Crack Paths 2009

,a

— g —46' 8 n m _Zrm [ K ' + ———1 ) ” ] S i n n 2 m — £ s 21 na( n} 6'

,a

n

(3)

aha)" sin

_ m H (" 46m)

2

2;!

2

2

E _40 l n m z r i K'—£+—1):|COSn"1+£cos(n m) ,

’

2,u

2

“1

fit "fn,1 gll gill

at

1 " m : f L m ‘ H - fg mLm m H ‘ agn m m v1 h1,1' hn,l l11 "1.1.1 [91

V

h m '

hn,l

l11 "'ln,1

bn

where m is the data point index.

By expanding equations 1 and 2, keeping the terms up to order r3/2 and comparing with

the morec o m m o notation, i.e. using stress intensity factors and T-stress, it can be shown

that

KI:a1\/2 , KH:—b1\/27t ,

T:4a2

(5)

in which K1 is the modeI stress intensity factor, K11 is modeII stress intensity factor and

Tis the T-stress.

Looking at equation 4 it is evident that no rigid body motion term has been considered in

that equation. This can be compensated for by adding constant terms in equation 4 to

compensate for the rigid body translations and another term to compensate for the rigid

body rotation as follows,

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