Abstract - Fatigue Behavior in Strain Cycling in The Low and Intermediate Cycle Range
Abstract - Fatigue Behavior in Strain Cycling in The Low and Intermediate Cycle Range
Abstract - Fatigue Behavior in Strain Cycling in The Low and Intermediate Cycle Range
fiA!I'IGUE
I1 /
'-
vJ!t' T
//?.6$
t3-t./'
.2/
/-,;-y
I!--
ABSTRACT
?/;i
,<-~~*~~~$~
were investigated.
c h a r a c t e r i s t i c s c o n s i s t s of a p l o t of l i f e versus t o t a l s t r a i n range
which i s t h e sum of e l a s t i c and t h e p l a s t i c components.
I n t h e low
Empirical r e l a t i o n s have
The v a l i d i t y of t h e s e
desigii f o r f i n i t e l i f e .
-..
- 2 -
However, before t h i s
For
a t about t h e same order of magnitude, and above 100,000 c y c l e s t h e p l a s t i c s t r a i n range i s n e g l i g i b l e compared t o t h e e l a s t i c s t r a i n range.
In
Thus, although
Experimental v e r i f i c a t i o n
of such r e l a t i o n s h i p s were subsequently shown ( r e f . 2 ) f o r s i x t e e n mater i a l s of various composition and heat treatment.
Thus, it h a s been
f a i r l y e x t e n s i v e l y v e r i f i e d t h a t l i f e i s governed by t h e t o t a l s t r a i n
range: cnnsisf,ing of
tiii
- 3 -
e - q e r h ~ z t z i-esiiits
l
anc tnose predicted by a method r e c e n t l y proposed by
- 4 -
For many a p p l i c a t i o n s
range
Nf,
the result i s
Thus t h e c y c l i c l i f e i s r e l a t e d
AP
where
M and
=mif
(1)
a r e m a t e r i a l constants.
z,
= -1/3.
z = -1/2
provided a b e t t e r representa-
is
appeared t o be a material
I f the s t r e s s range
This value
For t h e purpose of a n a l y s i s t h e s t r e s s
Au.
Thus
- 6 -
aEel = &/E
where
Aee,
cyclic l i f e
= (G/E)
Nf
(2)
i s t h e c y c l i c e l a s t i c s t r a i n range corresponding t o t h e
Nf,
i s t h e e l a s t i c modulus, and
and
are other
m a t e r i a l constants.
Although equation ( 2 ) adequately r e p r e s e n t s t h e c h a r a c t e r i s t i c
behavior of a l a r g e number of materials f o r engineering use, it i s
admittedlj only an approximation of t h e t r u e m a t e r i a l behavior.
For
even higher l i v e s .
Alternate e l a s t i c r e l a t i o n involving a n endurance l i m i t .
Equation ( 2 ) implies t h a t t h e l i f e i n c r e a s e s with a decrease i n
e l a s t i c s t r a i n since t h e exponent
e l a s t i c s t r a i n , corresponding t o a n applied s t r e s s , w i l l p r e d i c t a f i n i t e
life.
I n r e a l i t y , it i s w e l l recognized t h a t many m a t e r i a l s e x h i b i t an
I n order
l i m i t , t h e following d e r i v a t i o n i s made:
Let it be assumed t h a t t h e asymptotic s t r e s s range-strain range
rclatirjn coincides with t h e e l a s t i c l i n e up t o a c r i t i c a l s t r e s s range,
t h u s implying t h a t u n t i l t h i s s t r e s s range i s reached, no p l a s t i c flow
w i l l t a k e place.
By d e f i n i t i o n , then, t h i s
'end
bend,
and t h e s t r e s s
'end'
a"p
A(&
2aend)
S u b s t i t u t i n g i n equation ( 3 ) t h e value of
solving f o r
(3)
AD
aa = 2aend
- 2aend
(4)
I n p r i n c i p l e , therefore, equation ( 5 ) i s a
C . C ) E C P ~ cf
~
- 8 -
Thus from
equation (3)
limits.
It w a s concluded
Acel
versus
Nf
show
limit.
6
range ( f o r most m a t e r i a l s up t o 10 cycles).
Because of t h e s i m p l i c i t y
Of
el
For materials
versus
Nf
at
6
l i v e s w e l l below 10 cycles, t h e r e i s no d i f f i c u l t y i n re_nl%cir.gq d z t i o n ( 2 ) by i t s equivalent, equation (5), wherever t h e former appears
i n t h e discussions t o follow.
