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Wear properties of silicon nitride in rolling contact
285
Wear, 110 (1986) 285 - 293
WAR
PROPERT~S
OF SILICON NITRIDE IN ROLLING CONTACT*
M. AKAZAWA
Mechanical Engineering (Japan)
Department,
Miyagi National
College of Technology,
Natori
K. KATO
Mechanical Engineering Department,
Tohoku University, Sendai (Japan)
K. UMEYA
Emeritus Professor of Tohoku University, Sendai (Japan)
Summary The wear properties of silicon nitride were examined in dry rolling contact. The wear coefficient of silicon nitride in pure rolling was of the order of 1O-6 at the initial stage of wear and of the order of lo-* at the steady stage of wear under hertzian pressures of 1.06,1.30,1.50 and 1.83 GPa. The wear coefficient of silicon nitride in roll~g-sliding was of the order of low3 under hertzian pressures of 1.06, 1.50 and 1.83 GPa. The original grinding marks were decreased by the initial wear. Then a very smooth surface appeared in the steady state and its centre-line average roughness R, was 0.02 m. In contrast, pitting and the adhesive accumulation of thin film debris on the surface started to occur in the steady stage of wear. Three typical types of wear debris were distinguished. One of these, which was a glassy film, was confirmed to have an SiOz structure.
1. In~oduction Silicon nitride (Si3N4) is one of the most promising ceramics for bearing material. About 15 years ago, it was not good enough as a bearing material El], but the development of the m~ufacturing process made it possible to produce a tougher silicon nitride, with a fatigue life in rolling which has increased [2 - 61, Therefore, because of its popular usage, the wear mechanism of silicon nitride should be analysed more fundamentally and precisely. The rolling wear mechanism of silicon nitride was studied from this viewpoint in this paper and some new understanding was obtained 171. *Revised version of a paper presented at the Japan Society of Lubrication Engineers’ International Tribology Conference, Tokyo, Japan, July 8 - 10,1985. 0043-1648/86/$3.50
@ Elsevier Sequoia/Printed
in The Netherlands
286
2. Experimental procedure Ring specimens of Si3N4 were cold pressed in air and then heat treated. Wear tests were conducted in ring-on-ring rolling contact. The diameter of the driving ring specimen was 32 mm and its thickness 8 mm. The diameter of the following ring specimen was 32 mm and its thickness 6 mm. The contact surface was finished by grinding with a diamond grinding wheel. The maximum surface roughness R,,, and the centre-line average roughness R, of these rings were 1.7 E.trnand 0.24 pm respectively. The wear test was performed with a standard rolling test machine in dry friction at room temperature. The schematic representation of the rolling contact system is shown in the Fig. 1. The rotational frequency was 800 rev mm-‘. Followinq specimen
Driving specimen Fig. 1, Schematic
Directit 3n rrP r,T+z%+i,
representation
Fig. 2. Wear volume 1960 N; l, 2940 N.
1.0
Load
US. number
0
‘1
1
0 16
5x105
106 Number
of the rolling contact of revolutions
/
WI06
3x/o
of revolutions
system.
for various loads:
0, 980
N; 0, 1470
N; 0,
3. Results and discussion 3.1. Wear curves in pure rolling Wear curves of driving specimens under loads of 980 N, 1470 N, 1960 N and 2940 N are shown in Fig. 2. The hertzian pressures at these loads were 1.06 GPa, 1.30 GPa, 1.50 GPa and 1.83 GPa respectively. The wear volume was calculated from the change in the cross-sectional profile of the wear track. Every wear curve in the figure shows two distinctly different wear stages: initial severe wear and secondary steady wear. The initial wear ends before lo5 cycles in general. The wear coefficients K were calculated for both stages and are given in Table 1. The K values in the initial wear stage are quite close to the corresponding values for steel in average sliding lubrication, and the K values in the steady wear stage are smaller than the corresponding values for steel in excellent sliding lubrication after lo6 revolutions. So in practice we can apply Si&, as a rolling element under a moderate load from the viewpoint of volume loss.
