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Sliding sphere experiments on various single crystals of MnZn Ferrite
Wear, 131
353
(1989) 353 - 364
SLIDING SPHERE EXPERIMENTS OF MnZn FERRITE
ON VARIOUS
SINGLE
CRYSTALS
A. BROESE VAN GROENOU and S. E. KADIJK Philips Research
Laboratories,
(Received October 3,1988;
P.O. Box 80 000, 5600 JA Eindhouen
(The Netherlands)
accepted January 24,1989)
Summary By sliding a ruby sphere (0.25 mm in radius) on various MnZn ferrite crystals quantitative information has been obtained on the groove depth at speeds of 0.4 - 400 pm s-l at loads of 1 - 10 N and after 1 - 1000 passes. Above a certain threshold, a simple empirical relation is found between depth and load, lg,,(speed) and lg,,(passes) at 20 “C. The threshold is lowest for sliding on (111) and highest on (100). These planes also give the extremes of the wear rate of recording heads against video tape. For the (110) crystal the temperature was varied between 20 and 290 “C, showing a larger influence of load on depth, but without an extra speed effect. This result means that thermal propagation of slip is not the bottleneck in plastic deformation here.
1. Introduction In cubic materials with the spine1 structure, ABz04, wear and polishing rate show considerable anisotropy. For a sphere of the spine1 MgAl,O,, in contact with a mild steel at a calculated contact stress of 0.7 GPa, Duwel [l] found on the (100) plane along (100) wear a factor of 50 greater than along (011). The hardness on the same plane varied between 1.47 and 1.79 GPa, i.e. by +lO% [2]. Ferrite spinels, especially (Mn, Zn, Fe) Fez04, are commonly used as single crystalline materials for magnetic recording heads. Here again a factor of 50 is found for the variation in the wear rate, now for recording heads of different orientations, running against CrO, tape in a video tape recorder [3]. Wear is least on (100) and largest on (111). The Knoop [4] and Vickers [5, 61 hardness, however,‘vary between 5.9 and 6.8 GPa, i.e. by only + lo%, between the various directions. In lapping experiments on MnZn ferrite, the residual surface stress and the depth where the stress becomes zero, also depend on the plane [7]. The largest stress is found on (211), 2.3 GPa, the lowest on (loo), 1.0 GPa, while the depth of the stressed material varies from 0.1 pm (110) to more than 1 pm on (111). 0043-1648/89/$3.50
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in The Netherlands
354
Several authors have tried to model these phenomena by sliding indenters and observe the surface deformation. On MnZn ferrite, Yonezawa et al. [7] used diamond spheres with a radius of 3 - 5 pm at a load of 0.5 N (the calculated elastic stress is 49 GPa) and found cracking on {Ill) planes, Tanaka et al. [6] halved the contact stress by using sliders 20 pm in radius, but still observed mainly cracking around the grooves and no slip patterns that could be analysed. At about the same hertzian stress of 20 GPa, Miyoshi and Buckley [S] also observed cracks, but also a considerable anisotropy in friction, 0.21 to 0.29. An even larger variation in friction coefficient was seen when the diamond slider was replaced by a ferrite of the same composition [S]. Depending on the differences in orientation, the friction varied between 0.2 and 0.6. No cracks were observed for a sphere radius of 0.79 mm at an elastic stress of the order of 0.6 GPa. Other examples where the use of a larger sphere resulted in plastic deformation without cracking, are MgO and TiOz. On (100) planes of MgO, Dufrane and Glaeser [9] used a rolling steel sphere (0.6 GPa) and obtained slip patterns that correspond to (110) slip. The depth where slip could still be detected depends on the direction of rolling and on the speed, the largest dependence occurring in the 1 - 400 mm s-l range, Cracks were observed above 10’ passes. At a much higher stress (17 GPa) Miyoshi and Buckley [8] found considerable cracking after one pass. On TiO, Stein had the same experience [lo]. For small radius sliders cracking was seen at a stress of 9 GPa, while for larger radii, cracks were avoided and slip was observed. ‘Stein strongly advocated the use of sliding spheres to determine the mechanism of plastic deformation in brittle materials at room temperature. He identified the slip systems in TiO, and found these to be the same as those that operate above 600 “C. Swain and Lawn [ll, 121 did experiments on LiF and analysed the results of Dufrane and Glaeser on MgO. Their conclusion is that the sliding sphere allows the analysis of the onset of slip, whereas the Knoop indenter presumably samples the work hardening characteristics rather than the flow stress [ 121. The onset of slip in polycrystalline NiZn and MnZn ferrites was observed by the present authors [ 131. By increasing the number of passes, cracks occurred at the grain boundaries. Grain pull-out takes place at high loads, low speeds and under wet conditions. On a (100) plane of a single crystal of MnZn ferrite sliding and indentations showed simple slip patterns. By polishing and etching, subsurface slip could be observed as well. The patterns were attributed to slip on the {ill} and {loo) planes. The loaded sphere has another advantage, namely its known stress distribution (Hamilton and Goodman [14,15]). This was used to determine the resolved shear stress needed for slip to appear on MgO and LiF by Swain and Lawn [ll, 121. In a forthcoming publication the present authors will give the corresponding analysis of the slip patterns made by indenting various planes of MnZn ferrite crystals. The analysis requires slip on three systems, the {loo], (111) and (11Oj. The present work is an extension of
355
previous work on the deformation by a sliding sphere [ 131. Here grooves will be described made on crystal planes for which wear data are available [3]. The analysis of the slip patterns in the grooves will be given in later papers.
