112 FRETTING FATIGUE TEST METHODS AND EQUIPM- 123docz.net

i Specimen

~ ~Pad Strain gage[] 10

~- i: I __ i__i -~--~~ .... ~' ", Screw ~-~'l ' ...

Strain gage~A ~ ~ ~Press plate ~U

FIG. 15--FrettingJatigue test apparatus.

13.

v 13.

OJ :3 U~

E o

0 -100 -200

- 3 0 0

Time

MPa ~"--- "-"- -186MPa

N=2X105

FIG. 16--Change ()/contact pressure during fretting Jatigue test.

as shown in Fig. 16. Thus, there is little reduction of contact pressure. The fretting fatigue strengths of each strength improvement model are shown in Fig. 17. The fretting fatigue limit of grooved type specimens (184 MPa with groove depth of 1 ram, 208 MPa with groove depth of 2 ram) and knurled pad type specimen (216 MPa) increases significantly in comparison with the plain fretting fatigue limit ( 120 MPa) [ 7]. These experimental results of fretting fatigue limits coincided well with the estimated results shown in Figs. 9, 11 and 12. Fatigue fracture conditions of grooved type specimens, near fatigue limit stress levels, are shown in Fig. 18. For a groove depth of d = 1 m m the fracture occurred at a contact edge and for a groove depth of d = 2 m m the fracture occurred at the groove bottom. These conditions coincided well with the estimated results shown in Fig. 14. However, for high stress amplitude, the fracture occurred at the groove bottom regardless of the groove depth. This is shown in Fig. 17 with the 9 mark for a groove depth of 1 mm.

3 0 0

"13

u3 U)

200

100

. . ~ ' ~ - ~ . ~ . ~ Z & ~ z : ~ . . . ~ Knurled pad type

" ' ' - . ~ o "~'~A

" \ \ (R=Smm, cl=2mm) ./" ~ . O"

~'~\ (R=5mm, d=lmm) O-

"-... Grooved type

" ~ Plane fretting

"-.../

105

I I

10 6 10 7

Number of cycles to failure Nf

FIG. 17--Fretting fatigue test resin]Is".

10 8

FIG. 1 B--Fatigue fracture conditions of grooved type specimens.

114 FRETTING FATIGUE TEST METHODS AND EQUIPMENT Conclusions

T h e fretting fatigue strength of strength improved models is estimated using fracture m e c h a n i c s analysis o f small cracks formed at the contact edge. By c o m p a r i n g these estimated results with experimental results the following conclusions are drawn.

1. The fretting fatigue limit improves a b o u t 70-80% by m a k i n g a groove at the contact edge.

2. By increasing the groove depth the fatigue crack forms at the groove bottom. This tran- sitional p o i n t is the o p t i m u m groove shape (in o u r case groove depth o f d = 1.5 m m for a groove radius o f R = 5 m m ) .

3. Stress analysis a n d fracture m e c h a n i c s analysis o f a k n u r l e d pad type model can be performed easily by using equivalent stiffness for the k n u r l i n g region.

4. T h e fretting fatigue limit improves m o r e t h a n 80% by k n u r l i n g the pad surface.

References

[1] Gassner, E., "The value of surface-protective media against fretting corrosion on the basis of fatigue strength tests," Laboratorium fur Betrieb.~Jesligkeit TM 19/67, 1967.

[2] Buch, A., "Fatigue and fretting of pin-lug joints with and without interference fit," Wear, 43, 1977, pp. 9.

[3] Hattori, T., Kawai, S., Okamoto, N. and Sonobe, T., "Torsional fatigue strength of a shrink fitted shaft," Bulletin oftheJSME, 24, 197, 1981, pp. 1893.

[4] Cornelius, E. A, and Contag, D., "Die Festigkeits-minderung von Wellen unter dem Einfluj3 von Wellen-Naben-Verbindungen durch Lotung, Nut und Paflfeder, Kerbverzahnungen und Keilprofile bei wechselnder Drehung," Konstruktion, 14, 9, 1962, pp. 337.

[5] Hattori, T., Sakata, S. and Ohnishi, H., "Slipping behavior and fretting fatigue in the disk/blade dovetail region," Proceeding, s, 1983 Tokyo Int. Gas Turbine Cong., 1984, pp. 945.

[6] Johnson, R. L. and Bill, R. C., "'Fretting in aircraft turbine engines," NASA TM X-71606. 1974.

