NBSIR 75-740

Piezoelectric Polymer Transducer for

Impact Pressure Measurement

Aime S. DeReggi

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington, D. C. 20234

I

July. 1975

Final Report Covering Period

December 15, 1973 to December 31, 1974

Prepared for

IMational Highway Traffic Safety Administration

Department of Transportation

Washington, D. C. 20590

NBSIR 75-740

PIEZOELECTRIC POLYMER TRANSDUCER FOR

IMPACT PRESSURE MEASUREMENT

Aime S. DeReggi

Electronic Technology Division

Institute for Applied Technology

National Bureau of Standards

Washington. D. C. 20234

July. 1975

Final Report Covering Period

December 15. 1973 to December 31, 1974

The development and calibration efforts described in this report are exploratory in nature and are intended to serve as a basis for further work. The measurement results reported are derived from a statistically

small number of test transducers, and the conclusions that may be drawn

are therefore tentative.

Prepared for National Highway Traffic Safety Administration

Department of Transportation

Washington, D. C. 20590

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

John K. Tabor, Under Secretary

Dr. Betsy Ancker-Johnson, Assistant Secretary for Science and Technology

NATIONAL BUREAU OF STANDARDS. Ernest Ambler, Acting Director

ABSTRACT

Described are development efforts relating to the design, construction,

and calibration of a piezoelectric polymer transducer for the recording

of pressure transients developed over the interface between two bodies

as a result of impact. A bilaminate design was selected which uses electrically poled sheets of 25-um polyfvinyl idene fluoride) as the

active material. The intended primary response of the transducer is

to compression in the thickness direction, which is produced by either

hydrostatic or normal pressure; the transducer was also found to respond

to extension in the membrane direction. Individual-sheet activity in

the thickness-compression mode is approximately 15 pC/N, resulting in a bilaminate transducer pressure response of 4.5 uV/Pa (30 mV/psi).

Instructions for poling sheets and for constructing transducers are given

in detail. Static and dynamic methods for characterizing transducer output are described. In particular, in order to simulate field conditions

in which the transducer may bend or stretch, or both, during impacts, a drop-test procedure with curved impactors has been devised, and a theoretical analysis (simplified to the extent of considering the membrane-stress

contribution negligible) has been developed to yield the interface

pressure.

Piezoelectric Polymer Transducer

for Impact Pressure Measurement

Aime S. DeReggi

1. INTRODUCTION

This report describes the development of a pressure transducer design

utilizing a polymeric piezoelectric element [1]* for sensing impactinterface pressure. The measurement of interface pressure is of current

interest in studying injury sustained in vehicular crashes.

The results of recent impact-injury studies conducted elsewhere and also

sponsored by NHTSA [2] have demonstrated a correlation between the

interface pressure developed in the impact region and the severity of

local injury. These results were obtained in controlled tests in which

it was possible to instrument the impacting device in order to establish

the maximum pressure developed during impact. In less controlled tests,

such as crash tests with anthropomorphic dummies or with human cadavers,

it has not been feasible to make reliable interface-pressure measurements

with commercially available instrumentation.

A technique for measurement of peak pressures by using dye-filled microcapsules adhered to a flexible substrate which is placed over the impact

surface was studied elsewhere [3]. While this method of pressure gaging

yields the spatial distribution of the peak pressure and has the advantage

of requiring no electrical connections to the gage, it cannot provide the

pressure history.

The pressure history is important in establishing the duration of elevated

pressure, as well as in ordering the sequence of events which led to the

development of the peak pressure. Simultaneity with other impact observables such as the acceleration of the vehicle may readily be ascertained,

and effects of secondary impacts distinguished from those of the primary

impact. The pressure history also permits more general correlations to

be tested as, for example, whether there exists a correlation between the

time-rate-of-change of pressure and the extent of injury.

A pressure transducer made with piezoelectric polymer sheet material not

only can provide the pressure history, but also may be made sufficiently

thin and flexible to be mounted on curved surfaces. When mounted on human

skin or implanted in the body, the polymer material should provide a good

acoustical impedance match to skin or flesh because the densities of these

materials closely match that of the polymer. As results given in this

report demonstrate, prototype sensors have sensitivities approaching those

of piezoelectric ceramics, i.e., on the order of 1 -^V/Pa (10 mV/psi) for

*Figures in brackets refer to references, section 6.
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25-ym poly(vinyl idene fluoride) (PVF2). The dynamic range of pressure

based on the limit imposed by the polymer room- temperature yield stress

extends to approximately 40 MPa (6000 psi) in the case of PVF2. Morer

over, as the polymer material itself should provide low-Q resonance

behavior, a polymer sensor can be designed to exhibit a broad, flat

frequency response.

2. OBJECTIVES

The central objective of this program (DOT-HS-4-00835) is to develop a polymeric pressure transducer capable of measuring the interface pressure

developed when the surfaces of two bodies of different compliance come together under impact. The range of pressure specified is nominally zero

to a maximum of 1.4 MPa (200 psi), and the range of frequency a few hertz

to 10 kHz.

The detailed work statement originally called for the development, construction, and pressure calibration of at least ten polymer transducers suitable

for mounting on the surface of anthropomorphic dummies for impact studies.

The statement also specified that the sponsor would be supplied with ten

calibrated transducers sufficiently inert chemically to be suitable for

implantation into the brains of sub-human primates. The work statement

also called for the construction and test of a prototype sensing network

for use on the chest and on the head of an anthropomorphic dummy.

