Crack Paths 2009

As an important result it was found in [2] and [3] that a simple first-order evaluation

of mode-I stress intensity factors is even possible for arbitrarily shaped cracks with an

acceptable error margin if dy/dx≤0.2 and y/a<0.1 are fulfilled.

The mixed-mode stress intensity factors KI,II for non-linear cracks can be computed

by the weight function method as

xy

K

d x h

d x h

a

a

(2)

σ

τ

∫ 0

∫

I

11

12

=

+

n

0

K

d x h

d x h

a

a xy

(3)

σ

τ

∫ 0

∫

II

21

22

=

+

n

0

with the stresses normal on the crack, σn, and the shear stress parallel to the crack, τxy.

The weight function terms h11, h12, h21, and h22 necessary in Eqs 2 and 3 are of course

hardly available for a crack of arbitrary shape. In general these functions have to be

determined for any shape and any crack length. Such an approach of course would make

the weight function method highly inefficient.

Following the suggestion in [3] the weight functions for the rather complicated crack

can be approximately derived in a first-order analysis by superposition of knownstress

intensity factor and weight function solutions (for details see [3]). In the following

considerations, the stress intensity factor for the real crack is composed by a K of the

slant auxiliary crack (dash-dotted line in Fig 1b) and that of a kink under angle β

resulting in

(4)

)'(2 I K y O K K + + ≅ slantI, kinkI,

)'( II K y O K K + + ≅ kinkII, slantII,

(5)

Stress intensity factors for the slant crack

For the special case of a straight slant crack, the four weight functions were determined

in [4].

a

σ

τ

(6)

K

(

h

h

)

dx

∫ 0 a

slantI,

,11

n s l a n t

,12

xyslant

=

+

dx

σ

τ

(7)

K

(

h

h

)

∫

xy

slantII,

,21

slant

n

,22

slant

=

+

0

The mode-I and mode-II weight functions can be described by

617 3