Fatigue behaviour of composite tubes under multiaxial loading

46
where II A and II
Fifth International Conference on Fatigue of Composites
=
KI
II
IC
nII
da
A
dt
K
n denote a material constant and a crack propagation exponent, respectively. In
Model III, the Paris law is expressed as
nIII
Keq
= AIII
IC
da
dN
K
where III A denotes a material constant and n III a crack propagation exponent. It is proven in the
previous work [10] that the crack propagation exponent is identical among the three models. Thus,
hereafter, the crack propagation exponent is simply denoted by n . In addition, we assumed that n is a
linear function of R [10].
First, Model I is considered. The stress intensity factor range is given by
( )
K = Y - a
(4)
I max min
where Y represents a constant that depends on the geometry of the crack. Integrating Eq. (1) using Eq.
(4), we have
where 0 a and f
n-2 n-2
n
- - n-2 Y
2 2
n n
0 - f = I ( 1-
) max f
2 KIC
a a A R N
a are respectively referred to as the initial crack length and the crack length at the
number of cycles to failure N f . These crack lengths are related to the fracture toughness and the static
(or inert) strength S i . Then, we obtain
with
N
n-2
1
S
i
f = 1
2 -
hI( R) max max
n-2 Y
hI R AI R
2 K
( ) = ( 1-
)
2
IC
Through the manipulation of equations similar to the above, the number of cycles to failure for
Models I, II and III is expressed in a unified form as
with
Here, ( )
n-2
1
S
i
f 2
hi( R) max max
is the equivalent period defined as
e R
n
( )
N = - 1 i = I, II, III
n-2 Y
hII R = AII e R
2 KIC
( ) ( )
n-2 Y
hIII R AIII R
2 K
( ) = ( 1-
)
2
IC
2
( 1-
) n
(2)
(3)
(5)
(6)
(7)
(8)
(9a)
(9b)