2. Experimental details 2.1. Sliding apparatus The sliding apparatus consists of a balance, with a damping system on one arm, on the other arm an indenter, in this case a sphere. An x-y table carries the sample, which can be transported by a motor [16]. The indenter, a ruby sphere with a diameter of 0.25 mm, is loaded by means of a weight (giving loads of 0.1 - 10 N). If there is severe damage on the surface of the sample the ruby may be damaged as well. Sometimes fine ferrite wear particles adhere to the sphere and may be a cause of fine scratches on the sample. For these reasons the sphere was normally checked after each experiment. If damage was found, the sphere was rotated and fastened again in order to obtain a fresh area of the surface. In most cases it was sufficient to clean the sphere with acetone or ethanol. The scratching experiment can be followed by means of a camera, which is focused on the indenter. At the start of the experiment, the balance is brought into equilibrium and is then lowered as a whole until the indenter just touches the sample. Then a weight is put on the balance arm. The motor moves the x-y table up and down the same track. Every time the end of the track is reached, the x-y table trips a microswitch, the sample is moved in the opposite direction and the number of passes is counted automatically. Some typical values of the parameters of the experiment are as follows: the normal load, F,, is 1 - 10 N, the number of passes, N, is 1 - 1000 and the sliding velocity, u, is 0.4 - 400 pm s- l. The sliding experiments were done under laboratory conditions, at a relative humidity of approximately 50% and a temperature of 22 “C. Wet experiments were carried out with demineralized water, either as a droplet around the sphere, or, completely flooded, in a perspex container, before the experiment was started. Experiments above room temperature were made by fastening the sample on a heating table, mounted on the x-y table. A thermocouple near the sample gave the temperature. The temperature range is from 20 to 290 “C. The tangential force Ft was measured by means of strain gauges, connected to a bridge and a continuous recorder, the friction coefficient f being calculated from f = F,/F,. Above room temperature the strain gauges cannot be used and no friction data were obtained. 2.2. Observations The grooves on the sample were observed after the experiment under a microscope equipped with Nomarski interference contrast. The dimensions of the grooves were measured by means of a profiler, scanning perpendicular
356
to the sliding direction. Grooves with a depth of 10 - 500 nm could be measured in this way. 2.3. Materials Crystals of MnZn ferrite, Mn,,,Zno.~zFe2.0604, were used, grown by the Bridgman technique. Sliding was done on various faces, (OOl), (ill), (211) and (110) in the directions given in Table 1. The accuracy of cutting was within 2”. More extensive measurements were done on the (110) plane. The surface of the samples was diamond polished. TABLE 1 Empirical constants fitted to eqn. (1) for several of the sliding directions. Comparison with wear data from ref. 3 Direction
(loo)[oill
(111)[511] (lll)[oiii (llo)[iio] (2li)foil1 (211)[Illl
Cl (nm N-l)
C2 (um)
57(11)P 73(5) 65(Q) 74(5) 64(7) 66(4)
45(13) 55(7) QO(12) lOl( 12) 136(27) 78(61
c3
c4
(umt
Mm)
-28(13) -27(a) -49( 15) --58(g) -73(10) -35(4)
-133(62) -29( 24) -81( 46) -148( 32) -89(46) -69(20)
Wear rate (Pm h-l) 0.12 8.3 23 2.0 0.5 1.4
aThe numbers in parentheses give the standard deviation.
3. Groove dimensions 3.1. Groove dimensions On four crystal planes, grooves have been made along (110) and in some cases perpendicular to this direction as well. The conditions of load, speed and number of passes N were varied. The width of the grooves is somewhat smaller than the hertzian contact circle and is not influenced to a great extent by the experimental conditions. Depending on load, the width varies between 25 and 37 pm. In sliding, the time to traverse a distance equal to the width is of the order of 0.1 - 100 s, extending the range of the indentations [133 by a factor of 100. The mean pressure in the contact ranges between 5 and 9 CPa, not far from the Vickers hardness of 7 GPa. The coefficient of friction is 0.1 ?s0.05 for all samples. The loads were low enough to avoid cracks. The dependence of the groove depth on load F, is shown for sliding on (110) in Fig. 1. The lines for constant speed u are remarkably straight. The dependence on lg# and lg,,N is linear over a fairly large range (Figs. 2 and 3). For the other crystal planes the same behaviour was found (Fig. 4). In another experiment on the (110) crystal face, the sphere was surrounded by water and grooves were made at 3 N. On this plane the depth did not differ significantly from the data under dry conditions.
357 500
t F c 3 g b B
400
3OtJ
% $ 200
100
h(N) -
Fig. 1. Depth us. load for a single pass at various speeds on (110) along [ilO]. The lines have been drawn according to eqn. (1) with the coefficients fitted to all data: 0, u = 0.4 pm s-l; X, II = 4 pm s-l; A, LJ= 40 I.trns-l; 0, u = 400 pm s-l.
T.OO-
F C
400
f
3oo
B
2,,;
100
I
'"Ab_
X\\
1
I
0 0.1
-
k<\X
-
1
, , , ,...,I
,,,,
"h;
10
100
1000
Slidingvelocity(pm/s) -
Fig. 2. Depth us. lg&speed) for a single pass at various loads on (110) along [ilO]. The straight lines have been drawn according to eqn. (1) with the coefficients fitted to all data: A, F, = 3 N; x, Fn = 4 N; 0, F, = 6 N.
The linearity of these relationships suggests the following empirical formula for the depth d: d = C,F,
+ cz lg,,N + c3 lg,,u + CQ
(1)
The data available by varying load, speed and number of passes were used in fitting the data for the various crystal planes to this equation. The C values with the standard deviation are given in Table 1, with u expressed in
358 t
500
E
400
z 8 b 5
300
r, $ Q 200
100
Number of passes
-
Fig. 3. Depth us, lglo(number of passes, N), made in one direction,at variousloads, v = 40 Urns-* on (110) along [ilO], Lines drawn as in Fig, 2: X,F,= 2 N; A, Fn= 4 N; O,i,= 5 N; 0, k, = i N.