As the work progressed to the pressure-calibration stage, it became clear

that the sensitivity of the piezoelectrically active elements to bending

and stretching was sufficiently large and difficult to predict as to

require separate careful investigation before the transducers should be

delivered for use in the field. After a series of discussions between the

sponsor and project staff, it was deemed advisable to suspend the development of the pressure-calibration methods for the pressure and frequency

ranges specified, and to redirect the work toward defining the types and

magnitudes of outputs which can be expected when a transducer is subjected

to the imposition of curvature during impact. This change of emphasis

in the work was authorized by agreement between the sponsor and the

performing organization.

3. EXPERIMENTAL DEVELOPMENT

3.1 Principles Governing Transducer Performance and Design

3.1.1 Piezoeleotria Properties - The general relation between electric

displacement vector D, electric field vector £, and stress tensor X

tensor of second ranlT) is expressed [4] by the matrix equation

^ ^ij^j ^

^im'^m

" ° = 1. 2, 3 and m - 1, 2. ..6), (1)

where summation is implied by the repeated index. In (1), six-element

column matrix T represents the stress tensor. Conventionally, matrix

elements Ti, T2»...iTs represent tensor components Tn, T22. T33, T23»
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Ti3» in that order [4]. The elements of 3 x 6 matrix d-jm represent

components of a third-rank tensor. These elements are callea piezoelectric

strain moduli (with units C/N, equivalent to m/V). The matrix represents the ordinary permittivity tensor 4 (a tensor of second rankj.

The relation between D^, E_, and stress-induced polarization vector is

D. = c..Ej f P.. (2)

This equation and (1) show that moduli dj^ relate polarization components

to stress components T^ in the following way:

= d.Jn,. (3)

1 im m

For a flat sheet of PVF2 which has electrodes on both sides and which has

been poled across the sheet (i.e., in a direction defined as the 3-direction)

there exists a frozen-in, pol ing-f ield-induced polarization P3 distinct from

P in (3). The charge associated with P3 tends to become neutralized during

poling (by injected charge) or during storage (by stray atmospheric charge).

In any case, this polarization charge is not observable in dynamic measurements.

Equation (1) with D = 0 shows that an applied stress induces an electric

field, given by

The product (e'Mijdim is another matrix gj^, the elements of which are piezoelectric stress moduli. The d^-^^ and g. moduli are related generally

as follows*

The units of g^^^ are V • m/N.

For the flat-sheet geometry above, the relation

~ ^jm^m

implies that an open-circuit voltage will appear across the electrode under

applied stress.

The d-matrix for a poled PVF2 sheet, written out explicitly in rectangular

Cartesian coordinates, is [5,6]:

0 0 0 0 die 0

d =

15

0 0 0 d2^ 0 0

^31 ^32 d33 0 0 0

(6)
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The component determines the response to normal force. The d^i and d32

components determine the response to membrane forces, i.e., forces acting

in the plane of the sheet. In general, and d32 are not equal, especially

if the polymer material was stretched and rolled during the manufacturing

process or during the poling process. If stretching has occurred in the

1-direction, d^i > d^z. Recently, PVF2 sheet material which has been

biaxially stretched during manufacture has become available. For this

material, and no further stretching during poling, it is expected that

dsi a d32. The dis and d24 components determine the response to shear

stresses. As a rule dss > d^i > > ^is* [5,6].

For a given polymer-sheet material, the values of the components of d depend

on the poling procedures, that is, on the polarizing field, on the polarizing

temperature, and possibly also on the temperature and field histories.

Routinely achievable values of d^^ in this laboratory for 25-ym (0.001 in)

sheets of PVF2 are between 10 and 15 pC/N for the following poling conditions:

800 kV/cm polarizing field, 120''C polarizing temperature, temperature history

consisting of first heating to 120°C followed by cooling to room temperature,

the total cycle being completed within approximately 30 minutes, and applied

field at its maximum value throughout the thermal cycle. Corresponding values

of dsi are between 5 and 8 pC/N. Precise values for the shear components are not available.

The piezoelectric moduli are not expected to have a significant intrinsic

frequency dependence in the frequency range of interest.

The piezoelectric moduli are somewhat temperature-dependent. According to

data supplied by the manufacturer, the temperature coefficient of d^i for

PVF2 near room temperature is positive and Increases in an approximately

logarithmic fashion with temperature such that a d3i value of 10 pC/N at

20°C becomes 14 pC/N at 50°C. The transducer calibration should therefore

include a correction factor for the effect of ambient temperature.

In the foregoing discussion, it has been assumed that the strains imposed

upon the piezoelectric element of the transducer are homogeneous. Additional

effects associated with real charge (i.e., charge Injected during the poling

process that becomes trapped in the polymer and is therefore present after

poling) are possible if the strains are inhomogeneous [7,8]. Such effects

are not considered explicitly in this report.

3.1.2 Eteatriaal Response - The piezoelectric response of a polymer sheet

with electrodes on opposite surfaces can be measured with a charge amplifier

or a voltage amplifier. A charge amplifier measures the charge wh1,ch flows

in an external circuit to neutralize the stress-induced charge Q appearing

on the electrodes. In effect, measurements made with a charge amplifier

measure the short-circuit charge in that the electrodes are maintained at

the same potential. A voltage amplifier with sufficiently high input

resistance measures the open-circuit voltage V appearing across the

electrodes.
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From Gauss's law and the definition of the piezoelectric modulus g, it

follows that

Q = /eE • dA = -/egT • dA, (7)

where T is a general component of the stress tensor, E and g are components of the dielectric and piezoelectric tensors appropriate to the stress

component T, and where the integration is to be carried out over the surface

A of the piezoelectric sheet. In the general case, all components of the

T- tensor contribute to Q.

