DYNAMIC DEFORMATION EVALUATION BY ELECTROMOTIVE FORCE
Tetsuo Kumazawa, Noboru Nakayama
Department of Machine Intelligence and Systems Engineering
Akita Prefectural University
84-4 Tsuchiya-Ebinokuchi, Yurihonjyo, Akita,015-0055, JAPAN,
ABSTRACT
A deformation measurement with a thermocouple was intended to be applied for dynamic and impact deformation test. n
electromotive force (Emf) was caused by bending vibration, which was tensioned and compressed alternatively in a steel plate.
The Emf increased almost in proportion to the strain magnitude. The impact test was done using a Hopkinson bar made of steel
or solder. The Emf and strain were measured at same position. Both the Emf and strain were also generated in a Hopkinson bar
and agreed well with each other in timing, though they were different in the direction of increasing and decreasing. There was a
linear relationship between the absolute Emf and strain for the steel and the two solder bars.
1. Introduction
An electromotive force is generated during metal deformation and be measured with a thermocouple. Both the Emf–strain curve
and stress–strain curve were obtained simultaneously in a tension test [1]. The Emf curve is correlated with the stress curve
which depends on thermal change, i.e., strain energy. This Emf measurement is utilized in a static deformation test for strain
evaluation.
In the present paper, this method was applied to dynamic and impact deformation tests. The bending vibration for the dynamic
test was carried out using a steel narrow plate on which a thermocouple and a strain gauge were bonded. Both the Emf and the
strain were measured at the same time during the bending vibration. The impact test was done using a Hopkinson bar made of
steel or solder for which one end was hit by a striker, and the Emf and strain were measured. The Hopkinson bars made of steel
and solders were tested. It was shown that the Emf generated by the strain in the bar increased as the strain increased.
2. Electromotive force in bending vibration
2.1 Measurement method of electromotive force
A schematic for the emf measurement in bending vibration is shown in Fig.1. The thermocouple used was a combination of
copper (Cu) and Con. (constantan, NiCu alloy) wires, each 60cm long with a 0.1mm diameter. This material combination was
[2]
selected because it is a large Emf generation coupling material at room temperature . These wires were bonded separately on
a narrow steel plate (1x16x150 in mm unit), one end of which was fixed in a rigid block. The separation distance of the two wires
was 2mm. The non-bonded ends of the thermocouple wires were kept at 0 by immersing in an ice-filled vessel. A dummy
thermocouple was placed near the test plate for the purpose of compensating for the Emf caused by room temperature and
electric noises. The compensated Emf was amplified, displayed on the oscilloscope and recorded on a personal computer. A
strain gauge, i.e., an electric resistance gauge, was mounted at the same position as the thermocouple on the plate. The strain
generated was also amplified and recorded. This arrangement of the thermocouple and the strain gauge at the same position
and recording allowed the outputs from them during bending vibration to be compared.
2.2 Electromotive force and strain in bending vibration
The steel plate was bent at first and unloaded suddenly, which caused vibration. The plate surface was tensioned and
compressed alternatively by the vibration. The strain applied was within an elastic range. Both the Emf and the strain were
recorded, while the plate vibration was being dampened; typical curves are shown in Fig.2 The frequency of the plate vibration
was 160Hz, revolution time of which was about 6ms/cycle. It was clear that the Emf was generated during the dynamic
deformation and could be detected as a strain pattern.
Thermocouple
Steel plate
Vibration
Strain gauge
Dummy
plate
Thermocouple
0 Point of Amp. Oscilloscope
contact
Fig. 1 Schematic for electromotive force measurement with a thermocouple
measurement at tension
The Emf increased when the strain decreased and vice versa. In order to quantify the relationship between the strain and the
Emf, their peak values were plotted in a graph. The small fractional values in addition to the peak values are also suitable for
comparison, but they were not used in the present arrangement. The Emf values decreased proportionally to the strain, even
though the data showed a small fractional value in Fig.3 and the relationship was expressed as follows.
