Reversibility and hysteresis

In chapter 4.2, we obtain that the breakdown voltage is 2000 V. Properties of sample may alter when achieving breakdown point. Hence, we discuss the mechanism of VHB sample before breakdown phenomenon. It is important to understand whether process of applied voltage is reversible or not. If experimental process is reversible, VHB sample can reuse before breakdown phenomenon occurs.

In Figure 4–11, it is the first test in experiment. We can observe with the increase of applied voltage from 0 V to 1600 V, displacement gradually becomes large along upper path. Then, displacement gradually becomes small along lower path with the decrease of applied voltage from 1600 V to 0 V. The minus sign of displacement indicates that the equivalent direction is compressive.

Similarly, the second test is shown in Figure 4–12. We also can observe the trend of displacement with applied voltage. In Figure 4–11, we observe displacement of initial state and final state. After applied voltage increases from 0 V to 1600 V, then decreases from 1600V to 0 V, the final state is very close to the initial state. The same situation is observed in Figure 4–12. Hence, reversibility can be observed.

In Figure 4–13 and Figure 4–14, the third test and the forth test are obtained in experiment shown in figures. We can observe that the final state is almost equal to the initial state in Figure 4–13 and Figure 4–14. With the increase of test round, friction between VHB sample and sample stage is going to be canceled. Because of this, the final state is much more close to initial state. This experimental result shows reversibility.

Figure 4–11. Displacement vs. Voltage. The first test is in experiment. With the increase of applied voltage from 0 V to 1600 V, displacement gradually becomes large along upper path. Displacement gradually becomes small along lower path with the decrease of applied voltage from 1600 V to 0 V. The minus sign of displacement indicates that the equivalent direction is compressive.

Figure 4–12. Displacement vs. Voltage. The second test is in experiment. With the increase of applied voltage from 0 V to 1600 V, displacement gradually becomes large along upper path. Displacement gradually becomes small along lower path with the decrease of applied voltage from 1600 V to 0 V. The minus sign of displacement indicates that the equivalent direction is compressive.

Voltage increasing

Voltage decreasing

Voltage increasing

Voltage decreasing

Voltage (V)

Displacement (mm)

Voltage (V)

Displacement (mm)

Figure 4–13. Displacement vs. Voltage. The third test is in experiment. With the increase of applied voltage from 0 V to 1600 V, displacement gradually becomes large along upper path. Displacement gradually becomes small along lower path with the decrease of applied voltage from 1600 V to 0 V. The minus sign of displacement indicates that the equivalent direction is compressive.

Figure 4–14. Displacement vs. Voltage. The forth test is in experiment. With the increase of applied voltage from 0 V to 1600 V, displacement gradually becomes large along upper path. Displacement gradually becomes small along lower path with the decrease of applied voltage from 1600 V to 0 V. The minus sign of displacement indicates that the equivalent direction is compressive.

Voltage increasing

Voltage decreasing

Voltage increasing

Voltage decreasing

Voltage (V)

Displacement (mm)

Voltage (V)

Displacement (mm)

Using experimental data of four samples, we can re-compile the data and express as in Figure 4–15. Figure 4–15 shows mean value of measurement and standard deviation. Then, in order to confirm the fit of experimental result and theory, substitute applied voltage 0 V, 400 V, 800 V, 1200V, 1600V to equation (2.31. a) separately in order to obtain their normalized voltage. Next, substituting normalized voltage to equation (4. 1) and calculates normalized thickness by Matlab, then, actual thickness at applied voltage can be obtained from equation (2.2. c). Actual thickness at applied voltage is obtained, so does displacement. Depending on applied voltage and displacement by calculating, we can see the figure whose x-y coordinate, x-axis is applied voltage and y-axis is displacement. In Figure 4–16, the red curve represents displacement-applied voltage curve of theory and shows mean value of measurement and standard deviation. When dielectric constant is 3.0, the result of experiment most fits theoretical value.

According to Figure 4–15, we can observe the area bounded by curves of normalized thickness with the increase or decrease of voltage. This area expresses as the hysteresis. Some possibilities may result in this case. One possibility is friction between VHB sample and sample stage. Friction may loss a little energy which is generated by applied voltage. Because of energy loss, hysteresis is observed. Another possibility is power consumption. Because of high current occurs with the increase of applied voltage, high current can consume energy by transferring electrical energy to heat. According to possibilities, occurrence of hysteresis should be from consumptions of power and friction, not from properties of material.

Figure 4–15. Displacement vs. Voltage, show mean value of measurement and error bar.

With the increase of applied voltage from 0 V to 1600 V, displacement gradually becomes large along upper path. Displacement gradually becomes small along lower path with the decrease of applied voltage from 1600 V to 0 V. The minus sign of displacement indicates that the equivalent direction is compressive.

Figure 4–16. Displacement vs. Voltage, shows mean value of measurement and error bar.

Red curve is the value of substituting experimental data to theory.

Voltage increasing

Voltage decreasing

r

3.0

Voltage (V)

Displacement (mm)

Voltage (V)

Displacement (mm)