Crack Paths 2009

(10)

K K α ≥ =

c G

((),())cXmMα,AA

c

depends on α

he critical value Kα T

and the actual kink angle

maximizes the

c α

giving

denominator, i.e. mizesinim Kα

f K

(i.e. K

at failure).

α∀

(,(),())(,(),())ccXmMXmMcccαα≥AAAA

(11)

And

( ( ) , ( ) ) c c G

f

c

c

K

(

, A A 12)

=

X m M α

α

that Eq. 11 is not trivial since

is a function of

Note

(Eq. 9). This reasoning

c A

follows step by step that of the real case [1,5] (homo the physical ackground is less igo ecause f thgeneous material for instance) but

rous b

e oscillating terms met in G and

θ θ σ

.

A P P L I C A T I O N

/ 0.2 F L = 5 ,

0. = 2 .

Figure 2. 3-point bending test,

/ H L

Elastic simulations are carried out on a notched bimaterial specimen in flexion (figure

2) with a long debonding of the interface. The stiffer material is alternatively in the

upper ( R >1 )and lower ( R <1) position, R is the Young’s modulus ratio,

ν =

0.3

in

ateria. Two different materials are considered:

both m l s

Alumina,

1 E =

300 GPa,

1 c σ =400 M P a and

1 c G =0.05 MPa.mm(IcK =4.06 MPa.m1/2), and P M M A 2 E = 3

GPa, 1 c σ =75M P aand

1 c G =0.35 MPa.mm(IcK =1.07 MPa.m1/2). WhenAlumina is in

the upper position ( R >1 )various contrasts re analysed for a

R varying from 100 to 2.

Similarly, when P M M iAs in the upper position ( R <1) various contrasts are analysed

for R varying from 0.5 to 0.01. The particular case

R =1 (no contrast) is given for

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