For interface pressure measurements, the primary stress component is T33,

the normal stress in the 3-direction. The response associated with T33 is

a scalar quantity represented by Q33, which is proportional to /T33 • dA,

which is the total normal force, F3, applied to the sensitive area. Thus,

we have Q33 = -e33g33F3, and corresponding voltage (a scalar quantity)

represented by V33 = -e33g33F3/C.

The capacitance (C) in the above expression includes the capacitance of

the piezoelectric sheet and other capacitances, such as cable capacitances,

present in the measuring circuit. If the stray capacitances are neglected,

and the sheet capacitance is approximated by the parallel -pi ate formula,

C = eA/t, where A is the area and t the thickness of the active part, the

voltage V33 becomes

V33 = -g33tF3/A = -g33tPav» C8)

where Pgy - F3A is the average pressure over the sensitive area of the

sheet. Thus given arbitrary distribution of normal pressure acting on the

piezoelectric area A, Q33 is proportional to the force, and V33 to the

average pressure.

For a bilaminate transducer with two sheets connected electrically in

parallel and mechanically in series, the charge responses of the two

component sheets add. The voltage response of the transducer is that of

each sheet, assuming that the sheet responses are the same. If they are

not, the transducer voltage response is equivalent to the average of the

sheet responses.

As the resistivity of PVF2 before and after poling is of the order of

^0^^Q, ' cm, the leakage resistance of a polymer sheet will be very high.

In the case of a 1 -cm-diameter disk, the resistance is of order 10^^J2.

With a dielectric constant K of approximately 10, the capacitance will

be approximately 1 nF. Hence the source time constant will be of order

100 s. With suitable amplifiers, quasi-static pressure measurements are

thus possible. With ordinary a-c charge or voltage amplifiers, the measured response will have a low-frequency roll -off set by the instrumentation rather than by the polymer transducer.
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The frequency response 1n the audio range and beyond will depend on the

nature of mechanical resonances. The thickness -compress Ion resonance Is

In the 1 MHi range, but other modes such as membrane-extension modes may

have constraint-dependent resonances at much lower frequencies.

3,1.3 Effeate of Membrane Streeeea - In those applications In which a transducer Is mounted on the surface of a compliant body and adheres to

the surface during Impact with another body, the transducer active element

may be subjected to stretching and bending, in which cases membrane stresses

will be generated. Membrane stresses can result in significant contributions

to transducer response because relatively small membrane forces produce

large membrane stresses in thin transducer elements. For example, in the case of 1-cm-diameter element 25-ym (0.001-in) thick, the area resisting

membrane forces is 300 times smaller than the area resisting compressive

forces across the sheet due to the external pressure. Thus, the charge

outputs resulting respectively from pressure-related compressive forces

and from stretching forces will be comparable if the stretching force is

150 times smaller than the compressive force, assuming d33 = 2d3i.

3.1.3.1 Consider first the case of flat impacting surfaces. The impactinduced strains occurring within the impacting bodies along the impact

interface where a pressure transducer is located will tend to have components parallel to the interface, with magnitudes in roughly the same proportion to the magnitude of the component normal to the interface, as Poisson's ratio. It follows that if the impacting bodies do not have

compliances and values of Poisson's ratio identical to those of the transducer material, additional voltage contributions V31 = Q31/C and V32/C will

be present in the transducer output and will be respectively proportional

to d3iT22 and d32T22, where Tn and T22 represent mutually perpendicular

membrane stresses. If the impacting bodies have a common compliance which

is much greater than that of the transducer, then there will be a tendency

for the deforming bodies to impart tensile membrane forces to the transducer through frictional forces, or through the bonding material if one

is used. The signs of V31 and V32 will be the same as that of V33 since

these voltages arise from stresses tending to reduce the thickness of

the transducer. As frictional forces on the surfaces of the transducer

are difficult to avoid, it may be worthwhile to use lubrication as a means of reducing the coefficient of friction to the lowest possible value and

of ensuring that V33 » V3i, V32.

3.1.3.2 Case of imparted single curvature. Single curvature is imparted

to a transducer mounted on a compliant body when a relatively hard cylindrical object impacts the body (the direction of motion is understood .to be

normal to the surface of the body before impact, with elements of the

impactor cylindrical surface normal to the direction of motion). Membrane

forces again will be generated. If bending occurred with negligible

frictional forces present over opposite surfaces of the transducer, the

neutral surface would remain midway across the thickness of the transducer.

The membrane-stress distribution would be antisymmetric with respect to
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the neutral surface. Assuming the same d^i (and d32) for the transducer

material on both sides of the neutral surface, the piezoelectric responses

from regions on opposite sides of the neutral surface should cancel to a first approximation. In the presence of frictional forces which are different on opposite surfaces of the transducer, bending would result in a displacement of the neutral surface, a net membrane stress, and a net

response to bending. The extent to which lubrication can reduce neutral

surface displacement during bending is best determined by experiment. A

transducer made with two piezoelectric elements, back-to-back, might have

an unbalance related to differences in the d3i and values of the

component elements, and hence could exhibit a response to bending, even if

the neutral surface coincided with the contacting surfaces of the component

elements. In this case lubrication would not eliminate the net bending

response even though it would tend to eliminate the net membrane stresses.

