Figure 3-9. Stress distribution for the 4-Pt bending simulation at (a) room temperature;
(b) cryogenic temperature.
The fracture toughness can be calculated in two ways. The first method is similar to
the "stress matching" [29] as described by the equation below (see Figure 3-10):
K, = limu (r)r2
r-O
(3.1)
In the second method a logarithmic plot of a vs. r is used to determine the best
value ofK by fitting (see Figure 3-11)
o(r)= Ktr-
(3.2)
In both methods the singularity X derived from the analytical method was used.
8E+07
7E+07
6E+07
& 5E+07
4E+07
a 3E+07
L 2E+07
1E+07
Case 1
Case 2
Case 3
0 1E-05 2E-05 3E-05
Distance from a crack tip, r (m)
Figure 3-10. Variation of K = -r with the distance from the crack tip at room temperature.