes. For investigating the effect of initial coating thickness on a thermally sprayed coating, two different coating thicknesses were chosen. Fretting tests were performed under the same experimental conditions. It is apparent that durability of a coating increases with increasing initial coating thickness. Exponential evolution law of fretting damage was applied to friction coefficient evolutions. It is identified that the damage rate constant of a thick coating is higher than that of a thin one. In conclusion, obtained results offer fretting wear behaviour of a thermally sprayed coating used for aerospace components. In addition, proposed methods help to evaluate a low friction coating effectively. Further investigation will be focused on effects of experimental parameters such as normal force, temperature, etc. Acknowledgements The author wishes to acknowledge the support of Rolls-Royce plc and the Department of Trade and Industry (DTI) under project SMIGTE at Oxford University Technology Centre in Solid Mechanics, established in collaboration with Rolls-Royce plc. Particular thanks are due to John Schofield (Rolls-Royce plc) for his encouragement and advice. Appendix A. Calculation of dissipated energy Gauss-Green formula is useful for calculating areas within fretting loops in a gross slip regime and in a partial slip regime. The area of the fretting loop in the tangential force (Q)–displacement (d) plane is determined as 1 Area = 2
n (0.5(di+1 + di )(Qi+1 − Qi ) − 0.5(Qi+1 + Qi )(di+1 − di )) i=1
where n is the number of measured points in each fretting loop.
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Appendix B. Curve fitting Fit function: f = f0 + a × Sb , f0 is initial friction coefficient, S is accumulated sliding distance Index 1 2
Coating thickness (mm) 0.05–0.08 0.10–0.15
f0
a
B
Quality of fit (R)
0.11 0.11
1.02 × 10−12 3.33 × 10−13
3.05 3.40
0.99 0.99
References [1] D.A. Hills, D. Nowell, Mechanics of Fretting Fatigue, Springer, 1994. [2] A.M. Korsunsky, K. Kim, Dissipated energy and friction coefficient evolution during fretting wear of solid lubricant coatings, Tribology International 43 (5–6) (2010) 861–867. [3] A.M. Korsunsky, A.R. Torosyan, K. Kim, Development and characterization of low friction coatings for protection against fretting wear in aerospace components, Thin Solid Films 516 (16) (2008) 5690–5699. [4] K. Kim, A.M. Korsunsky, Dissipated energy and fretting damage in CoCrAlY–MoS2 coatings, Tribology International 43 (2010) 676–684. [5] K. Kim, A.M. Korsunsky, Exponential evolution law of fretting wear damage in low friction coatings for aerospace components, Surface and Coatings Technology 202 (2008) 5838–5846. [6] S. Fouvry, P. Kapsa, L. Vincent, Analysis of sliding behaviour for fretting loadings: determination of transition criteria, Wear 185 (1995) 35–46. [7] M. Varenberg, I. Etsion, G. Halperin, Slip index: a new unified approach to fretting, Tribology Letters 17 (2004) 569–573. [8] C.H. Hager, J.H. Sanders, S. Sharma, Characterization of mixed and gross slip fretting wear regimes in Ti6Al4V interfaces at room temperature, Wear 257 (2004) 167–180. [9] G.X. Chen, Z.R. Zhou, Study on transition between fretting and reciprocating sliding wear, Wear 250 (2001) 665–672. [10] O. Vingsbo, S. Soderberg, On fretting maps, Wear 126 (1988) 131–147. [11] O. Jin, S. Mall, Effects of independent pad displacement on fretting fatigue behaviour of Ti–6Al–4V, Wear 253 (2002) 585–596. [12] H. Lee, S. Mall, Fretting behavior of shot peened Ti–6Al–4V under slip controlled mode, Wear 260 (2006) 642–651. [13] H. Mohrbacher, J.P. Celis, J.R. Roes, Laboratory testing of displacement and load induced fretting, Tribology International 18 (5) (1995) 269–278. [14] G.R. Sabeya, J.-Y. Paris, J. Denape, Fretting wear of a coated titanium alloy under free displacement, Wear 264 (2008) 166–176. [15] Z.R. Zhou, L. Vincent, Lubrication by thin polystyrene coating in fretting, Wear 231 (1999) 179–184. [16] Q. Wei, Z.M. Yu, M. Ashfold, Z. Chen, L. Wang, L. Ma, Effects of thickness and cycle parameters on fretting wear behaviour of CVD diamond coatings on steel substrates, Surface and Coatings Technology 205 (2010) 158–167. [17] L. Kreines, G. Halperin, I. Etsion, M. Varenberg, A. Hoffman, R. Akhvlediani, Fretting wear of thin diamond films deposited on steel substrates, Diamond and Related Materials 13 (2004) 1731–1739. [18] A.L. Mohd Tobi, J. Ding, S. Pearson, S.B. Leen, P.H. Shipway, The effect of gross sliding fretting wear on stress distributions in thin W-DLC coating systems, Tribology International 43 (2010) 1917–1932.