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Variation of Electro-Conductive Property of SSF /PP System Under Impact Loading Using a Modified SHPB

Variation of Electro-Conductive Property of SSF /PP System Under Impact Loading Using a Modified SHPB Jin-tao Lei 1,a, Ming-hua Zhang 2,b and Jian-kang Chen 3,c

Faculty of Mechanical Engineering and Mechanics, Ningbo University, Ningbo 315211, China

1,2,3

Summary In order to detect the variation of electro-conductive property of short steel fiber (SSF) filled polypropylene (PP) under impact loading, a modified split Hopkinson pressure bar (M-SHPB) is suggested. Such M-SHPB is constructed by designing a new test electrocircuit, and connecting it to the specimen and oscillograph. On the other hand, a copper foil cover is designed and placed on the whole SHPB equipment for avoiding interference of electromagnetic wave existing in the testing environment. By means of M-SHPB, the relation between the resistance and dynamic stress or dynamic strain is effectively detected. The experimental results indicate that the resistance of the material decreases with the increase of strain or stress. The sensitive variation of the resistance appears at the beginning of the deformation of the material.

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Keywords: Polymeric composite; electroconductivity; modified split Hopkinson pressure bar (M-SHPB); impact loading

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1. Introduction

Electroconductivity of polymeric composite has been extensive researched since their first discovery in 1986 by Lundberg Band Sundqvist B.1. The establishment of effective synthesis techniques, By Rodrigues and Akcelrud, the conductivity of polyaniline and polyurethane was measured by the standard spring-loaded pressure contact four probe method2. Besides the electromechanical coupling, there is also a mechanical coupling between the axial deformation and the torsion, which can also modify electronic properties of polymeric composite and is rather important. Several methods, such as MTS, SEM and SHPB, have been used to describe this coupling response in polymeric composite. Limited by the instrument capability, the dynamic high-resistance of the polymeric composite is a knotty problem. Uttam Kumar Chakravarty

has reviewed the various closed cell polymeric from effect of strain rate and microstructure on the compressive strength and energy absorption behavior3. The C-SHPB technique has been continually modified by Maziar Ramezani to obtain more accurate dynamic properties of a variety of engineering materials4. Especially for the polymers and polymeric composite materials, it has been noted that serious experimental problems occur from the poor contact of between the soft specimen and the steel pressure bar5. In order to obtain valid experimental results on soft specimens, the dynamic stress equilibrium between the front and rear of the specimen is checked by Ouk Sub Lee, to provide more reliable experimental data. The C-SHPB technique has been modified to obtain more accurate dynamic compressive stress-strain data for PP specimens under varying strain rate conditions6. Correlated electrical

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[email protected], [email protected], [email protected]

a

Smithers Rapra Technology, 2012

©

Polymers & Polymer Composites, Vol. 20, Nos. 1 & 2, 2012

conductivity and mechanical property analysis of high-density polyethylene filled with graphite and carbon fiber is studied by Thongruang W.7. Though by the analytical method, mechanical behaviour of acrylic under high strain rate tensile loading is studied by N.K. Naik, high strain rate tensile stress–strain behaviour is presented8. Dynamic mechanical properties of composites, such as PP/PA, whisker/ PA66, using the split Hopkinson pressure bar technique at high strain rates are studied deeply9. In order to detect the variation of electroconductive property of short steel fiber (SSF) filled polypropylene (PP) under impact loading, a modified split Hopkinson pressure bar (M-SHPB) is suggested. Next work an aluminum bar set-up should be used in order to achieve constant strain rates in the specimen during M-SHPB experiment.

2. Experimental Methods

2.1 M-SHPB Apparatus The piezoresistive behavior of electroconductive polymeric

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Jin-tao Lei, Ming-hua Zhang and Jian-kang Chen

composite under static loading has been investigated10-11. However, in the case of impact loading, it is difficult to detect the piezoresistive behavior, because the variation of the resistance is sharply in this case. In this paper, a new modified split Hopkinson pressure bar (M-SHPB) is designed for measuring dynamic piezoresistive behavior of the polymeric composite. Two equipments are added to the typical split Hopkinson pressure bar, one is dynamic highresistance meter used for measuring the variation of dynamic resistance (shown in Figure 1), and the other is copper foil cover, which is placed on the SHPB for avoiding the interference of electromagnetic wave existing in environment (shown in Figures 1-2).

Incident and transmission bars are made of steels material, the resistance of them is under 100 W, which may be neglected comparing with the highresistance (108 W) of the polymeric composite. The two bars (striker bar and transmitter bar) are used as electric conduction poles. In order to improve the poor contact, DDG-A conductive paste is used between the bars and specimen. DDG-A conductive paste is so pivotal that the experiment data is flawed without it. The substrate of incident bar and SHPB apparatus are ground to decrease the electromagnetic interference. Compared with DDG-A conductive paste, insulation is also a key role, between the substrate of transmission bar and SHPB

apparatus, whose resistance is above 1015 W. Therefore, the resistance of the specimen can be measured by dynamic high-resistance meter.

