Wear Equation
Content
Wear 255 (2003) 579–592
Wear coefficient equation for aluminium-based matrix composites against steel disc
L.J. Yang
School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore
Abstract A new formulation of the wear coefficient was developed and tested experimentally. Two different types of pin-on-disc wear tests were conducted using three commercial, A6061 aluminum-based metal–matrix composites (MMCs). One type of test resulted in a spiral track and the other a circular track. Hardened tool steel discs were used as the sliding counterface for MMC pins having 10, 15 and 20% alumina reinforcements. A new wear equation was derived and shown to be a better predictor of steady-state wear coefficients. It is based on an exponential transient wear volume equation and Archard’s equation. © 2003 Elsevier Science B.V. All rights reserved.
Keywords: Metal–matrix composites (MMCs); Transient wear; Steady-state wear; Adhesive wear; Wear coefficient
1. Introduction Metal–matrix composites are widely used in industries because of their excellent mechanical properties and wear resistance. To understand the wear behaviour of different MMC materials, wear tests are often carried out with suitable wear testing techniques. There are different types of wear mechanisms involved, for example, adhesive wear, abrasive wear, or others. However, adhesive wear is by far the most dominant form of material loss among sliding components in machinery [1]. The pin-on-disc test is a classical method commonly used for adhesive wear experiments. During the experiment, the sliding between the pin and disc may result in wear on both contact surfaces of the pair. To facilitate measurement, the pin is generally the wearing member that has a lower hardness. Although weight loss and wear rate are often used for studying the wear characteristics of test specimens, recent investigations [2,3] have found that wear coefficient is a better parameter to be used instead. This is because the wear coefficient has taken into account not only the wear rate (V/L), the applied load, but also the hardness of the wear pin or counterface which can affect the wear rate significantly. Although there are some concerns in using the wear coefficient as a wear parameter, as variations by an order of 10–1 were observed [4], however, it can be seen from Section 2 that the variations can be minimized if suitable precautions are taken. Furthermore, more consistent
E-mail address: [email protected] (L.J. Yang).
wear coefficient values are also obtainable when a better analytical model is used in its computation [5,6]. Fig. 1(a) shows that a wear volume versus distance curve can be divided into two regimes, the transient wear regime and the steady-state wear regime. The volume (or weight) loss is initially curvilinear and the rate of volume loss per unit sliding distance decreases until at P, where it joins smoothly with the straight line PQ. The amount of volume loss in the regime given by OP is the transient (running-in or unsteady-state) wear and PQ is the steady-state wear. The slope of the linear steady-state regime is used to express the wear rate of a material per unit sliding distance and, at a given load and speed, it is constant for a material depending on the nature (e.g. hardness) of the counter-surface. The standard wear coefficient value obtained from a volume loss versus distance curve is a function of the sliding distance. Due to the higher initial running-in wear rates, it has a higher value initially and will reach a steady-state value when the wear rate becomes constant, as shown in Fig. 1(b). This is because the standard method to calculate the wear coefficient is to make use of the total volume loss and the total sliding distance covered [7]. This practice would give a higher standard steady-state wear coefficient value since the higher wear rate from the transient wear is included in its computation. It is also obvious that variations of the standard wear coefficient values can occur since those determined near the transient wear regime will have higher values than those from the steady-state wear regime. It will be shown in Section 5.11 that variations can range from 5 to 10 times, based on data obtained in this study. It should be noted that
0043-1648/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0043-1648(03)00191-1
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A6061 aluminum-based composites (MMC-A, MMC-B and MMC-C) reinforced with 10, 15 and 20% aluminium oxide (alumina) particles, respectively. Both the moving-pin technique developed at Nanyang Technological University [3] and the conventional pin-on-disc technique were used in the wear testing. The former technique used a spiral wear track while the latter a circular wear track. Both the standard and the net steady-state wear coefficient values of the specimens were determined by using the standard method and the first standard wear coefficient equation developed earlier [10]. In the present study, the new standard wear coefficient equation was again used to model both the transient and steady-state wear coefficients. Comparisons were then made between the corresponding wear coefficient values obtained previously and those obtained in the present study.
2. The adhesive wear model Fig. 2 shows the proposed mathematical wear model to cover the transient wear and steady-state wear of an Al–Al2 O3 (P)/steel system. The wear model consists of two parts, the transient wear and the steady-state wear. Point P represents the end of transient wear and Lt is the transient wear distance. Point P also represents the beginning of the steady-state wear. Hence, at point Q, the specimen will have covered a total sliding distance of Lq and the total volume loss will be Vq . An exponential equation is used to model the transient wear [5,6,11,12] while the Archard [13] equation is revised to model the net steady-state wear. The following sub-sections will describe the wear model in detail. 2.1. The transient wear The rate of volume removed per unit sliding distance is assumed to be a function of the volume of metal available at the junctions. dV = −BV dL (1)
Fig. 1. (a) Wear volume; and (b) standard wear coefficient vs. sliding distance curve.
the term “standard steady-state wear coefficient” is used to differentiate it from another one, the “net steady-state wear coefficient” to be introduced later in this section. Various techniques were proposed by previous investigators to solve the non-linear wear problem. Blau [8] suggested to segment the wear curve into various stages and to calculate linear wear coefficients, which were valid only for specific intervals of time. Another suggestion was to express Archard’s wear equation as a time-dependent relationship by incorporating time into the value of the wear coefficient. A mathematical expression containing time elements was also proposed by Peterson [9]. However, in this study, an exponential equation was used to model the transient wear; and Archard’s wear equation was modified to enable the net steady-state wear coefficient to be determined more precisely, based on the steady-state wear volume and sliding distance only. As the net steady-state wear coefficient was dependent on the steady-state wear volume and sliding distance, its accuracy would also depend on how accurate the transient distance was determined. Hence, a mathematical method was proposed to calculate the theoretical transient distance for the determination of the net steady-state wear coefficient value [5]. Section 2 of this paper will describe the wear model in detail while Section 3 will formulate two standard wear coefficient equations. The first standard wear coefficient equation was used in a previous study [10] and the second one is to be used in the present study. The presentation of the formulation of the first equation in this paper is to facilitate discussion and the understanding of the similar approach taken. In the previous study, weight loss data was collected from wear tests carried out on three types of commercial
Fig. 2. The proposed adhesive wear model.
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or re-arranging dV = −B dL V (2)
KS =
3HW PLρ
(11)
where V term denotes the volume, L the sliding distance and B is a constant which depends on the applied load and the surface condition of the wear surface. The negative sign describes a situation where the original volume at the junctions diminishes with sliding distance.Integrating Eq. (2) gives ln V = −BL + C (3)
where C is the constant of integration.Eq. (3) can also be expressed as V = exp−BL+C (4)
As mentioned previously, the standard wear coefficient value obtained from Eq. (10) is a function of the sliding distance as shown in Fig. 1(b). Due to the higher initial running-in wear rate, it has a higher value initially (in the transient wear regime) and will reach a steady-state value when the wear rate becomes constant. As the standard method to calculate the wear coefficient is to make use of the total volume loss and the total sliding distance covered, consequently Archard’s equation in its present form would give a higher steady-state wear coefficient value. Hence, there is a need to define the net steady-state wear coefficient (KN ). 2.2.2. Net steady-state wear coefficient (KN ) To model the net steady-state wear, Archard’s wear equation in its revised form as shown in Eq. (12), is used to represent the steady-state wear volume, VS : VS = KN PLS 3H (12)
If A is the volume at the junctions at zero sliding distance, putting L = 0 in Eq. (4), then A = expC That is, C = ln A Hence, V = A exp−BL (7) (6) (5)
Thus, the volume removed (Vt ) which is the transient wear volume, at a sliding distance L is: Vt = A − V = A − A exp−BL = A[1 − exp−BL ] that is, Vt = A[1 − exp−BL ] (8)
It should be noted that in Eq. (8), L should be ≤Lt , which is the transient wear distance. 2.2. Steady-state wear 2.2.1. Standard wear coefficient (KS ) For steady-state wear, Eq. (9) was proposed by Archard [13]. PL V = KS 3H (9)
where VS and LS are, respectively, the steady-state wear volume and sliding distance, to be defined by Eqs. (13) and (14), respectively. KN is the dimensionless net steady-state wear coefficient. Fig. 2 shows the proposed mathematical model to cover the transient wear and steady-state wear of an Al–Al2 O3 (P)/steel system. Point P represents the end of transient wear and Lt is the transient wear distance. Point P also represents the beginning of the steady-state wear. Hence, at point Q, the specimen will have covered a total sliding distance of Lq and the total volume loss will be Vq . The steady-state sliding distance (LS ) and the steady-state wear volume (VS ) can be calculated by using Eqs. (13) and (14), respectively. LS = Lq − Lt VS = Vq − Vt (13) (14)
Hence, the net steady-state wear coefficient (KN ) can be computed from Eq. (15). KN = 3HVS PLS (15)
where V is the volumetric loss of the softer material after sliding for a distance L at load P normal to the wear surface. H is the Brinell hardness of the softer wearing material while KS a dimensionless standard wear coefficient characterizing the particular pin–disc interface. For known values of V, P, L and H, the standard wear coefficient can be calculated from Eq. (10). For a particular material, it should be noted that V can also be estimated from the weight loss W and the density ρ. Hence, the standard wear coefficient can also be determined from Eq. (11). KS = 3HV PL (10)
With the revised Archard’s wear equation, a more precise net steady-state wear coefficient (KN ) can be obtained, to facilitate a better comparison of the wear properties of similar or non-similar materials, since the higher wear rate from the transient wear is excluded. Considerable time could also be saved in wear testing since a much longer sliding distance required by the conventional method would no longer be needed. Furthermore, more consistent results would be obtained, as the wear track is less likely to be damaged by a shorter sliding distance.
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2.3. Transient distance To determine the transient distance, it is assumed that the sliding distance L = Lt is the end of the transient wear and beginning of steady-state wear. From Fig. 2, it is obvious that at L = Lt the gradient of transient wear is equal to the gradient of the steady-state wear. Differentiate Eq. (8) gives, dV = AB exp−BL dL Differentiate Eq. (12) gives dVs KN P = dLs 3H Equating Eqs. (16) and (17) gives AB exp−BLt = or ln KN P = −BLt 3HAB KN P 3H (17) (16)
system. It is expressed as: Vc = g1 P d(1 − fv ) −g3 fv L 1 − exp g3 H fv d(1 − fv ) (20)
where Vc is the volumetric pin material loss, H the pin hardness, P the load, fv is the particle volume fraction, d the average particle size, L the distance, g1 and g3 are experimental constants to be determined from Eqs. (22) and (25), respectively. As will be mentioned later in this section, g1 is a function of the applied load (P), the pin hardness (H) and the gradient (mA ) of the Vc curve at L = 0. The g3 is a function of the average particle diameter (d), the volume fraction of particles (fv ), the transient distance (Lt ), the gradients of the Vc curve (mA and mB ) at L = 0 and L = Lt , respectively. Differentiating Eq. (20) with respect to L gives g1 P −g3 fv L dVc = exp dL H d(1 − fv ) (21)
Hence, −ln[KN P/3HAB] Lt = B Substitute Eq. (15) into Eq. (18) gives, Lt = −ln[Vs /ABLs ] B
(18)
(19)
Eq. (19) indicates that the transient distance Lt can be determined if the constants A and B as well as the LS and VS values are known. A and B values can be obtained from the transient data points from the respective volume loss versus distance curve by using standard softwares. However, both LS and VS values can not be determined from Eqs. (13) and (14) without a Lt value. To overcome this difficulty, a number of approximate transient distance values (Lta ) are selected to work out some approximate Lsa and Vsa values. With these values, a number of transient distance (Lt ) values can then be found from Eq. (19). The average Lt value is then used to calculate the LS and VS values, by using Eqs. (13) and (14), respectively. Consequently the net steady-state wear coefficient KN can be computed from Eq. (15). The choice of Lta is not critical and it will not affect the calculated results significantly. This is because the steady-state wear, as expressed by Eq. (12), generally has a linear relationship.