Emf - 0.005 (mV)100()
(1)
The thermal condition in a solid changes due to external loading[3] [4] ] [5]. The temperature increases in compression and
decreases in tension. At the same time, the temperature decreases and increases in accordance with thermal conduction. The
relative interaction of heat change by strain and conduction results in reduction of temperature deviation from room temperature,
which is considerd to be a reason why the Emf deviation diminished after several repetitionsof waves as shown in Fig.2. Though
there is reduction of temperature deviation, the strain values can be estimated at ealy atage of dynamic loading, i.e., in several
msec range. A linear relationship between them was required and was expressed by eq.(1).
Fig.2
Electromotive force and strain curves in bending
vibration of a steel plate
0.03
EmfmV
0.02
0.01
0
-0.01
-0.02
-0.03
-600
-400
-200
Strain
0
200
()
400
600
Fig.3 Relationship between electromotive force
and strain
3. Electromotive force by impact loading
3.1 Measurement of electromotive force
The Emf was investigated by a using round steel Hopkinson bar, in which the strain (or stress) wave was propagated (Fig.4).
The total length of the Hopkinson bar was 2000mm. The diameters of the bar and the barrel were 12mm. The steel bar ends
were both flat, but the barrel had an end which was spherical. The barrel started to move, accerated by compressed air and hit
the bar, when the valve of the compressor tank was opened.
A compressive strain wave which was generated in one bar end (end-L) propagated to the other end (end-R). The wave became
a tensile wave at the end-R and was reflected back to the bar end-L. The thermocouples were bonded at the position of 500mm
and 1500mm from end-L (Fig.5). The thermocouples (Cu wire and Con. wire) were bonded so that they faced each other at
opposite points on the bar circumference. The strain gauges were mounted at the same position as the thermocouples on the
bar, but in the direction of angle 90from( perpendicular to ) the thermocouples.
A dummy thermocouple was placed near the steel bar to compensate for the emf which was caused by room temperature and
electric noises. The compensated Emf was amplified, displayed on the oscilloscope and recorded on a personal computer in the
same manner as for the plate vibration test. The strain generated was also amplified and recorded.
3.2 Electromotive force in the steel bar by impact loading
The tensile and compressive strain waves at 500mm from the L-end which were generated and propagated repeatedly are
shown in Fig.6. Some overshooting in amplitude of emf was observed. The Emf increased when the strain decreased and vice
versa, which was similar to the plate vibration in behavior. Both parameters agreed well with each other in timing, though they
were different in the direction of inceasing and decreasing. The Emf goes together with the strain, the relation of which is
expressed as follows.
Emf - 1.33 (mV)100()
(2)
This Emf value was much larger than the emf value obtained at bending vibration, i.e., about 27 times larger. This was because
the enery dispersion was quite small, i.e., deformed at almost adiabatic condition as the impact deformation time was very
short.
Valve
Test Bar
Barrel
Pipe
Cushioning
Medium
Compressor
Fig.4
Striker
12
Cu Wire
Strain Gauge
Cu Wire
Con. Wire
Schematic forimpact test (Hopkinson bar test)
2000mm
500 mm
1500 mm
12
Impact
Strain Gauge
200
Strain ()
100
Con. Wire
Position of thermocouples and strain gauges
2
Emf
1
0
-100
-200
0
Con. Wire
0
Emf (mV)
Fig.5
Cu Wire
Cu Wire
-1
Strain
0.5
Time (ms)
-2
1
Fig.6 Electromotive force wave and strain wave
in a steel bar
Con. Wire
The damping of both the strain and Emf waves was very small, which was obseved from the alternating following propagations.
The above mentioned results were the same for the waves observed at 1500mm from the L-end.
The time difference between the first wave and a returned wave (i.e., second wave) is 0.193ms. As the wave propagates 1m
distance in the bar during that time, the velocity of propagation was calculated to 5180m/s. This velocity was almost the same
as the speed of an elastic longitudinal wave in steel, derived from the equation of density and Young’s modulus[6].
