Crack Paths 2006

lTi-(RR§‘})”j(R§‘})dF(R§’})

+ ]T,,(r,Rg+l)uj(Rg+l)dp(Rg+l)

:

FAT}

Flt}

[anewtame) = lW-(nR'éfialLwddR'é-ll

(17)

a Sc{

Fifi

However, for edge cracks problems when the displacements of the usaper and lower

crack surfaces only at the one of the crack tips coincide (i.e., ui(Ré‘<5}

M g } I ui(Rc ) and

ullRgfl ) I a, (R23 )), the lower-order singular integral can be expressed by

l(nRé*})Au.(R§*)dF(R2*)

=

P5‘

W.

“8)

rte-l

Sci

Therefore, for edge cracks problems the edge-discontinuous element is used at the

intersection between a crack and an edge to avoid a c o m m o node at the intersection.

Reduction of the order of the strongly singular integrals in the equality 12 can be

obtained by integration of both sides of this equality with respect to the field point,

R27}, along the lower crack surface, 172*}, that consists of smooth straight segments

from one crack tip AC to R ?

R{—} F~(R§)= ]r,~(R'é*})dF(

a“) =vAcRiilcAcBc-

(19)

1

Ac

For the internal crack problems, an additional constraint equation for the dislocation

densities, g,( g’})I6[Au,(R'C{’})]/6s§}, along the lower crack surface is given by

[g,(R{g})dF(R{g}).

Fi‘}

N U M E R I CTARLE A T M EO NFTTH EB O U N D AIRN YT E G R EA QL U A T I O N S

For a given source point, PM), the boundary forms of Eqs 8 and 19 can be discretized

into NB boundary contour segments and NC crack contour segments as follows: