Crack Paths 2009

The dependence of the notch stress intensity factors defined as K = lim t(21tr)1'X are

r—>0

shownin Fig. 7b for a 900 degree notch and various Poisson’s ratios.

The values for the notch stress intensity factor are significantly affected by Poisson’s

ratio and can reach almost the applied magnitude of the shear modefor crack problems

(notch angle, or: 0°). The most interesting finding of the numerical results is the

establishing of the fact of the existence of the out-of-plane singularity for the vertex

angles above 102.40 despite the disappearance of the coupled in-plane shear singular

mode[24]. This is contrary to manystudies stated that above this critical angle there is

no line singularity which would contribute to the failure of the notch loaded in modeII.

I ( O

k

M d II[16] ’‘

Kipp

‘

‘

0 e

I,’

O3 -

. Finite Element Result [25] .

\‘

_

\

1.2 -

,1

l

- Non-singular stress fields ,‘l

i‘

1

.

.'|

,

02_ v=0.1,0.3,0.5

:

_ Singular stress fi e l d s / 1 M o d eO [ 2 3 ] / / a / /

.

H

0.8 —

,"

,/’

‘J

1 '

/ ’

|

," , / "

0.1 -

i

0-6 ' ,L;;:,/"/

/ ModeI[l6]

\

"

\

0 . 4 . . . . . . . . . . . . . . . . O_

0

30 60

90 120 150 0‘

0

0.1

0.2

0.3

0.4

z/h

Fi .7a. Stren h of sin larit for in- gu y g

Fi . 7b. Normalized O-modeNSIF, in g 0242 -

plane modeI and II and O-mode

(m) '

, across the thickness for

(1:900 and various Poisson’s ratios

S O M 3EDE F F E C TISN C R A CPKR O B L E M S

The crack geometry, probably, is one of the most important for practical applications

and will be considered next in some detail. Below we discuss two cases: a crack

stressed in mode I and mode II, in other words we consider a through-the-thickness

crack in an infinite plate of thickness 2h subjected to K?” or xgpp stress intensity

factors. Because of the space limitations we will discuss only the most interesting

features of the three-dimensional solutions for both these problems.

Crack stressed in modeI

Fig. 8a shows the transition from plane strain (TZ I l) to plane stress conditions (TZ I O)

for a semi-infinite crack. Despite that the stress field in the vicinity of a crack tip

follows the plane strain solution the basic assumption of this theory (8Z I O) is not valid.

Fig. 8b summarises results of various numerical, analytical and experimental studies

demonstrating that the free surface has finite displacements at the crack tip. Thus, the

three-dimensional (actual) displacement and strain fields in the vicinity of the crack

cannot be approximated by either plane stress or plane strain assumptions.

197