Eq. (21) is valid in transient wear only and till the onset of steady wear. If it is allowed to progress from transient wear into steady wear, the curve will level off horizontally and this will violate Archard’s steady-state wear theory as mentioned previously. To determine g1 and g3 , let the gradients of the Vc graph be mA at L = 0, and mB at L = Lt , which is the onset of steady-state wear. Invoking the first boundary condition when the first derivative of Vc equals to mA and L = 0 in Eq. (21), g1 can now be determined from Eq. (22). HmA (22) g1 = P The second boundary condition is at L = Lt , which is the onset of steady-state wear, where gradient of Vc is mB : mB = −g3 fv Lt g1 P exp H d(1 − fv ) g1 P H g 3 f v Lt d(1 − fv ) (23)
By employing natural logarithm throughout Eq. (23), lnmB = ln − (24)
Substituting Eq. (22) into Eq. (24) and rearranging gives d(1 − fv ) (ln mA − ln mB ) (25) g3 = fv Lt With constants g1 and g3 determined, the transient wear volume loss for a steel–MMC system can be predicted from Eq. (20). By substituting Eq. (20) into Eq. (10), one gets KS = 3g1 d(1 − fv ) −g3 fv L 1 − exp g3 fv L d(1 − fv ) (26)
3. Formulations of wear coefficient equations 3.1. First standard wear coefficient equation proposed by Yang [10] Zhang et al. [14] postulated a mathematical model for the transient wear volume of an Al–SiC(P)/steel composite
It should be noted that the effects of load and pin hardness are taken into account in the determination of g1 , as indicated in Eq. (22). Hence, by substituting Eq. (22) into Eq. (26), one gets Eq. (27) which shows clearly the effects of load and pin hardness on the wear coefficient. KS = 3HmA d(1 − fv ) −g3 fv L 1 − exp PLg3 fv d(1 − fv ) (27)
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3.2. Effects of exponential factors FA and FB Eq. (20) can be re-written as Vc = where FA = 1 − exp −g3 fv L d(1 − fv ) (29) g1 P d(1 − fv ) [FA ] g3 H fv (28)
Eq. (20) was proposed for the transient wear volume only as it contains a function FA as shown in Eq. (29). FA is an exponential function of L and it has the effect of increasing the volume rapidly to reach a steady state. Hence, Eq. (20) can not be used for the determination of the steady-state wear volume since it violates the Archard’s equation for wear, Eq. (10). As Eq. (27) also contains such a function, one may wonder why Eq. (27) can be used successfully to determine the standard steady-state wear coefficient. To understand the rational, it is necessary to examine Eq. (27) carefully. Eq. (27) can be re-written as KS = 3HmA d(1 − fv ) 1 Pg3 fv L 1 − exp −g3 fv L d(1 − fv ) (30) or KS = where FB = 1 L FA L 1 − exp −g3 fv L d(1 − fv ) (32) 3HmA d(1 − fv ) [FB ] Pg3 fv (31)
Fig. 3. Characteristics of factors FA and FB vs. distance.
It will be shown in Section 5.7 that the average deviation of using this equation is about 19%. It should be noted that the value of FB is also equal to FA /L, as indicated by Eq. (33). The FA value will only increase very slowly after the initial period. Furthermore, factor FA can only have a maximum value of unity. Hence, the value of FB will decrease further as the distance (L) is increased, and will become zero when L is at infinity. Hence, due care should be exercised to select the correct distance L. The best distances to select should give a FA value that is close to, but slightly lower than unity. This is to reduce the risk of obtaining an inaccurate and lower wear coefficient value. 3.3. Current standard wear coefficient equation proposed by Yang
Comparing Eq. (32) with Eq. (29), it is obvious that FB = (33)
By substituting Eq. (8) into Eq. (10), one gets KS = 3HA [1 − exp−BL ] PL (34)
It is clear that Eq. (27) contains factor FB , which is related to FA as shown in Eq. (33). However, the behaviour of FB is different from that of FA . Fig. 3 shows the values of factors FA and FB plotted against distance, from 0.25 to 12 km, for MMC-A, MMC-B and MMC-C, respectively; and based on data obtained previously [10]. It can be seen from Fig. 3 that the average value of FA and FB varies from about 0.16 to 1.0 and 6.5×10−5 to 0.8× 10−5 , respectively, from a sliding distance of 0.25–12 km. FA increases rapidly and reaches almost 100% of the maximum value at 9 km. However, FB decreases more gradually, reaches to 1.1 at 9 km, or 83% reduction from its maximum value. Hence, Eq. (20), which contains factor FA , is unsuitable for the determination of the wear volume in steady-state wear since it will give a horizontal line in the steady-state wear regime which is different from the actual volume loss versus distance line. On the other hand, Eq. (27), which contains factor FB , was found to be capable of predicting the standard steady-state wear coefficients with a good accuracy.
By adapting the same approach used in Section 3.2 and let FA = [1 − exp−BL ] FB = 1 [1 − exp−BL ] L 3HA [FB ] P (35) (36)
then Eq. (34) becomes KS = (37)
As mentioned in Section 3.2, to obtain realistic values from Eq. (34) to predict the standard steady-state wear coefficients, L should be selected to give a FA value that is close to, but slightly lower than unity. Again, this is to reduce the risk of obtaining an inaccurate and lower wear coefficient value. It should be noted that Eq. (34) is similar to Eq. (27), both are of the exponential types. However, experience has
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indicated that there are some difficulties in using Eq. (27). First of all, the distribution of particles in a metal matrix composite is always non-uniform, to give different (fv ) values from one section to another. Next, different particle sizes (d) are present in a particular section. Furthermore, only two gradients, mA and mB are used to define the curve which may not turn up to be exact. In the case of Eq. (34), only two parameters (A and B) need to be determined, as the other parameters such as H, P, and L are known. With the use of established softwares, the values of A and B can be determined more accurately as all the transient data points are fully utilized to obtain the ‘best-fit’ curve for the transient wear volume. Hence, more accurate results can be obtained with Eq. (34). It will be shown in Section 5.7 that the average deviation of using this equation is about 14%.
on the same surface can also damage the wear track to affect the test results. In an attempt to overcome the above-mentioned shortcoming, the moving-pin technique with a spiral wear track was developed by Yang [3]. This technique was found particularly useful for testing hard pin material like cemented tungsten carbide. It was again used in the current study, as the aluminium-based matrix composites containing alumina can be abrasive to cause a rapid wear of the disc material. It can be seen from Eq. (38) that, for the same N, the linear speed of the disc is directly proportional to R. With the aid of computer numerical control (CNC) technology, R can be varied while the linear velocity of the disc is kept constant. The feed rate of the pin can also be specified. However, a high feed rate should be avoided in order not to affect the actual wear rate. 4.2. Experimental set-up Fig. 4 shows the schematic experimental set-up for carrying out the wear tests. The fixture is clamped onto the tool post of the CNC lathe and carries a square tool pin holder and a pneumatic cylinder which is used to provide the required load which is adjustable during the wear testing of the pins. A pressure gauge was used to monitor the load pressure and a throttle valve was used to adjust the required load. A Rikadenki Type R-63 multi-pen recorder and a Kistler Type 9121 force dynamometer were used to measure the force between the pin and the disc during wear testing [3]. The pin holder was designed to ensure that the pin specimen would be held firmly during the wear tests, with 20 mm of the pin held inside the holder and 5 mm of it protruding out for wear test purposes. The protruded pin surface must have full contact with the disc to obtain accurate experimental results. Thus, close dimension tolerance was maintained when machining the pin holder and the pins.
4. Experimental methodology used in the previous studies 4.1. The moving-pin technique With the conventional pin-on-disc wear test, the pin specimen is held stationary on top of a precision ground rotating disc, with the required load applied through the pin. With the use of a variable speed motor, the rotational speed of the disc can be varied. The linear speed of the disc at the point where the pin is located is: Vdisc = 2πRN (38)
where Vdisc is the linear speed of the rotating disc, R the distance from the centre of the pin to the centre of the disc and N the rotational speed of the disc. The conventional pin-on-disc wear test is conducted with a fixed R and only a small portion of the disc is utilized. The continuous rubbing
Fig. 4. Schematic experimental set-up for carrying out the wear tests.
L.J. Yang / Wear 255 (2003) 579–592 Table 1 Density and hardness of pin materials MMC-A Density (g/cm3 ) Measured Calculated Measured 2.817 2.823 611 MMC-B 2.895 2.885 554 MMC-C 2.973 2.946 579
585
were obviously manufactured in different batches, with different alumina sizes. 4.4. Experimental technique Wear tests for the MMC-A, MMC-B and MMC-C were carried out at distances of 250, 500, 1000, 1500, 2000, 2500, 3000, 6000, 9000 and 12,000 m. Both the moving-pin and the conventional pin-on-disc techniques were used. A constant load of 7.5 kgf, linear velocity of 4.58 m/s and a feed rate of 0.05 mm/rev was used for the moving-pin technique. The pin would start at a radius of 87.5 mm on the rotating disc and would travel to a radius of 20 mm before returning back to the initial point. A stopwatch was used to time the cycle time needed based on the wear distance and constant linear velocity of 4.58 m/s for the collection of weight loss data. As for the conventional pin-on-disc experiment, the pin was held stationary at a radius of 87.5 mm of the rotating disc and a constant sliding speed of 500 rpm. The other factors remained the same as the moving-pin technique. Three repetitions were carried out for each experiment [16].
HB (MPa)
4.3. Disc and pin materials The discs used in this study were made of Assab DF2 tool steel (equivalent to AISI 01) hardened and tempered to 60 HRC (697 Hv), and ground to a surface finish of 0.3 m (Ra ). The discs had a diameter of 180 mm and a thickness of 30 mm. The pins were machined accurately to a size of 10 mm × 10 mm and a length 25 mm by a wire-cut electro-discharge machining (EDM) process to fit the pin holder. The pin materials used in this experiment were A6061 aluminium-based matrix composites with different nominal volume fraction of alumina particles, MMC-A with 10% alumina, MMC-B with 15% alumina and MMC-C with 20% alumina. These materials were supplied by Comalco in the form of flat bars extruded from Duralcan billets. The density of the specimens was measured by using a Ultrapycnometer. The hardness of the three composite materials was tested using a Brinell hardness tester. Table 1 shows the density and hardness values of the pin materials. The [15] gives the density of A6061 as 2.70 and 3.75–3.93 g/cm3 for alumina. Based on the nominal volume fraction of alumina given by the manufacturer, the theoretical density was calculated, based on a value of 3.93 g/cm3 for alumina, and listed in Table 1. It can be seen from the table that the deviations of both the measured and calculated density values are small, indicating the nominal volume fraction of alumina in each material is approximately correct. However, MMC-A contains a lower volume fraction of alumina and should give a lower hardness value. This does not seem to be the case, presumably due to different processing parameters used in its manufacture. Scanning electron microscopy (SEM) was used to determine the cross-sectional area of the particles. Table 2 shows the average cross-sectional area of the alumina particles observed and the computed average diameter (d) of the particles for each type of material. The average diameter ranges from 24 to 36 m for the three composite materials, which
5. Results and discussions 5.1. Wear test data collected previously Weight loss data were collected from tests performed with both the moving-pin technique and the conventional pin-on-disc technique for MMC-A, MMC-B and MMC-C, at sliding distances from 250 to 12,000 m. Their average wear volume loss values, obtained by dividing the respective average weight loss value by its measured density, are presented in Table 3. 5.2. Wear volume loss curves Fig. 5 shows the wear volume loss against distance curves for MMC-A, MMC-B and MMC-C, with data obtained from both the moving-pin and the conventional pin-on-disc methods. In the figure, V(M)-A and V(C)-A indicate the wear volume loss values (V) of MMC-A tested under moving-pin and conventional pin-on-disc conditions, respectively. Fig. 5 indicates that the curves can generally be divided into two regimes, the transient regime and the steady-state regime. For each material, the actual wear volume loss curve is initially curvilinear and the rate of volume loss per unit
Table 2 Average area and diameter of alumina particles in MMC-A, MMC-B and MMC-C A1 ( m)2 MMC-A MMC-B MMC-C 754 958 447 A2 ( m)2 722 1050 454 A3 ( m)2 690 998 480 A4 ( m)2 701 1120 400 A5 ( m)2 662 986 460 Average area A ( m)2 706 1023 448 d ( m) 30 36 24
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Table 3 Volume loss and standard wear coefficient values (K1 , K2 and K3 ) obtained for MMC-A, MMC-B and MMC-C Distance (m) Moving-pin method Average MMC-A 250 500 1000 1500 2000 2500 3000 6000 9000 12000 MMC-B 250 500 1000 1500 2000 2500 3000 6000 9000 12000 MMC-C 250 500 1000 1500 2000 2500 3000 6000 9000 12000 2.47 4.24 6.42 8.15 9.17 9.71 10.40 13.45 17.54 21.84 1.89 3.16 4.24 4.95 5.69 6.52 7.08 9.42 12.99 17.74 1.36 2.12 3.52 4.62 5.18 5.35 5.60 7.46 9.81 13.7 V (mm3 ) K1 (× 24.6 21.1 16.0 13.5 11.4 9.7 8.6 5.6 4.9 4.5 17.1 14.3 9.6 7.5 6.4 5.9 5.3 3.6 3.3 3.3 12.8 10.0 8.3 7.3 6.1 5.1 4.4 2.9 2.6 2.7 10−5 ) K2 (× 22.3 20.3 17.0 14.4 12.3 10.7 9.4 5.2 3.5 2.6 15.4 14.1 11.9 10.1 8.7 7.6 6.7 3.7 2.5 1.9 11.9 11.1 9.1 8.6 7.6 6.8 6.1 3.6 2.5 1.9 10−5 ) K3 (× 22.6 20.3 16.5 13.6 11.5 9.8 8.5 4.5 3.0 2.3 13.6 12.2 9.9 8.1 6.8 5.8 5.0 2.7 1.8 1.3 11.7 10.5 8.6 7.1 6.0 5.1 4.4 2.4 1.6 1.2 10−5 ) Conventional pin-on-disc method Average 3.80 5.30 7.32 9.00 10.13 11.02 12.12 15.25 17.89 22.11 1.45 2.65 4.42 5.53 6.11 6.90 7.57 10.26 13.59 18.95 1.42 2.41 4.62 6.13 7.03 8.32 9.04 11.1 13.8 17.8 V (mm3 ) K1 (× 10−5 ) 37.8 26.4 18.2 14.9 12.6 11.0 10.1 6.3 5.0 4.6 13.1 12.0 10.0 8.3 6.9 6.2 5.7 3.9 3.4 3.6 13.4 11.4 10.9 9.6 8.3 7.9 7.1 4.4 3.6 3.5 K2 (× 10−5 ) 34.5 31.4 26.4 22.4 19.3 16.7 14.7 8.1 5.4 4.1 12.2 11.4 9.9 8.7 7.7 6.9 6.2 3.6 2.5 1.9 12.5 11.7 10.3 9.1 8.1 7.3 6.6 3.9 2.7 2.0 K3 (× 10−5 ) 27.5 24.4 19.4 15.8 13.1 11.1 9.5 5.0 3.3 2.5 12.6 11.6 9.8 8.4 7.2 6.3 5.5 3.1 2.1 1.5 12.6 11.9 10.6 9.5 8.6 7.8 7.1 4.4 3.0 2.3
Note: K1 , K2 and K3 were computed by using Eqs. (10), (27) and (34), respectively.