3.1.3.3 Case of imparted double curvature. Double curvature is imparted

to a transducer mounted on a compliant body when a relatively hard spherical

object impacts the body (the direction of motion is understood to be normal

to the undisturbed surface of the body before impact). Membrane stresses

are unavoidable, whether or not lubrication is used. To reduce the bending

response in such cases, it may be advantageous to reduce the area of the

transducer element. As the voltage output in response to pressure of a transducer element does not depend on sensing area, a negligible reduction

in voltage output will result, provided the stray capacitance is small

compared to the capacitance of the transducer element. The effects of

double curvature with and without lubrication are probably best determined

by experiment. A similar comment applies even more strongly for more

general compound curvature.

3.2 Transducer Construction

The following step-by-step procedure details the construction of a typical

polymeric pressure transducer. This procedure produces bi laminate transducers in lots of nine.

(1) Two rectangular sheets, 13 cm x 16 cm, are cut from a roll of capacitorgrade PVF2 sheet 25-ym thick.

(2) Each sheet of PVF2 is sandwiched between two sheets of glass. This

assembly is placed in an oven and is heat-treated at 130 ±10°C for

approximately two hours. This annealing treatment serves to reduce

permanent and severe dimensional changes during subsequent steps.

(3) On one side of each sheet (referred to as the electrical high side)

a mask-defined pattern of nine identical aluminum electrodes, as shown

in figure 1, is deposited by evaporation in a vacuum chamber. The

pattern is defined by an evaporation mask which is also shown in figure

1. Aluminum was selected as the electrode material because it is easy to

evaporate, adheres well to the polymer substrate, and has good electrical
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conductivity In th1n«f1lii! form. Each electrode consists of a l-cm-d1ameter

circular area connected to a 0.2-cm-d1ameter circular dot by a strip 10.1-cm

long and 0.04-cm wide. The l-cm-d1ameter spot defines the area which ultimately becomes active; the strip serves as an electrical lead, and the small

dot as a pad for later electrical connection to the center conductor of a low-noise cable. The nine electrodes are deposited side-by-slde, so that

the nine strip leads are parallel and 1.6-cm apart, while the l-cm-d1ameter

spots and the 0.2-cm-diameter pads form respective parallel linear arrays,

nominally 10 cm from each other. Approximately 0.2 ym of aluminum is

deposited, which results in a strip lead resistance of less than 100 fi. .

(4) On the opposite side of each sheet a strip electrode, 3-cm wide and

approximately 0.1 -ym thick, is deposited in line with the array of 1 -cm- diameter dots. During poling, this strip serves as a common electrical

ground electrode. Figure 1 shows how this strip is oriented.

(5) Each sheet, together with two strips of tin foil for electrical con- tact to the exterior, is then sandwiched between two insulating sheets of

250-ym-thiGk polyethylene terephthalate. One tin-foil strip contacts the common ground electrode, and the other contacts all nine high-side leads.

This assembly is mounted between the 23 x 23-cm platens of an hydraulic

hot press, and a load of approximately 40 kN (four-tonf gage reading) is

applied. The positive output terminal of a high-voltage d-c power supply

is connected to the high electrode, and the negative terminal is connected

to the ground electrode. The steel frame of the press and the negative

terminal of the power supply are connected to laboratory ground. A poling

voltage of 2000 ±50 V is applied, corresponding to a field of about 8 x 10^

V/cm across the polymer in the region defined by the l-cm-diameter areas. The PVF2 1s heated to a temperature of 120''C, as measured by a thermocouple

inserted between the insulating sheets, and cooled immediately thereafter

to room temperature. The heating part of the cycle takes approximately

20 min and the cooling part approximately 15 min. This procedure poles the

PVF2 selectively in the regions of' the 1-cm areas, and leaves the nine stripleads effectively inactive. Pressure is applied during poling to prevent

wrinkling of the polymer sheets under the combined effects of field and

temperature.

(6) After removal from the press, an aluminum shield electrode, 0.1-nm

thick, is deposited on the ground side of each sheet, extending the ground

electrode to cover nominally the entire surface of that side of the sheet.

To avoid depoling the nine activated areas during this evaporation, which

heats the polymer substrate, the part of the ground electrode used during

poling consisting of a 1.5-cm-wide strip opposite the set of l-cm-diameter

dots, and aligned with them, is masked off by a metal strip. Another strip,

also 1.5-cm wide, masks off another area, opposite the set of 0.2-cm-diameter

dots on which it is centered to provide a clear area for visual alignment of one sheet with another in a later step.
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(7) The high side of each sheet is then coated with a thin layer of

contact cement* by wiping the surface with a foam-rubber pad saturated

with a solution of contact cement diluted 5 to 1 with toluene. The

contact cement is allowed to dry at least 15 min to allow the solvent

to evaporate.

(8) Nine pieces of ZBO-ym-diameter, tinned-copper wire are cut to a length of 5 cm, and one end is flattened over a length of approximately

0.6 cm, by rolling the end in a bench-type rolling mill. The flattened

portions of the nine wires are coated with a thin layer of silver-bearing

epoxy and are laid on the nine high leads of one of the sheets, in a manner such that the flattened portion contacts the 0.2-cm-diameter dots

at the ends of the evaporated leads. A small drop of contact cement is

then applied to each wire immediately behind the flattened portion to

form a fillet for the round wire and to hold the wire in place on the

sheet.

(9) The two sheets are precisely positioned on separate, mating, vacuum- hold-down plates with the high, cement-coated, sides facing out. At the same time, they are stretched lightly to make them lie as flat as possible.