100 Number
of
passes ---w
Fig, 4. Depth us. number of passes for F, = 4 N on (111) afong [%l] and on (100) along foil] at 400 ,f_ims-l and on (211) along [Oil] at 40 pm s-l. Lines drawn as in Fig. 2:
x,(ioo)[oii];A,(ii~) @ii]; o,(zll)[oiil.
micrometres per second. It is remarkable that cross terms between F, and speed or N do not occur. The straight iines drawn in Figs. 1 -4 were derived from the fitted coefficients. The fit is clearly better for (110) than for (100) and (ill), as seen from the standard deviations in Table 1. For sliding along [llO] the effects of speed and number of passes is largest on (110) and (211). The data show that the ratio of Cz and C3 is about constant for the different experiments, an indication that the effects
359
of N and u are similar. Several C values depend on temperature, as will be shown later. The significance of the last term, Cq, is that a threshold is needed before the depth of the groove can be observed. For N = 1 and u = 1 pm s-l, and putting d = 0, the threshold for the load is given by -C4/C1. The ratio varies between 0.4 N for (111) and 2.3 N for (loo), confirming the difficulty of creating grooves on the latter plane. At higher N or lower speed the threshold is seen to decrease. 3.2. Higher temperatures on (110) A number of experiments were done above room temperature. In view of the increase in the number of variables, a variance analysis [17] was made for investigating the dependence of depth on load, speed, number of passes and temperature. In contrast to the data shown in Section 3.1, the dependence was not limited to linear terms, but a full rank second-order model was used,
i=l
i=l
j=j
i
The Xi are normalized variables, corresponding to F, (in the range 3, 4, 5 N), lg,,N (for N = 3,9,27), lgieu (with u = 4, 40 and 400 pm s-i) and the temperature T = 20, 113 and 290 “C. In comparison to eqn. (l), a limited number of new coefficients /3 is significant, the linear and quadratic terms in the temperature, the product term of load and temperature and the quadratic term in the speed. The presence of temperaturedependent terms is seen in Fig. 5, where the groove depth is seen to increase with temperature, for the 600
t
t
0
100
200
300
400
500 T(K)
Fig. 5. Depth us. temperature on (110) along [ho].
600 -
for Fn = 4 N, u = 40 pm s-l and N = 9 (both ways). Sliding
360
200
100
0
Fig. 6. Depth us. load for three temperatures, derived from the variance experiment. 40 pm s-l, N = 9, passes in both directions. Sliding on (110) along [ilO].
v=
centre of the chosen conditions, F, = 4 N, u = 40 pm s-i and 9 passes in both directions. The fit of the data can be presented as a depth-load curve for the central choice of parameters (Fig. 6). The effect of the temperature is seen in the increased slope. Moreover, the curve shifts to lower loads, indicating that the threshold for deformation is lower too. The experimental data show that the Tlg,,u term is absent (Fig. 7). There is a slight curvature of the lines, indicating that a small (lg1eu)2 term is present, with a coefficient of -30 z!z17.
4. Discussion 4.1. Groove depth
The groove depth varies with load, speed, number of passes, temperature, plane and direction of sliding. The specific form of the relation is of interest, as well as the relation with the line patterns in the groove. The groove width zu varied considerably less with the experiment& conditions than the depth d. This allows the interpretation of the depth data as strain values. An effective strain E, is derived from d and w by 2d E,= W
This definition of strain equals the profile ratio w/ZR introduced by Tabor [18] and used by Ishibashi and Shimoda [19]. The mean strain of indentation is obtained by multiplying eqn. (3) by 0.2. Since the w data show minor variations compared with d, eqn. (1) may be interpreted as an empirical relation between plastic strain and load, speed and number of passes.
361
z
woe
c
500
t
T x b z Si
400
0”
300
200
100
I
I
0’ 4
40
400 v @m/s)
+
Fig. 7. Depth us. speed for three temperatures. Sliding on (110) along [IlO].
Load 4 N. 9 passes in both directions.
4.2. Speed effects in the groove depth From eqn. (1) the threshold of load, below which no groove is detected, is clearly a function of v and N. This suggests that propagation is the bottleneck in the slip process. If the speed of dislocation propagation ds/dt is governed by a thermal process [20,21], we have ds z = v. exp{-(E,
+ Bo)/lzT}
(4)
where E, is the activation energy, v0 the pre-exponential factor, B the activation volume, k the Boltzmann constant and u the relevant resolved stress component. Assume that ds is related to the deformation, i.e. the depth, and that dt is the time available for slip. Putting
CIS -=-=dt
d Nrpps
dvpass NW
(5)
and assuming that stress u and strain e are linearly related, we find [20] that the depth, according to eqn. (3), contains -kT lg,# + kT lg,&. If these are compared with the terms in ref. 1, there are two differences. The coefficients Cz and C3 are not equal and not proportional to the temperature. The coefficients Cz and C3 in eqn. (1) are indeed correlated, but differ by a factor of two (Table 1). A repetition at the same speed is more effective
362
than one pass at half speed, maybe because the groove widens at every pass, or maybe because the stress cycle is different. The resolved shear stress first increases when the sphere approaches, reaches a maximum and decreases again. This variation may combine with the stress, owing to the deformation that is already present, and lead to more slip. The absence of a Tdependent Igieu term (Fig. 7) means that the speed of propagation is not limited by the low temperatures used in the experiment. The strain is clearly affected by the temperature, both by the load term and by the lower threshold. The depth is linear in temperature under otherwise constant conditions (Fig. 5). The temperature dependence is also found in the number of slip lines, It indicates that the small number of lines at room temperature is due to limitations in the nucleation of slip. 4.3. Groove depth anisotropy The groove width w for a given load on the sphere, did not show large variations between the crystals studied here. This agrees with the small anisotropy in Vickers’ or Knoop hardness [l - 31 which is derived from the size of pyramidal indentations. In the empirical eqn. (l), the C values depend on the crystal orientation. The coefficient of load, C,, varies from 57 nm N-i for “hard” (001) to 85 for “soft” (ill), a difference of about 50%, to be compared with a 10% difference in hardness. A much larger effect is seen in the ratio C4fCi that determines the threshold for the load at N = 1 and v = 1 pm s-l, It varies from 0.4 N for (111)[211] to 2.0 N for (llO)[ilOJ and 2.3 N for (001) [llO]. This is a considerable variation, which increases by (C,/C,) lgi,& when N is increased. When the speed is lowered, the threshold increases by (-C&i) lgleu, which ranges from 0.4 N for (lll)@ll] to 0.8 N for (110) [ilO] and 1.1 N for (211) [Oli]. Also in terms of stress this is an appreciable effect. The data for the depth should be compared with the changes in slip line patterns when the same parameters are changed. For sliding on (001) the pattern is much less affected [ 131, which agrees with the lower C,/C, ratio. A preliminary analysis of the patterns on (llO), (111) and (211) shows a pronounced influence of speed. The patterns will be investigated in more detail in later work. 4.4, Wear The ductile deformation in a groove does not bring material removal. Slip is necessary, but not sufficient. Wear occurs here by a process that destroys the protruding slip lines, thereby producing small debris particles, that may grow and cause fine scratches [13 1. The first process, slip, is the step that limits the wear rate in the groove formation by sliding. Is this also so in other cases? The wear data from the literature on video recording {3,223 are compared in Table 1 with the C data on the groove depth, measured on the same planes. In view of the dependence of groove depth on the number of passes the data may not be compared without further discussion. The experiment with a sliding sphere is a typical example of low cycle
363
fatigue, with up to 1000 passes at a load ranging from 1 to 10 N. The recording data are typical of high cycle fatigue, with lo8 passes at asperity loads in the 10 E.~N range. There is some correlation between the wear rate and the C4/C1 ratio, i.e. the threshold for the groove depth, but in view of the speed dependence discussed above, the low correlation is not surprising. A more basic quantity might be the resolved shear stress, since its value should be sufficiently large in all examples of ductile deformation. It would therefore be useful to analyse the resolved shear stress for the planes used in these experiments. The correlation with the wear data in video recorders is still not satisfactory and will be taken up after the analysis of the slip line data.