[7] Hattori, T., Nakamura, M. and Watanabe, T., "Fretting fatigue analysis by using fracture mechanics," ASME Paper No. 84- WA/DE- 10, 1984.

[8] King, R. N. and Lindley, T, C., "Fretting fatigue in a 3~ Ni-Cr-Mo-V rotor steel," Proc. ICF 5, 1980, pp. 631.

[9] Sakata, H., Hattori, T. and Hatsuda, T., "'An Application of Fracture Mechanics to Fretting Fatigue Analysis," Role (?[Fracture Mechanics in Modern Technology, G. C. Sih, H. Nishitani and T. lshi- hara, Ed., Elsevier Science Publishers B. V., 1987, pp, 303.

[10] Ezawa, Y. and Okamoto, N., "Singularity modeling in two and three-dimensional stress intensity factor computation using the boundary element method," Proceedings, 7th Int. Conf. on Boundary Elements VII, Como, Italy, 1985, pp. 7-3.

[ 11] Usami, S., "'Applications of threshold cyclic-plastic-zone-size criterion to some fatigue limit prob- lems," Proceedings, Int. Conf. on Fatigue Thresholds, Stockholm, 1981, pp. 205.

[12] El Haddad, M. H., Smith, K. N. and Topper, T. H., "Fatigue crack propagation of short cracks,"

Transactions, ASME, Vol. 101, 1979, pp. 42.

Effect of Contact Pressure on Fretting Fatigue of High Strength Steel and Titanium Alloy

REFERENCE: Nakazawa, K., Sumita, M., and Maruyama, N., "Effect of Contact Pressure on Fretting Fatigue of High Strength Steel and Titanium Alloy," Standardization of Fretting Fatigue Test Methods" and Equipment, ASTM STP 1159, M. Helmi Attia and R. B. Waterhouse, Eds., American Society for Testing and Materials, Philadelphia, 1992, pp. 115-125.

ABSTRACT: The effect of contact pressure on fretting fatigue behavior has been studied using a high strength steel and a Ti-6AI-4V alloy. In steel, at higher stress amplitude, the fretting fatigue life decreased monotonously with increasing contact pressure. At lower stress amplitude, it exhibited a minimum at a low contact pressure and a maximum at an intermediate contact pressure, then decreased again and became constant at high contact pressures. The fretting fatigue strength at l0 7 cycles was high at an intermediate contact pressure. In titanium alloy, the fretting fatigue life showed a similar contact pressure dependence. The frictional force increased monotonously with increasing contact pressure. The initiation site of the main crack depended on the contact pressure and had a close relation to the width of stick region at the fretted area. The contact pressure dependence was discussed in terms of stress concentration at the fretted area.

KEY WORDS: fretting fatigue, contact pressure, frictional force, crack initiation site, stick region, stress concentration, high strength steel, titanium alloy

Fretting d a m a g e is k n o w n to have a deleterious effect on fatigue behaviors o f steels and other alloys. Fretting fatigue behaviors have been investigated so far from the point of view m a k i n g clear their m e c h a n i s m . M a n y factors control the fretting fatigue. T h e effect of contact pressure on fretting fatigue has been studied by several researchers. Most o f these studies have shown that the fretting fatigue life decreased with an increase in contact pressure [ 1 - 7]. However, one a u t h o r reported [8] that the fretting fatigue life exhibited a m i n i m u m at a certain contact pressure. Thus, the effect o f c o n t a c t pressure is not yet fully understood. In this paper, fretting fatigue b e h a v i o r o f a high strength steel and a Ti-6AI-4V alloy was studied at various contact pressures,

Experimental Procedure Specimen Preparation

Materials used were a high strength steel o f 0.18C-0.32Si- 1.26Mn- 1.04Ni-0.60Cr-0.49Mo- 0.26Cu-0.059AI-0.001P-0.003S (in weight %) and a t i t a n i u m alloy of 6.34A1-4.11V-0.14Fe- 0 . 2 0 0 - 0 . 0 0 7 N - 0 , 0 0 8 C . T h e steel was q u e n c h e d and t e m p e r e d in the following sequence:

heated to 1173 K for 2 h t h e n air cooled; heated to 1153 K for 1 h then water cooled; t e m p e r e d at 838 K for 1 h then water cooled. T h e t i t a n i u m alloy was solution treated at 1213 K for 2 h, t h e n water cooled, and aged at 813 K for 5 h, then air cooled. T h e m e c h a n i c a l properties o f the steel and t i t a n i u m alloy along the rolling direction are shown in Table 1.