The plates are then mated so that the cement-coated sides are pressed

together to form a bi laminate assembly. Care must be exercised prior to

and during this step to insure that when the sheets are bonded, the pattern

of dots and leads on one sheet is in satisfactory alignment with the corre- sponding pattern on the other sheet, and that trapping of air bubbles is

minimized. The assembly is then placed in the hydraulic press and further

pressed under a load of approximately 250 kN (25-tonf gage reading).

(10) The bonded sheets are then cut to yield nine separate bi laminate

transducer elements. A 12-ym layer of unpoled PVF2 is then cemented

on each side of the elements, covering all but the small portion of the

shield electrode at the end where electrical contact is to be made.

These layers act as a protective coating to prevent damage to the shield

electrode.

(IT) The wire lead of each element is trimmed to leave approximately

0.3 cm protruding outside the polymer sheets. This lead is then soldered

to the center conductor of a female miniature bulkhead coaxial connector.

Care is taken not to damage the connection to the evaporated lead by

excessive soldering heat conducted by the wire.

(12) The exposed parts of the high lead between the connector and the end

of the transducer not covered by the shield electrode are potted in epoxy.

After the epoxy has hardened, electrical contact between the shield side

of the connector and the shield side of the transducer is made by applying

a thick coat of liquid, silver-bearing rubber, over the insulating epoxy

and the area surrounding it.

Considerable experimentation was conducted with various bonding agents.

Contact cement meeting Federal Specification MMM-A-130a has been

satisfactory.
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A well-made transducer has a high leakage resistance (usually greater than

10^* fl) and a capacitance of roughly 1 nF. The capacitance of the lead

between the active arta of the transducer and the coaxial connector contributes only about 10% of this capacitance.

3.3 Transducer Testing and Calibration

3,3*1 OuMing Prinoiptee - The preliminary transducer parameter used to

characterize performance Is pressure sensitivity. The pressure range of

interest is from nominally zero (or preferably slightly negative pressure)

to 1.4 MPa (200 psi), and the frequency range of interest from approximately 5 Hz to 10 kHz. However, in view of the transducer sensitivity to

membrane stresses as well as to pressure, it was felt that a pure-pressure

calibration would be of limited value unless an evaluation of all the

important contributions to transducer response was made. Further, the

evaluation should take account of conditions anticipated in crash studies,

in which bending of the transducer may occur in combination with compression.

Another guideline was that a transducer intended for use under impact conditions should be tested under impact conditions.

3.3.2 Teat and Calibration Methods Considered - The following quasi-static

and dynamic methods were evaluated in the process of selecting calibration

and test procedures:

(1) Static uniaxial compression produced by means of a small mechanical

press,

(2) Sinusoidal compression produced by means of a vibration exciter with

a rigid inertial loading mass (to generate periodic variations in

pressure),

(3) Sinusoidal hydrostatic pressure generated by a vibration exciter and

. a liquid column,

(4) Shock tests using a drop-testing machine, and

(5) Shock tests using a miniature shock tube.

Methods (1) and (4) were selected because they have the advantage over other

methods that they can produce pressures over the entire range of interest

(except for slightly negative pressures). In addition, measurements made

on the press and. the drop-testing machine were not significantly affected

by electrical noise or by 60-Hz pick-up. Methods using vibration exciters

available to the project could have achieved pressures only a small fraction

of the specified maximum and been useful over only the lower half of the

specified frequency range. [Exploratory measurements were made of the

frequency response using method (2). The absolute response at any given

frequency depended on the bonding agent used to hold the transducer to the

vibration-exciter table and the inertial mass to the transducer. The

regular use of a rigid bonding agent was precluded by the desirability

of recovering the transducer without damage.]
-nThe shock-tube methods were not considered after preliminary tests resulted

in anomalously high transducer outputs attributed provisionally to pyroelectric response and surface charging by ions carried in the compressed

gas.

3.3.3 Meohaniaal Press - Figure 2 shows the experimental arrangement of

the mechanical press. The transducer under test rests on the upper surface

of a cylindrical block with plane, parallel upper and lower surfaces. This

block is rigidly fastened to a commercial force transducer, which has a measuring range of -440 to +440 N (-100 to +100 Ibf). A flat-faced, cylindrical nylon rod 1.2 cm in diameter is placed over the transducer to cover

the entire 1-cm-diameter sensitive area. This rod serves as a mechanical

coupler between the polymer transducer and the ball-tipped drive screw.

In operation, the drive screw is manually advanced and withdrawn, varying

the uniaxial compression of the polymer transducer along its thickness

(i.e., along the 3-direction) . An x-y recorder plots the output of the

force transducer on the x-axis and the amplified output of the polymer

transducer on the y-axis. The amplifier used for most tests is an electrometer, and thus transducer charge output is the quantity normally

measured.

Figure 3 shows plots for two transducers. The pressure offset is due to

a preload applied to smooth out wrinkles in the transducer before the shorting [Switch of the charge amplifier is released. The slope of the curves,

which is not sensitive to initial charge or to initial pressure, is used

to obtain the pressure sensitivity of the transducer. This sensitivity is

reproducible from day to day to within a few percent. The range of sensitivity among a large number of transducers, however, was found to be

unexpectedly broad, as discussed in 4.1.

