Civil Engineering Reference
In-Depth Information
where
R
is the electrical resistivity,
L
part
is the length of the workpiece, and
A
contact
is the actual contact area at the specimen and die interface. The relation for the
actual contact area can be re-written as Eq. (
9.4
):
R
part
·
L
part
V
I
A
contact
=
(9.4)
This relation describes electrical resistance, but it does so assuming that the work-
piece and the top and bottom dies are essentially all one piece. However, there is
also some type of contact resistance between the specimen and dies since there is
a difference in the parts and in the die/workpiece materials. The total resistance
in the system (including electrical resistance and contact resistance) is shown as
Eq. (
9.5
):
R
total
=
R
electrical
+
R
contact
(9.5)
The electrical contact resistance was described above, but the contact resistance
can be written as Eq. (
9.6
):
4
·
N
asp
·
A
asp
+
R
part
+
R
die
R
part
+
R
die
R
contact
=
(9.6)
D
where
R
part
is the resistivity of the part,
R
die
is the resistivity of the die,
N
is the
number of asperities,
A
is the radius of the contact points, and
D
is the diameter
of the region where the asperities are located. When including both the electrical
resistance and the contact resistance, the equation for the total resistance can be
written as Eq. (
9.7
):
R
total
=
R
electrical
+
R
contact
=
R
part
·
L
4
·
N
asp
·
A
asp
+
R
part
+
R
die
R
part
+
R
die
A
contact
+
(9.7)
D
The final equation to be used to back-solve for the contact area, based on the
measured voltage, is Eq. (
9.8
):
R
part
·
L
part
A
contact
=
(9.8)
I
−
R
part
+
R
die
4
·
N
asp
·
A
asp
−
R
part
+
R
die
V
D
part
For 4.76-mm-diameter “Large CA” specimens in which stationary electrical tests
were run, Table
9.7
summarizes the recorded voltages, the apparent contact area
(i.e., the area calculated using Eq. (
9.1
), the contact areas calculated using Eq. (
9.4
)
(without the contact resistance), and the contact area calculated using Eq. (
9.8
)
(with the contact resistance). Figure
9.19
displays the contact areas with and with-
out the contact resistance accounted at the various static loads, along with a dashed
line representing the apparent contact area created from the EDM process dur-
ing the fabrication of the specimens. Please note that the area calculated with the
contact resistance is higher than the actual apparent area. This is possibly due to
the fact that the loads are in the plastic region and the total specimen height and
asperity height/width (i.e., cross-sectional area) has changed in this region. Of all