Fig. 5. Wear volume loss against distance curves for MMC-A, MMC-B and MMC-C.
sliding distance decreases until a point, i.e. at the transient distance, beyond which it becomes almost constant. By visual inspection of the curves, the end point of the transient region is about 2000–3000 m. The wear loss values for the specimens tested with the conventional pin-on-disc method, indicated by the dotted lines, were found to be higher, as compared with those tested with the moving-pin method. It should be noted that the wear volume of a pin from the pin-on-disc test depends greatly on the condition of the wear track. The single wear track generated by the conventional pin-on-disc method can be damaged more easily by alumina particles or wear debris, to give a higher wear rate. A slightly higher wear volume loss can also be observed on some specimens tested up to 12 km due to the same reason. The volume loss of MMC-A is also found to be higher than that of MMC-B and MMC-C. Again this is due to the presence of a smaller volume fraction of alumina particles in MMC-A. It seems that the presence of a larger volume fraction of alumina particles would increase the wear resistance of the
L.J. Yang / Wear 255 (2003) 579–592 Table 4 The g1 and g3 values for MMC-A, MMC-B and MMC-C Moving-pin method g1 (× MMC-A 8.2 MMC-B 5.65 MMC-C 4.25 10−5 ) g3 (× 2.14 1.56 0.547 10−7 )
587
Conventional pin-on-disc method g1 (× 10−5 ) g3 (× 10−7 ) 12.63 4.37 4.47 2.09 1.20 0.525
Fig. 6. Standard wear coefficient (K1 ) vs. distance curves for MMC-A, MMC-B and MMC-C.
MMC materials as in MMC-B and MMC-C, especially so in the transient wear regime. 5.3. Standard wear coefficient (K1 ) against distance curves Table 3 also contains the standard wear coefficient (K1 ) values, computed from their respective wear volume loss values with Eq. (10), against distance for MMC-A, MMC-B and MMC-C, respectively. Fig. 6 shows the standard wear coefficient (K1 ) curves versus distance for MMC-A, MMC-B and MMC-C, with data obtained from both the moving-pin and the conventional pin-on-disc methods. In the figure, K1 (M)-A and K1 (C)-A indicate the standard wear coefficient values (K1 ) of MMC-A tested under moving-pin and conventional pin-on-disc conditions, respectively. It can be seen from the figure that the standard wear coefficient (K1 ) decreases more rapidly as the distance increases initially, but more gradually when approaching the steady-state wear and eventually becomes almost a horizontal line in the steady-state wear. The standard wear coefficient values for the specimens tested with the conventional pin-on-disc method, indicated by dotted lines, were found to be higher, as compared with those tested with the moving-pin method, due to their higher wear volumes as discussed in Section 5.2. 5.4. Standard wear coefficient (K2 ) against distance curves To determine K2 with Eq. (27), g1 and g3 need to be calculated. The gradients mA and mB were firstly determined at L = 0 and at L = 2500 m, respectively. The latter was estimated from the volume loss versus distance curves, as shown in Fig. 5, to be the average distance at the end of transient wear and the beginning of steady wear. It will also be shown in Section 5.8 that the average calculated transient distance is 2502 m. The corresponding g1 and g3 values for the three composite materials, based on data obtained from both the
moving-pin and conventional pin-on-disc techniques, were then determined from Eqs. (22) and (25), respectively, and tabulated in Table 4. It should be noted from Table 4 that for MMC-A, the g1 value calculated from the data obtained with the conventional pin-on-disc method is considerably higher than that from the moving-pin method. Table 2 indicates that MMC-A has the highest hardness value despite the fact that it has the lowest volume fraction of alumina particles. Obviously a different hardening mechanism was probably involved in MMC-A which made it less wear resistance when tested with the conventional pin-on-disc method. The wear coefficient values, K2 , were computed by using Eq. (27) and were again presented in Table 3 for the three materials. It can be seen from Table 3 that similar trend and standard wear coefficient values were obtained for K2 and K1 . However, a more detailed comparison of K2 and K1 values will be discussed in Section 5.7. 5.5. Standard wear coefficient (K3 ) against distance curves The wear loss volumes, computed from data obtained by both the moving-pin and conventional pin-on-disc methods, and at distances of 500, 1000, 1500, 2000, 2500 and 3000 m, were input into a commercial software DataFit Version 6 [17], to determine their transient wear equation constants A and B. Table 5 shows the values of these constants. With the A and B values from Table 5, the wear coefficient values, K3 , were computed by using Eq. (34) and were again presented in Table 3. It should be noted that the K1 values were obtained directly from the measured weight loss data, the K2 values from the first standard wear coefficient equation Eq. (27) proposed by Yang [10] while K3 is from the newly proposed standard wear coefficient equation Eq. (34). It can again be
Table 5 Transient wear equation constants A and B, for MMC-A, MMC-B and MMC-C Moving-pin method A MMC-A MMC-B MMC-C 10.87 7.09 6.02 B (× 9.36 9.54 9.24 10−4 ) Conventional pin-on-disc method A 11.95 8.25 11.79 B (× 10−4 ) 10.51 7.43 4.80
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Fig. 7. Standard wear coefficient (K1 , K2 and K3 ) vs. distance (MMC-A).
seen from these figures that similar trend and standard wear coefficient values were obtained for K1 , K2 and K3 , both in the transient wear regime and in the steady-state wear regime. To facilitate comparison, the wear coefficient values, K1 , K2 and K3 for MMC-A are also plotted in Fig. 7, in which K1 (M)-A and K1 (C)-A indicate the wear coefficient values (K1 ) of MMC-A tested under moving-pin and conventional pin-on-disc conditions respectively. Similarly, K2 or K3 (M)-A and K2 or K3 (C)-A indicate the wear coefficient values (K2 or K3 ) of MMC-A tested again under moving-pin and conventional pin-on-disc conditions, respectively. It can be seen from Fig. 7 that K3 has given a slightly lower wear coefficient value in the steady-state wear. Similar trends were also observed for MMC-B and MMC-C. Section 5.10 will discuss the significance of this observation. 5.6. FA and FB values for K3 As indicated in Section 3.3, to obtain realistic standard wear coefficient values from Eq. (34), the FA values should be close to, but slightly lower than unity. Hence, the FA
Table 6 Values of factors FA and FB versus distance Distance (m) FA for MMC-A MP 250 500 1000 1500 2000 2500 3000 6000 9000 12000 0.209 0.374 0.608 0.754 0.846 0.904 0.940 0.996 1.000 1.000 CP 0.231 0.409 0.650 0.793 0.878 0.928 0.957 0.998 1.000 1.000 FA for MMC-B MP 0.212 0.379 0.615 0.761 0.852 0.908 0.943 0.997 1.000 1.000 CP 0.170 0.310 0.524 0.672 0.774 0.844 0.892 0.988 0.999 1.000
and FB values were determined, respectively, from Eqs. (35) and (36), and tabulated in Table 6 for the three materials from a distance of 0.25–12 km; and based on data obtained from both the moving-pin and the conventional pin-on-disc techniques. It can be seen from Table 6 that the average values of FA and FB have similar trends to those obtained previously and plotted in Fig. 3. However, it should be noted that the FA value of 0.944 at 6000 m for MMC-C is too low and it was excluded in calculating the average FA value as listed in Table 6. For the same reason, the corresponding K3 value was omitted in the calculation of the average K3 value plotted in Fig. 10. Table 6 shows again that factor FA are close to, but slightly lower than unity, with an average value of 0.995, 0.998 and 1.000 for the three materials, when the sliding distances are 6, 9 and 12 km, respectively. Hence, the standard steady-state wear coefficient (K3 ) values obtained earlier in Section 5.5 by Eq. (34) are realistic. 5.7. Deviations of K2 and K3 against K1 To evaluate the accuracy of Eq. (34), that is the K3 values, the percentage deviations of K2 and K3 values against K1 values ( K2 and K3 ) were calculated by using Eqs. (39) and (40), respectively, and plotted in Fig. 8. The K1 , K2 and K3 values were taken from Table 3 for MMC-A, MMC-B and MMC-C, respectively, from data obtained with the moving-pin method. K2 = K3 = K2 − K1 × 100 K1 K3 − K 1 × 100 K1 (39) (40)
It can be seen from Fig. 8 that the deviation of K3 , shown with solid lines in the figures, is generally lower than that of K2 . The deviation trend starts with a negative value and then increases slightly before it decreases again. However, for K3 , most of the negative deviations are found in
FA for MMC-C MP 0.206 0.370 0.603 0.750 0.842 0.901 0.938 0.996 1.000 1.000 CP 0.113 0.213 0.381 0.513 0.617 0.699 0.763 0.944 (a) 0.987 0.997
Average FA
Average FB (× 10−5 )
0.190 0.343 0.564 0.707 0.802 0.864 0.906 0.995 (b) 0.998 1.000
7.60 6.85 5.64 4.72 4.01 3.46 3.02 1.64 1.11 0.83
Notes: MP is moving-pin method; and CP conventional pin-on-disc method; (a) this value was too low and was omitted in the calculation of the average value as indicated in (b).
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a better accuracy than Eq. (27), since it contains lesser number of variables as mentioned in Section 3.3. As indicated in Section 5.5, as well as in Table 7 and Fig. 8, Eq. (34) seems to have given a lower standard steady-state wear coefficient value. Hence, Section 5.10 will compare the standard wear coefficient values (K1 , K2 and K3 ) with the net steady-state wear coefficient (KN ). 5.8. Transient distance values
Fig. 8. Deviations of K2 and K3 against K1 for MMC-A, MMC-B and MMC-C. Data obtained with the moving-pin method.