Senior Researcher, Head of Research Laboratory, and Researcher, respectiveIy, National Research Institute for Metals, 1-2-I Sengen, Tsukuba, 305 Japan.

115 Copyright 9 1992by ASTM International www.astm.org

116 FRETTING FATIGUE TEST METHODS AND EQUIPMENT

TABLE l--Mechanical properties of steel and titanium alloy.

0.2% P.S. U.T.$. El. R.A.

Material (MPa) (MPa) (%) (%)

Steel 920 1 010 15 70

Titanium alloy 1 010 1 100 15 30

Testing Procedure

The fretting fatigue device is shown schematically in Fig. 1. Dimensions of fatigue specimen and fretting pad are shown in Fig. 2. Bridge-type fretting pads (span length 20 mm) of the same materials as the fatigue specimens were used. The gage parts of the fatigue specimens and the fretting pads were polished with 0-grade emery paper, then degreased with acetone.

~-Fatigue Specimen

~ Fretting Pod

~ - ~ - N o r m a l L o ~

Cyclic Load

FIG. 1--Schematic representation offretting fatigue test.

10 e Fatigue Specimen

I I

Fretting Pad ~ 2 ~

FIG. 2--Dimensions ~ffatigue specimen and fretting pad.

The fretting fatigue tests were performed on a 100 kN capacity closed loop electrohydraulic fatigue testing machine. A constant normal pad load was applied by a small hydraulic actuator to which oil pressure was supplied from the main oil pressure source of the fatigue testing machine. The contact pressure, calculated by dividing a normal force by the apparent contact area o f the fretting pad, was maintained below 160 MPa. The tests were carried out using a sinusoidal wave at a frequency of 20 Hz, under tension-tension mode at a stress ratio of 0.1 in laboratory air of 40 to 70% relative humidity at room temperature. Relative slip amplitude between the fatigue specimen and the outer edge of fretting pad was measured using a cali- brated extension meter at various stress amplitudes and contact pressures. The relative slip amplitude agreed approximately with the value calculated by the equation, 6 = L cr~/2E, where 6, L, ~o and E are relative slip amplitude, span length of pad, stress amplitude and Young's modulus o f fatigue specimen, respectively. 6 / ~ in steel specimens was about 0.05 u m / M P a , and that in titanium alloy specimens was about 0.1 um/MPa. However, the relative slip amplitude was influenced slightly by contact pressures, because the pad was deformed elastically by the frictional force. The deviation of the relative slip amplitude from the above values was less than _+ 10% for the contact pressure range investigated in the present study. Frictional force between the fatigue specimen and the pad was measured using strain gages bonded to the side of the central part o f the pad. The plain fatigue life data were obtained with hourglass-shaped fatigue specimens (stress concentration factor Kt = 1.08 for steel specimens and 1.04 for titanium alloy specimens).

Results

Fretting Fatigue L f e

The effect of contact pressure on fretting fatigue life at stress amplitudes of 180, 250 and 350 MPa for the steel is shown in Fig. 3. Plain fatigue lives, those at a contact pressure of 0, are beyond 1 X 1 0 7 cycles for three stress amplitudes. The relative slip amplitudes at stress amplitudes of 180, 250 and 350 MPa are about 9.0, 12.5 and 17.5 urn, respectively. In specimens at a stress amplitude of 350 MPa, the fretting fatigue life decreases drastically below 1 X 105 cycles at a contact pressure of 15 MPa. With the further increase in contact pressure, it decreases gradually until it becomes constant at contact pressures of more than 80 MPa. How- ever, in specimens at a stress amplitude of 250 MPa, the fretting fatigue life reaches a mini- m u m , about 1.4 X 105 cycles at a contact pressure of about 25 MPa. With the increase in contact pressure, it increases and reaches a m a x i m u m , about 2 X 105 cycles at a contact pressure of about 55 M Pa, then decreases gradually again to become constant at contact pressures of more than 80 MPa. In specimens at a stress amplitude of 180 MPa, the fretting fatigue life decreases below 1 X 1 0 6 cycles at contact pressures of 15 to 35 MPa, then increases sharply with increasing contact pressure. At contact pressures of 55 to 80 MPa, it is beyond 1 X 107 cycles. However, it again decreases below 1 X 1 0 6 cycles at contact pressures beyond 90 MPa.