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2.2 Design of Dynamic HighResistance Meter

Usually, high-resistance meter and digital multi-meter are used for the static detect of resistance within the range from 106 W to 1016 W , and from 100 W to 108 W. However, under impact loading, the variation of resistance of specimens takes place in micro seconds, therefore, high-resistance meter and digital multi-meter are not valid for measuring the change of the resistance.

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Figure 1. Photo of modified SHPB apparatus

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In this paper, a new dynamic highresistance meter is designed, and the circuit diagram is shown in Figure 3. This circuit is composed by a battery with voltage of 10V, a diode, a protecting resistor, Rs, a rheostat, R2, a digital multimeter, 3 resistors, R1, R3, and R4, a digital phosphor oscilloscope, and a resistance, Rx, to be detected. It should be pointed out that the variation of Rx can not be directly detected from the voltage on Rx because of the effect of internal resistance of the digital phosphor oscilloscope. Therefore, it will be detected by the change of voltage on R4. Such a dynamic high-

Figure 2. Sketched diagram of M-SHPB apparatus

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resistance meter can be used to detect the variation of resistance, Rx, from 10 W to 1012 W continuously.

Figure 3. Schematic drawing of high-resistance meter circuitry

From Figure 3 one can see that the circuit will remain in balance if the resistance of R2, is adjusted to some value, and in this case R1/R2 = Rx/R3, Rx can be obtained from this formula as the following:

Rx = R1 R3 / R2

(1)

When R1 = 1MW, R3 = W1M, R2 = 1W, using the digital multi-meter can be obtained, the resistance of specimen at this time can be computed out Rx = 1TW. Changing the resistance of potentiometer in the circuit between 1W–1kW, then the current may be balance under the resistance of specimen R x between1GW–1TW. However, in order to amplify the measure range, the R1 = 0.1kW-10MW, R3 = -0.1kW-10MW can be adjusted, the result is that we can measure the resistance of specimen Rx between 10W–100TW. That is to say, the meter can be used to measure the magnitude of Rx in the range 10W–10W14.

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If the specimen is under impact loading, the variation of resistance of Rx will take place due to the piezoresistive behavior of specimen, and the balance of the circuit is then broken. Such a variation may be detected by the change of voltage on R4 appearing on the oscilloscope. If R1,R2,R3,R4,U0 are known, and U4 can be tested by digital phosphor oscilloscope, then Rx can be obtained by:

Rx =

Figure 4. Curve of Rx - U4

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R1 R3 R4U 0 − (R1 R2 + R2 R4 + R1 R4 )R3U 4 R2 R4U 0 +  R1 (R2 + R3 + R4 )+R2 (R3 + R4 )U 4

Eq. (2) will reduce to Eq. (1) if U4=0.

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(2)

If R1 = 1MW, R2=1W, R3 = 1MW, R4=10kW, U0=10V, then Rx can be obtained from Eq. (2) as the following:

Rx = (105 −10 4 *U 4 ) / (10−7 +U 4 )


(3)

The curve of Rx - U4 is plotted in Figure 4. One can see from Figure 4 that Rx is the monotone decreasing function of U4. Figure 4 indicates that the little change of U4 will bring great change of Rx. For instance, when U4 changes from 0.5 mv to 0.6 mv, Rx will decrease from 200 MW to 166 MW. Note that the value of U4 can be easily affected by electromagnetic waves in the environment, therefore, the electromagnetic interference should be considered.

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The electromagnetic interference on U4 includes the effects of electromagnetic waves on the SHPB apparatus and conveying wire. The SHPB apparatus has been covered by the copper foil, and the interference of electromagnetic waves on it is avoided. Now we consider how to decrease the electromagnetic interference on the conveying wire. In this study, the wire with electromagnetic shield function is selected as the conveying wire.

t = 2l0 / C0

(4)

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where l0 is the length of striker bar, l0 = 0.300 m, C0 is the velocity of the stress wave in the incident and transmission bar, C0 = 5190 m/s, substituting l0, C0 into Eq. (4), we obtain t = 115.607 ms, this means that the variation of U4 within 120 ms is effective data. In order to exactly detect the variation of the resistance of specimen, namely, Rx, the resistance of resistors and the magnitude of U0 in the circuit are chosen as:

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In order to further reduce the electromagnetic interference, grounding technique should be improved. In this experiment, the point of grounding is chosen far away from testing equipments. Otherwise, the direct current (DC) is adopted to power experiment equipments. Experimental results indicate that these methods can effectively minimize the noise-signal on digital oscilloscope.