287 TABLE 1 Wear coefficients Load (W
980
1470 1960 2940
K in pure rolling K Initial wear (X 10-h)
Steady wear (x10-8)
1.70 1.89 1.70 1.13
0.43 1.51 4.58 3.56
3.2. The change in the profile and pattern of the wear surface Figure 3(a) shows the initial surface profiles of the driving (lower) and following (upper) specimens. The surfaces of both specimens were carefully finished so that the contact of the surfaces was parallel. Figure 3(b) shows
Fig. 3. Surface profiles in the rolling process under a load of 1470 N: (a) 0 cycles; (b) lo5 cycles; (c) 2 X lo6 cycles.
288
the surface profiles after lo5 revolutions, at which stage the sharp asperity peaks have been rounded by wear and a wear track has formed on the driving specimen’s surface. Figure 4(a) shows the surface of the following specimen (upper), where the grinding marks have clearly remained and many pits can be observed. Figures 4(b) and 4(c) show the surfaces after 5 X lo5 and lo6 revolutions respectively. The grinding marks are disappearing and the size of the pits are not increasing.
Fig.
4. Optical
N: (a) lo5
micrographs
cycles;(b)
of the surface
5 x 10’
cycles;(c)
of the following lo6
cycles;(d)
specimen
2 X lo6
under
a load of 1470
cycles.
In Fig. 3(c) after 2 X lo6 revolutions, both surfaces are becoming smoother. In particular, the surface of the following (upper) specimen has become very smooth. Grinding marks have completely disappeared, but some wear debris has begun to adhere at the right-hand edge of the upper specimen surface. This is shown in Fig. 4(d) more clearly, where grinding marks cannot be observed but many wear debris particles are adhering to the right-hand side of the surface. These wear debris particles are very thin and a glassy transparent film can be seen when the film is viewed in an optical microscope. 3.3. The change Figures 5 mens in rolling debris particles
in surface
roughness
in rolling
and 6 show the change in roughness of the following speciunder a load of 1470 N and 2940 N respectively; adhering were avoided in these measurements as far as possible. So
0’
Id
Id
Fig. 5. The change in roughness in pure rolling under a load of 1470 N: 0, R,,, Fig. 6. The change in roughness in pure rolling under a load of 2940 N: 0, R,,,
; 0, R,. ; 0, R,.
IO3
Id
Number of revolutions
Fig. 7. The change in surface profile of the following specimen under a load of 1960 N: (a) 0 cycles;(b) lo6 cycles.
decreases in the maximum roughness R,,, and the centre-line average R, in Figs. 5 and 6 indicate the disappearance of the original grinding marks and increases in R,,, and R, indicate the generation of pits. It is surprising that the value of R, at lo6 cycles in Fig. 5 is about 0.2 E.cmas a lifetime of 10’ cycles might be expected in dry rolling. When Fig. 6 is compared with Fig. 5, it is evident that a load of 2940 N is too large to have a long lifetime without large pits. If the surface of the following specimen is rounded off a little as in Fig. 7(a), stress concentration at the corner is avoided and glassy film debris is generated uniformly all over the contact area. Figure 8 has this appearance together with pits and Fig. 8(b) shows adhering debris and pits. 3.4. The type of wear debris 3.4.1. Flake-like large debris particles (100 - 200 pm) Figure 9(a) shows large thin flake-like debris particles growing on the wear surface. The general size of this type of debris particle is about 100 200 ,um in diameter; some particles are transparent and others are opaque
Fig. 8. Optical micrograph load of 1960 N.
of the surface
of the following
Fig. 9. Flake-like large debris particles: (a) debris ent debris particle; (c) an opaque debris particle.
adhering
specimen
at 10” cycles
to the surface;
under a
(b) a transpar-
when viewed in an optical microscope. Figure 9(b) shows a transparent flake-like debris particle and Fig. 9(c) shows an opaque debris particle. Wear debris particles similar to those in Fig. 9 were formed in the initial wear stage (0 - lo5 cycles) under ail loads. In the transition period from initial wear to steady wear, grinding marks were decreased and the size of the debris particles became smaller.
291
3.4.2. Glassy film small debris particles (10 - 50 pm) Figure 10(a) shows a group of white thin fine wear debris particles deposited from the interface in the steady wear state (10’ - 10’ cycles) and Fig. 10(b) shows a single wear debris particle in the group. Wear debris particles of this type look like thin glass films when viewed in an optical microscope and their diameter ranges from about 10 to about 50 pm. If wear debris particles of this type are sandwiched at the rolling interface and pressed together, they would adhere to the surface and form islands as shown in Figs. 4(d) and 6. The structures of the debris particles shown in Fig. 10 were analysed using IR spectroscopic analysis and the results are shown in Fig, 11. In Fig. 11 the spectrum of the glassy film debris coincides with that of quartz (SiO*). So these debris particles have an SiOZ structure, and this means that Si,N4 changes its structure during rolling wear.