- 9 -
Plotted
however, not a s t r a i g h t l i n e .
The t o t a l s t r a i n range,
&,
with t h e s t r a i g h t l i n e f o r t h e p l a s t i c component.
A t t h e higher c y c l i c
&
el
tangency t o t h e e l a s t i c l i n e .
line.
Thus, t h e
&
curve approaches
10
cycles.
Thus, i f
On t h e o t h e r
Basically, it i s probably s t i l l l o c a l i z e d
10
p l a s t i c f l o w t h a t induces fatigue, even a t t h e very high l i v e s , but measurement of t h e p l a s t i c flow i s d i f f i c u l t , and t h e s t r e s s range apparently
becomes an adequate measure of t h i s l o c a l i z e d p l a s t i c flow.
One f i n a l p o i n t can be made i n connection with f i g u r e 1 t h a t i s of
p r a c t i c a l i n t e r e s t i n t h e experimental determination of material behavior.
This
A s already indicated, t h e t y p e s of r e l a t i o n s
e n t i r e l y on d a t a obtained i n f a t i g u e t e s t s .
Measurement of constants.
I n t h e most general sense t h e constants
M,
z,
G,
and
must be
Al-
From t h e s t r e s g r-e,
the e l a s t i c
A logarithmic
and y
can be determined.
z1
Such a p l o t permits c a l c u l a t i o n of
N1
and
ACT,
and
Au2,
(nEl - T)
-z
N1
= (&2
4)
Acl
-Z
N2
The optimum s t r a i g h t
12
M and
z,
i s t h e range
and
i s t h a t a t high
y,
In
Eliminating
Nf
between equations
but it i s t o be
& has
Thus equa-
t i o n ( 9 ) r e p r e s e n t s e s s e n t i a l l y a r e l a t i o n between t h e t o t a l s t r a i n
range and t h e asymptotic s t r e s s range.
13
i s u s u a l l y done f o r a s t a t i c s t r e s s - s t r a i n curve.
No l i m i t a t i o n s a r e
Thus approx-te
r e l a t i o n s involving r e a d i l y a v a i l a b l e d a t a can
The approximate r e l a t i o n s t o be
The l e a s t square
l i n e s used a r e t h e
In c a l c u l a t i n g these l i n e s , t h e f o l -
f o r t h e p l a s t i c l i n e , t h e d a t a p o i n t s used
what d i f f e r e n t m a t e r i a l i s being t e s t e d ,
The
s t a t i c t e n s i l e p r o p e r t i e s t o be used i n t h e following a n a l y s i s a r e l i s t e d
i n t a b l e I.
Parameters,
where
is the ductility,
.A
and Af
a r e t h e i n i t i a l and f i n a l a r e a s
- *o
Thus
t h e conven-
- Af
-7
If the
Another form of
16
AE
P
is
fi D
at
(ref. IC)
a r r i v e d a t another e f f e c t i v e value of
of 1.5 D
at
Nf = 1/4 cycle,
In reality,
Thus,
its validity.
( k p / D ) 1/4
versus
Nf = 1 / 4
( f i g u r e s ZA through 17A).
at
I f t h e assumption t h a t
AE = D
P
Nf = 1 / 4
were v a l i d , a l l t h e p o i n t s would l i e on a h o r i z o n t a l s t r a i g h t l i n e
(&p/D)1/4
= 1.
A d e t a i l e d a n a l y s i s of t h e i n t e r c e p t of t h e
N,
was tried.
It w a s
D3/4
(14)
17
This
life.
e l a s t i c l i n e s a t a number o f d i f f e r e n t c y c l i c l i v e s (figs. 2A
through 17A) versus ultimate t e n s i l e strength f o r a l l t h e m a t e r i a l s
investigated.
shown i n f i g u r e ( 2 0 ) .
mation
18
or
--
t h e l i f e a t 10 cycles.
The f r a c t u r e s t r e s s i s determined by
I n a l l cases, therefore,
19
f a t i g u e t e s t , it i s n a t u r a l t o expect t h a t t h e l i n e of e l a s t i c s t r a i n
N = 1/4
Nf = 1 / 4
of t h e optimized l i n e a r r e l a -
(+j1/& 0
where
= 2.5
i s t h e f r a c t u r e s t r e s s i n t h e uniaxial t e n s i l e test.
It i s merely
necessary t o p l o t
2,5
f
E
at
Nf = 1/4.