5. Conclusions (1) The sliding sphere applied to MnZn ferrite crystals provides quantitative data on the dependence of groove depth on load, sliding speed and number of passes, at temperatures up to 290 “C, and in a water environment when necessary. (2) The relation between depth and the parameters mentioned can be presented in an empirical formula. The number of passes and the speed of sliding are not equivalent, a repetition is more effective than a slower pass. (3) At higher temperatures there is a cross term between temperature and load, but not between temperature and speed. (4) In all cases investigated there is a threshold for the groove depth. At lower speed, after more passes and at higher temperatures the threshold is lower, while on (110) a water environment does not have much influence on the depth results. (5) The threshold is lowest for the (111) plane, highest for (100). Data from the literature on the wear of video heads show that wear is highest on (111) and lowest on (100).
References 1 E. J. Duwell, Wear rates of rutile and spine1 single crystals in water-lubricated slide interfaces, ASLE Tmns., 12 (1969) 34 - 35. 2 Y. Akimune and R. C. Brad& Knoop microhardness anisotropy of single crystal stoichiometric MgAlaO,, J. Am. Cemm. Sot., 70 (1987) C84 - C86. 3 K. Kugimiya, E. Hirota and Y. Bando, Magnetic heads made of crystal-oriented spine1 ferrite, IEEE Trans. Magn., IUAG-10 (1974) 907 - 909. 4 T. Ito, Knoop hardness anisotropy and plastic deformation in Mn-Zn ferrite single crystals, J. Am. Ceram. Sot., 54 (1971) 24 - 26. 5 K. Miyoshi and D. H. Buckley, Friction and wear of single-crystal manganese-zinc ferrite, Wear, 66 (1981) 157 - 173. 6 K. Tanaka, K. Miyoshi and T. Murayama, Friction and deformation of Mn-Zn ferrite single crystals, Frictional properties and deformation, Bull. Jpn. Sot. Prec. Eng., 9 (2) (1975) 27 - 29.
364 7 T. Yonezawa, K. Yokoyama and N. Ito, Residual stress of Mn-Zn ferrite polished surface and effect on magnetic properties, National Technical Rep. 25(l), 1979, pp. 6 - 17. 8 K. Miyoshi and D. H. Buckley, Ceramic wear in indentation and sliding contact, ASLE Trans., 28 (1985) 296 - 302. 9 K. F. Dufrane and W. A. Glaeser, Rolling-contact deformation of MgO single crystals, Wear, 37 (1976) 21 - 32. 10 R. P. Stein, Friction and wear of rutile single crystals, ASLE Trans., 12 (1969) 21 33. 11 M. V. Swain and B. R. Lawn, A study of dislocation arrays at spherical indentations in LiF as a function of indentation stress and strain, Phys. Status Solidi, 35 (1969) 909 - 923. 12 M. V. Swain, Dislocation generation beneath static and rolling contact with a sphere, Wear, 48 (1978) 173 - 180. 13 A. Broese van Groenou and S. E. Kadjik, Sliding sphere wear test on NiZn and MnZn ferrites, Wear, 126 (1988) 91 - 110. 14 G. M. Hamilton and L. E. Goodman, The stress field created by a circular sliding contact, J. Appl. Mech., 33 (1966) 371 - 376. 15 G. M. Hamilton, Explicit equations for the stresses beneath a sliding spherical contact, Proc. Inst. Mech. Eng., London, 197C (1983) 53 - 59. (The equation for u, due to a tangential load contains a term x2z2/3; the three in the denominator should be replaced by the expression S, defined in the paper.) 16 N. Maan and A. Broese van Groenou, Low speed scratch experiments on steels, Wear, 42(1977)365-390. 17 D. M. Himmelblau, Process Analysis by Statistical Methods, Wiley, New York, 1970, Chapter 8 (Strategy for efficient experimentation). 18 D. Tabor, Hardness of MetaZs, Oxford University Press, Oxford, 1951. 19 T. Ishibashi and S. Shimoda, The correlation between hardness and flow stress, JSME Znt., J., 31 (1988) 117 - 125. 20 D. Kuhlmann, Zur Theorie der Nachwirkungserscheinungen, 2. Phys., 124 (1948) 468 - 481. 21 J. P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968, pp. 540. 22 E. Hirota, K. Hirota and K. Kugimiya, Recent developments of ferrite heads and their materials. In H. Watanabe, S. Iida and M, Sugimoto (eds.), FERRITE& Proc. Znt. Conf., Japan, 1980, Centre for Academic Publications Japan, 1981, pp. 670 - 674.