the steady-state wear regime. Similar trend was also observed with data obtained from the conventional pin-on-disc method. Table 7 shows the average deviations of the K2 and K3 against K1 for MMC-A, MMC-B and MMC-C, based on data obtained by both the moving-pin technique and the conventional pin-on-disc technique. It should be noted that, in the calculation of the average deviations, only absolute values were used. It can be seen from Table 7 that the average values for K3 are 15.0 and 12.2% for data obtained with the moving-pin and the conventional pin-on-disc techniques, respectively; while the corresponding values for K2 are 18.7 and 18.9%. Hence, the over-all average values for K3 and K2 are about 14 and 19%, respectively. It should again be noted that the K1 values were obtained directly from the measured weight loss data, the K2 values from the standard wear coefficient equation Eq. (27) while K3 from the newly proposed standard wear coefficient equation Eq. (34). It is, therefore, obvious that Eq. (34) has given
To compare the accuracy of the standard wear coefficient values, K1 , K2 and K3 , with the net steady-state wear coefficient (KN ) values for the three types of MMC materials, it is necessary to determine their respective transient distances in order to calculate the latter. Table 8 shows an example of transient distance calculation for MMC-A, by using data from the moving-pin method. The Lta values used were 2000, 2500 and 3000 m. The average transient distance values obtained, with Eq. (19), for MMC-A, MMC-B and MMC-C were, respectively, 2311, 1999 and 2228 m when the moving-pin method was used; and 2301, 2334 and 3838 m when the conventional pin-on-disc method was used. The average value of the calculated transient distance was 2502 m. Hence, it was reasonable to use an average transient distance of 2500 m to calculate the g1 and g3 values in Section 5.4. 5.9. Net Steady-state wear coefficient values (KN ) for MMC-A, MMC-B and MMC-C With the transient distance values determined, the net steady-state wear coefficient values (KN ) for MMC-A,
Table 7 Average deviations of K2 and K3 against K1 for MMC-A, MMC-B and MMC-C Method MMC-A K2 (%) MP CP 13.2 32.1 K3 (%) 12.6 15.9 MMC-B K2 (%) 23.1 13.1 K3 (%) 19.1 13.7 MMC-C K2 (%) 19.9 11.6 K3 (%) 13.3 7.0 Average K2 (%) 18.7 18.9 K3 (%) 15.0 12.2
Based on the absolute values of the deviations; MP is moving-pin method; and CP conventional pin-on-disc method. Table 8 An example of transient distance calculation for MMC-A with different Lta values (Data from moving-pin method) Lta (m) 2000 Vta (mm3 ) 9.17 L2 (m) 6000 9000 12000 6000 9000 12000 6000 9000 12000 V2 (mm3 ) 13.45 17.54 21.84 13.45 17.54 21.84 13.45 17.54 21.84 Lsa (m) 4000 7000 10000 3500 6500 9500 3000 6000 9000 Vsa (mm3 ) 4.28 8.37 12.67 3.74 7.83 12.13 3.05 7.14 11.44 Lt (m) 2406 2288 2226 2408 2278 2217 2461 2293 2222 Average Lt (m)
2307
2500
9.71
2301
3000
10.40
2325 Overall average Lt (m), 2311
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Table 9 An example of net steady-state wear coefficient calculation for MMC-A Lt (m) 2300 Vt (mm3 ) 9.49 L2 (m) 6000 9000 12000 V2 (mm3 ) 13.45 17.54 21.84 Ls (m) 3700 6700 9700 Vs (mm3 ) 3.96 8.05 12.35 KN (× 10−5 ) 2.67 3.00 3.18 Average KN (× 10−5 )
2.95
Note: Data from moving-pin method.
MMC-B and MMC-C were calculated with Eq. (15). Table 9 shows an example of net steady-state wear coefficient calculation for MMC-A, with data from the moving-pin method. Fig. 9 shows the net steady-state wear coefficient (KN ) plotted against the steady-state sliding distance (LS ). It should be noted that, in most cases, the net steady-state wear coefficient increases slightly with an increase of steady-state sliding distance. This was due to the occurrence of damaged wear tracks caused by fractured alumina particles when a longer sliding distance was used. The average net steady-state wear coefficient values (KN ), for MMC-A, MMC-B and MMC-C were, respectively, found to be 2.95 × 10−5 , 2.86 × 10−5 and 1.66 × 10−5 when the moving-pin method was used; and 2.91 × 10−5 , 2.50 × 10−5 and 1.97 × 10−5 when the conventional pin-on-disc method was used. 5.10. Comparison of the standard wear coefficient values (K1 , K2 and K3 ) with the net steady-state wear coefficient (KN ) As indicated in Sections 5.5 and 5.7, there is some indication that K3 has given a slightly lower standard wear coefficient value in the steady-state wear. One may wonder about the accuracy of Eq. (34), and how its steady-state K3 values are compared with the net steady-state wear coefficients. Fig. 10 shows the average standard wear coefficients
(K1 , K2 and K3 ) and the average net steady-state wear coefficient (KN ) for MMC-A, MMC-B and MMC-C. These values were obtained by taking the average of their respective values at distances of 6000, 9000 and 12,000 m, tested with both the moving-pin and the conventional pin-on-disc techniques. However, for MMC-B, the average values were based on those obtained with 9000 and 12,000 m only, as the FA value at 6000 m was only 0.944 which was too low to be classified as steady-state wear, as discussed in Section 5.7. It should be noted that, as K1 , K2 , and K3 are obtained by using Eqs. (10), (27) and (34), respectively, they are standard wear coefficients. They would, therefore, give a higher steady-state wear coefficient value, as compared with the net steady-state wear coefficient as can be seen generally in Fig. 10, since the higher wear rate from the transient wear is included in its computation, as discussed in Section 2.2. To facilitate comparisons, the deviations of K1 , K2 and K3 from their respective KN values were calculated by using Eqs. (41)–(43) for the three types of materials. Dev( K1 ) = Dev( K2 ) = Dev( K3 ) = K1 − KN × 100 KN K2 − KN × 100 KN K3 − KN × 100 KN (41)
(42)
(43)
The average deviation, for each type of material was obtained by taking the average values from those tested with the moving-pin technique and those tested with the conventional pin-on-disc technique. Although negative deviation values were observed, however, for each type of material
Fig. 9. Net steady-state wear coefficient (KN ) vs. distance (MMC-A, MMC-B and MMC-C).
Fig. 10. Average standard steady-state wear coefficients (K1 , K2 and K3 ) and the average net steady-state wear coefficient (KN ) for MMC-A, MMC-B and MMC-C.
L.J. Yang / Wear 255 (2003) 579–592 Table 10 Ratio of maximum and minimum standard wear coefficient values MMC-A Moving-pin method K1 5.5 K2 8.6 9.8 K3 MMC-B 5.2 8.1 10.5 MMC-C 4.7 6.3 9.8 3.8 6.3 5.5
591
Average 5.1 7.7 10.0 5.2 7.0 8.3
Conventional pin-on-disc method K1 8.2 3.6 K2 8.4 6.4 11.0 8.4 K3 Fig. 11. Average deviations (%) of K1 , K2 , and K3 , based on KN , for MMC-A, MMC-B and MMC-C.
and, for each K value, the average deviation was calculated by using the absolute deviation values only. Fig. 11 shows the average deviations (%) of the standard wear coefficients K1 , K2 , and K3 , based on their respective KN values. It is clear from Fig. 10 that K3 , calculated from Eq. (34), has the lowest standard wear coefficient values for all the three types of materials. It is also clear from Fig. 11 that K3 has the lowest average deviation from KN , that is, about 18% against 37 and 59% for K2 and K1 , respectively. Obviously, K3 has given the lowest standard steady-state wear coefficient value which is closest to the net steady-state wear coefficient (KN ), unlike K2 and K1 . Hence, Eq. (34) is a more accurate equation to be used for predicting the standard wear coefficient of the Al–Al2 O3 (P)/steel system, in both transient and steady-state wear. As mentioned in Section 3.3, this is also an easier equation to use since there are lesser number of variables (only A and B) involved. The [18] reported a sliding wear coefficient value of 6.3× 10−5 for a 2014 Al–20 wt.%SiC (T6) composite on SAE 52100 steel (63 HRC) with a block-on-ring type wear rig. The applied normal load was 9.35 N and a sliding velocity of 0.1 m/s was used. The average standard wear coefficient values for MMC-C with 20% alumina particles obtained from the present study are K1 = 3.3 × 10−5 , K2 = 2.8 × 10−5 and K3 = 2.2 × 10−5 which are lower than the value of 6.3×10−5 reported in [18]. However, it should be noted that different materials, testing process and parameters were used in both the studies. Furthermore, the standard wear coefficient value is a function of the sliding distance, as mentioned in Section 2.2. Due to the higher initial running-in wear rate, it has a higher value near the transient wear regime. It is also clear from Section 5.7 that, with a lower FA value, a higher wear coefficient value would be obtained, as the wear might not have reached the steady-state yet. 5.11. Ratio of maximum and minimum standard wear coefficient values Table 10 shows the ratios of the maximum standard wear coefficient value (at 250 m) against the minimum one (at
12,000 m) calculated from data listed in Table 3. It can be seen from the table that, on the average, it varies from about 5 (based on K1 ) to 10 (based on K3 ). This agrees with earlier report that variation up to 10–1 was possible [4]. Obviously, it is extremely important to distinguish between transient wear coefficients and the steady-state wear coefficients determined from a wear test. Failure to do so may have been the main reason behind the variations of wear coefficients reported previously.
6. Conclusion (i) It was found that Eq. (34) proposed in this paper was capable to model standard wear coefficients in both the transient wear and steady-state wear of the Al–Al2 O3 /steel system. The unique characteristic of factor FB was again significant in contributing to the successful use of the equation. (ii) By comparing K3 (obtained from Eq. (34)) and K2 (obtained from Eq. (27)) with the K1 values obtained directly from the measured weight loss data, the average deviation of K3 was generally lower than that of K2 . The over-all average values for K3 and K2 were about 14 and 19%, respectively. (iii) With sliding distances of 6, 9 and 12 km, the standard steady-state wear coefficient (K3 ) was found to have the lowest average deviation from the net steady-state wear coefficient (KN ), i.e. about 18% against 37 and 59% for K2 and K1 , respectively. (iv) Obviously, Eq. (34) had given to more accurate standard wear coefficient values (K3 ). Eq. (34) was also found to be easier to use since it contained lesser number of variables, only A and B involved with the transient equation; and these variables could be measured more accurately than those contained in Eq. (27). (v) The predictive power of Eq. (34) is also of great significance. Although the equation was established with the transient wear data, i.e. the A and B values, however, it is capable of predicting the standard steady-state wear coefficients as well. This is, therefore, a significant contribution to the modeling of standard wear coefficient of Al–Al2 O3 /steel system.
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L.J. Yang / Wear 255 (2003) 579–592 Proceedings of the Second Asiatrib International Conference, Jeju Island, Korea, October 2002, pp. 217–218. L.J. Yang, Steady-state wear coefficient of A6061 aluminium alloy reinforced with alumina particles, in: Proceedings of the Sixth Austrib International Conference, Perth, Australia, December 2002, pp. 575–582. E. Rabinowicz, Wear coefficients—metals, in: M.B. Peterson, W.O. Winer (Eds.), Wear Control Handbook, The American Society of Mechanical Engineers, New York, 1980. P. Blau, Friction and Wear Transitions of Materials: Break-in, Run-in, Wear-in, Noyes Publications, Park Ridge, New Jersey, USA, 1989. M. Peterson, Design considerations for effective wear control, in: M.B. Peterson, W.O. Winer (Eds.), Wear Control Handbook, The American Society of Mechanical Engineers, New York, 1980. L.J. Yang, The transient and steady wear coefficients of A6061 aluminium alloy reinforced with alumina particles, Compos. Sci. Technol. 63 (2003) 575–583. C.A. Queener, T.C. Smith, W.L. Mitchell, Transient wear of machine parts, Wear 8 (1965) 391–400. A.D. Sarkar, Wear of Metals, Pergamon Press, Oxford, New York, 1976. J.F. Archard, Contact and rubbing of flat surfaces, J. Appl. Phys. 24 (1953) 981. Z.F. Zhang, L.C. Zhang, Y.W. Mai, Running-in wear of steel/Si(CP)–Al composite system, Wear 194 (1996) 38–43. P.K. Mallick, Composites Engineering Handbook, Marcel Decker, New York, 1980. P.K. Low, Wear characteristics of aluminium alloy (A6061) reinforced with alumina, B.E. Final Year Project Report, School of Mechanical and Production Engineering, Nanyang Technological University, May 2001. Oakdale Engineering, http://www.oakdaleengr.com. A.T. Alpas, J.D. Embury, Wear mechanisms in particle reinforced and laminated metal matrix composites, Wear of Materials, vols. 159–166, ASME, 1991.
(vi) This work has also explained the possible cause of variations in the determination of wear coefficients. A variation of up to 10–1 between wear coefficients in the transient regime and that in the steady-state regime was observed. This paper has, therefore, contributed to a better understanding of the characteristic of standard wear coefficients. Acknowledgements The author would like to thank the support of this project by Applied Research Fund #72/93 provided by Nanyang Technological University; Dr. Malcolm Couper, Comalco Research Centre, Thomastown, Australia for supplying the composite materials used in the investigation. References
[1] A.R. Lansdown, A.L. Price, Materials to resist wear, Wear, Pergamon Press, Oxford, 1986. [2] L.J. Yang, N.L. Loh, The wear properties of plasma transferred arc cladded stellite specimens, Surf. Coat. Technol. 71 (1995) 196– 200. [3] L.J. Yang, Pin-on-disc wear testing of tungsten carbide with a new moving-pin technique, Wear 225–229 (1999) 557–562. [4] M. Godet, Modeling of friction and wear phenomena, in: F.F. Ling, C.H.T. Pan (Eds.), Approaches To Modeling Of Friction And Wear, Springer–Verlag, Berlin, 1988. [5] L.J. Yang, Determination of transient wear distance in the adhesive wear of A6061 aluminium alloy reinforced with alumina, in:
[6]
[7]
[8] [9]
[10]
[11] [12] [13] [14] [15] [16]
[17] [18]
Wear coefficient equation for aluminium-based matrix composites against steel disc
L.J. Yang
School of Mechanical and Production Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore
Abstract A new formulation of the wear coefficient was developed and tested experimentally. Two different types of pin-on-disc wear tests were conducted using three commercial, A6061 aluminum-based metal–matrix composites (MMCs). One type of test resulted in a spiral track and the other a circular track. Hardened tool steel discs were used as the sliding counterface for MMC pins having 10, 15 and 20% alumina reinforcements. A new wear equation was derived and shown to be a better predictor of steady-state wear coefficients. It is based on an exponential transient wear volume equation and Archard’s equation. © 2003 Elsevier Science B.V. All rights reserved.
