Page 163 - Plastics Engineering

146 Mechanical Behaviour of Plastics

Hence a graph of log(da/dN) against log(AK) will be a straight line of
slope n as shown Fig. 2.77. Now, in Section 3.4 it was shown that the range
of stress intensity factor could be represented by a general equation of the form
K = YC(XU)'/~ or AK = Y(AO)(XU)'/~ (2.118)

where Y is a geometry function.

1 o-~ -.
I

1 o-'
0.1 1 5
Ak (MN m42)

Fig. 2.77 Crack growth rate as a function of stress intensity factor

Thus, combining equations (2.1 17) and (2.1 18) gives
da
- = C~{Y(AO)(XU)'/~)"
dN
Assuming that the geometry function, Y, does not change as the crack grows
then this equation may be integrated to give the number of cycles, Nf, which
are necessary for the crack to grow from its initial size (2q) to its critical size
at fracture (kc).
a. Nf
1 da

ai 0