353
(1989) 353 - 364
SLIDING SPHERE EXPERIMENTS OF MnZn FERRITE
ON VARIOUS
SINGLE
CRYSTALS
A. BROESE VAN GROENOU and S. E. KADIJK Philips Research
Laboratories,
(Received October 3,1988;
P.O. Box 80 000, 5600 JA Eindhouen
(The Netherlands)
accepted January 24,1989)
Summary By sliding a ruby sphere (0.25 mm in radius) on various MnZn ferrite crystals quantitative information has been obtained on the groove depth at speeds of 0.4 - 400 pm s-l at loads of 1 - 10 N and after 1 - 1000 passes. Above a certain threshold, a simple empirical relation is found between depth and load, lg,,(speed) and lg,,(passes) at 20 “C. The threshold is lowest for sliding on (111) and highest on (100). These planes also give the extremes of the wear rate of recording heads against video tape. For the (110) crystal the temperature was varied between 20 and 290 “C, showing a larger influence of load on depth, but without an extra speed effect. This result means that thermal propagation of slip is not the bottleneck in plastic deformation here.
1. Introduction In cubic materials with the spine1 structure, ABz04, wear and polishing rate show considerable anisotropy. For a sphere of the spine1 MgAl,O,, in contact with a mild steel at a calculated contact stress of 0.7 GPa, Duwel [l] found on the (100) plane along (100) wear a factor of 50 greater than along (011). The hardness on the same plane varied between 1.47 and 1.79 GPa, i.e. by +lO% [2]. Ferrite spinels, especially (Mn, Zn, Fe) Fez04, are commonly used as single crystalline materials for magnetic recording heads. Here again a factor of 50 is found for the variation in the wear rate, now for recording heads of different orientations, running against CrO, tape in a video tape recorder [3]. Wear is least on (100) and largest on (111). The Knoop [4] and Vickers [5, 61 hardness, however,‘vary between 5.9 and 6.8 GPa, i.e. by only + lo%, between the various directions. In lapping experiments on MnZn ferrite, the residual surface stress and the depth where the stress becomes zero, also depend on the plane [7]. The largest stress is found on (211), 2.3 GPa, the lowest on (loo), 1.0 GPa, while the depth of the stressed material varies from 0.1 pm (110) to more than 1 pm on (111). 0043-1648/89/$3.50
0 Elsevier Sequoia/Printed
in The Netherlands
354
Several authors have tried to model these phenomena by sliding indenters and observe the surface deformation. On MnZn ferrite, Yonezawa et al. [7] used diamond spheres with a radius of 3 - 5 pm at a load of 0.5 N (the calculated elastic stress is 49 GPa) and found cracking on {Ill) planes, Tanaka et al. [6] halved the contact stress by using sliders 20 pm in radius, but still observed mainly cracking around the grooves and no slip patterns that could be analysed. At about the same hertzian stress of 20 GPa, Miyoshi and Buckley [S] also observed cracks, but also a considerable anisotropy in friction, 0.21 to 0.29. An even larger variation in friction coefficient was seen when the diamond slider was replaced by a ferrite of the same composition [S]. Depending on the differences in orientation, the friction varied between 0.2 and 0.6. No cracks were observed for a sphere radius of 0.79 mm at an elastic stress of the order of 0.6 GPa. Other examples where the use of a larger sphere resulted in plastic deformation without cracking, are MgO and TiOz. On (100) planes of MgO, Dufrane and Glaeser [9] used a rolling steel sphere (0.6 GPa) and obtained slip patterns that correspond to (110) slip. The depth where slip could still be detected depends on the direction of rolling and on the speed, the largest dependence occurring in the 1 - 400 mm s-l range, Cracks were observed above 10’ passes. At a much higher stress (17 GPa) Miyoshi and Buckley [8] found considerable cracking after one pass. On TiO, Stein had the same experience [lo]. For small radius sliders cracking was seen at a stress of 9 GPa, while for larger radii, cracks were avoided and slip was observed. ‘Stein strongly advocated the use of sliding spheres to determine the mechanism of plastic deformation in brittle materials at room temperature. He identified the slip systems in TiO, and found these to be the same as those that operate above 600 “C. Swain and Lawn [ll, 121 did experiments on LiF and analysed the results of Dufrane and Glaeser on MgO. Their conclusion is that the sliding sphere allows the analysis of the onset of slip, whereas the Knoop indenter presumably samples the work hardening characteristics rather than the flow stress [ 121. The onset of slip in polycrystalline NiZn and MnZn ferrites was observed by the present authors [ 131. By increasing the number of passes, cracks occurred at the grain boundaries. Grain pull-out takes place at high loads, low speeds and under wet conditions. On a (100) plane of a single crystal of MnZn ferrite sliding and indentations showed simple slip patterns. By polishing and etching, subsurface slip could be observed as well. The patterns were attributed to slip on the {ill} and {loo) planes. The loaded sphere has another advantage, namely its known stress distribution (Hamilton and Goodman [14,15]). This was used to determine the resolved shear stress needed for slip to appear on MgO and LiF by Swain and Lawn [ll, 121. In a forthcoming publication the present authors will give the corresponding analysis of the slip patterns made by indenting various planes of MnZn ferrite crystals. The analysis requires slip on three systems, the {loo], (111) and (11Oj. The present work is an extension of
355
previous work on the deformation by a sliding sphere [ 131. Here grooves will be described made on crystal planes for which wear data are available [3]. The analysis of the slip patterns in the grooves will be given in later papers.