Keywords: Metal–matrix composites (MMCs); Transient wear; Steady-state wear; Adhesive wear; Wear coefficient
1. Introduction Metal–matrix composites are widely used in industries because of their excellent mechanical properties and wear resistance. To understand the wear behaviour of different MMC materials, wear tests are often carried out with suitable wear testing techniques. There are different types of wear mechanisms involved, for example, adhesive wear, abrasive wear, or others. However, adhesive wear is by far the most dominant form of material loss among sliding components in machinery [1]. The pin-on-disc test is a classical method commonly used for adhesive wear experiments. During the experiment, the sliding between the pin and disc may result in wear on both contact surfaces of the pair. To facilitate measurement, the pin is generally the wearing member that has a lower hardness. Although weight loss and wear rate are often used for studying the wear characteristics of test specimens, recent investigations [2,3] have found that wear coefficient is a better parameter to be used instead. This is because the wear coefficient has taken into account not only the wear rate (V/L), the applied load, but also the hardness of the wear pin or counterface which can affect the wear rate significantly. Although there are some concerns in using the wear coefficient as a wear parameter, as variations by an order of 10–1 were observed [4], however, it can be seen from Section 2 that the variations can be minimized if suitable precautions are taken. Furthermore, more consistent
E-mail address: [email protected] (L.J. Yang).
wear coefficient values are also obtainable when a better analytical model is used in its computation [5,6]. Fig. 1(a) shows that a wear volume versus distance curve can be divided into two regimes, the transient wear regime and the steady-state wear regime. The volume (or weight) loss is initially curvilinear and the rate of volume loss per unit sliding distance decreases until at P, where it joins smoothly with the straight line PQ. The amount of volume loss in the regime given by OP is the transient (running-in or unsteady-state) wear and PQ is the steady-state wear. The slope of the linear steady-state regime is used to express the wear rate of a material per unit sliding distance and, at a given load and speed, it is constant for a material depending on the nature (e.g. hardness) of the counter-surface. The standard wear coefficient value obtained from a volume loss versus distance curve is a function of the sliding distance. Due to the higher initial running-in wear rates, it has a higher value initially and will reach a steady-state value when the wear rate becomes constant, as shown in Fig. 1(b). This is because the standard method to calculate the wear coefficient is to make use of the total volume loss and the total sliding distance covered [7]. This practice would give a higher standard steady-state wear coefficient value since the higher wear rate from the transient wear is included in its computation. It is also obvious that variations of the standard wear coefficient values can occur since those determined near the transient wear regime will have higher values than those from the steady-state wear regime. It will be shown in Section 5.11 that variations can range from 5 to 10 times, based on data obtained in this study. It should be noted that
0043-1648/03/$ – see front matter © 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0043-1648(03)00191-1
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A6061 aluminum-based composites (MMC-A, MMC-B and MMC-C) reinforced with 10, 15 and 20% aluminium oxide (alumina) particles, respectively. Both the moving-pin technique developed at Nanyang Technological University [3] and the conventional pin-on-disc technique were used in the wear testing. The former technique used a spiral wear track while the latter a circular wear track. Both the standard and the net steady-state wear coefficient values of the specimens were determined by using the standard method and the first standard wear coefficient equation developed earlier [10]. In the present study, the new standard wear coefficient equation was again used to model both the transient and steady-state wear coefficients. Comparisons were then made between the corresponding wear coefficient values obtained previously and those obtained in the present study.
2. The adhesive wear model Fig. 2 shows the proposed mathematical wear model to cover the transient wear and steady-state wear of an Al–Al2 O3 (P)/steel system. The wear model consists of two parts, the transient wear and the steady-state wear. Point P represents the end of transient wear and Lt is the transient wear distance. Point P also represents the beginning of the steady-state wear. Hence, at point Q, the specimen will have covered a total sliding distance of Lq and the total volume loss will be Vq . An exponential equation is used to model the transient wear [5,6,11,12] while the Archard [13] equation is revised to model the net steady-state wear. The following sub-sections will describe the wear model in detail. 2.1. The transient wear The rate of volume removed per unit sliding distance is assumed to be a function of the volume of metal available at the junctions. dV = −BV dL (1)
Fig. 1. (a) Wear volume; and (b) standard wear coefficient vs. sliding distance curve.
the term “standard steady-state wear coefficient” is used to differentiate it from another one, the “net steady-state wear coefficient” to be introduced later in this section. Various techniques were proposed by previous investigators to solve the non-linear wear problem. Blau [8] suggested to segment the wear curve into various stages and to calculate linear wear coefficients, which were valid only for specific intervals of time. Another suggestion was to express Archard’s wear equation as a time-dependent relationship by incorporating time into the value of the wear coefficient. A mathematical expression containing time elements was also proposed by Peterson [9]. However, in this study, an exponential equation was used to model the transient wear; and Archard’s wear equation was modified to enable the net steady-state wear coefficient to be determined more precisely, based on the steady-state wear volume and sliding distance only. As the net steady-state wear coefficient was dependent on the steady-state wear volume and sliding distance, its accuracy would also depend on how accurate the transient distance was determined. Hence, a mathematical method was proposed to calculate the theoretical transient distance for the determination of the net steady-state wear coefficient value [5]. Section 2 of this paper will describe the wear model in detail while Section 3 will formulate two standard wear coefficient equations. The first standard wear coefficient equation was used in a previous study [10] and the second one is to be used in the present study. The presentation of the formulation of the first equation in this paper is to facilitate discussion and the understanding of the similar approach taken. In the previous study, weight loss data was collected from wear tests carried out on three types of commercial
Fig. 2. The proposed adhesive wear model.
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or re-arranging dV = −B dL V (2)
KS =
3HW PLρ
(11)
where V term denotes the volume, L the sliding distance and B is a constant which depends on the applied load and the surface condition of the wear surface. The negative sign describes a situation where the original volume at the junctions diminishes with sliding distance.Integrating Eq. (2) gives ln V = −BL + C (3)
where C is the constant of integration.Eq. (3) can also be expressed as V = exp−BL+C (4)
As mentioned previously, the standard wear coefficient value obtained from Eq. (10) is a function of the sliding distance as shown in Fig. 1(b). Due to the higher initial running-in wear rate, it has a higher value initially (in the transient wear regime) and will reach a steady-state value when the wear rate becomes constant. As the standard method to calculate the wear coefficient is to make use of the total volume loss and the total sliding distance covered, consequently Archard’s equation in its present form would give a higher steady-state wear coefficient value. Hence, there is a need to define the net steady-state wear coefficient (KN ). 2.2.2. Net steady-state wear coefficient (KN ) To model the net steady-state wear, Archard’s wear equation in its revised form as shown in Eq. (12), is used to represent the steady-state wear volume, VS : VS = KN PLS 3H (12)
If A is the volume at the junctions at zero sliding distance, putting L = 0 in Eq. (4), then A = expC That is, C = ln A Hence, V = A exp−BL (7) (6) (5)
Thus, the volume removed (Vt ) which is the transient wear volume, at a sliding distance L is: Vt = A − V = A − A exp−BL = A[1 − exp−BL ] that is, Vt = A[1 − exp−BL ] (8)
It should be noted that in Eq. (8), L should be ≤Lt , which is the transient wear distance. 2.2. Steady-state wear 2.2.1. Standard wear coefficient (KS ) For steady-state wear, Eq. (9) was proposed by Archard [13]. PL V = KS 3H (9)
where VS and LS are, respectively, the steady-state wear volume and sliding distance, to be defined by Eqs. (13) and (14), respectively. KN is the dimensionless net steady-state wear coefficient. Fig. 2 shows the proposed mathematical model to cover the transient wear and steady-state wear of an Al–Al2 O3 (P)/steel system. Point P represents the end of transient wear and Lt is the transient wear distance. Point P also represents the beginning of the steady-state wear. Hence, at point Q, the specimen will have covered a total sliding distance of Lq and the total volume loss will be Vq . The steady-state sliding distance (LS ) and the steady-state wear volume (VS ) can be calculated by using Eqs. (13) and (14), respectively. LS = Lq − Lt VS = Vq − Vt (13) (14)
Hence, the net steady-state wear coefficient (KN ) can be computed from Eq. (15). KN = 3HVS PLS (15)
where V is the volumetric loss of the softer material after sliding for a distance L at load P normal to the wear surface. H is the Brinell hardness of the softer wearing material while KS a dimensionless standard wear coefficient characterizing the particular pin–disc interface. For known values of V, P, L and H, the standard wear coefficient can be calculated from Eq. (10). For a particular material, it should be noted that V can also be estimated from the weight loss W and the density ρ. Hence, the standard wear coefficient can also be determined from Eq. (11). KS = 3HV PL (10)
With the revised Archard’s wear equation, a more precise net steady-state wear coefficient (KN ) can be obtained, to facilitate a better comparison of the wear properties of similar or non-similar materials, since the higher wear rate from the transient wear is excluded. Considerable time could also be saved in wear testing since a much longer sliding distance required by the conventional method would no longer be needed. Furthermore, more consistent results would be obtained, as the wear track is less likely to be damaged by a shorter sliding distance.
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2.3. Transient distance To determine the transient distance, it is assumed that the sliding distance L = Lt is the end of the transient wear and beginning of steady-state wear. From Fig. 2, it is obvious that at L = Lt the gradient of transient wear is equal to the gradient of the steady-state wear. Differentiate Eq. (8) gives, dV = AB exp−BL dL Differentiate Eq. (12) gives dVs KN P = dLs 3H Equating Eqs. (16) and (17) gives AB exp−BLt = or ln KN P = −BLt 3HAB KN P 3H (17) (16)
system. It is expressed as: Vc = g1 P d(1 − fv ) −g3 fv L 1 − exp g3 H fv d(1 − fv ) (20)
where Vc is the volumetric pin material loss, H the pin hardness, P the load, fv is the particle volume fraction, d the average particle size, L the distance, g1 and g3 are experimental constants to be determined from Eqs. (22) and (25), respectively. As will be mentioned later in this section, g1 is a function of the applied load (P), the pin hardness (H) and the gradient (mA ) of the Vc curve at L = 0. The g3 is a function of the average particle diameter (d), the volume fraction of particles (fv ), the transient distance (Lt ), the gradients of the Vc curve (mA and mB ) at L = 0 and L = Lt , respectively. Differentiating Eq. (20) with respect to L gives g1 P −g3 fv L dVc = exp dL H d(1 − fv ) (21)
Hence, −ln[KN P/3HAB] Lt = B Substitute Eq. (15) into Eq. (18) gives, Lt = −ln[Vs /ABLs ] B
(18)
(19)
Eq. (19) indicates that the transient distance Lt can be determined if the constants A and B as well as the LS and VS values are known. A and B values can be obtained from the transient data points from the respective volume loss versus distance curve by using standard softwares. However, both LS and VS values can not be determined from Eqs. (13) and (14) without a Lt value. To overcome this difficulty, a number of approximate transient distance values (Lta ) are selected to work out some approximate Lsa and Vsa values. With these values, a number of transient distance (Lt ) values can then be found from Eq. (19). The average Lt value is then used to calculate the LS and VS values, by using Eqs. (13) and (14), respectively. Consequently the net steady-state wear coefficient KN can be computed from Eq. (15). The choice of Lta is not critical and it will not affect the calculated results significantly. This is because the steady-state wear, as expressed by Eq. (12), generally has a linear relationship.
