Forgeabilité des aciers inoxydables austéno-ferritiques

tel-00672279, version 1 - 21 Feb 2012
154 Chapter IV. STRAIN PARTITIONING
The macroscopic flow properties are denoted as m
0
� , m
� , and β m and their corresponding numerical
values obtained via the non-linear least square fitting procedure are given in Table IV.22. The elastic
modulus is estimated from the slope of the tangent drawn at 0.2% strain on the flow curve. This value
is approximated as 70 GPa and the Poisson’s ratio is taken as 0.3.
m
� 0 (MPa)
0
m
� 0 (MPa) β m
155.8 1626.5 17.8
Table IV.22. Numerical values for the three parameters of the Kocks-Mecking hardening law de-
� macro-
m
scribing the macroscopic flow properties of the specimen D2_W deformed at 850°C; 0
scopic yield stress, m
� and β 0
m are parameters that describe the macroscopic rate of hardening.
� Step2.
Using the macroscopic flow properties, now for each phase, two initial guesses for every flow parame-
ter are considered such that a mismatch of 20%-50%, as anticipated from the literature, is maintained
between the flow parameters of the two phases, see Table IV.23.
� 0
� �
� 0
� �
1. 1�
, 1.
2�
m
0
m
0
m
0
0. 8�
, 0.
9�
m
0
� 1. 1�
, 1.
2�
� � β γ = 1.1β m , 1.2β m
0
0
m
0
m
0
m
0
� 0. 9�
, 0.
8�
� � β δ = 0.9β m , 0.8β m
m
0
Table IV.23. Initial guesses for every flow parameter.
The elastic properties of both phases are considered the same as that of the macroscopic material.
� Step3.
A two-dimensional FE simulation of the plane strain compression-test is performed in
Abaqus/Standard that uses implicit-integration scheme [138] choosing the first of the above 64 combi-
nations of the flow parameters for the two phases. As mentioned in the previous section, it was difficult
to achieve truly plane strain deformation conditions in the experiments. It is also clear from Figure
IV.49.a that the observed shear strains are quite significant. In order to closely reproduce the experi-
mental conditions, the displacements observed along the four edges of each micrograph are imposed
in the finite element analysis. Many points are considered along each edge in order to capture the
local strain fields with sufficient accuracy. Furthermore, to overcome numerical singularities and also
to improve the rate of convergence in FE analyses, the displacement profile on these edges is slightly
smoothened in highly distorted regions along the edges.