S - N curves of fretting fatigue at contact pressures of 25, 80, and 120 MPa for the steel are shown in Fig. 4. They depend on the contact pressure as predicted from Fig. 3. The fretting fatigue strength at 107 cycles is higher at a contact pressure of 80 MPa than at 25 and 120 MPa.

The effect of contact pressure on fretting fatigue life at a stress amplitude of 150 MPa for the titanium alloy is shown in Fig. 5. The relative slip amplitude was about 15 um. The fretting fatigue life takes a m i n i m u m at a contact pressure of about 20 MPa. The contact pressure dependence of fretting fatigue life is similar to that of the steel specimens at a stress amplitude o f 250 MPa as shown in Fig. 3. S - N curves at contact pressures of 20 and 50 MPa for the titanium alloy are shown in Fig. 6. At the lower stress amplitude, the fretting fatigue life is shorter at a contact pressure of 20 MPa than at 50 MPa. The effect of contact pressure on S-N curves is also similar to that in the steel specimens.

118 FRETTING FATIGUE TEST METHODS AND EQUIPMENT

I I I l I I

,o,k ~

u l /

u I /

",', J

',', [

106 \

1 ~ D D

i I I

S t r e s s a m p .

o 180 MPa o 250 MPa A 350 MPa

0 n

[]

o ;; \ . o - R ~ z ~ o o

- Steel

10 4 I I J i I , , 1 J

0 20 40 60 80 100 120 140 16(

Contact Pressure / MPa

FIG. 3 - - L ~ ' c t (?/contact pressure on /rettingJatigue /t72) for steel.

500 n 400 o

:E 30O

~.2oo

100

i f )

I I I 1

Steel

. ~ Plain fatigue Fretting fatigue ",.,'~ . ~ _

- " Z X ~

Contact pressure - -L~- - 25 MPa

80 MPa - . - o - . - 120 MPa

I I I I

1 0 4 1 0 5 1 0 6 1 0 7 C y c l e s to F a i l u r e

F I G . 4--Effect ~)Jcontact pressure on fretting fatigue S - N curves for steel.

10 7

I I 1 1 I I I I I

Titanium alloy Stress amplitude

150 MPa

--IO

10 1 , , l , J i , ,

0 20 40 60 80 100 120 140 160

Contact Pressure / MPa

FIG. 5--Effect o/contact pressure on /ketting,/atigue l~/ejbr titanium alloy.

6 0 0 I I I I

Titanium alloy gsoo

fatigue

" 400

"~ Fretti n

300 fatigue ~ ~

"._.~

n s .<

2 0 0 -

(/1

(/1 Contact pressure ~

~ 1 0 0 - zs 20MPa

o 50 MPa

1 I I I

03 104 105 106 107

Cycles to Failure

FIG. 6--Effect qf contact pressure on J?ettingjatigue S-N curves for titanium alh)y.

Frictional Force

Frictional force between the fatigue specimen and the pad varied with the number of cycles.

The degree o f variation was small at high contact pressures but somewhat larger at low contact pressures. In fretting fatigue, the crack initiation and the acceleration of the crack growth by fretting usually occur after 104 to l0 s cycles [2,5,9-1l]. Hence, a frictional force determined around 104 cycles was used.

120 F R E T T I N G F A T I G U E T E S T M E T H O D S A N D E Q U I P M E N T

Relations between frictional stress amplitude and contact pressure for the steel specimens at stress amplitudes of 180, 250 and 350 MPa are shown in Fig. 7. The frictional stress amplitude is defined as a shear stress amplitude acting on the contact area whose value is calculated by dividing frictional force amplitude by the apparent contact area. At low contact pressures, the frictional stress amplitudes increase almost linearly with increasing contact pressure. At high contact pressures, the rate of increase drops and the frictional stress amplitude appears saturated irrespective of stress amplitude, and the higher the stress amplitude, the larger the frictional stress amplitude. For the titanium alloy, the relation of the frictional stress amplitude and the contact pressure was similar to the steel specimens.