2. Experimental details 2.1. Sliding apparatus The sliding apparatus consists of a balance, with a damping system on one arm, on the other arm an indenter, in this case a sphere. An x-y table carries the sample, which can be transported by a motor [16]. The indenter, a ruby sphere with a diameter of 0.25 mm, is loaded by means of a weight (giving loads of 0.1 - 10 N). If there is severe damage on the surface of the sample the ruby may be damaged as well. Sometimes fine ferrite wear particles adhere to the sphere and may be a cause of fine scratches on the sample. For these reasons the sphere was normally checked after each experiment. If damage was found, the sphere was rotated and fastened again in order to obtain a fresh area of the surface. In most cases it was sufficient to clean the sphere with acetone or ethanol. The scratching experiment can be followed by means of a camera, which is focused on the indenter. At the start of the experiment, the balance is brought into equilibrium and is then lowered as a whole until the indenter just touches the sample. Then a weight is put on the balance arm. The motor moves the x-y table up and down the same track. Every time the end of the track is reached, the x-y table trips a microswitch, the sample is moved in the opposite direction and the number of passes is counted automatically. Some typical values of the parameters of the experiment are as follows: the normal load, F,, is 1 - 10 N, the number of passes, N, is 1 - 1000 and the sliding velocity, u, is 0.4 - 400 pm s- l. The sliding experiments were done under laboratory conditions, at a relative humidity of approximately 50% and a temperature of 22 “C. Wet experiments were carried out with demineralized water, either as a droplet around the sphere, or, completely flooded, in a perspex container, before the experiment was started. Experiments above room temperature were made by fastening the sample on a heating table, mounted on the x-y table. A thermocouple near the sample gave the temperature. The temperature range is from 20 to 290 “C. The tangential force Ft was measured by means of strain gauges, connected to a bridge and a continuous recorder, the friction coefficient f being calculated from f = F,/F,. Above room temperature the strain gauges cannot be used and no friction data were obtained. 2.2. Observations The grooves on the sample were observed after the experiment under a microscope equipped with Nomarski interference contrast. The dimensions of the grooves were measured by means of a profiler, scanning perpendicular
356
to the sliding direction. Grooves with a depth of 10 - 500 nm could be measured in this way. 2.3. Materials Crystals of MnZn ferrite, Mn,,,Zno.~zFe2.0604, were used, grown by the Bridgman technique. Sliding was done on various faces, (OOl), (ill), (211) and (110) in the directions given in Table 1. The accuracy of cutting was within 2”. More extensive measurements were done on the (110) plane. The surface of the samples was diamond polished. TABLE 1 Empirical constants fitted to eqn. (1) for several of the sliding directions. Comparison with wear data from ref. 3 Direction
(loo)[oill
(111)[511] (lll)[oiii (llo)[iio] (2li)foil1 (211)[Illl
Cl (nm N-l)
C2 (um)
57(11)P 73(5) 65(Q) 74(5) 64(7) 66(4)
45(13) 55(7) QO(12) lOl( 12) 136(27) 78(61
c3
c4
(umt
Mm)
-28(13) -27(a) -49( 15) --58(g) -73(10) -35(4)
-133(62) -29( 24) -81( 46) -148( 32) -89(46) -69(20)
Wear rate (Pm h-l) 0.12 8.3 23 2.0 0.5 1.4
aThe numbers in parentheses give the standard deviation.
3. Groove dimensions 3.1. Groove dimensions On four crystal planes, grooves have been made along (110) and in some cases perpendicular to this direction as well. The conditions of load, speed and number of passes N were varied. The width of the grooves is somewhat smaller than the hertzian contact circle and is not influenced to a great extent by the experimental conditions. Depending on load, the width varies between 25 and 37 pm. In sliding, the time to traverse a distance equal to the width is of the order of 0.1 - 100 s, extending the range of the indentations [133 by a factor of 100. The mean pressure in the contact ranges between 5 and 9 CPa, not far from the Vickers hardness of 7 GPa. The coefficient of friction is 0.1 ?s0.05 for all samples. The loads were low enough to avoid cracks. The dependence of the groove depth on load F, is shown for sliding on (110) in Fig. 1. The lines for constant speed u are remarkably straight. The dependence on lg# and lg,,N is linear over a fairly large range (Figs. 2 and 3). For the other crystal planes the same behaviour was found (Fig. 4). In another experiment on the (110) crystal face, the sphere was surrounded by water and grooves were made at 3 N. On this plane the depth did not differ significantly from the data under dry conditions.
357 500
t F c 3 g b B
400
3OtJ
% $ 200
100
h(N) -
Fig. 1. Depth us. load for a single pass at various speeds on (110) along [ilO]. The lines have been drawn according to eqn. (1) with the coefficients fitted to all data: 0, u = 0.4 pm s-l; X, II = 4 pm s-l; A, LJ= 40 I.trns-l; 0, u = 400 pm s-l.
T.OO-
F C
400
f
3oo
B
2,,;
100
I
'"Ab_
X\\
1
I
0 0.1
-
k<\X
-
1
, , , ,...,I
,,,,
"h;
10
100
1000
Slidingvelocity(pm/s) -
Fig. 2. Depth us. lg&speed) for a single pass at various loads on (110) along [ilO]. The straight lines have been drawn according to eqn. (1) with the coefficients fitted to all data: A, F, = 3 N; x, Fn = 4 N; 0, F, = 6 N.
The linearity of these relationships suggests the following empirical formula for the depth d: d = C,F,
+ cz lg,,N + c3 lg,,u + CQ
(1)
The data available by varying load, speed and number of passes were used in fitting the data for the various crystal planes to this equation. The C values with the standard deviation are given in Table 1, with u expressed in
358 t
500
E
400
z 8 b 5
300
r, $ Q 200
100
Number of passes
-
Fig. 3. Depth us, lglo(number of passes, N), made in one direction,at variousloads, v = 40 Urns-* on (110) along [ilO], Lines drawn as in Fig, 2: X,F,= 2 N; A, Fn= 4 N; O,i,= 5 N; 0, k, = i N.
