Forgeabilité des aciers inoxydables austéno-ferritiques

tel-00672279, version 1 - 21 Feb 2012
180 Appendices
A.3 Calculation of pressure and equivalent strain εeq
To determine the flow stress of the material, the load exerted by the ram L�was converted into an
average pressure p�using the instantaneous breadth b�and the platen width w, such that
L
p� eq A.6
wb
eq A.7 presented the equation for equivalent tensile strain εeq and eq A.8 was for the ideal plane strain
conditions, i.e. ε3 = 0 and ε1 = -ε2.
2
� � [( � ��
)² � ( � ��
)² � ( � ��
)²]
3
1/
2
eq 1 2 2 1 3 1
eq A.7
� eq
�
h f
2 �
ln
�
�
3 � h
0
�
�
�
�
eq A.8
However accounting for the lateral spread, ε3 = ln(b/b0), ε1 = ln(h/h0) and therefore ε2 = -ε1-ε3. Then by
substitution, εeq is given through eq A.9.
2
� � [ � ��
� ��
]
3
2
2 1/
2
eq 1 1 3 3
eq A.9
From eq A.9, εeq�may be determined from the instantaneous width and thickness measurements. As
shown, ε1 is related to ε3 by eq A.3 and a factor f can be defined as:
� ��
f
eq
�1
eq A.10
For example, in the limit of zero spread, then f � 2/ 3�
1.
155 . However, as there is a clear lateral
spread for all these tests, the equivalent strain was determined using eq A.9, then f�may be deter-
mined from eq A.11.
� eq
� eq A.11
f �
�
1
With f�determined this factor was then used to determine the equivalent stress and strain rate for the
deformation.
A.4 Determination of equivalent flow stress σeq
The equivalent flow stress σeq�was calculated from the maximum shear stress k. This was deduced
from the instantaneous pressure using the method described in Ref. [127] where the friction conditions
were determined to be either predominantly sliding, sticking or a combination of the two. Sliding friction
assumed that contact stress at the tool/specimen interface was equal to the material flow stress in