3.3 Electromotive force in the solder bar by impact loading
The Emf for solder bar, when impacted in the same manner as the steel Hopkinson bar test, was evaluated here. Knowing
impact characteristics of the solder is important for reliable design of impact-proof in electronic appliances [7] . The 2m long bar
with 12mm diameter made of Sn-37Pb or Sn-3.5Ag-0.75Cu solder was used in the test. The strain gauge and thermocouple
were bonded at 500mm and 1500mm from the L-end in the case of the steel bar.
The Emf and strain waves of Sn-37Pb measured at 500mm from the L-end are shown in Fig.7. The compressive strain
propagated and returned as a tesile strain. A positive Emf was clearly generated by the compressive strain. The Emf wave
propagated and no returned wave was observed, though the strain wave was reflected as a second wave. This was considered
to be diminishment of the reflected wave, owing to large degradation in a soft solder material like Sn-37Pb. The strain velocity in
the Sn-37Pb bar, which was calculated from propagated time and distance, was 2220 m/s. It could be seen that the Emf wave
moved slightly faster than the strain wave, though the Emf waves was generated by the impact strain (loading).
Next, Emf and strain waves in a Sn-3.5Ag-0.75gCu bar measured at 500mm from the L-end are shown in Fig.8. The generation
and propagation of the strain and Emf waves were almost the same as for the Sn-37Pb bar. The strain velocity in the
Sn-3.5Ag-0.75Cu bar was 2760 m/s.
200
S t r a in
Strain ( )
100
0
-1 0 0
-2 0 0
Emf (mV)
0 .1
Emf
0
-0 .1
0
1
T im e ( m s )
2
Fig.7 Electromotive force wave and strain wave
in a Sn-37Pb bar (measured at 500mm )
Fig.8 Electromotive force wave and strain wave
in a Sn-3.5Ag-0.75Cu bar (measured at 500mm )
0.20
Emf (mV)
0.15
0.10
0.05
0
0
100
200
300
-Strain ( )
400
Fig.9 Relationship between electromotive
force and strain in Sn-37Pb bar
3.4 Relationship between electromotive force and strain
The Emf wave in the Sn-37Pb bar was caused by the first strain wave. In order to investigate the relationship between the
strain and the Emf, the peak values of both waves were plotted on a negative strain–Emf graph (Fig.9). The Emf value was
proportional to the strain value, even though the data showed a fraction. The proportional relationship was expressed as
follows.
Emf - 0.04 (mV)100()
(3)
As for the Sn-3.5Ag-0.75Cu bar, the proportional relationship is shown in Fig.10 and expressed as follows.
Emf - 0.03 (mV)100()
(4)
The proportionality rates of the steel and solder bars were different. This was because the strain energy differed depending on
materials, even though the same strain was induced.
0.20
Emf ( mV )
0.15
0.10
0.05
0
0
100
200
-Strain ()
300
400
Fig.10 Relationship between electromotive
force and strain in Sn-3.5Ag-0.75Cu bar
4.
Conclusions
An electromotive force method was applied to the dynamic bending and impact deformation tests. Both the Emf and the strain
were measured effectively at same time during deformation. The tested materials were steel and two types of solders (tin alloy
metal). The conclusions were as follows.
1.The Emf was caused by bending vibration, which was tensioned and compressed alternatively in a steel plate .
The generated absolute Emf increased almost in proportion to the strain magnitude.
2. Both the strain and Emf were also generated in a Hopkinson bar and agreed well with each other in timing,
though they were different in the direction of increasing and decreasing. There was a linear relationship between
the absolute Emf and strain for the steel and the two solder bars.
3. The results suggested that the Emf measurement method can be used as a dynamic and an impact deformation
test for strain energy evaluation.
References
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[2]
[3]
[4]
[5]
[6]
[7]
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