3. Experimental

R1 = 100 k Ω, R2 = 100Ω,

Substituting Eq. (5) into Eq. (2) yields:

R3 = 100 k Ω, R4 = 10 k Ω, U 0 = 10 V

(

)(

Rx = 105 −10 4 U 4 / 10−3 +1.101U 4

)

(6)

The variation of Rx can be obtained from Eq. (6) because U4 is detected and plotted in Figures 6-7. The dynamic behavior of specimen may be studied by analyzing the signals of CH1 and CH2 (shown in Figure 5). According to 1-D theory of stress wave9, the strain rate, strain, and stress can be respectively expressed by:

(

)(

d ε / d t = C0 / l0 ε I − ε R − εT

)

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(5)

(7)

Figure 5. Typical oscilloscope recorded signals of the M-SHPB

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In this study, the variation of resistance of polypropylene filled by short steel fiber (PP/SSF) under impact loading is carried out. Mass fraction of filler of the material is 6%, and thickness and diameter of specimen is 3 mm and 5 mm, respectively. The oscilloscope is selected as Tektronix TDS 3014C Digital Phosphor Oscilloscope. The striker bar in SHPB is fired under the external pressure of 0.15 MPa. The variation of voltage on R4, and on strain gages placed at incident and transmitter bars are appeared in the oscilloscope (shown in Figure 5), the CH1 is the signal of incident bar, the CH2 is the signal of transmission bar, and the CH3 is the voltage signal of the material.

Figure 6. Curves of resistance-time and strain-time of specimen

In order to determine the change of resistance of specimen, the signal of CH3 (shown in Figure 5) is investigated. This signal represents the imbalance voltage of R4. The total time (including incident and reflection time) of propagation of stress wave in specimen can be calculated by:

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Figure 7. Curves of resistance-time and stress-time of specimen

t

ε = (C0 / l0 ) ∫ (ε I − ε R − εT ) d t 0

σ (t) =

(8)

EA ε +ε +ε 2 A0 I R T

(

)

(9)

where E is Young’s modulus of the incident or transmitted bar, A is the area of cross-section of the bars, A0 is the area of cross-section of the specimen, e1 is incident strain pulse, eR is reflected strain pulse, eT is transmitted strain pulse. The average value of strain rate, strain, and stress of specimen can be approximately defined as the following12:

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Figure 8. Curve of strain rate - time of specimen

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dε / dt = 2C0 / l0ε R

(10)

t

ε = −2C0 / l0 ∫ ε R (t)dt 0

σ = EA / A0εT

(11)

(12)

Substituting the experimental results shown in Figure 5 into Eqs. (7), (8) and (9), we obtain the variation of resistance of specimen under impact loading and plot it in Figures 8-9. In this experiment, the variation of resistance of the specimen, the dynamic strain and stress of specimen are obtained at the same time, the relation between the resistance and dynamic strain or dynamic stress is effectively detected and plotted (shown in Figures 6-7). One can see from Figure 6 that the resistance of specimen is descending firstly, and then remains constant, although there is small changing.

In order to research the variation law of electro-conductive property of SSF/ PP under impact loading, curves of stress-strain and resistance-strain of specimen are fitted.

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Figure 9. Curve of stress-strain of specimen

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In order to derive formulas for the resistance-strain curve, it is necessary to establish the mathematical model of resistance-strain curve. From the relation of resistance - strain curve shown in Figure 10, it is


clear that the resistance-strain curve is more complicated. Therefore, according to the analysis on the characteristics of resistance-strain curve, the mathematical model of resistance - strain curve may be

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Figure 10. Fitted model curve of resistance-train of specimen

composite under impact loading within micro-seconds.

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2. Different from the situation of static loading, there are a sensitive and a non-sensitive region for the variation of resistance of conductive polymeric composite under impact loading with respect to time. The resistance decreases suddenly from initial deformation of specimen to 31.3 µs, and then keeps almost a constant.

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Figure 11. Curve of gauge factor-strain of specimen

Rx = 6 × 106 e−125ε + 8 ×105

(13)

dRx / Rx dε

(14)

To calculate the gauge factor of the SSF/PP, the Young’s modulus of the material is known from [13~15]. Substituting Eq. (13) into Eq. (14) yields:

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(

Acknowledgements

K = −7500e−125ε / 60e−125ε + 8

The piezoresistive coefficient, K (also known as gauge factor), of a material is defined as16:

K=

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described as piecewise experimental formulas as follows:

3. The experimental results state that the new modified SHPB can effectively eliminate the yawp produced in the testing environment, and test the variation of resistance of electro-conductive polymer under impact loading.

)

(15)

This work was financially supported by the National Natural Science Foundation of China (No.10872099), the Natural Science Foundation of Zhejiang Province (No.Y6100728), Financial support by the Scientific Research Fund of Zhejiang Provincial Education Department (No.Y200804458), K.C. Wong Magna Fund in Ningbo University are acknowledged, 2010 Excellent Degree Thesis Foster Fund of Ningbo University (No.PY20100009), and the Scientific Research Foundation of Graduate School of Ningbo University (No. G10JA016, G11JA013).

As shown in Figure 11, the SSF-PP is sensitive material related to strain.

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4. Summary

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The variation of a conductive polymeric composite under impact loading is firstly studied by M-SHPB technique, and some new results are obtained as the following: 1. The new modified SHPB system can effectively detect the variation of a conductive polymeric

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