Crack Paths 2006

under the condition of AKH (point A) I AKHI (point B). Now, the value of K11 for the

leading edge of the major axis of the elliptical crack (point A) is expressed for b < a by

ab3 %

kzz'sinfl

K n = [ J

1

a

[(k2 —v)E(k)+ vk'2K(k)Kb2 sin2 e + a2 cos2 5 %

{ W V k2’ a [(k2 —v)E(k)+vk' K(k)](b)%

Similarly, the value of K mfor the edge of the minor axis of elliptical crack (point B) is

expressed for b < a

1

—(l—v)k22'cosfl

(7m ) [(k2 - v)E(k)+ vk'2K(k)](b2

1 sin2 3 + a2 @052 p%

Kill I b A

I (rz'ab)%

_ (l _ V)k2T

......................

[(k2 — v)E(k)+ v k'2K(k)ka)%

Where,

l 2 A kI£l—b—] ,k'zb

2

T

S

E(k): _['/2(1—k2sin2¢)%d¢,

/2 d¢ K(k) I I — 1 (1 - k2 sinz qM

Here, w eassumev I0.3.

FromEqs. (1) and (2), we can derive the aspect ratio (b/a) which satisfies the condition

of AKH (point A) = AKHI (point B), is b/a I 0.49.

Figure 9. A 3D elliptical crack in an infinite

body under shear stress [15].