Fig. 10. Glassy film small debris particles: (a) a group of debris particles; view of a single debris particle with an interference fringe.
Fig. 11. The results of the IR spectroscopic
analysis.
(b) a magnified
Fig. 12. Crystalline small debris view of a single debris particle.
3.4.3.
C~sta~li~e
particles:
(a) a group
of debris particles;
(b) a magnified
small debris ~ar~~~~es (2 0 - 50 pm)
Figure 12(a) shows a group of grey massive wear debris particles which were formed in rolling-sliding contact and Fig. 12(b) shows a single wear debris particle in this group. Wear debris of this type is transparent and looks like a crystal when viewed in an optical microscope. The debris particles have a cubic, round bar-like or plate-like shape and their diameters range from about 10 to about 50 pm. These wear debris particles occurred frequently in rolling-sliding contact, but similar particles were observed in the very early stages of wear in pure rolling. The result of an IR spectroscopic analysis of the debris in Fig. 12 is shown in Fig. Il. It is evident that the spectrum of these debris particles agrees well with that of the base material of the specimen (Si&). So the debris particles in Fig. 12 have an Si3N4 structure. 3.5. The effect of slip oa wear in ratting ~0~~~~~ It was shown in Table 1 that SiJN4 has a satisfactory low value of the wear coefficient Ii; in rolling with no slip. In order to know whether S&N4 would be available or not under the existence of slip in rolling, a certain amount of slip was introduced into the rolling test. Table 2 shows the results obtained.
TABLE
2
Wear coefficient Load
fN) 980
1960 2940
K in rolling sliding
Slip ratio (%I
R
9 30 30
1.57 6.61 2.52
(X10+)
293
The values of the wear coefficient are very large under all loads and their order does not change because of the change in slip ratio from 9% to 30%. It is concluded, therefore, that Si3N4 is not available in practice when slip is introduced into rolling.
4. Conclusions (1) The rolling wear coefficient of SisN4 was of the order of 10e6 in the initial wear stage and 10m8 in the steady wear stage. (2) Three types of wear formed in rolling: thin flake-like debris particles of 100 - 200 m diameter, glassy film debris particles of 10 - 50 pm diameter and crystalline debris particles of 10 - 50 pm diameter. (3) The glassy film debris has an SiOz structure, and the crystallme debris an S&N4 structure.
References 1 D. Scott, J. Blackwell and P. J. McCullagh, Sihcon nitride ss a rolling bearing material - a preliminary assessment, Wear, 17 (1971) 73 - 82. 2 K. Kikuchi, T. Yoshioka, T. Kitahara, K. Okazaki, K. Nakayama and T. Fujiwara, Rolling contact fatigue life of ceramics for rolling bearing materials, J. Jpn. Sot. Lubr. Eng., 28 (1983) 465 - 471. 3 H. M. Dalal, D. Hahn and W. L. Rhoads, Effect of surface and mechanical properties on silicon nitride bearing element performance, Final Rep., SKF Rep. AL75T002, February 1975 (Naval Air Systems Command) (Contract NOOOl9-74~-0168). 4 J. M. Raddecliff and R. Valori, The performance of a high-speed ball thrust bearing using silicon nitride balk, J. Lubr. TechnoL, 98 (1976) 553 - 663. 5 G. Hamburg, P. Cowley and R. Valori, Operation of an all-ceramic mainshaft roller bearing in a J-402 gas-turbine engine, Lubr. Eng., 37 (1981) 407 - 415. 6 J. R. Miner, W. A. Grace and R. Valori, A demonstration of high-speed gas turbine bearings using silicon nitride roiling elements, L&r. &kg., 37 (1981) 462 - 478. 7 T. E. Fischer and H. Tomizawa, Interaction of t~~chemistry and microfracture in the friction and wear of silicon nitride, Proc. Int. Co& on Wear of Materials, Vancouver, April 14 - 18, 1985, American Society of Mechanical Engineers, New York, 1985, pp. 22 - 32.
