Page 150 - Fiber Fracture

STRENGTH OF GLASS FIBERS I35

some (not too low) temperature, T, and in an environment of relative humidity, X, is
called the fatigue strength. Strength is frequently measured under conditions of constant
strain rate, called the 'dynamic fatigue' experiment.

Delayed Failure (Static Fatigue)

Another consequence of fatigue (which is of significant technological importance) is
that a sample may fail after a long time under constant stress which is much less than
the short-term fracture stress. This phenomenon is known as 'delayed failure' or 'static
fatigue'. Experimental results show that the time to failure, t(T, X,o), decreases rapidly
with increase in applied stress, o, with increase in relative humidity of the environment,
X, and with increase in temperature, T.

Slow Crack Growth Model of Extrinsic Fatigue

Denoting the size of a crack by, C, the rate of growth of this crack (or the crack
velocity) due to fatigue increases with relative humidity, X, and temperature, T, of the
testing environment and the stress at the crack tip (characterized by the stress intensity
factor K) according to the following empirical power law relation (Charles, 1958;
Wiederhorn, 1967; Freiman, 1980):
V dC/dt = V,X"~X~[--Q/RT][K/K,]~ (8)
Here Q is the activation energy of the reaction, Kc the critical stress intensity factor
(also known as the fracture toughness and is considered an intrinsic property of a
homogeneous material), N the stress corrosion susceptibility, a! the humidity exponent,
and V, the pre-exponential factor. The stress intensity factor, K, is given by:
K = YoC"' (9)
where o is the applied stress (far from the crack tip) and Y is a dimensionless coefficient
(- &), the exact value of which depends on crack/sample geometrical configuration
(Rooke and Cartwright, 1976; Hertzberg, 1989). It should be clear that a larger N
implies less susceptibility to fatigue.
A much discussed alternative to Eq. 8 is the exponential equation (Wiederhorn, 1975;
Michalske et al., 1993):
V = VoX"exp[-Q/RT]exp[b(K - K,)/RT] (10)
By comparing Eqs. 8 and 10, Gupta (1982) has shown that
N x bK,/RT
Experimentally, the values of the stress corrosion susceptibility range from about 15 to
40 and are known to vary with T (Hibino et al., 1984) and the environment (Armstrong
et al., 1997). Clearly, N is not a material parameter.
While Eq. 10 has a more sound basis, as follows directly from the phenomenology
of chemical kinetics (Wiederhorn et a]., 1980), than Eq. 8, both equations appear to fit
the data equally well and have the same number of fitting parameters. Since analytical
expressions can be readily obtained for Eq. 8, it is more convenient to use.