Crack Paths 2012

order to be always smaller than the radius of the domain where the singular stress field

(1) prevails.

10

G3

˜

1 0 2 , m a x 1 0 . 6 1 1 0 M P a . m b G 3 ˜

p

2

9.9810 MPa.m

,max

Figure 7. Variation of the change of the potential energy G 3with the angle of the crack

extension for a) single crack deflection and b) crack bifurcation. Crack extension length ap=25μm, H2r=0.39 MPa.m1-G2 and H2m=1.1 MPa.m1-G2 (flexure load 220N).

The obtained numerical results showed that both crack bifurcation or crack deflection

are preferred modes of fracture with respect to straight crack propagation. The angle of

Mp, was predicted to be in the range 20° – 30° which is in a good

deflection/bifurcation,

agreement with experimental observations. However, contrary to experimental data, the

crack propagation was predicted even for the loading force about of 10 N, i.e. much

lower value then the threshold value of 220 N found experimentally, see Figure 2. This

discrepancy made us reexamine the real crack path. By inspection of the fractographic

observations in Figure 3 it could be found that crack does not bifurcate and/or deflect

just at the interface but at a distance 'a # 25 P m behind the interface. This is due to the

energy accumulated in the system during the unstable crack propagation (in the ATZ

layer which is subjected to tensile residual stress) before the crack reaches the interface.

The accumulated energy allows the crack to penetrate inside the compressive layer. The

stress field around the edge of the penetrating crack is square-root singular with the

regular stress intesity factor KI. It is worth mentioning that the radius of the dominance

domain of the square-root singular field is only few microns as detailed numerical

calculations revealed. Outside this domain the singular stress field (1) still prevails.

However, it was found that the intensity of the singular stress field (1) caused by pure thermal loading, H2r, is significantly reduced. This is associated with the sharp change

of residual stress between A T Zand A M Zlayer. From linearity and dimensional considerations wecan relate the GSIFH2r and the regular stress intesity factor KIr as:

2 1

r r I A T Z 2 A T Z K t a k ' ˜ ,

H t G

(8)

where tATZ denotes the thickness of the A T Zlayer and k is a dimensionless coefficient which describes the reduction of GSIF H2r. The coefficient k can be found from the

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