102 Part of the SPIE Conference on Optical Fiber Reliability and Testing
Boston, Mass achusetts • September 1999
SPIE Vol. 3848 • 0277-786X/99/$10.00
Fatigue behavior of silica fibers of different strength
Sergei L. Semjonov
a∗
, G. Scott Glaesemann
b
and Mikhail M. Bubnov
a
a
Fiber Optics Research Center, 38 Vavilov Street, Moscow 117756, Russia
b
Corning Inc., Corning, NY
ABSTRACT
It was obtained that (t
s
S
i
2
)-(
σ
s
/S
i
) and (
σ
d
/S
i
)-(
σ′
/S
i
3
) are universal coordinates for presentation of static fatigue and
dynamic fatigue data respectively. Usage of these coordinates helps to correctly compare the results of tests of different
kinds of fibers (strong and weak) regardless of the initial defect size. Presentation of the dynamic fatigue data for pristine
and indented fibers in universal coordinates shows a very similar behavior of both fiber types in spite of their difference in
strength.
Keywords: fiber strength, static fatigue, dynamic fatigue, fiber reliability
1. INTRODUCTION
A single-region power law for crack growth into silica glass is widely used to predict the lifetime of optical fibers in
communication networks. This model is based on numerous investigations of fatigue of high-strength fibers (5-6 GPa).
However, long-term reliability of optical fibers in communication systems depends on large flaws, which can survive proof
testing at a level of ~0.7 GPa. A few earlier works showed that the fatigue behavior of low-strength fibers was similar to the
behavior of high-strength fibers (more or less linear log-log graphs with fatigue parameter n~20)
1-4
. Fresh results of
dynamic fatigue measurements in a wide region of stressing rates
5-7
demonstrate a complicated multi-region behavior of the
fatigue curve for abraded and indented fibers. In a previous work
8
, a different behavior of dynamic fatigue curves was
predicted, owing to a different size of the initial defects. The aim of this report is to find a method for correctly comparing
fatigue data of weak and strong fibers.
In earlier papers
9,10,11
, a so-called “universal fatigue curve” was used to correlate the results of static fatigue measurements
for different kinds of samples. Coordinates (t/t
0.5
) – (σ/S
i
) were used for this purpose, where t is the time-to-failure under
stress
σ, S
i
is the initial inert strength of the sample, t
0.5
is the time-to-failure at σ = 0.5S
i
. There exist several reasons to
continue research in this direction:
- the above “universal” presentation was deduced using simple power or exponential laws of crack growth;
- it is useful only for static fatigue measurements;
- it requires knowledge of an additional parameter t
0.5
.
Therefore, it is desirable to solve the problem of correlating fatigue measurements of different fibers in a more general form.
2. THEORY
Stress concentration in a crack tip is characterized by stress intensity factor K
I
, which is defined in terms of applied stress
σ
and crack length a
aYσK
I
= , (1)
where Y ~ 1 is a constant determined by the crack geometry.
An effect of subcritical crack growth or fatigue in brittle materials, such as glass or ceramics, is usually described as a
dependence of crack growth rate on stress concentration in the crack tip:
∗
Correspondence: E-mail: sls@fo.gpi.ac.ru; Telephone: 7(095)135-7402; Fax: 7(095)135-8139
103
=
Φ
IC
I
K
K
dt
da
, (2)
where K
IC
is the critical stress intensity factor depending on the properties of a specific material. Power or exponential laws
are often used in equation (2), but we will deal with an arbitrary positive function defined in the range 0< K
I
< K
IC
.
One more term to be introduced is inert (or intrinsic) strength S:
aY
K
S
IC
= . (3)
This is the strength in the absence of slow crack growth or fatigue. The strength in liquid nitrogen is close to the inert
strength.
Two types of tests are widely used to observe fatigue effects; namely, static and dynamic. In the first case, constant stress
σ
s
is applied to the sample, and time-to-failure t
s
is measured. In the second test, an increasing load with a constant loading rate
σ′
= d
σ
/dt is applied to the sample, until it breaks at some load
σ
d
. The dependence of time-to-failure on the applied stress is
called static fatigue, the dependence of breaking strength on the loading speed is called dynamic fatigue. The both
dependencies can be derived from equation (2), taking into account that the point of K
I
= K
IC
is the point of failure.
For static fa tigue
(
σ
= const. =
σ
s
) the following two equations can be taken into account
SK
K
k
IC
I
σ
== , (4)
and
2
⋅
⋅
=
σ
Y
Kk
a
IC
. (5)
As the result, equation (2) can be transformed into
()
dtk
Y
Kk
d
s
IC
⋅Φ=
⋅
⋅
2
σ
. (6)
At the beginning of the test the initial crack size is a
i
, the corresponding initial inert strength is S
i
, and the following relation
is created:
i
s
i
S
k
σ
= . (7)
Thus,
()
k
dk
SkY
K
dt
ii
IC
Φ
⋅⋅
=
2
2
. (8)
The solution of equation (8) is
()
()
Ψ=Ψ=
Φ
⋅
⋅
⋅
=⋅
∫
i
s
i
k
i
IC
is
S
k
k
dkk
kY
K
St
i
σ
1
2
2
. (9)