Wear, 110 (1986) 285 - 293
WAR
PROPERT~S
OF SILICON NITRIDE IN ROLLING CONTACT*
M. AKAZAWA
Mechanical Engineering (Japan)
Department,
Miyagi National
College of Technology,
Natori
K. KATO
Mechanical Engineering Department,
Tohoku University, Sendai (Japan)
K. UMEYA
Emeritus Professor of Tohoku University, Sendai (Japan)
Summary The wear properties of silicon nitride were examined in dry rolling contact. The wear coefficient of silicon nitride in pure rolling was of the order of 1O-6 at the initial stage of wear and of the order of lo-* at the steady stage of wear under hertzian pressures of 1.06,1.30,1.50 and 1.83 GPa. The wear coefficient of silicon nitride in roll~g-sliding was of the order of low3 under hertzian pressures of 1.06, 1.50 and 1.83 GPa. The original grinding marks were decreased by the initial wear. Then a very smooth surface appeared in the steady state and its centre-line average roughness R, was 0.02 m. In contrast, pitting and the adhesive accumulation of thin film debris on the surface started to occur in the steady stage of wear. Three typical types of wear debris were distinguished. One of these, which was a glassy film, was confirmed to have an SiOz structure.
1. In~oduction Silicon nitride (Si3N4) is one of the most promising ceramics for bearing material. About 15 years ago, it was not good enough as a bearing material El], but the development of the m~ufacturing process made it possible to produce a tougher silicon nitride, with a fatigue life in rolling which has increased [2 - 61, Therefore, because of its popular usage, the wear mechanism of silicon nitride should be analysed more fundamentally and precisely. The rolling wear mechanism of silicon nitride was studied from this viewpoint in this paper and some new understanding was obtained 171. *Revised version of a paper presented at the Japan Society of Lubrication Engineers’ International Tribology Conference, Tokyo, Japan, July 8 - 10,1985. 0043-1648/86/$3.50
@ Elsevier Sequoia/Printed
in The Netherlands
286
2. Experimental procedure Ring specimens of Si3N4 were cold pressed in air and then heat treated. Wear tests were conducted in ring-on-ring rolling contact. The diameter of the driving ring specimen was 32 mm and its thickness 8 mm. The diameter of the following ring specimen was 32 mm and its thickness 6 mm. The contact surface was finished by grinding with a diamond grinding wheel. The maximum surface roughness R,,, and the centre-line average roughness R, of these rings were 1.7 E.trnand 0.24 pm respectively. The wear test was performed with a standard rolling test machine in dry friction at room temperature. The schematic representation of the rolling contact system is shown in the Fig. 1. The rotational frequency was 800 rev mm-‘. Followinq specimen
Driving specimen Fig. 1, Schematic
Directit 3n rrP r,T+z%+i,
representation
Fig. 2. Wear volume 1960 N; l, 2940 N.
1.0
Load
US. number
0
‘1
1
0 16
5x105
106 Number
of the rolling contact of revolutions
/
WI06
3x/o
of revolutions
system.
for various loads:
0, 980
N; 0, 1470
N; 0,
3. Results and discussion 3.1. Wear curves in pure rolling Wear curves of driving specimens under loads of 980 N, 1470 N, 1960 N and 2940 N are shown in Fig. 2. The hertzian pressures at these loads were 1.06 GPa, 1.30 GPa, 1.50 GPa and 1.83 GPa respectively. The wear volume was calculated from the change in the cross-sectional profile of the wear track. Every wear curve in the figure shows two distinctly different wear stages: initial severe wear and secondary steady wear. The initial wear ends before lo5 cycles in general. The wear coefficients K were calculated for both stages and are given in Table 1. The K values in the initial wear stage are quite close to the corresponding values for steel in average sliding lubrication, and the K values in the steady wear stage are smaller than the corresponding values for steel in excellent sliding lubrication after lo6 revolutions. So in practice we can apply Si&, as a rolling element under a moderate load from the viewpoint of volume loss.
