Materials Letters 62 (2008) 3632–3635

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Materials Letters

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Energy-harvesting characteristics of PZT-5A under gunfire shock

Sang-Hee Yoon ⁎, Young-Ho Lee, Seok-Woo Lee, Chan LeeAgency for Defense Development, Yuseong P.O. Box 35, Daejeon 305-600, Korea

⁎ Corresponding author. He is now with the UniversitE-mail address: shyoon@me.berkeley.edu (S.-H. Yoon

0167-577X/$ – see front matter © 2008 Elsevier B.V. Aldoi:10.1016/j.matlet.2008.04.042

A B S T R A C T

A R T I C L E I N F O

Article history:

The energy-harvesting beha Received 12 February 2008Accepted 7 April 2008Available online 15 April 2008

Keywords:Energy-harvestingEnergy-transfer efficiencyGunfire shockPiezoelectric elementShock-aging

viors of a ring-shaped PZT-5A element exposed to gunfire shock are investigatedfor military applications such as an in-flight power source for electronic fuze. A laboratory test using apneumatic shock machine up to 3000 g's and a gunfire test accompanied by the acceleration of 65,000 g'shave been performed. The PZT-5A element subjected to gunfire shock has worked in its strong-depolarization region, thereby generating the electric energy whose quantity is about 140.4 times largerthan that measured in its linear operation region. The experimental studies on the PZT-5A element underdynamic load have demonstrated three physico-electric characteristics: the dependence of piezoelectricconstant on load-rate, the shock-aging of piezoelectric effect, and the dependence of energy-transferefficiency on the change in normalized impulse.

© 2008 Elsevier B.V. All rights reserved.

1. Introduction

Energy recovery fromwasted power has been a topic of discussionfor a long time [1]. A gunfire shock is a typical example of wastedpower. Although direct exposure to gunfire shock is seriously harmfulto the survivability of a spring-mass type device [2], gunfire shock canbe used as a source of mechanical stress for piezoelectric ceramicswhich generate electric energy. Since F. W. Neilson's research [3],many experimental studies on the energy-harvesting characteristicsof piezoelectric ceramics traversed by mechanical stress waves havebeen conducted. The previous researches [1,4–6] dealt with thebehaviors of piezoelectric elements in the linear region where thepiezoelectric constant g33 and the permittivity ε33 are constant and nostrong-depolarization occurs. The dynamic behaviors of piezoelectricelement in the nonlinear region, however, still remain unknownexcept for the shape of the current pulse generated [7,8].

The present research investigates the energy-harvesting andenergy-charging characteristics of a lead zirconate titanate (PZT-5A)ceramic element under gunfire shock, thereby showing the depen-dence of piezoelectric constant on load-rate, the shock-agingphenomenon of the piezoelectric effect, and the dependence ofenergy-transfer efficiency on the change in normalized impulse.

2. Theory of piezoelectric phenomenon

It is well known to express the relationship between mechanicalstress and electric potential difference of piezoelectric element operat-

y of California at Berkeley.).

l rights reserved.

ing in the linear region. Assuming that the piezoelectric behavior islinear during deformation, the mechanical work Wm done by mechan-ical stress σ is expressed as Wm=0.5σAδh=0.5S33σ2Ah where A, h, δh,and S33 are the cross-sectional area, height, height displacement of thePZT-5A element, and the longitudinal elastic compliance at constantcharge density, respectively.

For a capacitor with capacitance C charged to an electric potentialdifference V under mechanical stress, the available electric energyWel

is represented as Wel=0.5CV2=0.5V2ε33A /h where ε33 is the permit-tivity at constant strain. Using the longitudinal coupling factor k33defined as (Wel /Wm)1/2, the relation between the electric potentialdifference and the mechanical stress [9,10] is given by

V ¼ k33 S33=e33ð Þ1=2hrcg33hr: ð1ÞThis is because the longitudinal piezoelectric constant at constantstress g33 in electric field-stress relation is approximated as g33≈k33(S33/ε33)1/2. In this theoretical analysis, the PZT-5A under gunfireshock is assumed to operate in the nonlinear region. Its electricpotential difference therefore depends on load-rate σ̇ defined as dσ/dtand the longitudinal piezoelectric constant can be represented asV=g33(σ̇)hσ.