20
l i n e , but rather,use
f o r predicting a p o i n t on t h e e l a s t i c
e l a s t i c s t r a i n range predicted a t
5
1 0 cycles from
The average
lo4
cycles.
Thus f a r
of t h e s e two l i n e s .
It i s i n t e r e s t i n g t o observe t h a t
Actually, t h e r e l a t i o n t h a t i s most
A p l o t of
bel
A s t r a i g h t l i n e does
21
(Ap)104 = a01
i n s t e a d of
lo4
cycles.
cycles approaches or i s
lo4
np
high s t r e n g t h m a t e r i a l s i s -0.6
Endurance l i m i t ,
a s w i l l ??e discussed l a t e r .
i s t h e s t r e s s a t t h e outermost f i b e r s i n a n a l t e r n a t i n g bending t e s t
h-1
vLAvw
--L4-L
WLIILll
applied.
3 - - I U L U ~U U ~ S
D-3 7---;-
22
Choice of an a r b i t r a r y l i f e i s
a0
p r e c i s e l y t h e knee of t h e
Nf
Failure
OCCUTB
a t almost any
point on t h e
Au
Nf
curve, e i t h e r by implication as t o c y c l e s t o f a i l -
we, or by d i r e c t s p e c i f i c a t i o n of cyclic l i f e .
endurance l i m i t a t a l i f e of
-1
. -c 4
aena
i s the
cycles, one p o i n t on t h e l i n e of
Nend
s t r a i n i=Zlige v e r s u s life is
c I Q I D ~ ~ ~
Thus i f
?fl--2
at
--=uL
= Mend,
where
is
t h e e l a s t i c modulus,
i n a l t e r n a t i n g b ending t e s t s
axial straining.
, whereas
= 0.65
bend
send
y = 0.
Thus
23
or
G = 2uend
The "knee",
7
assumed a t 10 cycles.
the relation
s t a n t s i n equation ( 2 ) .
Figure 24 shows a p l o t of
z
A better
24
r i a l s as w a s previously discussed.
The slope of t h e l i n e f i t t i n g the e l a s t i c component of t h e t o t a l
s t r a i n range ( t h e same as t h e exponent
i n eq. ( 2 ) ) w a s found t o
Where no other
y = -0.1
m y be
cannot be measii~ed
accurately.
Relation involving d u c t i l i t y and endurance l i m i t .
A n extremely single r e l a t i o n was proposed by Langer ( r e f . 3), which
a)
b)
c)
-1/2
D
CV = CVp + Ace1 =
(Nf)
+ - 20end
E
25
I n p r a c t i c e a graphi-
The l i n e f o r t h e e l a s t i c com-
5 -___ n
C Y C L C ~ ILUIII
~n
IU
Y - ?
t,~lt: IracLur.e
LT..
af
can-
from t h e p r e d i c t e d s t r a i g h t l i n e .
From t h e e l a s t i c s t r a i n range t h e
The
4
point a t 10 c y c l e s i s t h e n joined by a s t r a i g h t l i n e t o t h e p o i n t a t
AEP
For t h e case
The o r d i n a t e s a t se-
z,
G,
and
i n terms of
D,
up
and
uf.
26
where
y =
z =
= 0.827D
0.52
0.083
-1 log
4
(3
(.)($) ]
0.166 l o g
0.179
82
D + 1l o g
3
[ (2)(;0*177
1- 82
I n t h i s case it i s l o g i c a l t o c o n s t r u c t t h e l i n e f o r e l a s t i c
I f the
For m a t e r i a l s i n which t h e e l a s t i c
is
ha.rnna
u+JvILu
+L-
m~.p--+~,-,
c A L I G L u L V G
_.--(1
It1
AllCC
-n
U
I
AL-
~ L I CC U L V ~ ,
of t h e e l a s t i c l i n e .
27
by t h e p o i n t a t t h e endurance l i m i t .
fer G,
Nend,
-;,
Lm--.,.-
?4, a&
C-<-l--
vcLulIlc
Ia..LILY
---l<--.L-J
2.0
LulllyLLcabcu
The formulas
Nend
II
i s i11duGed
as a l i t e r a l t e r m .
s p e c i f i c values of
Nend.
Nend
= 10
0.92
(&)
= 2*5 end
M = 0.827D
2,
= 0,052
0.394
166
-u3
(
endy
(
)2)
nd
- -14
RESULTS
zT3ilzilZlL4y of c
AND DISCUSSION
~
a&&
~ oii
~i-el&ti-cel>~
~laygec ii-(jij2uez-.