287 TABLE 1 Wear coefficients Load (W
980
1470 1960 2940
K in pure rolling K Initial wear (X 10-h)
Steady wear (x10-8)
1.70 1.89 1.70 1.13
0.43 1.51 4.58 3.56
3.2. The change in the profile and pattern of the wear surface Figure 3(a) shows the initial surface profiles of the driving (lower) and following (upper) specimens. The surfaces of both specimens were carefully finished so that the contact of the surfaces was parallel. Figure 3(b) shows
Fig. 3. Surface profiles in the rolling process under a load of 1470 N: (a) 0 cycles; (b) lo5 cycles; (c) 2 X lo6 cycles.
288
the surface profiles after lo5 revolutions, at which stage the sharp asperity peaks have been rounded by wear and a wear track has formed on the driving specimen’s surface. Figure 4(a) shows the surface of the following specimen (upper), where the grinding marks have clearly remained and many pits can be observed. Figures 4(b) and 4(c) show the surfaces after 5 X lo5 and lo6 revolutions respectively. The grinding marks are disappearing and the size of the pits are not increasing.
Fig.
4. Optical
N: (a) lo5
micrographs
cycles;(b)
of the surface
5 x 10’
cycles;(c)
of the following lo6
cycles;(d)
specimen
2 X lo6
under
a load of 1470
cycles.
In Fig. 3(c) after 2 X lo6 revolutions, both surfaces are becoming smoother. In particular, the surface of the following (upper) specimen has become very smooth. Grinding marks have completely disappeared, but some wear debris has begun to adhere at the right-hand edge of the upper specimen surface. This is shown in Fig. 4(d) more clearly, where grinding marks cannot be observed but many wear debris particles are adhering to the right-hand side of the surface. These wear debris particles are very thin and a glassy transparent film can be seen when the film is viewed in an optical microscope. 3.3. The change Figures 5 mens in rolling debris particles
in surface
roughness
in rolling
and 6 show the change in roughness of the following speciunder a load of 1470 N and 2940 N respectively; adhering were avoided in these measurements as far as possible. So
0’
Id
Id
Fig. 5. The change in roughness in pure rolling under a load of 1470 N: 0, R,,, Fig. 6. The change in roughness in pure rolling under a load of 2940 N: 0, R,,,
; 0, R,. ; 0, R,.
IO3
Id
Number of revolutions
Fig. 7. The change in surface profile of the following specimen under a load of 1960 N: (a) 0 cycles;(b) lo6 cycles.
decreases in the maximum roughness R,,, and the centre-line average R, in Figs. 5 and 6 indicate the disappearance of the original grinding marks and increases in R,,, and R, indicate the generation of pits. It is surprising that the value of R, at lo6 cycles in Fig. 5 is about 0.2 E.cmas a lifetime of 10’ cycles might be expected in dry rolling. When Fig. 6 is compared with Fig. 5, it is evident that a load of 2940 N is too large to have a long lifetime without large pits. If the surface of the following specimen is rounded off a little as in Fig. 7(a), stress concentration at the corner is avoided and glassy film debris is generated uniformly all over the contact area. Figure 8 has this appearance together with pits and Fig. 8(b) shows adhering debris and pits. 3.4. The type of wear debris 3.4.1. Flake-like large debris particles (100 - 200 pm) Figure 9(a) shows large thin flake-like debris particles growing on the wear surface. The general size of this type of debris particle is about 100 200 ,um in diameter; some particles are transparent and others are opaque
Fig. 8. Optical micrograph load of 1960 N.
of the surface
of the following
Fig. 9. Flake-like large debris particles: (a) debris ent debris particle; (c) an opaque debris particle.
adhering
specimen
at 10” cycles
to the surface;
under a
(b) a transpar-
when viewed in an optical microscope. Figure 9(b) shows a transparent flake-like debris particle and Fig. 9(c) shows an opaque debris particle. Wear debris particles similar to those in Fig. 9 were formed in the initial wear stage (0 - lo5 cycles) under ail loads. In the transition period from initial wear to steady wear, grinding marks were decreased and the size of the debris particles became smaller.
291
3.4.2. Glassy film small debris particles (10 - 50 pm) Figure 10(a) shows a group of white thin fine wear debris particles deposited from the interface in the steady wear state (10’ - 10’ cycles) and Fig. 10(b) shows a single wear debris particle in the group. Wear debris particles of this type look like thin glass films when viewed in an optical microscope and their diameter ranges from about 10 to about 50 pm. If wear debris particles of this type are sandwiched at the rolling interface and pressed together, they would adhere to the surface and form islands as shown in Figs. 4(d) and 6. The structures of the debris particles shown in Fig. 10 were analysed using IR spectroscopic analysis and the results are shown in Fig, 11. In Fig. 11 the spectrum of the glassy film debris coincides with that of quartz (SiO*). So these debris particles have an SiOZ structure, and this means that Si,N4 changes its structure during rolling wear.