The coefficient of friction # is defined by the relation, u = f/P, w h e r e f a n d p are frictional stress amplitude and contact pressure, respectively. The coefficients of friction were large at low contact pressures, about 1.0 at a stress amplitude of 350 MPa, 0.9 at 250 MPa, and 0.7 at 180 MPa. However, they decreased with increasing contact pressure in accordance with the saturation in frictional stress amplitude. In addition, at high contact pressures, the higher the stress amplitude, the larger the coefficients of friction.

Crack Initiation

Initiation sites of the main cracks responsible for the failures for the steel specimens fractured at a stress amplitude of 250 MPa (Fig. 3) are shown in Fig. 8. Their frequencies, at sec- tions of fretted surface divided into five equal parts along the cyclic stress axis, are shown for two contact pressure ranges. Most of the crack initiations at contact pressures of 55 to 160 MPa occur near the outer edge of the contact area. However, at contact pressures of 15 to 35 MPa where the fretting fatigue life took a m i n i m u m , the crack initiations occur most frequently at the middle portion of the contact area. In specimens of a stress amplitude of 180 MPa and contact pressures of 15 to 35 MPa and in those of a stress amplitude of 350 M Pa and contact pressures below 55 MPa, the crack initiation also occurred at the middle portion. At the higher contact pressures, it occurred near the outer edge of the contact area at both stress amplitudes.

In the titanium alloy specimens, the effect of contact pressure on crack initiation was the same as that in the steel specimens.

Figure 9 shows scanning electron micrographs of fretted surfaces near the initiation sites of fracture in the steel specimens fractured at a stress amplitude of 250 MPa. At a contact pressure of 80 MPa, the inner area of the fretted surface remains as polished. This area is the so-called

~ 1 0 0

~ 8o

~ o

~- o

I I I I I I I I

Stress amp. Steel

n 180 MPa 250 MPa o

zx 350 MPa . ~ j x ~

J i I I I I I I I

20 40 60 80 100 120 140 160 Contact Pressure I MPo

F I G . 7 - - R e / a l i o n belweenJHcziona] stress amplilude and contact pressure for steel.

Cyclic Lood Specimen

3 Fretting Pod

< 2ram ~,

(a) p = 55-160MP,

(b) p=lS-35MPo

l~tiation Site of Fracture

FIG. 8--Initiation sites q/i/?acture in specimens at a stress amplitude ~f 250 MPa shown in Fig. 3.

stick (non-slip) region. The outer area is the slip region. The stick region is wide. However, at a contact pressure of 25 MPa, the stick region is very narrow. The main cracks are seen near the boundaries between the stick region and the slip region. These boundaries were nearer to the initiation sites of the main cracks when the cracks were initiated, since the boundaries moved inward with the number of cycles. There was a tendency that the higher the contact pressure, the wider the stick region. At the lower contact pressures, there was no stick region, The a m o u n t of wear debris produced during testing was much more at low contact pressures than at high contact pressures.

D i s c u s s i o n

In fretting fatigue, the frictional shear stress acts on the fretted surface and stress concentration occurs there. The decrease in fatigue life caused by the fretting damage is thought to be brought about by the decrease in crack initiation life due to this stress concentration and also by the acceleration of the early stage of crack growth by fretting [2,12,13]. Hence, the larger the frictional stress, the shorter the life would be. As shown in Fig. 3, the fretting fatigue life at a stress amplitude of 350 MPa decreased monotonously with increasing contact pressure. This result was the same as those reported so far [1-7]. The frictional stress amplitude shown in Fig. 7 also increased with increasing contact pressure. There was a good correlation between the life and the frictional stress amplitude.

On the other hand, the fretting fatigue lives at stress amplitudes of 180 and 250 MPa exhibited a m i n i m u m at contact pressures of 15 to 35 MPa, and a m a x i m u m at contact pressures of 55 to 80 MPa, then decreased again and became constant at high contact pressures. In the titanium alloy, the fretting fatigue life also took a m i n i m u m at a contact pressure of 20 MPa.

