Crack Paths 2012

2 _ r R

I 2 H j i g, ;'M"R I a

(17)

It)»

2 rR 8a 4at

Then, the radial and the circumferential normalstresses are:

L

r;

2

o’E’aq t H 4m

1 2

—r2 2

—"R

,t = _ —- + _ E _ - E 75),]? 2 6 orlr )

18 ( )

8a l(4at) FR (4at)

ot'E'qa t i H2) 1 r2 ’ t : — _ 4 a t _ 4at + _2 E - _R _ Gelr ) “M2 2 e 8 8a "R I 4at r ’ 4at —I"2

( )

These radial and circumferential normal stresses are then calculated with the

following typical values for steel: a Youngmodulus E=210GPa, a Poisson ratio v=0.29,

a thermal expansion coefficient of the material ot:1.2><10‘5 K4, and the line heat source is taken equal to the unity (qzl W.m‘l). The figure 3 gives for rRI4 p mthe evolution of

the radial stress as it varies with the radius for two times tzl s and t:l0 s. Note that the

radial stress is always negative because the material is under compression due to the

thermal expansion of the material near the crack tip. The figure 3 is an enlargement of

the curve around the reverse cyclic plastic zone. This figure shows a minimumof the

radial stress. After t=l s and t=l0 s, the minimumradial stresses are respectively equal

to —2.2xl072 M P aand -l .9>

the reverse cyclic plastic zone (r = 0) are 17 u mand 16 p mfor a unit line heat source

—l=10s -———l=1s

H‘

F

CL

ll

2.

,

2.

§

1}

-—t=10s

g

l:

l‘

----l=15

:

w

j

m

1; 0.015

d

*5 41,015

8

B

ms

on

I

I!

43020

0 0 m

4 1 m-

I

|

|

|

|

|

{ W 5|,

1

0.00

0,0:

i102

cws

0.0:

0.05

40 a‘

.

RECIIUS [m]

Radius[pm]

_a_

_b_

Figure 3: The distribution of the radial normal stress for various times for a unit heat

source q = 1 Wm‘1and rR = 4 pm; a) general view, b) enlargement near the reverse

cyclic plastic zone.

54