Crack Paths 2006

priori and they depend on the applied load. The knowledge of the closed crack region is

necessary for the evaluation of the contact stresses on the crack surfaces, by which the

effective SIFs can be determined via WF, as a superimposition of their effects to those of

external stresses. The problem can be efficiently faced if the Green Function (GF) giving

the C O Dcomponents for a general loading condition is determined.

10

0.4

r=1

r=10

-1-2-272.1.-50505

-0.86420

0

K I/ K 0 , K II /K

W F

WKI(IF(A(B)AB)FFE

KI(A)FE

KII (A) FE

KI(B)FE

KII(B)FE

-5 -4 -3 -2 -1 0 1 2 3 4 5

L/a

-3

-2

-1

0 L/a

1

2

3

Fig. 3 SIF produced by the normal (compressive) force Py travelling on the surface for two r ratios

-0.54321012345

r=1

r=10

WKIF(A)FE I (BA)B)

K I/ K 0 , K I, K 0

W F

-21.-521 -0120.5012 -3

-2

-1

0 L/a

1

2

3

KI(A)FE

KII (A) FE

KI (B) FE

KII(B)FE

-8

-6

-4

-2

0 2 4 6 8

L/a

Fig. 4 SIF produced by the tangential force Px travelling on the surface for two r ratios

E V A L U A T I OFNT H EG R E E N ’FSU N C T I OFNO RT H EC O D

On the basis of the W Fdefinition, the C O Dcomponents u and v, indicating the relative

displacements of corresponding points C+,C- and D+,D- on crack edges (figure 1), in the x

and y direction, can be calculated for symmetrical and anti-symmetrical load cases by using

the symmetrical and anti-symmetrical components of the W F respectively. Any loading

condition can be subdivided into a symmetric and an anti-symmetric components, so that

the corresponding C O Dcomponents can be calculated as the summation of the CODs

originated by the two loading conditions. By generalizing the formulation reported in [10]

the following equations hold:

˜

a

B A

S I

SI d b r b K r b x h r b K r ) , ( ) , , (

³

x H r a x v 2 ) , , ( /

(7a)

@

) , (

˜

) , , (

>

V

V

S I I S I I

³ a

r

˜

˜

> A I A I d b r b K r b x h r b K H ) , ( ) , , ( ) , ( ) , , ( 2 V V @ AII A I I

x