Page 365 - Mechanical Behavior of Materials

366 Chapter 8 Fracture of Cracked Members

(a) (b)
a
2a

c
2c

Figure 8.21 Nomenclature for cracks growing from notches.

P P
e M = Pe
b/2

a a a
K = K + K
1 2
b

Figure 8.22 Eccentric loading of a plate with an edge crack, and the superposition used to
obtain K.

then be obtained from the preceding equations:
c
(8.26)
2
l =
k tg
1.12 − 1
F
The resulting values of l are typically in the range 0.1ρ to 0.2ρ, where ρ is the notch-tip radius.

More refined estimates of K for cracks at notches may be made, as described by Kujawski
(1991) and in earlier work that he references. Also, the various handbooks give solutions for
specific cases.

8.5.3 Superposition for Combined Loading

Stress intensity solutions for combined loading can be obtained by superposition—that is, by adding
the contributions to K from the individual load components. For example, consider an eccentric load
applied a distance e from the centerline of a member with a single edge crack, as shown in Fig. 8.22.
This eccentric load is statically equivalent to the combination of a centrally applied tension load and
a bending moment. The contribution to K from the centrally applied tension may be determined
from Fig. 8.12(c):

√ P
K 1 = F 1 S 1 πa, S 1 = (8.27)
bt