Compressive Electrically Assisted Forming Model - Electrically Assisted Forming - page 87

σ = C ε n ε m (5.11)

where C is the strength of the material, ε is the effective strain rate, and m is the
strain rate sensitivity.

5.1.5 Current Density Relationship During Electrically
Assisted Compression

Work by Ross et al. [ 10 ] shows that the electricity in an EAF process had to be
applied differently for different forms of metal deformation. In particular, Ross et
al. determines that applying EAF continuously for a tensile process caused detri-
mental effects. This is due to the increasing current density throughout a tensile
process, due to the shrinking cross-sectional area. Conversely, the cross-sectional
area of a workpiece in a compression-based process increases, leading to a
decreasing current density over the duration of the test.
The term “current density” will be used frequently throughout this chapter.
When used, it represents the starting current density, not the instantaneous cur-
rent density. For the forging experiments in this chapter, the current density will
decrease since the cross-sectional area of the workpiece will increase during
deformation. Equation ( 5.12 ) shows this relation as:

A o
A f

CD act = CD nom ·

(5.12)

where CD act is the actual current density during the deformation process, CD nom is the
nominal current density (i.e., the starting current density), A o is the initial cross-sec-
tional area, and A f is the final cross-sectional area. As decreases, the current den-

sity decreases as well. Equation ( 5.12 ) can be rewritten in terms of strain as Eq. ( 5.13 ):

A o
A f

1
e ε

= CD nom · e − ε CD act = CD nom ·

(5.13)

where ε is the material strain.
Figure 5.2 shows the change in current density over the duration of an electri-
cally assisted forging test. The specific tests in the figures are of SS304 specimens
(7.154 mm × 4.761 mm diameter) that were deformed at dies speeds of 12.7 and
25.4 mm/min. From the figure, the ending current density is about 41 % of the start-
ing current density, hence there is a significant change in the current density over the
duration of the EAF tests if current is held constant. Note that derivations in this chap-
ter are based on current level, and not current density; these approaches are contrasted
in Chap. 4 . The modeling includes electrical power, which is obtained by the current
(which is held constant in all tests). The starting current density value of any EAF test
is used purely as a classification mechanism and not as a modeling variable, because
it is dependent on the cross section of the part and this is constantly changing.