Eq. (21) is valid in transient wear only and till the onset of steady wear. If it is allowed to progress from transient wear into steady wear, the curve will level off horizontally and this will violate Archard’s steady-state wear theory as mentioned previously. To determine g1 and g3 , let the gradients of the Vc graph be mA at L = 0, and mB at L = Lt , which is the onset of steady-state wear. Invoking the first boundary condition when the first derivative of Vc equals to mA and L = 0 in Eq. (21), g1 can now be determined from Eq. (22). HmA (22) g1 = P The second boundary condition is at L = Lt , which is the onset of steady-state wear, where gradient of Vc is mB : mB = −g3 fv Lt g1 P exp H d(1 − fv ) g1 P H g 3 f v Lt d(1 − fv ) (23)
By employing natural logarithm throughout Eq. (23), lnmB = ln − (24)
Substituting Eq. (22) into Eq. (24) and rearranging gives d(1 − fv ) (ln mA − ln mB ) (25) g3 = fv Lt With constants g1 and g3 determined, the transient wear volume loss for a steel–MMC system can be predicted from Eq. (20). By substituting Eq. (20) into Eq. (10), one gets KS = 3g1 d(1 − fv ) −g3 fv L 1 − exp g3 fv L d(1 − fv ) (26)
3. Formulations of wear coefficient equations 3.1. First standard wear coefficient equation proposed by Yang [10] Zhang et al. [14] postulated a mathematical model for the transient wear volume of an Al–SiC(P)/steel composite
It should be noted that the effects of load and pin hardness are taken into account in the determination of g1 , as indicated in Eq. (22). Hence, by substituting Eq. (22) into Eq. (26), one gets Eq. (27) which shows clearly the effects of load and pin hardness on the wear coefficient. KS = 3HmA d(1 − fv ) −g3 fv L 1 − exp PLg3 fv d(1 − fv ) (27)
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3.2. Effects of exponential factors FA and FB Eq. (20) can be re-written as Vc = where FA = 1 − exp −g3 fv L d(1 − fv ) (29) g1 P d(1 − fv ) [FA ] g3 H fv (28)
Eq. (20) was proposed for the transient wear volume only as it contains a function FA as shown in Eq. (29). FA is an exponential function of L and it has the effect of increasing the volume rapidly to reach a steady state. Hence, Eq. (20) can not be used for the determination of the steady-state wear volume since it violates the Archard’s equation for wear, Eq. (10). As Eq. (27) also contains such a function, one may wonder why Eq. (27) can be used successfully to determine the standard steady-state wear coefficient. To understand the rational, it is necessary to examine Eq. (27) carefully. Eq. (27) can be re-written as KS = 3HmA d(1 − fv ) 1 Pg3 fv L 1 − exp −g3 fv L d(1 − fv ) (30) or KS = where FB = 1 L FA L 1 − exp −g3 fv L d(1 − fv ) (32) 3HmA d(1 − fv ) [FB ] Pg3 fv (31)
Fig. 3. Characteristics of factors FA and FB vs. distance.
It will be shown in Section 5.7 that the average deviation of using this equation is about 19%. It should be noted that the value of FB is also equal to FA /L, as indicated by Eq. (33). The FA value will only increase very slowly after the initial period. Furthermore, factor FA can only have a maximum value of unity. Hence, the value of FB will decrease further as the distance (L) is increased, and will become zero when L is at infinity. Hence, due care should be exercised to select the correct distance L. The best distances to select should give a FA value that is close to, but slightly lower than unity. This is to reduce the risk of obtaining an inaccurate and lower wear coefficient value. 3.3. Current standard wear coefficient equation proposed by Yang
Comparing Eq. (32) with Eq. (29), it is obvious that FB = (33)
By substituting Eq. (8) into Eq. (10), one gets KS = 3HA [1 − exp−BL ] PL (34)
It is clear that Eq. (27) contains factor FB , which is related to FA as shown in Eq. (33). However, the behaviour of FB is different from that of FA . Fig. 3 shows the values of factors FA and FB plotted against distance, from 0.25 to 12 km, for MMC-A, MMC-B and MMC-C, respectively; and based on data obtained previously [10]. It can be seen from Fig. 3 that the average value of FA and FB varies from about 0.16 to 1.0 and 6.5×10−5 to 0.8× 10−5 , respectively, from a sliding distance of 0.25–12 km. FA increases rapidly and reaches almost 100% of the maximum value at 9 km. However, FB decreases more gradually, reaches to 1.1 at 9 km, or 83% reduction from its maximum value. Hence, Eq. (20), which contains factor FA , is unsuitable for the determination of the wear volume in steady-state wear since it will give a horizontal line in the steady-state wear regime which is different from the actual volume loss versus distance line. On the other hand, Eq. (27), which contains factor FB , was found to be capable of predicting the standard steady-state wear coefficients with a good accuracy.
By adapting the same approach used in Section 3.2 and let FA = [1 − exp−BL ] FB = 1 [1 − exp−BL ] L 3HA [FB ] P (35) (36)
then Eq. (34) becomes KS = (37)
As mentioned in Section 3.2, to obtain realistic values from Eq. (34) to predict the standard steady-state wear coefficients, L should be selected to give a FA value that is close to, but slightly lower than unity. Again, this is to reduce the risk of obtaining an inaccurate and lower wear coefficient value. It should be noted that Eq. (34) is similar to Eq. (27), both are of the exponential types. However, experience has
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indicated that there are some difficulties in using Eq. (27). First of all, the distribution of particles in a metal matrix composite is always non-uniform, to give different (fv ) values from one section to another. Next, different particle sizes (d) are present in a particular section. Furthermore, only two gradients, mA and mB are used to define the curve which may not turn up to be exact. In the case of Eq. (34), only two parameters (A and B) need to be determined, as the other parameters such as H, P, and L are known. With the use of established softwares, the values of A and B can be determined more accurately as all the transient data points are fully utilized to obtain the ‘best-fit’ curve for the transient wear volume. Hence, more accurate results can be obtained with Eq. (34). It will be shown in Section 5.7 that the average deviation of using this equation is about 14%.
on the same surface can also damage the wear track to affect the test results. In an attempt to overcome the above-mentioned shortcoming, the moving-pin technique with a spiral wear track was developed by Yang [3]. This technique was found particularly useful for testing hard pin material like cemented tungsten carbide. It was again used in the current study, as the aluminium-based matrix composites containing alumina can be abrasive to cause a rapid wear of the disc material. It can be seen from Eq. (38) that, for the same N, the linear speed of the disc is directly proportional to R. With the aid of computer numerical control (CNC) technology, R can be varied while the linear velocity of the disc is kept constant. The feed rate of the pin can also be specified. However, a high feed rate should be avoided in order not to affect the actual wear rate. 4.2. Experimental set-up Fig. 4 shows the schematic experimental set-up for carrying out the wear tests. The fixture is clamped onto the tool post of the CNC lathe and carries a square tool pin holder and a pneumatic cylinder which is used to provide the required load which is adjustable during the wear testing of the pins. A pressure gauge was used to monitor the load pressure and a throttle valve was used to adjust the required load. A Rikadenki Type R-63 multi-pen recorder and a Kistler Type 9121 force dynamometer were used to measure the force between the pin and the disc during wear testing [3]. The pin holder was designed to ensure that the pin specimen would be held firmly during the wear tests, with 20 mm of the pin held inside the holder and 5 mm of it protruding out for wear test purposes. The protruded pin surface must have full contact with the disc to obtain accurate experimental results. Thus, close dimension tolerance was maintained when machining the pin holder and the pins.
4. Experimental methodology used in the previous studies 4.1. The moving-pin technique With the conventional pin-on-disc wear test, the pin specimen is held stationary on top of a precision ground rotating disc, with the required load applied through the pin. With the use of a variable speed motor, the rotational speed of the disc can be varied. The linear speed of the disc at the point where the pin is located is: Vdisc = 2πRN (38)
where Vdisc is the linear speed of the rotating disc, R the distance from the centre of the pin to the centre of the disc and N the rotational speed of the disc. The conventional pin-on-disc wear test is conducted with a fixed R and only a small portion of the disc is utilized. The continuous rubbing
Fig. 4. Schematic experimental set-up for carrying out the wear tests.
L.J. Yang / Wear 255 (2003) 579–592 Table 1 Density and hardness of pin materials MMC-A Density (g/cm3 ) Measured Calculated Measured 2.817 2.823 611 MMC-B 2.895 2.885 554 MMC-C 2.973 2.946 579
585
were obviously manufactured in different batches, with different alumina sizes. 4.4. Experimental technique Wear tests for the MMC-A, MMC-B and MMC-C were carried out at distances of 250, 500, 1000, 1500, 2000, 2500, 3000, 6000, 9000 and 12,000 m. Both the moving-pin and the conventional pin-on-disc techniques were used. A constant load of 7.5 kgf, linear velocity of 4.58 m/s and a feed rate of 0.05 mm/rev was used for the moving-pin technique. The pin would start at a radius of 87.5 mm on the rotating disc and would travel to a radius of 20 mm before returning back to the initial point. A stopwatch was used to time the cycle time needed based on the wear distance and constant linear velocity of 4.58 m/s for the collection of weight loss data. As for the conventional pin-on-disc experiment, the pin was held stationary at a radius of 87.5 mm of the rotating disc and a constant sliding speed of 500 rpm. The other factors remained the same as the moving-pin technique. Three repetitions were carried out for each experiment [16].
HB (MPa)
4.3. Disc and pin materials The discs used in this study were made of Assab DF2 tool steel (equivalent to AISI 01) hardened and tempered to 60 HRC (697 Hv), and ground to a surface finish of 0.3 m (Ra ). The discs had a diameter of 180 mm and a thickness of 30 mm. The pins were machined accurately to a size of 10 mm × 10 mm and a length 25 mm by a wire-cut electro-discharge machining (EDM) process to fit the pin holder. The pin materials used in this experiment were A6061 aluminium-based matrix composites with different nominal volume fraction of alumina particles, MMC-A with 10% alumina, MMC-B with 15% alumina and MMC-C with 20% alumina. These materials were supplied by Comalco in the form of flat bars extruded from Duralcan billets. The density of the specimens was measured by using a Ultrapycnometer. The hardness of the three composite materials was tested using a Brinell hardness tester. Table 1 shows the density and hardness values of the pin materials. The [15] gives the density of A6061 as 2.70 and 3.75–3.93 g/cm3 for alumina. Based on the nominal volume fraction of alumina given by the manufacturer, the theoretical density was calculated, based on a value of 3.93 g/cm3 for alumina, and listed in Table 1. It can be seen from the table that the deviations of both the measured and calculated density values are small, indicating the nominal volume fraction of alumina in each material is approximately correct. However, MMC-A contains a lower volume fraction of alumina and should give a lower hardness value. This does not seem to be the case, presumably due to different processing parameters used in its manufacture. Scanning electron microscopy (SEM) was used to determine the cross-sectional area of the particles. Table 2 shows the average cross-sectional area of the alumina particles observed and the computed average diameter (d) of the particles for each type of material. The average diameter ranges from 24 to 36 m for the three composite materials, which
5. Results and discussions 5.1. Wear test data collected previously Weight loss data were collected from tests performed with both the moving-pin technique and the conventional pin-on-disc technique for MMC-A, MMC-B and MMC-C, at sliding distances from 250 to 12,000 m. Their average wear volume loss values, obtained by dividing the respective average weight loss value by its measured density, are presented in Table 3. 5.2. Wear volume loss curves Fig. 5 shows the wear volume loss against distance curves for MMC-A, MMC-B and MMC-C, with data obtained from both the moving-pin and the conventional pin-on-disc methods. In the figure, V(M)-A and V(C)-A indicate the wear volume loss values (V) of MMC-A tested under moving-pin and conventional pin-on-disc conditions, respectively. Fig. 5 indicates that the curves can generally be divided into two regimes, the transient regime and the steady-state regime. For each material, the actual wear volume loss curve is initially curvilinear and the rate of volume loss per unit
Table 2 Average area and diameter of alumina particles in MMC-A, MMC-B and MMC-C A1 ( m)2 MMC-A MMC-B MMC-C 754 958 447 A2 ( m)2 722 1050 454 A3 ( m)2 690 998 480 A4 ( m)2 701 1120 400 A5 ( m)2 662 986 460 Average area A ( m)2 706 1023 448 d ( m) 30 36 24
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Table 3 Volume loss and standard wear coefficient values (K1 , K2 and K3 ) obtained for MMC-A, MMC-B and MMC-C Distance (m) Moving-pin method Average MMC-A 250 500 1000 1500 2000 2500 3000 6000 9000 12000 MMC-B 250 500 1000 1500 2000 2500 3000 6000 9000 12000 MMC-C 250 500 1000 1500 2000 2500 3000 6000 9000 12000 2.47 4.24 6.42 8.15 9.17 9.71 10.40 13.45 17.54 21.84 1.89 3.16 4.24 4.95 5.69 6.52 7.08 9.42 12.99 17.74 1.36 2.12 3.52 4.62 5.18 5.35 5.60 7.46 9.81 13.7 V (mm3 ) K1 (× 24.6 21.1 16.0 13.5 11.4 9.7 8.6 5.6 4.9 4.5 17.1 14.3 9.6 7.5 6.4 5.9 5.3 3.6 3.3 3.3 12.8 10.0 8.3 7.3 6.1 5.1 4.4 2.9 2.6 2.7 10−5 ) K2 (× 22.3 20.3 17.0 14.4 12.3 10.7 9.4 5.2 3.5 2.6 15.4 14.1 11.9 10.1 8.7 7.6 6.7 3.7 2.5 1.9 11.9 11.1 9.1 8.6 7.6 6.8 6.1 3.6 2.5 1.9 10−5 ) K3 (× 22.6 20.3 16.5 13.6 11.5 9.8 8.5 4.5 3.0 2.3 13.6 12.2 9.9 8.1 6.8 5.8 5.0 2.7 1.8 1.3 11.7 10.5 8.6 7.1 6.0 5.1 4.4 2.4 1.6 1.2 10−5 ) Conventional pin-on-disc method Average 3.80 5.30 7.32 9.00 10.13 11.02 12.12 15.25 17.89 22.11 1.45 2.65 4.42 5.53 6.11 6.90 7.57 10.26 13.59 18.95 1.42 2.41 4.62 6.13 7.03 8.32 9.04 11.1 13.8 17.8 V (mm3 ) K1 (× 10−5 ) 37.8 26.4 18.2 14.9 12.6 11.0 10.1 6.3 5.0 4.6 13.1 12.0 10.0 8.3 6.9 6.2 5.7 3.9 3.4 3.6 13.4 11.4 10.9 9.6 8.3 7.9 7.1 4.4 3.6 3.5 K2 (× 10−5 ) 34.5 31.4 26.4 22.4 19.3 16.7 14.7 8.1 5.4 4.1 12.2 11.4 9.9 8.7 7.7 6.9 6.2 3.6 2.5 1.9 12.5 11.7 10.3 9.1 8.1 7.3 6.6 3.9 2.7 2.0 K3 (× 10−5 ) 27.5 24.4 19.4 15.8 13.1 11.1 9.5 5.0 3.3 2.5 12.6 11.6 9.8 8.4 7.2 6.3 5.5 3.1 2.1 1.5 12.6 11.9 10.6 9.5 8.6 7.8 7.1 4.4 3.0 2.3
Note: K1 , K2 and K3 were computed by using Eqs. (10), (27) and (34), respectively.
