Crack Paths 2012

Kf, (z) = V21r lirré rxy (x, 0, Z) J }

(431)

x — )

and the definition of the stress intensity of the shear coupled m o d eis similar to

m o d e111, or

Kf”(z) = V21r 16kg ryz (x, 0,Z)\/;

(4b)

wherex is the distance from the crack tip along the bi-sector direction.

To determine the stress intensities, the corresponding stress componentsare

first calculated and extracted from FE analysis and then substituted into the above

equations to identify the value of the stress intensity for the coupled modesat

certain z - coordinate along the crack front. Someconditions have to be met in

order to get correct values of the stress intensities, which are exhaustively

described in the literature.

First, we consider the case when a through-the-thickness crack is loaded by shear or

anti-plane loading when only the first (singular) term in the asymptotic expansion is

non-zero (b1 at 0 and CO at 0) and all other terms are zero i.e. bn = an = 0 for all other

11. Figures 3a and 3b show the results of careful 3D FE studies for shear and anti-plane

loading of a through-the-thickness crack, respectively.

K

KI‘?

1.5

1.0

J

1/- increasing

05 V

o O v:0.;0.1;0.3and 0.5

1'

o O o O O

KICII(Z)

O O o

I

O 8

I n n l m n g g gOgO O O _O O

I

g

0

0.1

0.2

0.3

0.4

Z / h

Fig.3a The dependence of the intensity of the primary (mode 11) KH (Z) and the coupled

modeK0 (2) = K16;, (2) across the plate thickness in the area near the crack tip. The

influence of Poisson’s ratio on the intensity of the primary modeis very weakand

results are not shownfor the sake of the clarity of the figure.

140