Crack Paths 2012

Ferrite/Austenite

i"' Layer

7

/ —

I | 1

Increase Hardness —

Q) a

1 1 1 1 1 1

.

-1-1

m

=1

\

1 1 1 1 | | |

0 u in

g Q a --1 Q -—1

N

1ii 1

091

F

Figure 1. Profile of the plastic region in front of the notch tip in the graded region of a

F G S(crack arrester configuration)

In order to determine the mechanical properties of the layer containing the notch tip,

it has been supposed that the fracture toughness (KIC) and yield stress (0,) vary

exponentially with respect to the direction X:

KIC (X ) : D 1 e X p ( D 2 X )

(4)

6,, ( X ) : eDX3P ( D 4 X )

where X is the distance of the layer from the crack divider specimen edge, D,- are the

constants that can be obtained by imposing the appropriate boundary conditions shown

in Table l.

The fracture toughness (Klcw) and the yield stress (a,.(dy) corresponding with the

layer containing the notch tip could be obtained by substituting X I X*-d in the Eqs. 4

and 5.

By considering Eq. 2, A,;, can be obtained as follows:

_ 1

2

_ K1001) 4 *

2

AM, _2%LI, was] _ a2

Lfw) d6

,

<6)

I a2

Xexp[4(D2 —D4)(X* —d):|XI,

3

w h e r e

1 I j: cos22[(1—2v)2+3sin22] 20o

(7)

1

I)

2

2

Eq. 7 gives values independent of the type of the composite and the values of the

distance d. I1 is equal to 2.2594for vI0.33.

508