A similar result has been found in fretting fatigue by torsion in an aluminum alloy [8], in which the life took a m i n i m u m at a certain intermediate contact pressure. This phenomenon was explained by the m a x i m u m fretting damage at a specific contact pressure, which resulted probably from the decrease in relative slip amplitude accompanied by the increase in contact

122 FRETTING FATIGUE TEST METHODS AND EQUIPMENT

FIG. 9--Scanning electron micrographs of/ketted surfaces near the initiation sites o/J?acture in steel specimens at a stress amplitude ~ f 250 MPa. Contact pressure. (a) 80 MPa, (b) 25 MPa.

pressure. In the present study, the relative slip amplitude between the fretting pad and the specimen decreased slightly with the increase in contact pressures at a given stress amplitude. It is difficult to explain a m a x i m u m and a m i n u m u m in fatigue lives in Fig. 3 by the slight change in relative slip amplitude. The contact pressure dependence of fretting fatigue lives at stress amplitudes of 180 and 250 MPa cannot be explained simply or directly by the change in frictional stress amplitude, since the frictional stress amplitude increased monotonously with increasing contact pressure as shown in Fig. 7.

The fretting damage is shown schematically in Fig. 10. Under a certain testing condition, there exist a stick region at the middle portion of the fretted area and slip regions on either side o f it. The relative slip mode depended on the contact pressure, relative slip amplitude [14], and n u m b e r of cycles. Hereafter, the relative slip mode is restricted to the situation around 104 to 105 cycles when the crack was initiated. The stick region was narrow when the contact pressure was low as shown in Fig. 9. When the contact pressure was very low, the whole area was occupied only by the slip region, which could be obviously judged from observing the fretted area or the wave form o f frictional force. In the steel specimens, the contact pressures for the no stick region were limited below 10 MPa at a stress amplitude o f 180 MPa, below 15 MPa Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:01:55 EST 2015

Normat Load Fretting Pad

l ~ }"P Stick R ion sI,p Weor

~, Debris

Cyclic Load

FIG. lO--Schematic representation of~'etting damage.

at 250 MPa, and below 55 MPa at 350 MPa, respectively. The relative slip mode thus changed with increasing contact pressure as follows: only slip r e g i o n - - n a r r o w stick region plus wide slip r e g i o n - - w i d e stick region plus narrow slip region.

The contact pressure and the frictional stress amplitude used in the present study were.the average values and were calculated by dividing the normal load and the frictional force by the apparent fretted area determined by the size of the pad shown in Fig. 2, respectively. Therefore, it was assumed that they were distributed uniformly over the whole fretted area. In the slip region, the contact surface was heavily damaged and wear debris was produced, and a part of wear debris was removed out o f the fretted area. The large a m o u n t of wear debris was removed near contact pressures where the life exhibited a m i n i m u m . The net contact pressure acting in the slip region was probably lower than the average contact pressure, since the normal load was given through the m e d i u m of wear debris. On the other hand, in the stick region, the net contact pressure was probably higher than the average contact pressure, since the normal load was increased by the decrease in normal load in the slip region. Hence, the net contact pressure and the net frictional stress amplitude acting in the stick region were higher, while those in the slip region were lower than the average values. Therefore, stress concentration occurred near the boundaries between the stick and slip regions, and the crack could be easily initiated. The main crack was initiated near the outer edge of the pad when the contact pressure was high and the stick region was wide. However, the main crack was initiated at the middle portion of the fretted area, when the contact pressure was low and the stick region narrow. This correlation between the crack initiation site and stick region width also implies that the crack was initiated near the boundaries between the stick and slip regions.

In the steel specimens at stress amplitudes of 180 and 250 MPa, the fretted areas were occupied only by the slip regions at very low contact pressures, while they were occupied by the wide stick regions at high contact pressures. In both cases, the contact pressure was distributed presumably uniformly over the whole fretted area. At a contact pressure where the life exhibited a m i n i m u m , the existing stick region was very narrow as shown in Fig. 9b. To this narrow stick region, a contact pressure greater than average was applied, and the net contact pressure and resulting frictional stress amplitude equal to or greater than those at high contact pressures must have acted on this narrow stick region. The m i n i m u m life was probably caused by this high concentration of frictional stress amplitude. The effect of contact pressure on fretting fatigue life at a given stress amplitude is shown schematically in Fig. 1 1. There are two life curves. The first has A B D E drawn assuming that the contact pressure is distributed uniformly over the whole fretted area; the second with BCD assumes that the contact pressure is concen- trated at the narrow stick region. Point C corresponds to a m i n i m u m in life observed at a low

112 FRETTING FATIGUE TEST METHODS AND EQUIPMENT

106 FRETTING FATIGUE TEST METHODS AND EQUIPMENT