Crack Paths 2006

constant radius around the crack tip. For the case of mode I and II loadings, the strain

energy density factor S was given by Sih [3] as follows:

S : ankl2 + 2a12k1k2 + a22k22

(5)

where the coefficients ail, which vary with the spherical angles (19, d) measured from the

crack tip, were given by

K+l

K—1

all 16/1AK2cost9i (

V)+ K i

(a)

_ fl [1_2 l] l2_8/1)a<2cost9 K ( V)

_ 6b

( )

1 1 a22 = W [ 4 ( I _ V ) ( K — D + Z ( K + 1 ) ( 3 — K ) ] (66)

where a and v are the shear modulus of elasticity and Poisson’s ratio, and the parameters

A and Kare given by Sih [3]. It is assumedthat the crack will start to extend in a direction

for which the strain energy density factor possesses a relative minimumvalue, i.e.,

(all)

=0,

>0

(7)

2

60 ,z,

a9 6:60

Based on a" S /o"t9 I 0 at 190, the directions of fatigue crack growth (90 can be

determined. Note that the above total strain energy is evaluated along a constant circle

with radius r around the crack tip based on the theory of elasticity.

Tensile stress criterion

In the present case, the tensile stress under the combinationof m o d eI and II loadings was

given by Sih [2] as the following equation,

k

K+l £2—K—3K2) k

K-l £2+K—K2] (8)

: _ l

+ 2

U2 5 21 cos (9

2K3

5 21 cos (9

2K3

It is assumed that the crack growth direction coincides with the direction of maximum

tensile stress along a constant radius around the crack tip. Therefore, the angle (90 of the

fatigue crack growth direction can be determined by maximizing the 0; value, i.e.,

2

{601) : 0a

< 0

(9)

66 6:90

66 6:90