>
~
It should be recognized, of
28
The t e n s i l e d a t a f o r
a r e p l o t t e d i n f i g u r e s 25 through 30.
~ . V Q ~&hnds
Comparisons of p r e d i c t i o n s wi-th e x p r i n e n t , a l i3-~t,.zf ~ r
In
It can be seen
and
31b).
29
t h e m a t e r i a l s investigated.
were obtained.
I n f i g u r e 31b t h e p r e d i c t i o n s a r e base& on equation (22), using an
experimentally determined d u c t i l i t y and endurance l i m i t .
The endurance
uu
*IvAwIAI
1 ,.PA
lL1c U
I
A *
n 7 L,YUCS.
----- - -
1
IU
I n general it i s seen t h a t
Where
a t all.
The p r e d i c t i o n s of f i g u r e 31a a r e based on making use of t h e duct i l i t y , f r a c t u r e s t r e s s , and u l t i m a t e t e n s i l e s t r e n g t h as determined i n
the s t a t i c uniaxial tensile t e s t .
An improvement i s obtained r e l a t i v e
It i s
30
possible t o make t h e method using t e n s i l e data alone predominantly conservative by dividing t h e predicted s t r a i n by approximately 1.5; t h e
r e s u l t i s s t i l l an improvement ( i n the sense t h a t b e t t e r c o r r e l a t i o n i s
obtained) over t h e method using equation ( Z Z ) , d e s p i t e t h e f a c t t h a t no
f a t i g u e p r o p e r t i e s a r e required t o make t h e analysis.
A f i n a l p o i n t t o be made i n comparing t h e two methods i s t h e very
important by-product r e s u l t i n g from t h e method t h a t f i t s t h e e l a s t i c
s t r a i n range data b e s t as well as the t o t a l s t r a i n range data.
This
The predic-
r i a l s investigated.
31
It
r i a l s from t h e i r u n i a x i a l t e n s i l e p r o p e r t i e s i s presented.
Predictions
LE
Sata foi-
G,
l a r g e iimfuer
0;
materiais.
me
The
32
APPENDIX
y = a
bx
I n practice,
w i l l c o r r e l a t e t h e d a t a according t o t h i s equation.
a,
b,
and
and
x,
which
versus
by t h e authors i s as follows:
a ) s e l e c t a value of t h e exponent n,
b) plot
versus
xn,
and
r e s u l t i n g f r o m t h e b e s t fit straight l i n e
through t h e data,
d ) determine t h e s u i t a b i l i t y of t h e choice of exponent
by
n.
initially,
of
and
b.
33
n.
The
s o l i d l i n e s a r e i d e a l i z a t i o n s of m a t e r i a l p r o p e r t i e s where t h e endurance
l i m i t i s taken as zero.
Thus, t h e
& = &
small i n t h e v i c i n i t y of t h e o r i g i n j while t h e
f e c t l y straight.
Nf l i n e i s per-
nEel
z/d
Nf
curve
i n equa-
z/d,
z/d
Nf
&/E
versus
z/d,
t h e standard devia-
z/d =
The standard
0.085,
since
34
z/d.
z/d
pro-
z/d,
L1-f
io5
cycies, it i s c l e a r t h a t t h e choice o f
small d e v i a t i o n s i n t h e "data",
so c h a r a c t e r i s t i c i n f a t i g u e experiments,
limit.
A s before, b e s t r e s u l t s a r e obtained f o r
aend
l/d,
0,
but the
and correspond-
l/d
a r e shown i n f i g u r e 32(a).
No
endurance l i m i t of 50,000 p s i .
35
be
0.246
(32)
and
= EE
el
E = 32.5,:iC:6 psi.
where
= 100,000
300,000
(Nf)
0.160
(35)
However, f o r t h e p r e s e n t c a l c u l a t i o n cogni-
+-1
percent
to
5 5 percent,
In this
By comparing
t h e standard d e v i a t i o n s i n t a b l e s I V and V and t h e d o t t e d curves i n f i g ure 33 (of which o n l y two a r e shown, t o avoid congestion), it can be seen
that considerable ambiguity e x i s t s a t t h e optimum endurance l i m i t .
The
limit.
A f i n a l computation i s shown i n f i g u r e 34.
t.ioml
"cL8.t.B."
computations a r e shown i n t a b l e V I .
L
-.
J-L-Li C
nD
-.
ll*e
rm-
of endurance l i m i t d e t e r m i m t i o n i s g r e a t l y reduced.
