Fatigue behaviour of composite tubes under multiaxial loading

22
Fifth International Conference on Fatigue of Composites
Where, N is fatigue life, S is stress, and C is undetermined constants. Using log function on both
sides of Eq. (1)
When
Eq. (2) can be written
lg N = lgC - lg S
(2)
y = lg N, x = lg S, a = lg C, b = -
(3)
y = a + bx
(4)
Eq. (4) shows that there exists linear log relationship between the structural fatigue life and the stress.
A larger number of fatigue test data suggest that lgN obey normal distribution and the standard
deviation of it will linear increase with the stress decrease if the S-N or P-S-N curves are linear in log
coordinate. The relationship between and the stress is expressed as
Where, 0, , x0are
undetermined parameters [1].
( x) = [1 + (
x - x )]
(5)
0 0
Independence fatigue test of single specimen was performed for ni times in the same stress S i and
the fatigue life is denoted by Nij ( i = 1,2, , m; j = 1,2, , ni
), transform Nij to a set of data
[ x , y ]( i = 1,2, , m; j = 1,2, , n ) by using Eq.(3), then the formula of P-S-N curve with high
i ij i
confidence and high reliability can be obtained by method of heteroscedastic regression analysis [2].
And
yp = ap + bp x
(6)
u ˆ c0 0 ( c2x + 2 c3)
a ˆ ˆ p = a + c00(1 -x0) u p -
2 c x + c x + c
2
1 2 3
ˆ
ˆ
u c0 0 (2 c1x + c2
)
b ˆ
p = b + c0 0 u p -
2 c x + c x + c
0
n i=
1
2
1 2 3
(7)
(8)
1 m
x = n x
(9)
x =
i i
nx
( )
m
i i
2
i= 1 I xi
m ni
2
i= 1 I xi
( )
0
(10)
I( x) = 1 + (
x - x )
(11)
2
-1
m
- u
i
- w
i=
1
21 c0= 1 - , = n - 3
(12)
22
2 2 2
u p 1 u
c1
= + 1- w l
xx w
2 2
2 (1 -x0)
up 2x
u
c2
= - 1- w l
xx w
(13)
(14)