100 Number
of
passes ---w
Fig, 4. Depth us. number of passes for F, = 4 N on (111) afong [%l] and on (100) along foil] at 400 ,f_ims-l and on (211) along [Oil] at 40 pm s-l. Lines drawn as in Fig. 2:
x,(ioo)[oii];A,(ii~) @ii]; o,(zll)[oiil.
micrometres per second. It is remarkable that cross terms between F, and speed or N do not occur. The straight iines drawn in Figs. 1 -4 were derived from the fitted coefficients. The fit is clearly better for (110) than for (100) and (ill), as seen from the standard deviations in Table 1. For sliding along [llO] the effects of speed and number of passes is largest on (110) and (211). The data show that the ratio of Cz and C3 is about constant for the different experiments, an indication that the effects
359
of N and u are similar. Several C values depend on temperature, as will be shown later. The significance of the last term, Cq, is that a threshold is needed before the depth of the groove can be observed. For N = 1 and u = 1 pm s-l, and putting d = 0, the threshold for the load is given by -C4/C1. The ratio varies between 0.4 N for (111) and 2.3 N for (loo), confirming the difficulty of creating grooves on the latter plane. At higher N or lower speed the threshold is seen to decrease. 3.2. Higher temperatures on (110) A number of experiments were done above room temperature. In view of the increase in the number of variables, a variance analysis [17] was made for investigating the dependence of depth on load, speed, number of passes and temperature. In contrast to the data shown in Section 3.1, the dependence was not limited to linear terms, but a full rank second-order model was used,
i=l
i=l
j=j
i
The Xi are normalized variables, corresponding to F, (in the range 3, 4, 5 N), lg,,N (for N = 3,9,27), lgieu (with u = 4, 40 and 400 pm s-i) and the temperature T = 20, 113 and 290 “C. In comparison to eqn. (l), a limited number of new coefficients /3 is significant, the linear and quadratic terms in the temperature, the product term of load and temperature and the quadratic term in the speed. The presence of temperaturedependent terms is seen in Fig. 5, where the groove depth is seen to increase with temperature, for the 600
t
t
0
100
200
300
400
500 T(K)
Fig. 5. Depth us. temperature on (110) along [ho].
600 -
for Fn = 4 N, u = 40 pm s-l and N = 9 (both ways). Sliding
360
200
100
0
Fig. 6. Depth us. load for three temperatures, derived from the variance experiment. 40 pm s-l, N = 9, passes in both directions. Sliding on (110) along [ilO].
v=
centre of the chosen conditions, F, = 4 N, u = 40 pm s-i and 9 passes in both directions. The fit of the data can be presented as a depth-load curve for the central choice of parameters (Fig. 6). The effect of the temperature is seen in the increased slope. Moreover, the curve shifts to lower loads, indicating that the threshold for deformation is lower too. The experimental data show that the Tlg,,u term is absent (Fig. 7). There is a slight curvature of the lines, indicating that a small (lg1eu)2 term is present, with a coefficient of -30 z!z17.
4. Discussion 4.1. Groove depth
The groove depth varies with load, speed, number of passes, temperature, plane and direction of sliding. The specific form of the relation is of interest, as well as the relation with the line patterns in the groove. The groove width zu varied considerably less with the experiment& conditions than the depth d. This allows the interpretation of the depth data as strain values. An effective strain E, is derived from d and w by 2d E,= W
This definition of strain equals the profile ratio w/ZR introduced by Tabor [18] and used by Ishibashi and Shimoda [19]. The mean strain of indentation is obtained by multiplying eqn. (3) by 0.2. Since the w data show minor variations compared with d, eqn. (1) may be interpreted as an empirical relation between plastic strain and load, speed and number of passes.
361
z
woe
c
500
t
T x b z Si
400
0”
300
200
100
I
I
0’ 4
40
400 v @m/s)
+
Fig. 7. Depth us. speed for three temperatures. Sliding on (110) along [IlO].
Load 4 N. 9 passes in both directions.
4.2. Speed effects in the groove depth From eqn. (1) the threshold of load, below which no groove is detected, is clearly a function of v and N. This suggests that propagation is the bottleneck in the slip process. If the speed of dislocation propagation ds/dt is governed by a thermal process [20,21], we have ds z = v. exp{-(E,
+ Bo)/lzT}
(4)
where E, is the activation energy, v0 the pre-exponential factor, B the activation volume, k the Boltzmann constant and u the relevant resolved stress component. Assume that ds is related to the deformation, i.e. the depth, and that dt is the time available for slip. Putting
CIS -=-=dt
d Nrpps
dvpass NW
(5)
and assuming that stress u and strain e are linearly related, we find [20] that the depth, according to eqn. (3), contains -kT lg,# + kT lg,&. If these are compared with the terms in ref. 1, there are two differences. The coefficients Cz and C3 are not equal and not proportional to the temperature. The coefficients Cz and C3 in eqn. (1) are indeed correlated, but differ by a factor of two (Table 1). A repetition at the same speed is more effective
362
than one pass at half speed, maybe because the groove widens at every pass, or maybe because the stress cycle is different. The resolved shear stress first increases when the sphere approaches, reaches a maximum and decreases again. This variation may combine with the stress, owing to the deformation that is already present, and lead to more slip. The absence of a Tdependent Igieu term (Fig. 7) means that the speed of propagation is not limited by the low temperatures used in the experiment. The strain is clearly affected by the temperature, both by the load term and by the lower threshold. The depth is linear in temperature under otherwise constant conditions (Fig. 5). The temperature dependence is also found in the number of slip lines, It indicates that the small number of lines at room temperature is due to limitations in the nucleation of slip. 4.3. Groove depth anisotropy The groove width w for a given load on the sphere, did not show large variations between the crystals studied here. This agrees with the small anisotropy in Vickers’ or Knoop hardness [l - 31 which is derived from the size of pyramidal indentations. In the empirical eqn. (l), the C values depend on the crystal orientation. The coefficient of load, C,, varies from 57 nm N-i for “hard” (001) to 85 for “soft” (ill), a difference of about 50%, to be compared with a 10% difference in hardness. A much larger effect is seen in the ratio C4fCi that determines the threshold for the load at N = 1 and v = 1 pm s-l, It varies from 0.4 N for (111)[211] to 2.0 N for (llO)[ilOJ and 2.3 N for (001) [llO]. This is a considerable variation, which increases by (C,/C,) lgi,& when N is increased. When the speed is lowered, the threshold increases by (-C&i) lgleu, which ranges from 0.4 N for (lll)@ll] to 0.8 N for (110) [ilO] and 1.1 N for (211) [Oli]. Also in terms of stress this is an appreciable effect. The data for the depth should be compared with the changes in slip line patterns when the same parameters are changed. For sliding on (001) the pattern is much less affected [ 131, which agrees with the lower C,/C, ratio. A preliminary analysis of the patterns on (llO), (111) and (211) shows a pronounced influence of speed. The patterns will be investigated in more detail in later work. 4.4, Wear The ductile deformation in a groove does not bring material removal. Slip is necessary, but not sufficient. Wear occurs here by a process that destroys the protruding slip lines, thereby producing small debris particles, that may grow and cause fine scratches [13 1. The first process, slip, is the step that limits the wear rate in the groove formation by sliding. Is this also so in other cases? The wear data from the literature on video recording {3,223 are compared in Table 1 with the C data on the groove depth, measured on the same planes. In view of the dependence of groove depth on the number of passes the data may not be compared without further discussion. The experiment with a sliding sphere is a typical example of low cycle
363
fatigue, with up to 1000 passes at a load ranging from 1 to 10 N. The recording data are typical of high cycle fatigue, with lo8 passes at asperity loads in the 10 E.~N range. There is some correlation between the wear rate and the C4/C1 ratio, i.e. the threshold for the groove depth, but in view of the speed dependence discussed above, the low correlation is not surprising. A more basic quantity might be the resolved shear stress, since its value should be sufficiently large in all examples of ductile deformation. It would therefore be useful to analyse the resolved shear stress for the planes used in these experiments. The correlation with the wear data in video recorders is still not satisfactory and will be taken up after the analysis of the slip line data.