When the electric energy generated from a piezoelectric ceramicwith parasitic capacitance Cp is charged to a storage capacitor withcapacitance Cs of the load circuit (shown in Fig. 1), the total electriccharge Qt is given by

Q t ¼ CpVp ðwithout storage capacitorÞ¼ CpVs þ CsVs with storage capacitorÞð

ð2Þ

where Vp and Vs are the charged voltage at the piezoelectric ceramicwithout storage capacitor and the charged voltage at the storage

Fig. 1. Experimental setup for characterizing the ring-shaped PZT-5A element.

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capacitor, respectively. The piezoelectric ceramic is modeled as aparasitic capacitor (not shown) with capacitance of Cp in the loadcircuit. The charged voltage at the storage capacitor is thereforewritten as Vs=Vp{Cp / (Cp+Cs)}. The total charged energy Et is expressedas Et=0.5CpVs

2+0.5CsVs2=0.5CpVp

2{Cp / (Cp+Cs)}=Eg{Cp/ (Cp+Cs)} whereEg=0.5CpVp

2 is the energygenerated from the piezoelectric ceramic. Theenergy-transfer efficiency η is consequently given by

g kð Þ ¼ Et=Eg � 100 ¼ Cp= Cp þ Cs� �� 100

¼ 1= 1þ Cs=Cp� �� 100: ð3Þ

3. Experimental details

For experimental studies, the ring-shaped PZT-5A elements withouter radius ro of 5 mm, inner radius ri of 2.4 mm, and height h of3 mm are prepared. The material properties are as follows: theparasitic capacitance Cp is 300 pF; the relative permittivity ε33

r is 830;the longitudinal elastic compliance S33 is 9.46×10−12 m2/N; thelongitudinal coupling factor k33 is 0.705; the piezoelectric constantg33 is 0.0248 V m/N [11]. To explore their dynamic behavior, two kindsof tests – a laboratory test using a pneumatic impacter up to 2000 g'sand a gunfire test accompanied by the acceleration of 65,000 g's – areperformed, as shown in Fig. 1.

In the experimental studies, a PZT-5A element is deformed andgenerates electric energy as a proof mass smashes the piezoelectricelement by pneumatic impact or gunfire shock. The applied mechan-ical stress is calculated from themeasured acceleration. The generated

Fig. 2.Measured voltage and load-rate of the ring-shaped PZT-5A element as a functionof mechanical stress, compared with theoretical voltage in a pneumatic impacter test.

electric energy is measured by a digital oscilloscope in order tocharacterize the energy-harvesting behavior, whereas the electricenergy charged at a storage capacitor of 0.1, 1, or 10 µF through arectifying diode is recorded in order to examine the energy-chargingbehavior.

4. Results and discussion

To investigate the energy-harvesting characteristics of PZT-5A element underdynamic load, the output voltage is measured at the peak mechanical stress range of 10to 100MPa. Fig. 2 shows themeasured voltage and load-rate as a function ofmechanicalstress in an impacter test. There is a large discrepancy between the measured voltageand the theoretical one calculated from (1) due to the piezoelectric constant varia-tion with load-rate. The theoretical voltage mentioned above is analyzed under staticloading condition in which the piezoelectric constant is kept a constant. The piezo-electric constant under dynamic loading condition, however, changes with load-rate. Toexplore the effect of load-rate on piezoelectric constant, the piezoelectric constantunder dynamic load is calculated and comparedwith the static piezoelectric constant of0.0248 Vm/N, as shown in Fig. 3. As the load-rate gets higher, the piezoelectric constantdecays exponentially and converges finally. The duration of dynamic load below 58.4±5.6 GPa/s is on the order of ms (ms region) and that above 58.4±5.6 GPa/s is on theorder of µs (µs region), showing that the piezoelectric constant of PZT-5A elementdecays in the ms region, whereas is almost constant in the µs region. The piezoelectricconstant is therefore assumed a function of load-rate, which can be written as g33(σ ̇)=ae− σ̇/b+c where a, b, and c are the material constants whose values are determined tobe a=0.0138, b=15.55×109, and c=0.011 from the measured voltage shown in Fig. 2.

