Crack Paths 2012

Moreprecisely, the evolution of the three principal stresses have been computedat four places

in the cylindrical specimen, denoted by A, B, C, D (see fig la) and are plotted on fig 4.

b

a) 6507

) 1,E+08

4,E+07 -

SE07

1,‘ 2,E+O7 -

96.507

%

v, 0,E+00

m 4,E+07

80

17,-2,|5+07

-

£2,507

-4,E+07 *

“ MO E+OO

‘6507

-2 E+O7

80

time (s)

l

c) 1,2E+O8

(1)1 4E+0a

A1,OE+08

1,2E+08

9Z8,0E+07

g?‘ 1,0E+O8

g 6,0E+07

I B'OEJ'W

U ,& 4,OE+07

& 60507

in

,_ 4,0E+07 ‘0 2,0E+O7

2,0E+O7

0,0E+00

.

-

-

0,0E+00

t

t

i

o

20

40

60

80

0

20

40

60

80

time (s)

time (s)

Figure 4: evolution of the three principal stresses at points A, B, C, D for AT2344°C

Peak stresses occur earlier near a free surface - where loading is non-proportional- but are

smaller than at points located deeper inside. Near the center-point, loading is proportional and

the principal directions are r, 0 and z. The stress state and triaxiality are quite different from

one place to the other. Only one principal stress is always positive at point A, two at point B,

while points C and D experience triaxial tension all the time. The stress concentration near the

pores thus varies, depending on their position in the specimen, as shownbelow.

Goodier [2] provided analytical expressions of the stresses near a spherical pore in an elastic

infinite mediumunder uniform loading. For a Poisson’s ratio v20.3, the stress concentration factor

near a pore is 2.04, 1.36 and 1.5 for uniaxial, equibiaxial and equitriaxial tension, respectively. But

these results are not valid near the edges of specimens in which stress gradients exist. The stress

concentration near pores in the specimens was thus evaluated numerically, by applying the three

principal stresses computedat A, B, C or D at peak value of the first principal stress in flawless glass

on the boundary of the FE. model shownon Fig 2a. Figure 5 compares the evolution of the first

principal stress at A, B, C and D. The stress concentration factor, KI induced by a pore at each point is

also indicated, as well as the resulting local stress (Kttimes the peak value of the first principal stress).

1,4E+O8

p(1rinsctPirspeaslsat)

1,2E+O8

1,0E+O8

8,0E+O7

6,0E+O7

4,0E+O7

2,0E+O7

0,0E+00

0

20

4O

60

80

time (s)

Figure 5: Comparedevolution of the first principal stress and of Kt at points A, B, C, D

362