Page 151 - Fiber Fracture

136 P.K. Gupta

According to fracture mechanics, catastrophic fracture (fast crack growth) occurs at
the Griffith-Irwin criterion (Lawn, 1993) given by
K = Kc (12)
Eqs. 8, 9, and 12 together are referred to as the slow crack growth model and describe
fatigue completely in non-pristine fibers. Important consequences of the slow crack
growth model are summarized in the following.

The Inert Strength

The inert strength is given by:

so = Kc/[Ycy]
where CO is the initial size of the most severe crack in a sample.

The Time to Failure, t(T,X,a)

As a function of the applied stress u, relative humidity X, and temperature T (Gupta,
1983), it is given by:

dT,X,u) 25 {2/[(N - 2)v031x-* exP(e/RT)[K,/ySo12rSo/~lN (14)

The Strain Rate Dependence of Strength

At a constant T and X, strength increases with increase in strain rate, E~, according to
the following equation (Gupta, 1983):

Ins = [I/(N+ l)]ln~~+constant (15)
This equation for dynamic fatigue provides a convenient way of measuring the stress
corrosion susceptibility N.

The Temperature Dependence of Strength

Gupta (1983) has also shown that the temperature dependence of strength caused by
fatigue can be expressed as:
InS(T) = { Q/((N+ I)RT]} +constant (16)
According to Eq. 16, strength decreases with increase in T approximately in an
Arrhenius manner with an apparent activation energy equal to [ Q/(N + I)]. This
decrease is caused by the increased slow crack growth rate at higher temperatures. Eq.
16 is valid as long as fatigue is present. It is not valid at sufficiently low temperatures
(such as the Iiquid N2 temperature where the fatigue reaction is frozen). At sufficiently
low temperatures, strength is constant (= SLN).
Eq. 16 has been derived assuming constant relative humidity of the testing environ-
ment. If the experiment is performed under conditions of constant absolute humidity, a