Page 362 - Mechanical Behavior of Materials

Section 8.5 Additional Topics on Application of K 363

S S
(a) (b)

y z t
b b D y
a
x x
t 2c
2t

2b
y
c c
D
P
a
φ
E a E x
a

D

a 1.65
!
πa
K D = F D S , Q ≈ 1 + 1.464 (a/c ≤ 1)
Q c

Case Values for small a/t, c/b Limits for 10% accuracy
(a) F D = 1 a/t < 0.4, c/b < 0.2
1
(b) F D ≈ 1.12 a/t < 0.3, c/b < 0.2
1
Note: Except limit to a/t < 0.16 if a/c < 0.25.
Figure 8.19 Stress intensity factors for (a) an embedded elliptical crack and (b) a similar
half-elliptical surface crack. The equations give K D at point D for a uniform tension
normal to the crack plane. (Based on [Newman 86].)

with a/c ≤ 1, equations giving F D for any a/t are

2 4
F D = g 1 + g 2 (a/t) + g 3 (a/t) f w , g 1 = 1.13 − 0.09(a/c)
0.89 1 24
g 2 =−0.54 + , g 3 = 0.5 − + 14(1 − a/c)
0.2 + a/c 0.65 + a/c (8.23)

πc a
!
f w = sec (c/b < 0.5)
2b t