3.3.4 Drop Test

3.3.4.1 Figure 4 shows the overall experimental arrangement for the drop

tests. (The drop- testing machine shown in the photograph is a modification of the commercially available instrument used in this work. Modifications were carried out after the work described here was completed and

are therefore not described.) A commercial accelerometer, screwed to the

upper face of the dropping carriage, records acceleration as a function

of time for each drop. The accelerometer response is specified by the

manufacturer as 7.9 mV/^p over a frequency range of 5 Hz to 15 kHz. Figure

5 shows the selection of interchangeable rigid impactors which are fastened,

by means of bolts, to the lower face of the carriage. Each impactor is

designed to impart a given shape to the transducer under test during the

time at impact that interface pressure is generated between impactor and

the compliant pad fastened to the base of the drop tester. As the various

impactors have different masses, the total dropped mass depends on the

impactor used. Precise values for these masses are given in table 1.

The recording electronics consists of a two-channel transient recorder, a monitor oscilloscope, and an X-Y1-Y2 plotter. A charge-sensitive amplifier

was sometimes used between the transducer under test and the transient
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recorder. These Instrumpnts are shown in figure 4. In normal, operation,

the polymer output and the carriage accelerometer output are recorded

simultaneously. However, in order to relate the accelerometer signal to

the interface pressure for the various impactors, the penetration depth

of the impactor into the pad must also be recorded. This measurement is

performed separately with an eddy-current proximity sensor, which can be

positioned vertically and horizontally by means of a micrometer-driven

stage. In use, the sensor is positioned low enough so that the bottom

of the carriage cannot hit it at the lowest point of carriage travel.

Simultaneous records are made (using the transient recorder) of the outputs of the proximity sensor and of the accelerometer in a series of drops

in which the proximity sensor is raised in small increments until the

recorded signal indicates incipient contact. As figure 6 illustrates,

the slightest contact produces an easily resolved flat spot on the

proximity-sensor record, when the rms voltage becomes zero. The micrometer reading is recorded at this point and also at the point when the

impactor just comes into contact with the pad as the carriage is slowly

lowered by hand. The difference between the two readings provides the

peak penetration depth with a resolution of ±25 ym (±0.001 in). The

absolute error. is estimated to be no more than ±130 ym (±0.005 in). This

error is principally due to the inherent limited accuracy with which it is

possible to define initial contact between impactor and pad and the mechanical relaxation time of the pad after impact. The full recorded trace represents carriage displacement as a function of time. Because the penetration

depths chosen for tests (on the order of 1 cm) far exceed the linear range

of the proximity sensor (2 mm), the recorded trace is highly non-linear at

separations between carriage and proximity sensor exceeding a few millimeters.

To date, the main use which has been made of the simultaneous records

as a function of time of the outputs of the proximity sensor and

the accelerometer has been to ensure that peak acceleration occurred at

peak penetration. A similar comment applies to the simultaneous records

of the outputs of the polymer transducer and the accelerometer. Once it was determined that peak transducer output occurred at peak acceleration,

only peak values were analyzed in detail. The general features of the

acceleration levels and penetration depths for various impactors as a function of drop height are shown in figures 7 and 8 for a 2.5-kg (5.5-lb

mass) carriage and for the flat-surfaced half-sine pad supplied by the

manufacturer. This pad was used only in the earlier work, because its

construction (three layers of different thicknesses with two different

compliances) unnecessarily complicated the theoretical analysis used to

relate the dynamic quantities measured to the interface pressure developed.

This pad was subsequently replaced by a homogeneous, small -pore, foamrubber pad, which also had a flat surface. Time limitations did not permit

a complete set of measurements to be taken for this pad. The method of

mounting the polymer transducer to the pad, which normally involves a few

layers of double-sided adhesive tape, affects the detailed mechanical

response of the pad (as manifested in the measured penetration depth) for

small drop heights which proved useful. Because of the presence of factors

affecting the measurement, such as those introduced by the transducer
-13-

mounting, measurements for a given transducer normally all were made under

the same conditions and during the same period. Drop height could not be

varied arbitrarily because, for a given pad and impactor, the drop height

had to be adjusted so that the penetration depth was smaller than the

impactor radius of curvature but deep enough (1) to impart the curvature

of the impactor to the entire sensitive area of the transducer under test

and (2) to develop interface pressures in a realistic range.

3,3.4.2 Drop-Test and Calibration Procedure - The following test and

calibration procedure was devised to characterize the dynamic response of

the polymer transducer when bending with single curvature occurs in com- bination with compression. The procedure involves two series of tests,

normally carried out at constant drop height.

For each series, the imparted radius of curvature is varied systematically,

through the use of one flat impactor and either two or three cylindrical

impactors. The first series is run with the transducer mounted flat on the

pad between two sheets of polytetrafl uoroethyl ene , with ethylene glycol used

as lubricant. The second series is run identically, except that the transducer is turned over.

The difference between the outputs of the transducer in the face-up and

face-down tests, which was found to vary greatly among transducers, is

interpreted as the bending-induced response of the transducer related to

unbalance in the piezoelectric properties of the two component sections

of the piezoelectric element. This difference in outputs was found to

decrease with increasing radius of curvature at constant drop height.

The average of the face-up and face-down outputs is interpreted as the

transducer pressure response with an additive term resulting from tension

(which causes the polymer to stretch in the direction normal to the axis

of the cylindrical impactor). This average value also decreases with

increasing radius of curvature at constant drop height. The observed

decrease results from both a decrease in interface pressure, as the theoretical analysis of 3.3.5 shows, and a decrease in the magnitude of the

tension term. Figure 9 shows illustrative plots of peak output signals

of both transducer and accel erometer as a function of inverse imparted

radius of curvature.

