Fatigue Crack Paths 2003

propagation processes. Depending on the ModeII- and ModeIII-portions a more or less

intense crack deflection can be observed (Figure 10).

−ψ 0

ϕ

0

Figure 10. Definition of crack deflection angles ϕ0 and ψ0.

Fracture Criteria for Unstable Crack Growth

For 3D-Mixed Modeproblems only very few fracture criteria do exist. The important

ones will be described in the following.

Criterion by Sih

At first sight, the well-known Strain Energy Density Criterion by Sih [3, 9] seems to be

able to handle three-dimensional crack growth by taking the stress intensity factors KI,

KII and KIII that are related to the three fracture modes into consideration. The strain

energy density factor is defined as follows:

2III33 2 I I 2 2 I I I 1 2 2 I 1 1 K a K a K K a 2 K + + + = (11)

with

4 3 ( c o s 1 6 1

+ − ϕ + ϕ − ν − ψ π μν =+ − ϕ ϕ π μ ϕ= + ϕ ν − ψ π ) c o s 1 ) ( c o s (12)

a

{

}

1322132

) 2 1

a

c o1 s 8

(cossin

}

{

cos)

a

c o 1s 1 6

1)(1 c o s 3 ( ) c o s 1 ) ( 1 4

{

}

4 1

cos

= πμ ψ

where μ is the shear modulus of elasticity and ν the Poisson's ratio. The crack angles ϕ0

and ψ 0 are derived by minimising S of Eq. (11):

∂S

0

and

∂S

(13)

= 0

ϕ∂ ϕ = ϕ

ψ∂

0 ψ = ψ

=

0

The formulation of ϕ0 resulting from the partial derivative of S by ϕ is depending on

Mode-I and Mode-II stress intensity factors and ν but independent of ψ0 as well as KIII.

With respect to the second crack deflection angle the minimum of S is given while

maximising the term cos(ψ 0). Therefore, the minimumof S is always in the direction of

“ψ=0 –plane” independently of the Mixed-Mode combination. Therefore, this criterion

has to be regarded as insensitive to Mode-III. A similar observation can be found in

[13].