Fig. 5. Wear volume loss against distance curves for MMC-A, MMC-B and MMC-C.
sliding distance decreases until a point, i.e. at the transient distance, beyond which it becomes almost constant. By visual inspection of the curves, the end point of the transient region is about 2000–3000 m. The wear loss values for the specimens tested with the conventional pin-on-disc method, indicated by the dotted lines, were found to be higher, as compared with those tested with the moving-pin method. It should be noted that the wear volume of a pin from the pin-on-disc test depends greatly on the condition of the wear track. The single wear track generated by the conventional pin-on-disc method can be damaged more easily by alumina particles or wear debris, to give a higher wear rate. A slightly higher wear volume loss can also be observed on some specimens tested up to 12 km due to the same reason. The volume loss of MMC-A is also found to be higher than that of MMC-B and MMC-C. Again this is due to the presence of a smaller volume fraction of alumina particles in MMC-A. It seems that the presence of a larger volume fraction of alumina particles would increase the wear resistance of the
L.J. Yang / Wear 255 (2003) 579–592 Table 4 The g1 and g3 values for MMC-A, MMC-B and MMC-C Moving-pin method g1 (× MMC-A 8.2 MMC-B 5.65 MMC-C 4.25 10−5 ) g3 (× 2.14 1.56 0.547 10−7 )
587
Conventional pin-on-disc method g1 (× 10−5 ) g3 (× 10−7 ) 12.63 4.37 4.47 2.09 1.20 0.525
Fig. 6. Standard wear coefficient (K1 ) vs. distance curves for MMC-A, MMC-B and MMC-C.
MMC materials as in MMC-B and MMC-C, especially so in the transient wear regime. 5.3. Standard wear coefficient (K1 ) against distance curves Table 3 also contains the standard wear coefficient (K1 ) values, computed from their respective wear volume loss values with Eq. (10), against distance for MMC-A, MMC-B and MMC-C, respectively. Fig. 6 shows the standard wear coefficient (K1 ) curves versus distance for MMC-A, MMC-B and MMC-C, with data obtained from both the moving-pin and the conventional pin-on-disc methods. In the figure, K1 (M)-A and K1 (C)-A indicate the standard wear coefficient values (K1 ) of MMC-A tested under moving-pin and conventional pin-on-disc conditions, respectively. It can be seen from the figure that the standard wear coefficient (K1 ) decreases more rapidly as the distance increases initially, but more gradually when approaching the steady-state wear and eventually becomes almost a horizontal line in the steady-state wear. The standard wear coefficient values for the specimens tested with the conventional pin-on-disc method, indicated by dotted lines, were found to be higher, as compared with those tested with the moving-pin method, due to their higher wear volumes as discussed in Section 5.2. 5.4. Standard wear coefficient (K2 ) against distance curves To determine K2 with Eq. (27), g1 and g3 need to be calculated. The gradients mA and mB were firstly determined at L = 0 and at L = 2500 m, respectively. The latter was estimated from the volume loss versus distance curves, as shown in Fig. 5, to be the average distance at the end of transient wear and the beginning of steady wear. It will also be shown in Section 5.8 that the average calculated transient distance is 2502 m. The corresponding g1 and g3 values for the three composite materials, based on data obtained from both the
moving-pin and conventional pin-on-disc techniques, were then determined from Eqs. (22) and (25), respectively, and tabulated in Table 4. It should be noted from Table 4 that for MMC-A, the g1 value calculated from the data obtained with the conventional pin-on-disc method is considerably higher than that from the moving-pin method. Table 2 indicates that MMC-A has the highest hardness value despite the fact that it has the lowest volume fraction of alumina particles. Obviously a different hardening mechanism was probably involved in MMC-A which made it less wear resistance when tested with the conventional pin-on-disc method. The wear coefficient values, K2 , were computed by using Eq. (27) and were again presented in Table 3 for the three materials. It can be seen from Table 3 that similar trend and standard wear coefficient values were obtained for K2 and K1 . However, a more detailed comparison of K2 and K1 values will be discussed in Section 5.7. 5.5. Standard wear coefficient (K3 ) against distance curves The wear loss volumes, computed from data obtained by both the moving-pin and conventional pin-on-disc methods, and at distances of 500, 1000, 1500, 2000, 2500 and 3000 m, were input into a commercial software DataFit Version 6 [17], to determine their transient wear equation constants A and B. Table 5 shows the values of these constants. With the A and B values from Table 5, the wear coefficient values, K3 , were computed by using Eq. (34) and were again presented in Table 3. It should be noted that the K1 values were obtained directly from the measured weight loss data, the K2 values from the first standard wear coefficient equation Eq. (27) proposed by Yang [10] while K3 is from the newly proposed standard wear coefficient equation Eq. (34). It can again be
Table 5 Transient wear equation constants A and B, for MMC-A, MMC-B and MMC-C Moving-pin method A MMC-A MMC-B MMC-C 10.87 7.09 6.02 B (× 9.36 9.54 9.24 10−4 ) Conventional pin-on-disc method A 11.95 8.25 11.79 B (× 10−4 ) 10.51 7.43 4.80
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Fig. 7. Standard wear coefficient (K1 , K2 and K3 ) vs. distance (MMC-A).
seen from these figures that similar trend and standard wear coefficient values were obtained for K1 , K2 and K3 , both in the transient wear regime and in the steady-state wear regime. To facilitate comparison, the wear coefficient values, K1 , K2 and K3 for MMC-A are also plotted in Fig. 7, in which K1 (M)-A and K1 (C)-A indicate the wear coefficient values (K1 ) of MMC-A tested under moving-pin and conventional pin-on-disc conditions respectively. Similarly, K2 or K3 (M)-A and K2 or K3 (C)-A indicate the wear coefficient values (K2 or K3 ) of MMC-A tested again under moving-pin and conventional pin-on-disc conditions, respectively. It can be seen from Fig. 7 that K3 has given a slightly lower wear coefficient value in the steady-state wear. Similar trends were also observed for MMC-B and MMC-C. Section 5.10 will discuss the significance of this observation. 5.6. FA and FB values for K3 As indicated in Section 3.3, to obtain realistic standard wear coefficient values from Eq. (34), the FA values should be close to, but slightly lower than unity. Hence, the FA
Table 6 Values of factors FA and FB versus distance Distance (m) FA for MMC-A MP 250 500 1000 1500 2000 2500 3000 6000 9000 12000 0.209 0.374 0.608 0.754 0.846 0.904 0.940 0.996 1.000 1.000 CP 0.231 0.409 0.650 0.793 0.878 0.928 0.957 0.998 1.000 1.000 FA for MMC-B MP 0.212 0.379 0.615 0.761 0.852 0.908 0.943 0.997 1.000 1.000 CP 0.170 0.310 0.524 0.672 0.774 0.844 0.892 0.988 0.999 1.000
and FB values were determined, respectively, from Eqs. (35) and (36), and tabulated in Table 6 for the three materials from a distance of 0.25–12 km; and based on data obtained from both the moving-pin and the conventional pin-on-disc techniques. It can be seen from Table 6 that the average values of FA and FB have similar trends to those obtained previously and plotted in Fig. 3. However, it should be noted that the FA value of 0.944 at 6000 m for MMC-C is too low and it was excluded in calculating the average FA value as listed in Table 6. For the same reason, the corresponding K3 value was omitted in the calculation of the average K3 value plotted in Fig. 10. Table 6 shows again that factor FA are close to, but slightly lower than unity, with an average value of 0.995, 0.998 and 1.000 for the three materials, when the sliding distances are 6, 9 and 12 km, respectively. Hence, the standard steady-state wear coefficient (K3 ) values obtained earlier in Section 5.5 by Eq. (34) are realistic. 5.7. Deviations of K2 and K3 against K1 To evaluate the accuracy of Eq. (34), that is the K3 values, the percentage deviations of K2 and K3 values against K1 values ( K2 and K3 ) were calculated by using Eqs. (39) and (40), respectively, and plotted in Fig. 8. The K1 , K2 and K3 values were taken from Table 3 for MMC-A, MMC-B and MMC-C, respectively, from data obtained with the moving-pin method. K2 = K3 = K2 − K1 × 100 K1 K3 − K 1 × 100 K1 (39) (40)
It can be seen from Fig. 8 that the deviation of K3 , shown with solid lines in the figures, is generally lower than that of K2 . The deviation trend starts with a negative value and then increases slightly before it decreases again. However, for K3 , most of the negative deviations are found in
FA for MMC-C MP 0.206 0.370 0.603 0.750 0.842 0.901 0.938 0.996 1.000 1.000 CP 0.113 0.213 0.381 0.513 0.617 0.699 0.763 0.944 (a) 0.987 0.997
Average FA
Average FB (× 10−5 )
0.190 0.343 0.564 0.707 0.802 0.864 0.906 0.995 (b) 0.998 1.000
7.60 6.85 5.64 4.72 4.01 3.46 3.02 1.64 1.11 0.83
Notes: MP is moving-pin method; and CP conventional pin-on-disc method; (a) this value was too low and was omitted in the calculation of the average value as indicated in (b).
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a better accuracy than Eq. (27), since it contains lesser number of variables as mentioned in Section 3.3. As indicated in Section 5.5, as well as in Table 7 and Fig. 8, Eq. (34) seems to have given a lower standard steady-state wear coefficient value. Hence, Section 5.10 will compare the standard wear coefficient values (K1 , K2 and K3 ) with the net steady-state wear coefficient (KN ). 5.8. Transient distance values
Fig. 8. Deviations of K2 and K3 against K1 for MMC-A, MMC-B and MMC-C. Data obtained with the moving-pin method.