In principle, a similar test and calibration procedure could be performed

to characterize the dynamic response of the transducer when bending with

double curvature occurs in combination with compression. Such tests would

require spherical, rather than cylindrical, impactors with different radii

of curvature. These impactors are available, as well as the theoretical

analysis required to determine the interface pressure. However, time did

not permit extensive tests to be carried out. One test was conducted to

compare the results for a spherical impactor with a large radius to the

results for a flat impactor.
-14-

2.2.5 Theoretiaal Analysis for Interfaae Pressure in Drop Tests - The

theoretical analysis given below develops relationships between interface

pressure and the two measured dynamic variables (the acceleration and maxi- mum penetration depth) for three impactor-face geometries: flat, spherical,

and cylindrical, as shown in figure 10.

For the analysis, the impactors in figure 10 are assumed to have penetrated

to maximum depth. The penetration depth d refers to the penetration depth

at the center of impact. The interface boundary is assumed to be a circle

of radius a for the flat impactor, a circle of radius r^^g^^ for the spherical

impactor, and a rectangle of dimensions Xp^^^ by li for the cylindrical

impactor. In the case of flat and spherical impactors, the interface pressure is P(r), a function of position coordinate r of the set of cylindrical

coordinates { y, r, (f) } with the y-axis pointing in the vertical direction.

In the case of cylindrical impactors, the interface pressure is P(x), a function of position coordinate x of the set of rectangular Cartesian

coordinates { x, y, z } with the y-axis again pointing in the vertical

direction, which is perpendicular to the generator of the cylindrical sur- face of the impactor. The above coordinates are spatial coordinates as opposed to the coordinates { 1, 2, 3 } used in the discussion of piezoelectric properties, which are material coordinates.

The theory is based on the underlying assumption that the interface pressure

P(r) or P(x) at any point on the interface is proportional to the impactor

penetration depth 6(r) or 6(x) at the same point measured vertically from a reference plane formed by the upper surface of the pad before impact. The

assumption represents an approximation which reduces the otherwise difficult

actual wave-mechanical problem to a problem which is solvable in closed form.

The actual pad-stress-distribution problem is difficult even if wave effects

are neglected. In that case, the problem reduces to a three-dimensional

elasticity problem, the solution of which requires specification of boundary

conditions over the entire surface of the pad, including the interface. The

specification of realistic strain boundary conditions over the interface is

greatly complicated by poor knowledge of the degree of involvement of static

and sliding frictional forces. Hence the boundary conditions are most poorly

known in the region where the stress distribution is sought.

From the starting assumption, it follows that

P(r) = K 6(r) for flat or spherical impactor, or (9)

P(x) = K 6(x) for cylindrical impactor, (10)

where the proportionality factor K (different for each impactor) is independent of 6 for a particular d. An explicit dependence of K on d is not

excluded. The numerical value of K is expected to depend not only on properties and dimensions of the pad material, such as E/Iq where E is an elastic modulus and Iq the thickness of the pad, but also on the impactor

geometry, which determines the strain distribution within the pad and

hence the degree of material containment against flow in the horizontal
-15-

plane. For example, the pad is expected to appear softer to a curved

impactor than to a flat impactor because the pad material near the center

of impact has more freedom to flow radially outward in the former case

than in the latter case. In this theory, it is not necessary to know the

detailed relationship of K to pad properties and impactor geometry because

K can be expressed in terms of experimentally measured quantities as discussed below.

The penetration function 6(r) or 5(x) depends on the maximum penetration

depth d, but otherwise is a purely geometric function determined by the

impactor geometry. Referring to the three cases in figure 10, the penetration function is

6(r) = d for the flat impactor, (11)

6(r) = d - R + /R^ - for the spherical impactor, and (12)

6(x) = d - R + /R-^ - x^ for the cylindrical impactor, (13)

where d is the maximum penetration depth and R the radius of curvature of

the impactor and deformed pad. The interface pressure or pad-reaction

pressure is then

P(r) = Kd flat, (14)

P(r) = K (d - r + /R2 - rz ) spherical, and (15)

P(x) = K (d - r + /R2 - x2 cylindrical. (16)

The integral over the interface area of the vertical component of the

differential contribution to the pad reaction force dF.y = (P_ • dS_)_y

gives the total pad reaction force F_y, which, by. Newton's law of

inertia, is the product of the dropping mass m and the acceleration y.

This integral is equivalent to the integral /P dSh » the horizontal

projection of the differential element of area dS. Hence,

F_y = 2Tr P(r) r dr = my flat, (17)

F_y = 2tt J^^^^ P(r) r dr = my spherical, and (18)

F.y = 2li /J^max p(x) dx = my cylindrical, (19)

where a and r^^^ are the radii of the impact circles for the flat case

and for the spherical case, respectively, and where Xmax is half the

maximum value of the x-dimension of the impact rectangle and li its

other dimension for the cylindrical case. By geometry, r^^v = ^m^v

' ;2Rd -

'"^^ "'^^

The quantities d and y are measured dynamic variables. Substituting for

P(r) and P(x), performing the integration, and solving for K, it follows

that

'-SS fl^t. (20)
-16-

spherical , and (21

2. {(d » R) + ^CR3 - (R2 - r^^^) 3/2]}

K

= M.

li CR2 sin-i (R - d) x^^^] cylindrical. (22)

The maximum pressure sampled by a transducer with dimensions small compared

to the imparted radius of curvature is approximately P(0), the pressure at

the center of the impact surface (i .e, , at r * 0 or x * 0). Combining the

results of (14), (15). and (16) and (20), (21), and (22) evaluated at r = 0 or X « 0, yields:

P(0)=^ flat, (23)

P(0) = ^

^

spherical, and (24)

2Tr {(d - R) J^+^[r3 . (R2 . r^^^)3/2]}

P(0) J^d

li [R2 sin-1 (R - d) x„, 1 cylindrical. (25) K mdX

The formal range of validity of the last two formulas is that for which d/R <

1. However, in practice, the formulas are expected progressively to lose

accuracy as d/R approaches 1, because the membrane forces which have been

neglected have negligible vertical components only when d/R « 1.

