Crack Paths 2012

Q(r,8) : g 0 )+ klrt (21(9) + m 22(9)) + o'(r,9) k1rA“_1(s1(9)+m s2(9))+...

withmziirM11

(1)

7(1", 9) : k,rt-1(t,(e)+m r,(8))+...

1

Where 0' and 7' hold for the tensile (0'66) and shear (are) components of the stress

tensor. The coefficients kl and k2 are the generalized stress intensity factors (GSIF) of

the two singular terms characterized by the exponents l1 and 2.2 and the two modes

21(0) and @(6), respectively symmetric and antisymmetric with respect to the

bisector. The functions s1(6l) and t1(6) (resp. s2(6l) and 5(6)) are associated with the

components 619 and r0 of the stress field derived from %(6) (resp. a2 (6)) through the

elastic constitutive law. Note that the definition of m implies k1 ¢ 0 , the particular case

k1 = 0 refers to the pure mode11 that can be treated similarly to the pure mode1. Energy

and stress conditions give

W012 J: 6.1mm» ; e z 6.00;

r]27'f(,u) for 0Sr§lwith/.i:

Where Gc is the toughness, and where 0'].

. and If are the tensile and shear strength at

failure under mix modeloading (the mixity is characterized by ,u ). According to (1)

k5!” (446,) + m(l)A12 (6,) + m(l)2 A, (90)) 2 £0,006»

k1f‘A1_1(S1

+ m(r)s2 ) z 0' f(r) for 0 g r g 7

(3)

Jere-101+ m(r)t2] 2 1,0») for 0 g r g 7

The scaling functions A, were defined in [8] and 60 is the crack direction. With the

additional relation (q = 2 holds for an elliptical criterion)

+]’f(”)] :1; eimzwfim

O - C

T L ‘

0' T 3 6,01) I # 1 ; 7,0,1) I lwf-(,a)

(If + ,uqo'f)

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