Forgeabilité des aciers inoxydables austéno-ferritiques

tel-00672279, version 1 - 21 Feb 2012
46 Chapter III. HOT CRACKING RESISTANCE
work dissipated within the plastic zone from the total work of fracture in order to provide an estimate of
the work spent per unit area within the fracture process zone (FPZ) to break the material [71].
For thin sheets, the double edge notch tension (DENT) geometry is particularly well suited owing to
the symmetry and advantage of avoiding buckling problems (Figure III.1). If the ligament of a sheet
specimen is, as shown in Figure III.1, completely yielded before initiation, and the plastic zone is con-
fined to the ligament, then the plastic work dissipated for the complete fracture is proportional to the
plastic volume at initiation and the work in the FPZ is proportional to the fracture area. That is, the
plastic work and the EWF scale differently with specimen dimensions.
L
l 0
Diffuse Plastic
Zone
t 0
Fracture Process Zone (FPZ)
Figure III.1. DENT geometry showing the diffuse plastic zone as well as the localized necking zone in
front of the crack tips.
The total work of plasticity dissipated during the test is proportional to the square of the ligament
length, l0² and thickness t0. The work performed in the FPZ is proportional to l0 time t0. The total work
of fracture, Wtot, can be written as the sum of the essential work, We, and the plastic work, Wp:
W
�
2
tot � We
�W
p � t0l0
we
� t0l0
wp
, eq III-1
where we is the specific essential work of fracture (work per unit area), wp is an average plastic work
density, t0 is the initial sheet thickness and α is a shape factor (π/4 for a circular plastic zone). Norma-
lizing the previous equation, the total specific work of fracture, wtot = Wtot/t0l0 is given by
w �
tot � we
� l0
wp
. eq III-2
It means that if the term αwp in eq III-2 does not depend on the ligament length, hence the variation of
wtot as a function of l0 has to follow a linear relationship. Thus, if several DENT specimens with differ-
ent ligament lengths l0 are tested, the specific essential work of fracture, we is the constant term in the
linear regression, i.e. the work obtained by extrapolating to a zero ligament length the linear evolution
of the total specific work of fracture, wtot against ligament length (Figure III.2). The total specific work of
fracture was calculated from the areas under the load-displacement curves and depends on the
specimen thickness [72].