Forgeabilité des aciers inoxydables austéno-ferritiques

tel-00672279, version 1 - 21 Feb 2012
Chapter IV. STRAIN PARTITIONING 115
(ii) Then, a database containing the intersections coordinates was processed using the same
software, which provided the strain components ε11, ε22, ε33, ε12 and the equivalent Von Mises
strain, for every microgrid intersection following the procedure described in the next section. Note
that according to the axes shown in Figure IV.16, ε11 and ε22 are the uniaxial strain components in
the directions parallel and perpendicular, respectively, to the loading (vertical) direction, and ε12 is
the shear strain component.
(iii) The distributions of the calculated strain components were then plotted using CorrelManuV,
with different colours depending on the strain value.
(iv) Finally, the SEM micrographs of the undeformed microstructure were edited using the image
software Gimp to generate the contour of the grain and interphase boundaries. These contours
were then superimposed on the strain map in order to analyze how the strains were distributed in
the microstructure.
IV.4.3.2 Calculation of the local strain components
The displacement gradient tensor can be written as indicated by eq IV-1:
�F11
F12
F13�
F �
� �
�
F21
F22
F23
.
�
��
F �
31 F32
F33�
eq IV-1
The program developed by Bornert and Doumalin [129] provides the in-plane displacement compo-
nents of each microgrid intersection, which leads to the in-plane components of the local transforma-
tion gradient tensor (F11, F22, F12, and F21). The procedure and equations required for calculating the
local in-plane gradient components are described in details in the paper published by Allais et al. [98],
in reference [128], and are also indicated in Appendix B.
Additional assumptions have to be formulated in order to estimate the unknown gradient components
(F13, F23, F31, F32 and F33).
Traditionally, it is considered that the direction orthogonal to the image (direction 3 in Figure IV.16), is
a principal direction for the transformation.
It is also assumed that there is no rotation outside the plane (ND, RD). Thus, only the F33 component
is not equal to zero whereas Fi3=F3i=0 for i = [1; 2] (eq IV-2), hence
�F11
F12
0 �
F �
� �
�
F21
F22
0 .
�
��
0 0 F � 33�
eq IV-2