Page 348 - Mechanical Behavior of Materials

Section 8.4 Application of K to Design and Analysis 349

P (a) S g (b) S g (c) S g
b
h a h a h
t
a t b t
S g b

6

5 K = FS πa
g
F S = P (a,b)
4 g 2bt
(c)
P
S = (c)
3 g bt
(a)
2 (b)

1

0 0.2 0.4 0.6 0.8 1.0
α = a/b

Values for small a/b and limits for 10% accuracy:
√ √ √
(a) K = S g πa (b) K = 1.12S g πa (c) K = 1.12S g πa
(a/b ≤ 0.4) (a/b ≤ 0.6) (a/b ≤ 0.13)

Expressions for any α = a/b:

1 − 0.5α + 0.326α 2
(a) F = √ (h/b ≥ 1.5)
1 − α
!
πα 2 πα

(b) F = 1 + 0.122 cos 4 tan (h/b ≥ 2)
2 πα 2
0.857 + 0.265α
4
(c) F = 0.265 (1 − α) + 3/2 (h/b ≥ 1)
(1 − α)
Figure 8.12 Stress intensity factors for three cases of cracked plates under tension.
Geometries, curves, and equations labeled (a) all correspond to the same case, and similarly
for (b) and (c). (Equations as collected by [Tada 85] pp. 2.2, 2.7, and 2.11.)