5. Conclusions (1) The sliding sphere applied to MnZn ferrite crystals provides quantitative data on the dependence of groove depth on load, sliding speed and number of passes, at temperatures up to 290 “C, and in a water environment when necessary. (2) The relation between depth and the parameters mentioned can be presented in an empirical formula. The number of passes and the speed of sliding are not equivalent, a repetition is more effective than a slower pass. (3) At higher temperatures there is a cross term between temperature and load, but not between temperature and speed. (4) In all cases investigated there is a threshold for the groove depth. At lower speed, after more passes and at higher temperatures the threshold is lower, while on (110) a water environment does not have much influence on the depth results. (5) The threshold is lowest for the (111) plane, highest for (100). Data from the literature on the wear of video heads show that wear is highest on (111) and lowest on (100).
References 1 E. J. Duwell, Wear rates of rutile and spine1 single crystals in water-lubricated slide interfaces, ASLE Tmns., 12 (1969) 34 - 35. 2 Y. Akimune and R. C. Brad& Knoop microhardness anisotropy of single crystal stoichiometric MgAlaO,, J. Am. Cemm. Sot., 70 (1987) C84 - C86. 3 K. Kugimiya, E. Hirota and Y. Bando, Magnetic heads made of crystal-oriented spine1 ferrite, IEEE Trans. Magn., IUAG-10 (1974) 907 - 909. 4 T. Ito, Knoop hardness anisotropy and plastic deformation in Mn-Zn ferrite single crystals, J. Am. Ceram. Sot., 54 (1971) 24 - 26. 5 K. Miyoshi and D. H. Buckley, Friction and wear of single-crystal manganese-zinc ferrite, Wear, 66 (1981) 157 - 173. 6 K. Tanaka, K. Miyoshi and T. Murayama, Friction and deformation of Mn-Zn ferrite single crystals, Frictional properties and deformation, Bull. Jpn. Sot. Prec. Eng., 9 (2) (1975) 27 - 29.
364 7 T. Yonezawa, K. Yokoyama and N. Ito, Residual stress of Mn-Zn ferrite polished surface and effect on magnetic properties, National Technical Rep. 25(l), 1979, pp. 6 - 17. 8 K. Miyoshi and D. H. Buckley, Ceramic wear in indentation and sliding contact, ASLE Trans., 28 (1985) 296 - 302. 9 K. F. Dufrane and W. A. Glaeser, Rolling-contact deformation of MgO single crystals, Wear, 37 (1976) 21 - 32. 10 R. P. Stein, Friction and wear of rutile single crystals, ASLE Trans., 12 (1969) 21 33. 11 M. V. Swain and B. R. Lawn, A study of dislocation arrays at spherical indentations in LiF as a function of indentation stress and strain, Phys. Status Solidi, 35 (1969) 909 - 923. 12 M. V. Swain, Dislocation generation beneath static and rolling contact with a sphere, Wear, 48 (1978) 173 - 180. 13 A. Broese van Groenou and S. E. Kadjik, Sliding sphere wear test on NiZn and MnZn ferrites, Wear, 126 (1988) 91 - 110. 14 G. M. Hamilton and L. E. Goodman, The stress field created by a circular sliding contact, J. Appl. Mech., 33 (1966) 371 - 376. 15 G. M. Hamilton, Explicit equations for the stresses beneath a sliding spherical contact, Proc. Inst. Mech. Eng., London, 197C (1983) 53 - 59. (The equation for u, due to a tangential load contains a term x2z2/3; the three in the denominator should be replaced by the expression S, defined in the paper.) 16 N. Maan and A. Broese van Groenou, Low speed scratch experiments on steels, Wear, 42(1977)365-390. 17 D. M. Himmelblau, Process Analysis by Statistical Methods, Wiley, New York, 1970, Chapter 8 (Strategy for efficient experimentation). 18 D. Tabor, Hardness of MetaZs, Oxford University Press, Oxford, 1951. 19 T. Ishibashi and S. Shimoda, The correlation between hardness and flow stress, JSME Znt., J., 31 (1988) 117 - 125. 20 D. Kuhlmann, Zur Theorie der Nachwirkungserscheinungen, 2. Phys., 124 (1948) 468 - 481. 21 J. P. Hirth and J. Lothe, Theory of Dislocations, McGraw-Hill, New York, 1968, pp. 540. 22 E. Hirota, K. Hirota and K. Kugimiya, Recent developments of ferrite heads and their materials. In H. Watanabe, S. Iida and M, Sugimoto (eds.), FERRITE& Proc. Znt. Conf., Japan, 1980, Centre for Academic Publications Japan, 1981, pp. 670 - 674.