Crack Paths 2012

211-1

1 * A * * nZLfl + _ 12 * ,where F = 1P5]

(15)

a i fl - l - *i

A S

orH‘F*

or H1F

f f

The case of a symmetric loading (pure mode 1) corresponds to mm I 71,. I 0 then

of I06, If I0, Gf IGIC, A; IA;-IA1, S1 IS; IT, and F* I1, through proper

normalization of the singular modes.

The stress conditions (6) and (7) lead to

2,-1 _ 0' 2' klmlm (s1+mms2)2o'f(lm) _—

°q° q M]

q

(To + l u m O - c )

'

ltl ‘l' m a t Z

with lag I a I f , m f

0'62",

s1+mas2

kHz/171s, +mfs,)z 6,0,.) I — , , q

(15+,ujof)

(16)

These inequalities refer only to tensions but by virtue of (7) inequalities in tension and

shear are equivalent. It comes finally

1

l—/l

i

‘51*

L * 1-2,

or: ‘I

if

3 lmzlfal-i S’:

(17)

If

S,

S.

l

fl + A i* S * 1321

1 5 4 i

azlzlfor 1741A’;

:lfot ‘_‘1H*

(18)

n

f

In the symmetric case H* I 1. Parameter ,6 can be identified so that (18) coincides

with the Paris law of the material in case of a pre-existing long crack: 2, I 1/ 2 then

,6 I p — 4 where p is the Paris exponent (p 2 4).

Remark 1: If klm Iklf then Gm I Gf, or I1, F* I1 and n =1, failures occurs at the

first cycle. In other terms, the fatigue criterion remains valid for a monotonic loading.

Remark2: In this model, the crack growth under fatigue loading is intermittent, every n

cycles, the crack length increases by lm. W eput forward the idea that this length could

be identified to the striations spacing observed in fatigue in quasi-brittle materials [12].

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