36
el
The conclusions
Nf
show d i s t i n c t curvature, i n
I n t h e absence of
of an endurance l i m i t ( i n f i n i t e l i f e ) , but i n p r a c t i c e i s
For
equivalent ( 5).
- 37
REFERENCES
1. Manson, S. S., Thermal Stress in Design, Machine Design (a) Part 18,
June 1960; (b) Part 1 9 , July 1960; (e) Part 21, September 1960.
2. Smith, R. W.,
E.,
11. Manson, S.
S.,
3%
pp. 45-49.
13. Worthing, Archie G.,
-Data
,
TIlBLE I.
- MATERIAL PROPERTIES
w
MATERIAL
NWINAL CWPOSITION,
PERCENT
FGZiL,
SAME H U T As IN REF. 2
A(KxTRII
I S 1 52100
-)
TITANISIM
(5A1*
C 0.022,
02 0.067,
1528'
400
sn)
I,
0.06, N2 0.014, A1 5 . 1 ,
H+ 0.0096, TI RWAMDER
Sn 2 . b .
VASCOMAX
300 C W
2024 T 4
ALDMI~
7075 T 6
AS
SUPPLIER
RC 4 8
RC 61-62
RC 31-32
SOIIITION
By SIiPPLIBR
900' F i 1 w1, AIR W O L
RC 54-55
AS P W NAW SPECIFICATION
apll-sa CONDITION T
A3 RBCEIVE
RB 9 4
PBR NAW S P E C P I C A T I O N
AS R B C 6 I V E
RB 1 9
QW-262 CONDITION T
ALuMlNUM
mmss
CONDITION
.IO
.o I
.oo I
I
IO-'
F i g u r e 1.
loo
10' lo2
lo3
104
(CYCLES TO FAILURE)
I
lo5
lo6
io7
CS-22507
PLASTIC
-LEAST
SQUARED FIT
OF DATA I
I
TOTAL
EQ. ,24THROUGH 20
DUCTILITY
ENDURAI
.I
.01
,001
100
io*
104
io'
105
103
CYCLES TO FAILURE
Figvre 2 .
107
CS-28Yb6
eee
ELASTIC
TO PL
.I
c .01
1
w
W
.I
,001
z
U
lE
v)
.Oi
.I
A .OI
.Ool
100
102
104
'
106
102
CYCLES TO FAILURE
F l g u r e 3 . - F a t i g u e b e h a v i o r of AIS1 304 (hard), material numbei. 2 .
,001
lo4
io6
CS-28952
CYCLES TO FAILURE
-
Flgore I .
CYCLES TO FAILURE
F:gure
5.
m
PLASTIC
Plgure 6 .
- Patlgue
PLASTIC
100
102
104
106
CYCLES TO FAILURE
Plgure 7 .
CS-28948
ELASTIC
TOTAL
PLASTIC
.I
.01 B
.001
100
102
104
106
CYCLES TO FAILURE
Plgure 8.
ELASTIC
PLASTIC
TOTAL
.I
(
a
P
z
(3
W
1: c.001
. o ~
(1:
Iv)
.Irn
A.01
,001
.
I
a
1'0
102
100
102
104
CYCLES TO FAILURE
II
104
cs-L'BYSI
PLASTIC
TOTAL
.I
.01 B
\
.OOl
11
103
CYCLES TO F A I L U R E
105
CS - 2696 2
ELASTIC
I
TOTAL
z c,001
E
a
W
p
. o
.I
!Y
+
.01 B
rn
.OOl
A .01
I!
,001 I
ULLU
IO'
CYCLES TO FAILURE
Flgure i l .
F a t i g u e behavior
Of
105
CS-BBYS3
107
107
ELASTIC
PLASTIC
TOTAL
.01
c .OOl
.I
W
(3
a
Ly:
za
.01 B
Ly:
I-
o
.I
.OOl
A .01
.OOl
100
104
102
106
101
103
105
CS-29960
CYCLES TO F A I L U R E
F i e u r e 12. - F a t i g u e b e h a v i o r of beryllium, m a t e r i a l number 11.
ELASTIC
PLASTIC
TOTAL
.I
.01
4a
.OOl
.I
(I:
z
a
(I:
.01 B
I-
cn
.oo I
.I
A .01
.OOl
1+!1141
100
I111I
102
104
106
..
CYCLES TO FAILURE
F l g u r e 13.
