Crack Paths 2009

o'xx (x,0) + io'xy (00,0) I (K1 + l-Kz). (2m)-1/2 ris

(6)

where K1 and K2 can be considered as the conventional mode I and mode II stress

intensity factors, rzx-a, and e=(1/2rt)ln((1-,b)/(1+,b)).

Dimensional considerations

require that:

K1+iK2 I k1a1/2_l[d(a,fl)aig

+e(a,fl)a_’f]

(7)

where d and e are dimensionless complexfunctions of a and ,6, which have been

evaluated through integral equation methods by IHI in [26].

Thus, the energy release rate of the deflected crack results in:

Gd I H1 _ "A j +

+ K22)/(4 00002 10)

(8)

# A

#B

Where

K12 + K,2 I kid-“[1012 +1612 + 2Re(d - 6)]

(9)

In order to establish a criterion for crack deflection/penetration the ratio Gal/Gp must

be evaluated. It can be observed that this ratio is independent of a (and k1) and is given

by:

Gd /(;p I [(1- ,B2)/(1— (1)] - [1012 +1612 + 2Re(d - e)]/02

(10)

The ratio Gal/Gp is plotted in Fig. 2 as a function of a.

__1.0

penetration

\

_

;

deflection

in I

0.5 I

0.0

I

015

I

110

or: (Eg-EQ/(EfEl'g)

Figure 2. Crack deflection/penetration criterion for a crack propagating

normal to the interface of two dissimilar materials B and A.

182