Fig. 10. Glassy film small debris particles: (a) a group of debris particles; view of a single debris particle with an interference fringe.
Fig. 11. The results of the IR spectroscopic
analysis.
(b) a magnified
Fig. 12. Crystalline small debris view of a single debris particle.
3.4.3.
C~sta~li~e
particles:
(a) a group
of debris particles;
(b) a magnified
small debris ~ar~~~~es (2 0 - 50 pm)
Figure 12(a) shows a group of grey massive wear debris particles which were formed in rolling-sliding contact and Fig. 12(b) shows a single wear debris particle in this group. Wear debris of this type is transparent and looks like a crystal when viewed in an optical microscope. The debris particles have a cubic, round bar-like or plate-like shape and their diameters range from about 10 to about 50 pm. These wear debris particles occurred frequently in rolling-sliding contact, but similar particles were observed in the very early stages of wear in pure rolling. The result of an IR spectroscopic analysis of the debris in Fig. 12 is shown in Fig. Il. It is evident that the spectrum of these debris particles agrees well with that of the base material of the specimen (Si&). So the debris particles in Fig. 12 have an Si3N4 structure. 3.5. The effect of slip oa wear in ratting ~0~~~~~ It was shown in Table 1 that SiJN4 has a satisfactory low value of the wear coefficient Ii; in rolling with no slip. In order to know whether S&N4 would be available or not under the existence of slip in rolling, a certain amount of slip was introduced into the rolling test. Table 2 shows the results obtained.
TABLE
2
Wear coefficient Load
fN) 980
1960 2940
K in rolling sliding
Slip ratio (%I
R
9 30 30
1.57 6.61 2.52
(X10+)
293
The values of the wear coefficient are very large under all loads and their order does not change because of the change in slip ratio from 9% to 30%. It is concluded, therefore, that Si3N4 is not available in practice when slip is introduced into rolling.
4. Conclusions (1) The rolling wear coefficient of SisN4 was of the order of 10e6 in the initial wear stage and 10m8 in the steady wear stage. (2) Three types of wear formed in rolling: thin flake-like debris particles of 100 - 200 m diameter, glassy film debris particles of 10 - 50 pm diameter and crystalline debris particles of 10 - 50 pm diameter. (3) The glassy film debris has an SiOz structure, and the crystallme debris an S&N4 structure.
References 1 D. Scott, J. Blackwell and P. J. McCullagh, Sihcon nitride ss a rolling bearing material - a preliminary assessment, Wear, 17 (1971) 73 - 82. 2 K. Kikuchi, T. Yoshioka, T. Kitahara, K. Okazaki, K. Nakayama and T. Fujiwara, Rolling contact fatigue life of ceramics for rolling bearing materials, J. Jpn. Sot. Lubr. Eng., 28 (1983) 465 - 471. 3 H. M. Dalal, D. Hahn and W. L. Rhoads, Effect of surface and mechanical properties on silicon nitride bearing element performance, Final Rep., SKF Rep. AL75T002, February 1975 (Naval Air Systems Command) (Contract NOOOl9-74~-0168). 4 J. M. Raddecliff and R. Valori, The performance of a high-speed ball thrust bearing using silicon nitride balk, J. Lubr. TechnoL, 98 (1976) 553 - 663. 5 G. Hamburg, P. Cowley and R. Valori, Operation of an all-ceramic mainshaft roller bearing in a J-402 gas-turbine engine, Lubr. Eng., 37 (1981) 407 - 415. 6 J. R. Miner, W. A. Grace and R. Valori, A demonstration of high-speed gas turbine bearings using silicon nitride roiling elements, L&r. &kg., 37 (1981) 462 - 478. 7 T. E. Fischer and H. Tomizawa, Interaction of t~~chemistry and microfracture in the friction and wear of silicon nitride, Proc. Int. Co& on Wear of Materials, Vancouver, April 14 - 18, 1985, American Society of Mechanical Engineers, New York, 1985, pp. 22 - 32.