0
0.1
0.05
d = l ~ m \
o o'.5 11o
Crack length.a (mm)
FIG. 6--Relalionship between constants C and crack length a (groow.d type).
where Kmi~ and Km=~ are the m i n i m u m and m a x i m u m M o d e I stress intensity values; and (2) the crack length, a, especially in the short crack region.
Here, we consider the effect o f the stress intensity factor ratio, R, and the crack length, a, on dxK, h. W e t h e n d e t e r m i n e the relationships between dxK~h and the stress intensity factor ratio, R, using various e x p e r i m e n t a l results derived [11] as
AKth(R} = &K~h{R:o) " (1 -- R) ~ (when R < 0) and
dxK, h(R) = &K,~(R:o~ " (1 -- R ) 1~176 R~/~o~ (when 0 ~< R < 1) (5)
T o predict/XK~h in the short crack region, El H a d d a d et al. [12] derived the e q u a t i o n
a (6)
/XK~h(~) = 3,Kth(a=~o) 9 a + ao In their e q u a t i o n , the critical crack length, ao, is d e t e r m i n e d by
2
ao \ Ao-.,o / 7r (7)
Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:01:55 EST 2015
0.1
Knuri:ingi i
O
0.05
o o15 1.o
C r a c k l e n g t h a (mm)
FIG. 7--Relationship between constants C and crack length a (knurled pad type).
where A~w,, is the fatigue l i m i t of a plain specimen a n d ~K,h~ .... ~ is the threshold stress intensity factor range of the long crack. The value, a0 is assumed to be c o n s t a n t for all R. Using Eqs 5 a n d 6, the threshold stress intensity thctor range, AK,h, considering both R a n d a, is derived as
AK, h = AK, h(R.O . . . . )" (1 -- R) ~ - @ a @ a o (when R < 0) a n d
a (when 0 ~ R < 1) (8) AK, h = AKn,IR=o . . . . )" ( l - - R ) (0"5+l~ R)/10) ,
~ 3 + a 0
Using Eq 3, the Mode I stress intensity factor range, LXK, a n d the stress intensity factor ratio, R, can be calculated as
2xK = Act 0 9 C (9)
A + ( ~ m i n + B ) - C
n = (10)
A + (c~ .... + B) 9 C
The c o m p a r i s o n s of AK with 'XK, h, for a grooved type model with a 1 m m groove depth, are shown in Figs. 8, 9 a n d 10. In each figure the stress amplitudes, era, are 137 MPa, 147 M P a a n d
1 0 8 FRETTING FATIGUE TEST METHODS AND EQUIPMENT
n 3O
<1
t ~
.~ 20
0
m
an
.f''" ^If~ tq, - ~O'a= | 3 7 M P a
..-'"
,'/" LkKth
Crack length a (ram)
FIG. 8 - - R e l a t i o n s h q ) betweo? A K a~d ~K'~h (grooved type, d ~ I ram. ~ = I57 MPa).
<I
t ~
O
t"
U~
30
20
10
, I
5 . . . . AKth
0 . 5 " - ~ i 0
Crack length a (rnm)
FIG. 9 - - R e l a t i o n s h i p beLwee/~ ~ K a n d ~K,,~ (gtr type, d = 1 ram, a~ = 147 MPa).
157 MPa, respectively. In the case of Fig. 8 (~,, = 137 MPa) the small carck formed by the fretting damage stops at 20 ~rn. For Fig. ~13 (a~ = 157 MPa) the crack formed by the fretting damage grows s|owly unt;,l the specimen breaks. Figure 9 shows the critical condition where the crack stops at 45 urn. h is important to note that this is the fretting fatigue limit. In Figs.
11 and 12 the fretting fatigue limit conditions for each grooved type with a 2 m m groove depth and knurled pad type are shown.
Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:01:55 EST 2015
<1
i -
r-
ul
30
20
10
:::::::::::::::::::::::::: AK .... -''"
.. " " " " " " / ~ - ~ G a = 157 M P a 1 " UJ-I / I ' -
. / V L, ~m=O
f
f A K t h
#
0
I . .. . .
o.s I.'o
C r a c k l e n g t h a (ram)
F I G . l O~Re[ationship between ,~K and &Kfh (grooved o'pe, d = 1 ram, c~ = 157 MPa).
v
<1
t'-
2 o
r"
.E 30
20
10
0
.::i!iiii!iiiii! R5 ~! &K _ -
J
"" 10"a'- 201MPa
f '
z 0 - -
/ / O'm=0
A K t h
Crack length a (ram)
F I G . i l--Relationship belween ~ K and AK~t, (grooved O,pe d = 2 ram, ~ = 201 MPa).
110 FRETTING FATIGUE TEST METHQDS AND EQUIPMENT
n
(-
if) r-
~
O9
/ AK,,.
30t- / .-..r
| / " .:ifiii!!iJ~Knufling / ~ . . ~ . . .
0 =~SMPa
AKth
10
015 1 .'0
Crack length a (mm)
F I G . 1 2 - - R e l a t i o n s h i p bet ween ,SK a n d AKrh (knurled p a d type, d = 1 m m , a. = 265 MPa).
i iiiiiiiiiiiii!ii:i: "
<1
d~
(-
oO 4.a
200
100
~" 98MPa
Distance from groove bottom r (ram)
F I G . 1 3 - - S t r e s s distribution near the groove bottom.
Copyright by ASTM Int'l (all rights reserved); Wed Dec 23 19:01:55 EST 2015
Optimization of Fretting Fatigue Strength Improvement Methods
F r o m the estimated results of the fretting fatigue limits for a grooved type (see Figs. 9 and 11) we can see that fretting fatigue strength improves with increased groove depths. However, the fatigue strength of the groove bottom decreases with increased groove depths. We must consider both the fretting fatigue limit and groove bottom fatigue limit for optimization of the groove shape. Stress distribution near a groove's bottom is shown in Fig. 13. Here, the stress concentration factor is 2.18. The fatigue limit of the groove bottom can be estimated from these stress concentration conditions. Estimated results of the fretting fatigue limit and groove b o t t o m fatigue limit for grooved type models are shown in Fig. 14. From these estimated results it was concluded that the o p t i m u m groove depth is about 1.5 ram.
Fretting Fatigue Test Experimental Procedure
The fretting fatigue test apparatus is shown in Fig. 15. The contact pressure, P0 = 196 MPa, is achieved by tightening the four screws and measured by strain gauges mounted at the spe- cimen's center (strain gauge A in Fig. 15). The fluctuating axial stress G~, is achieved using a closed loop servo controlled electro-hydraulic test machine with a load capacity of _+ 100 KN.
The test specimen and fretting pads are made, respectively, from Ni-Mo-V steel and c~/rbon steel. The frictional coefficient of the contact surface is estimated by measuring the strain hys- teresis near the contact edge by strain gauge B in Fig. 15. Using this method the frictional coef- ficient o f the fretting damaged surface can be obtained as 0.7.
Experimental Results
For the knurled pad type test, the wear loss of contact apexes and reduction of contact pres- sure were assumed, so the contact pressure change during the fretting fatigue test was measured
%
o.. 200
b ~
~
E
g
.~
" :+:+:::,::::-o F r e t t i n g fatigue limit
Groove bottom fatigue limit
0
Groove depth d (mm)
FIG. 14--Fatigue strength comparison qf grooved-type models.