Fatigue Crack Paths 2003

compared with findings from experimental investigations obtained by the aid of a spe

cially designed specimen with a circular hole under lateral force bending.

T W O - D I M E N S I OCNRAAL CPKA T HP R E D I C T I O N

Consider a crack in a two-dimensional linear elastic body under proportional mixed

mode loading conditions. The stresses ahead of the crack tip are given by

( ) 0,x

( ) 1 2 x I x O b T +

k

1

+

+

I = σ 1 1 1

π

,

1 xπ 2 ( ) ( ) 1 2 x I 1 I 1 2 2 0,x 1 + = σ π

,

(1)

x O b x 2 k

+

π

2 x I I π + = σ π 1 I I x 2 k 1 1 2 b 0,x

x O

1 +

,

( ) 1

( )

where kI and kII are the stress intensity factors (SIFs). T, bI and bII are the included

higher order stress field parameters. It is known that in such a situation the crack will

propagate in a smoothly curved manner after an abrupt deflection out of its original

plane, Fig. 1.

The generalisation of the local symmetry criterion can be regarded as the basis for the

evolution of the crack path. Therefore the state of stress ahead of the deflected new crack

tip exhibits no KII and is given by

( )

()*12 x * I * * 1 I * 1 x O b T x 2 K 0 , x * 1 + + + π = π ,

( ) ()*12 I x ** I * 1 2 2 x O b x 2 K 0 , x * 1 + + π = σ π , (2)

1

( ) ()*1 2 x * II *1 12 x O b 0 , x * 1 + = σ π .

It can be stated that continuous crack deflections can be caused only by the existing non

singular stresses.

According to Sumi [2,3] the crack path prediction can be performed by using the first

order perturbation solution of a slightly kinked and curved crack. A virtually extended

slightly kinked and smoothly curved crack path profile (Fig. 2) is assumed in the form

( )

()2/51 21 2/31 1 1 x O x x x xl + γ + β + α = , (3)

where α, β and γ are the shape parameters.