the steady-state wear regime. Similar trend was also observed with data obtained from the conventional pin-on-disc method. Table 7 shows the average deviations of the K2 and K3 against K1 for MMC-A, MMC-B and MMC-C, based on data obtained by both the moving-pin technique and the conventional pin-on-disc technique. It should be noted that, in the calculation of the average deviations, only absolute values were used. It can be seen from Table 7 that the average values for K3 are 15.0 and 12.2% for data obtained with the moving-pin and the conventional pin-on-disc techniques, respectively; while the corresponding values for K2 are 18.7 and 18.9%. Hence, the over-all average values for K3 and K2 are about 14 and 19%, respectively. It should again be noted that the K1 values were obtained directly from the measured weight loss data, the K2 values from the standard wear coefficient equation Eq. (27) while K3 from the newly proposed standard wear coefficient equation Eq. (34). It is, therefore, obvious that Eq. (34) has given
To compare the accuracy of the standard wear coefficient values, K1 , K2 and K3 , with the net steady-state wear coefficient (KN ) values for the three types of MMC materials, it is necessary to determine their respective transient distances in order to calculate the latter. Table 8 shows an example of transient distance calculation for MMC-A, by using data from the moving-pin method. The Lta values used were 2000, 2500 and 3000 m. The average transient distance values obtained, with Eq. (19), for MMC-A, MMC-B and MMC-C were, respectively, 2311, 1999 and 2228 m when the moving-pin method was used; and 2301, 2334 and 3838 m when the conventional pin-on-disc method was used. The average value of the calculated transient distance was 2502 m. Hence, it was reasonable to use an average transient distance of 2500 m to calculate the g1 and g3 values in Section 5.4. 5.9. Net Steady-state wear coefficient values (KN ) for MMC-A, MMC-B and MMC-C With the transient distance values determined, the net steady-state wear coefficient values (KN ) for MMC-A,
Table 7 Average deviations of K2 and K3 against K1 for MMC-A, MMC-B and MMC-C Method MMC-A K2 (%) MP CP 13.2 32.1 K3 (%) 12.6 15.9 MMC-B K2 (%) 23.1 13.1 K3 (%) 19.1 13.7 MMC-C K2 (%) 19.9 11.6 K3 (%) 13.3 7.0 Average K2 (%) 18.7 18.9 K3 (%) 15.0 12.2
Based on the absolute values of the deviations; MP is moving-pin method; and CP conventional pin-on-disc method. Table 8 An example of transient distance calculation for MMC-A with different Lta values (Data from moving-pin method) Lta (m) 2000 Vta (mm3 ) 9.17 L2 (m) 6000 9000 12000 6000 9000 12000 6000 9000 12000 V2 (mm3 ) 13.45 17.54 21.84 13.45 17.54 21.84 13.45 17.54 21.84 Lsa (m) 4000 7000 10000 3500 6500 9500 3000 6000 9000 Vsa (mm3 ) 4.28 8.37 12.67 3.74 7.83 12.13 3.05 7.14 11.44 Lt (m) 2406 2288 2226 2408 2278 2217 2461 2293 2222 Average Lt (m)
2307
2500
9.71
2301
3000
10.40
2325 Overall average Lt (m), 2311
590
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Table 9 An example of net steady-state wear coefficient calculation for MMC-A Lt (m) 2300 Vt (mm3 ) 9.49 L2 (m) 6000 9000 12000 V2 (mm3 ) 13.45 17.54 21.84 Ls (m) 3700 6700 9700 Vs (mm3 ) 3.96 8.05 12.35 KN (× 10−5 ) 2.67 3.00 3.18 Average KN (× 10−5 )
2.95
Note: Data from moving-pin method.
MMC-B and MMC-C were calculated with Eq. (15). Table 9 shows an example of net steady-state wear coefficient calculation for MMC-A, with data from the moving-pin method. Fig. 9 shows the net steady-state wear coefficient (KN ) plotted against the steady-state sliding distance (LS ). It should be noted that, in most cases, the net steady-state wear coefficient increases slightly with an increase of steady-state sliding distance. This was due to the occurrence of damaged wear tracks caused by fractured alumina particles when a longer sliding distance was used. The average net steady-state wear coefficient values (KN ), for MMC-A, MMC-B and MMC-C were, respectively, found to be 2.95 × 10−5 , 2.86 × 10−5 and 1.66 × 10−5 when the moving-pin method was used; and 2.91 × 10−5 , 2.50 × 10−5 and 1.97 × 10−5 when the conventional pin-on-disc method was used. 5.10. Comparison of the standard wear coefficient values (K1 , K2 and K3 ) with the net steady-state wear coefficient (KN ) As indicated in Sections 5.5 and 5.7, there is some indication that K3 has given a slightly lower standard wear coefficient value in the steady-state wear. One may wonder about the accuracy of Eq. (34), and how its steady-state K3 values are compared with the net steady-state wear coefficients. Fig. 10 shows the average standard wear coefficients
(K1 , K2 and K3 ) and the average net steady-state wear coefficient (KN ) for MMC-A, MMC-B and MMC-C. These values were obtained by taking the average of their respective values at distances of 6000, 9000 and 12,000 m, tested with both the moving-pin and the conventional pin-on-disc techniques. However, for MMC-B, the average values were based on those obtained with 9000 and 12,000 m only, as the FA value at 6000 m was only 0.944 which was too low to be classified as steady-state wear, as discussed in Section 5.7. It should be noted that, as K1 , K2 , and K3 are obtained by using Eqs. (10), (27) and (34), respectively, they are standard wear coefficients. They would, therefore, give a higher steady-state wear coefficient value, as compared with the net steady-state wear coefficient as can be seen generally in Fig. 10, since the higher wear rate from the transient wear is included in its computation, as discussed in Section 2.2. To facilitate comparisons, the deviations of K1 , K2 and K3 from their respective KN values were calculated by using Eqs. (41)–(43) for the three types of materials. Dev( K1 ) = Dev( K2 ) = Dev( K3 ) = K1 − KN × 100 KN K2 − KN × 100 KN K3 − KN × 100 KN (41)
(42)
(43)
The average deviation, for each type of material was obtained by taking the average values from those tested with the moving-pin technique and those tested with the conventional pin-on-disc technique. Although negative deviation values were observed, however, for each type of material
Fig. 9. Net steady-state wear coefficient (KN ) vs. distance (MMC-A, MMC-B and MMC-C).
Fig. 10. Average standard steady-state wear coefficients (K1 , K2 and K3 ) and the average net steady-state wear coefficient (KN ) for MMC-A, MMC-B and MMC-C.
L.J. Yang / Wear 255 (2003) 579–592 Table 10 Ratio of maximum and minimum standard wear coefficient values MMC-A Moving-pin method K1 5.5 K2 8.6 9.8 K3 MMC-B 5.2 8.1 10.5 MMC-C 4.7 6.3 9.8 3.8 6.3 5.5
591
Average 5.1 7.7 10.0 5.2 7.0 8.3
Conventional pin-on-disc method K1 8.2 3.6 K2 8.4 6.4 11.0 8.4 K3 Fig. 11. Average deviations (%) of K1 , K2 , and K3 , based on KN , for MMC-A, MMC-B and MMC-C.
and, for each K value, the average deviation was calculated by using the absolute deviation values only. Fig. 11 shows the average deviations (%) of the standard wear coefficients K1 , K2 , and K3 , based on their respective KN values. It is clear from Fig. 10 that K3 , calculated from Eq. (34), has the lowest standard wear coefficient values for all the three types of materials. It is also clear from Fig. 11 that K3 has the lowest average deviation from KN , that is, about 18% against 37 and 59% for K2 and K1 , respectively. Obviously, K3 has given the lowest standard steady-state wear coefficient value which is closest to the net steady-state wear coefficient (KN ), unlike K2 and K1 . Hence, Eq. (34) is a more accurate equation to be used for predicting the standard wear coefficient of the Al–Al2 O3 (P)/steel system, in both transient and steady-state wear. As mentioned in Section 3.3, this is also an easier equation to use since there are lesser number of variables (only A and B) involved. The [18] reported a sliding wear coefficient value of 6.3× 10−5 for a 2014 Al–20 wt.%SiC (T6) composite on SAE 52100 steel (63 HRC) with a block-on-ring type wear rig. The applied normal load was 9.35 N and a sliding velocity of 0.1 m/s was used. The average standard wear coefficient values for MMC-C with 20% alumina particles obtained from the present study are K1 = 3.3 × 10−5 , K2 = 2.8 × 10−5 and K3 = 2.2 × 10−5 which are lower than the value of 6.3×10−5 reported in [18]. However, it should be noted that different materials, testing process and parameters were used in both the studies. Furthermore, the standard wear coefficient value is a function of the sliding distance, as mentioned in Section 2.2. Due to the higher initial running-in wear rate, it has a higher value near the transient wear regime. It is also clear from Section 5.7 that, with a lower FA value, a higher wear coefficient value would be obtained, as the wear might not have reached the steady-state yet. 5.11. Ratio of maximum and minimum standard wear coefficient values Table 10 shows the ratios of the maximum standard wear coefficient value (at 250 m) against the minimum one (at
12,000 m) calculated from data listed in Table 3. It can be seen from the table that, on the average, it varies from about 5 (based on K1 ) to 10 (based on K3 ). This agrees with earlier report that variation up to 10–1 was possible [4]. Obviously, it is extremely important to distinguish between transient wear coefficients and the steady-state wear coefficients determined from a wear test. Failure to do so may have been the main reason behind the variations of wear coefficients reported previously.
6. Conclusion (i) It was found that Eq. (34) proposed in this paper was capable to model standard wear coefficients in both the transient wear and steady-state wear of the Al–Al2 O3 /steel system. The unique characteristic of factor FB was again significant in contributing to the successful use of the equation. (ii) By comparing K3 (obtained from Eq. (34)) and K2 (obtained from Eq. (27)) with the K1 values obtained directly from the measured weight loss data, the average deviation of K3 was generally lower than that of K2 . The over-all average values for K3 and K2 were about 14 and 19%, respectively. (iii) With sliding distances of 6, 9 and 12 km, the standard steady-state wear coefficient (K3 ) was found to have the lowest average deviation from the net steady-state wear coefficient (KN ), i.e. about 18% against 37 and 59% for K2 and K1 , respectively. (iv) Obviously, Eq. (34) had given to more accurate standard wear coefficient values (K3 ). Eq. (34) was also found to be easier to use since it contained lesser number of variables, only A and B involved with the transient equation; and these variables could be measured more accurately than those contained in Eq. (27). (v) The predictive power of Eq. (34) is also of great significance. Although the equation was established with the transient wear data, i.e. the A and B values, however, it is capable of predicting the standard steady-state wear coefficients as well. This is, therefore, a significant contribution to the modeling of standard wear coefficient of Al–Al2 O3 /steel system.
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L.J. Yang / Wear 255 (2003) 579–592 Proceedings of the Second Asiatrib International Conference, Jeju Island, Korea, October 2002, pp. 217–218. L.J. Yang, Steady-state wear coefficient of A6061 aluminium alloy reinforced with alumina particles, in: Proceedings of the Sixth Austrib International Conference, Perth, Australia, December 2002, pp. 575–582. E. Rabinowicz, Wear coefficients—metals, in: M.B. Peterson, W.O. Winer (Eds.), Wear Control Handbook, The American Society of Mechanical Engineers, New York, 1980. P. Blau, Friction and Wear Transitions of Materials: Break-in, Run-in, Wear-in, Noyes Publications, Park Ridge, New Jersey, USA, 1989. M. Peterson, Design considerations for effective wear control, in: M.B. Peterson, W.O. Winer (Eds.), Wear Control Handbook, The American Society of Mechanical Engineers, New York, 1980. L.J. Yang, The transient and steady wear coefficients of A6061 aluminium alloy reinforced with alumina particles, Compos. Sci. Technol. 63 (2003) 575–583. C.A. Queener, T.C. Smith, W.L. Mitchell, Transient wear of machine parts, Wear 8 (1965) 391–400. A.D. Sarkar, Wear of Metals, Pergamon Press, Oxford, New York, 1976. J.F. Archard, Contact and rubbing of flat surfaces, J. Appl. Phys. 24 (1953) 981. Z.F. Zhang, L.C. Zhang, Y.W. Mai, Running-in wear of steel/Si(CP)–Al composite system, Wear 194 (1996) 38–43. P.K. Mallick, Composites Engineering Handbook, Marcel Decker, New York, 1980. P.K. Low, Wear characteristics of aluminium alloy (A6061) reinforced with alumina, B.E. Final Year Project Report, School of Mechanical and Production Engineering, Nanyang Technological University, May 2001. Oakdale Engineering, http://www.oakdaleengr.com. A.T. Alpas, J.D. Embury, Wear mechanisms in particle reinforced and laminated metal matrix composites, Wear of Materials, vols. 159–166, ASME, 1991.
(vi) This work has also explained the possible cause of variations in the determination of wear coefficients. A variation of up to 10–1 between wear coefficients in the transient regime and that in the steady-state regime was observed. This paper has, therefore, contributed to a better understanding of the characteristic of standard wear coefficients. Acknowledgements The author would like to thank the support of this project by Applied Research Fund #72/93 provided by Nanyang Technological University; Dr. Malcolm Couper, Comalco Research Centre, Thomastown, Australia for supplying the composite materials used in the investigation. References
[1] A.R. Lansdown, A.L. Price, Materials to resist wear, Wear, Pergamon Press, Oxford, 1986. [2] L.J. Yang, N.L. Loh, The wear properties of plasma transferred arc cladded stellite specimens, Surf. Coat. Technol. 71 (1995) 196– 200. [3] L.J. Yang, Pin-on-disc wear testing of tungsten carbide with a new moving-pin technique, Wear 225–229 (1999) 557–562. [4] M. Godet, Modeling of friction and wear phenomena, in: F.F. Ling, C.H.T. Pan (Eds.), Approaches To Modeling Of Friction And Wear, Springer–Verlag, Berlin, 1988. [5] L.J. Yang, Determination of transient wear distance in the adhesive wear of A6061 aluminium alloy reinforced with alumina, in:
[6]
[7]
[8] [9]
[10]
[11] [12] [13] [14] [15] [16]
[17] [18]
