Forgeabilité des aciers inoxydables austéno-ferritiques

tel-00672279, version 1 - 21 Feb 2012
Appendices 185
� The local transformation gradient at a given grid intersection p is computed as the average of
the true local gradient over a small volume � p around the grid intersection. The chosen vo-
lume is a cylinder with its axis orthogonal to the surface of the sample, height e arbitrarily
small, and a polygonal upper surface � p whose vertices are neighbours of the considered
grid intersection (see Figure B.1). Let � � p be the boundary of� p , S�p its area and n�p its
normal. � p� is the lower surface of the cylinder.
Considered micro-grid intersection
Neighbour micro-grid intersection
Then, eq B.5 gives:
Surface of the sample
1
F p F � � x�
n
�p
V
F
� �
�p
��p
Figure B.1. Averaging volume for local strain computation [98].
� � �
� � � � �
� ���
� � � � �
� ���
�
��
��
� xde
xds
xds
1 e
p p
ndl
p
S p e
e
p
ds
p n
With e tending to 0, one gets then:
F
since x is continuous.
� � xds
�
1 � �p
�
� ���
x�
ndl�
� �p�
S�p
� �n
��p
�p
�
��
��
p n
�
�
,
�
eq B.7
. eq B.8
, eq B.9