- Fatigue
b e h a v i o r of 3 5 0 ( h a r d ) , materlal nuiber 1:
IO'
103
105
CS-28961
107
107
.
PLASTIC
TOTAL
.I
iZ
I
.01 0
.001
,001
ioo
io2
io4
io4
io2
106
CYCLES TO FAILURE
Figure 1 4 .
106
CS-dB,b,
TOTAL
.I
.01 0
,001
101
CYCLES TO FAILURE
103
105
"S-
,,I
107
TOTAL
.I
.01 B
.oo I
103
CYCLES TO FAILURE
F i g u r e 16.
105
107
cs-28942
TOTAL
ELASTIC
!.
.I
.01 B
.oo I
'0
CYCLES TO FAILURE
Pimure 17. .F a t l g d e b e h a v i o r o f 2014 T6 aluminum. material number 1 6
io5
CS-L'MJb7
10'
.4
.8
1.2
DUCTILITY
2.0
1.6
cs-2BY37
. 2 t
.02
.o I
.02
.04 .06
.I
.2
DUCTILITY
Figure 19.
.4
.6
2
CS-28939
P l a s t i c strain range a t l i f e of 10 c y c l e s v e r s u s d u c t i l i t y .
14
100
200
300
400
ULTIMATE STRENGTH, KSI
E-28934
F i g u r e 20. - C o r r e l a t i o n o f s t r e s s range
a t 105 c y c l e s with u l t i m a t e s t r e n g t h .
See Table I for m a t e r i a l i d e n t i f i c a t i o n .
1000
I-
a
W
W
z
a
ac
I
cn
cn
W
ac
Icn
200
300
400
FRACTURE STRENGTH, KSI cs-28933
100
F i g u r e 2 1 . - C o r r e l a t l o n of s t r e s s r a n g e
a t 1/4 c y c l e with f r a c t u r e s t r e s s . S e e
T a b l e I for m a t e r i a l i d e n t i f i c a t i o n .
SYMBOL
NUMBER
I
7
4
3
5
0
Q
6
2
8
13
12
9
IO
II
16
15
0
Q
v)
13
0
.OlO
dr
13
.OOl
IO0
I,1#1
101
, I t 1
, I n 1 1 1
I
I
I B I I I
I0 3
I02
IIIII
I04
CYCLES TO FAILURE,
IO5
Nf
I\
.004
.006
.008
PLASTIC STRAIN RANGE AT
104 CYCLES
.002
CS-28936
Figure 23. - Correlation of elastic and plastic
strain components at l o 4 cycles. See Table I
f o r material identification.
.I
IIIII
IO6
C S - 2 2 L,
-.4IL
-0''
.017
-
a.
0
1
-.2
ELASTIC
TOTAL
.I
.01 B
.OOl
io2
lo4
106
lo3
10'
CYCLES TO FAILURE
Flgvre 2 5 .
Fatlgue behavior
r i
lo5
CS-28947
-7.
10'
TOTAL
CYCLES TO FAILURE
F i g u r e 26. - Fatlglle b e h a v i o r O f 52100 X-hard RC 6 2 , material number 18.
ELASTIC
Plgure 28.
- Fatlwue
AL
.I
.01 B
.OOl
)4
F l g u r e 29.
- Fatigue
b e h a v l o - o f ?024 T4 alurnlnum, m a l e r i a : n u m b e r 2 :
I06
ELASTIC
PLASTIC
TOTAL
.I
.01 B
.OOl
102
104
CYCLES TO FAILURE
0A
I- LL
no
.I
106
102
104
106
Au=-I10+408(Ar,)0'080 2~0.42
KSI
Au=+60+278(Arp)o'200 2 ~ 0 . 5 9KSI
(0
.04
.06
.08
.IO
TOTAL STRAIN RANGE, A
(AI STRESS-RANGE VERSUS STRAIN-RANGE RELATION
.02-
,001
10-1
IO
IO'
I
102
103
104
I
105
I
106
107
CYCLES TO FAILURE, N f
cs-21I:Is
(81 STRESS-RANGE VERSUS LIFE RELATION
Figure 3 2 .
erlduranoe
.04
.06
.08
.IO
STRAIN RANGE, A s
(AI STRESS-RANGE VERSUS STRAIN-RANGE RELATION
0
.02
CYCLES TO FAILURE, N t
CS-"-'801
CUrYeS
t o c o n s t a n t s In equations l n v o l v l n g
NASA-CLEVELAND,
orno
E-2256