Forgeabilité des aciers inoxydables austéno-ferritiques

tel-00672279, version 1 - 21 Feb 2012
Chapter III. HOT CRACKING RESISTANCE 85
By applying eq III-11 to each morphology, gives respectively:
we, D2
_ E � k��
c,
D2
_ E�
X 0,
D2
_ E�
(exp( � c,
D2
_ E ) �1)
, and eq III-16
w �
e,
D2
_W
� k��
c,
D2
_W
� X 0,
D2
_W
�(exp(
c,
D2
_W
) �1)
. eq III-17
Considering that the critical strain is the equivalent strain to fracture: � c, D2
_ E � � , see Table III.10;
c,
D2
_W
and as the maximum of the load-displacement curves corresponds to the same point,
i.e. � c, D2
_ E � � , see Figure III.39; the ratio between the specific essential work of fracture of the
c,
D2
_W
equiaxed morphology, we D2
_ E
mated by:
w
w
e,
D2
_ E
e,
D2
_W
X
over that of the Widmanstätten one, , we, D2
_W
0,
D2
_W
can be approximately esti-
0,
D2
_ E
� , eq III-18
X
where X0 is a characteristic length as defined in Figure III.45. Considering that X0_E is approximately
equal to 65μm and that X0_W is about 30μm, the ratio X0_E/X0_W is about 2.2 and gives the correct
order of magnitude. Indeed, the ratio we D2
_ E
/ , we, D2
_W
III.6.3 To go further…necking vs. damage
III.6.3.1 Question
is approximately equal to 2.
As indicated in section III.1 “Literature review about the Essential Work of Fracture concept”, the total
work of fracture of deep double edge notched specimens plates (DENT) can be expressed as the sum
of an essential work of fracture, We spent in the end regions ahead of the crack tips, i.e. in the fracture
process zone, and a non-essential plastic work, Wp dissipated in the outer region:
W �
tot � We
Wp
. eq III-19
In the case of ductile materials where fracture occurs with constant thickness reduction, Pardoen et al.
[76] showed that the essential work of fracture We can be separated into two contributions:
W �
tot � W0
�Wn
Wp
, eq III-20
where W0 is the work spent for growing voids to final material separation and Wn is the plastic work
spent in the localized neck which develops in front of the crack tip and which includes the region
where material separation takes place.
This separation between the work of necking and the work spent for growing voids could help us ans-
wering the following questions.
� What is the origin of the difference between D2_E and D2_W?
� Does it originate from a difference in the necking contribution (Wn) or a difference of the dam-
age contribution (W0)?