To examine the energy-charging characteristics of PZT-5A element, the chargedenergies of storage capacitors are measured in the laboratory and gunfire tests, asshown in Fig. 4. In these experiments, two remarkable physico-electric phenomena, theshock-aging of piezoelectric effect and the strong-depolarization of PZT-5A elementunder gunfire, are proved and analyzed. In the gray-colored box of Fig. 4, substantial

Fig. 3. Measured piezoelectric constant g33 under dynamic load as a function of load-rate, compared with that under static load.

Fig. 5. Measured and theoretical energy-transfer efficiencies η, FWHM, and change in normaenergy-transfer efficiency measured in gunfire test is shown within an orange-colored box.

Fig. 4. Generated and charged energies of the ring-shaped PZT-5A element as a function ofmechanical stress in laboratory test, comparedwith those ingunfire test (orange-coloredbox).

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discrepancy between charged energies of new PZT-5A element and that of reused one isshown. The deterioration in energy-harvesting characteristics of PZT-5A element byrepeated mechanical shocks – the shock-aging of piezoelectric effect – is due toaccumulation of residual polarization by poling and its deterioration induces thelongitudinal coupling factor k33 to decrease [12–14]. The gunfire test is made to explorethe dynamic behavior of PZT-5A element under the gunfire shock of 65000 g's and2 msec, as shown in the orange-colored box of Fig. 4. The over-stressed PZT-5A elementgenerates the electric energy whose quantity is about 140.4±15.8 times larger than thatmeasured under pneumatic impact on the average, although the applied mechanicalstress is on the same level. The gunfire shock makes the PZT-5A element stronglydepolarized and has the piezoelectric constant sharply changed. The experimentalresults demonstrate that the PZT-5A element experiences a strong-depolarization if thepeak acceleration is as high as that of gunfire in spite of the low mechanical stress.

To make use of PZT-5A element as a power source, the generated electric energyfrom PZT-5A element should be transferred into a storage capacitor because the PZT-5Aworks only under mechanical stress. The energy-transfer efficiency η of the PZT-5Ais therefore one of the most important characteristics. Fig. 5 illustrates the mea-sured energy-transfer efficiency η, full width at half maximum (FWHM), andchange in normalized impulse as a function of acceleration for storage capacitors of0.1, 1, and 10 µF. The normalized impulse is expressed as ΔI= ∫F/mdt where F and mare the applied force and the mass, respectively. The integration range is 0 to2×FWHM. The measured energy-transfer efficiencies η defined by Eq. (3) at the

lized impulse as a function of acceleration for storage capacitors of 0.1, 1, and 10 µF. The

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fixed capacitance ratios Cs/Cp of 333 (0.1 µF), 3333 (1 µF), and 33333 (10 µF) aremuch larger than the theoretical efficiency calculated from Eq. (2), and it increases asthe applied acceleration increases. This is because the parasitic capacitance of PZT-5Aelement increases as the applied acceleration increases. In the gunfire test, electricenergies of 1251 and 166 ergs are transferred to the storage capacitors of 1 and 10 µFwith the energy-transfer efficiencies of 2.97 and 0.39%, respectively, as shownwithinorange-colored box of Fig. 5. The measured energy-transfer efficiency η at a fixedcapacitance ratio increases as the normalized impulse ΔI= ∫F/mdt increases. Theexperimental results shown in Figs. 4 and 5 demonstrate that the energy-transferefficiency of PZT-5A element is directly related to the amplitude and duration of themechanical stress.

5. Conclusions

The energy-harvesting and energy-charging characteristics of thePZT-5A element exposed to gunfire shock of 65,000 g's have beeninvestigated for military applications. The experimental studies havedemonstrated three physico-electric phenomena. First of all, thepiezoelectric constant is a function of load-rate and decays exponen-tially with increasing load-rate. Secondly, the energy-harvestingcharacteristics deteriorate under repeated mechanical shock. Finally,the PZT-5A element subjected to gunfire shock experiences strong-depolarization and its energy-transfer efficiency is proportional to thechange in normalized impulse.

Acknowledgements

The authors wish to acknowledge the support of Hanwha Corpora-tion, as well as the assistance of K.-H. Kim and D.-L. Kim, withoutwhomthe experimental work would not have been completed.

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