Figure 11 shows the interface pressure at the center of the impact surface

as a function of the imparted radius of curvature for the case of cylindrical

impactors. These curves were obtained using (25) with the acceleration and

penetration-depth data of figures 7 and 8 and with the masses given in

table 1. The curves are shown in the range d/R < 1 but, as indicated above,

they are expected to be most realistic physically in the range d/R « 1. A

few constant-d/R contours are also included in the figure.

A comparison of figure 9 with figure 11 suggests that a large part of the

dependence on radius of curvature observed experimentally for the output of

the polymer pressure transducer may be attributed to a systematic variation

of the interface pressure. The dependence of the pressure on the impactor

curvature comes partly from variation of the interface contact area, and

partly from variation of the pressure distribution.

4. RESULTS AND DISCUSSION

4.1 Mechanical Press Test Method

Table 2 shows the d-c pressure sensitivity obtained in the mechanical press

for 20 polymer pressure transducers in order of increasing sensitivity. (The
-17-

first four entries in table 2 are representative of the sensitivity levels

obtained early in the program, while the last ten entries represent sensitivity levels achieved toward the end of the program.) The d-c sensitivity

is expressed by the modulus d33*, which is defined as the induced charge per

unit normal force applied to the sensitive area of the transducer, with the

top and bottom surfaces of the transducer constrained in a manner specific

to the apparatus and to the transducer-mounting method. Apparatus details

are specified in 3.3.3. The mounting method consisted of placing each

transducer between and in direct contact with the nylon coupler on one side

and the aluminum flat on the other, taking care that the coupler face con- tacted the entire sensitive area of the transducer. No lubrication or bonding agent was used. In obtaining d33*, it was assumed that the piezoelectric

region is confined to a circle of 1-cm diameter. In fact, fringe effects may

cause the effective electrode to extend 1 or 2 mm beyond the 1 -cm-diameter

circle. No correction was made for fringe effects. The highest d33* listed

in table 2 is approximately twice as great as the maximum d33 values quoted

elsewhere in this report. This is expected because the two sections of a given bilaminate transducer are mechanically in series and electrically in

parallel, and hence their charge outputs add. More quantitative comparisons

between d33* and 2d33 are not appropriate since the relationship between

the two quantities, which is not general, was not worked out for the specific

conditions of the press-test. Significant differences can be expected

between d33*/2 and d33, since d33*/2 is measured on a specimen in the form

of a sheet, while the conventional method of measuring d33 employs specimens

in the form of a needle.

4.2 Drop Tests

4.2.1 Single Curvature Imparted to Transduaer - Table 3 summarizes the

results of a series of drop tests performed on a polymer transducer with a large sensitivity to bending. The transducer was sandwiched between two

thin polytetrafl uoroethylene sheets with ethylene glycol as lubricant.

The sandwich was mounted flat on a homogeneous foam-rubber pad by means

of double-sided adhesive tape. All drops were done at the same nominal

drop height of 25 cm (10 in). Three impactors were used, a flat and two

cylindrical impactors, giving radii of curvature of °°, 2.54, and 1.27 cm

1.00, and 0.50 in), respectively. The impactor with the smallest radius

of curvature.of -0.63 cm was found to produce a d/R of approximately unity

at the drop height of 25 cm (lo in) and hence was not used. The measured

quantities, transducer outputs with side 1 facing up and with side 2 facing

up, acceleration, and penetration depth, have been plotted as functions of

inverse imparted radius of curvature R--^ in figure 9.

The "footprint area" shown in the table is the area of the horizontal projection of the interface area obtained by calculation for each impactor

using the measured penetration-depth. The "average pressure over footprint area"_ is obtained by dividing the decelerating force supplied by

the pad (my) by the footprint area. The "calculated pressure at center

of footprint" is the pressure obtained using (23) and (25). The
-18-

"calculated pressure sensitivity" is the sensitivity obtained by dividing

the measured charge output by the calculated pressure. A transducer which

is highly responsive to normal pressure and weakly responsive to membrane

stresses would have a pressure sensitivity which is insensitive to the

imparted radius of curvature. A bi laminate transducer with component

sections matched elastlcally and piezoelectrically would have the same response whether side 1 or side 2 is facing up.

The differences In sensitivity between the side 1-up and side 2-up cases

reveal the high degree of mismatch in the elastic and piezoelectric properties, or both, of the component sections of the particular transducer tested.

This result points up the need for careful matching of component sections as

a part of the transducer construction procedure.

The fact that a sensitivity difference Is found between the side 1-up and

side 2-up cases with the flat impactor is believed to Indicate the existence of a residual contribution to the output related to membrane forces.

This observation indicates that, even when the flat impactor is used In

conjunction with lubrication, the dynamic stress distribution imposed to

the transducer Is more complicated than purely uniaxial.

The calculated pressure sensitivity as a function of imparted radius of

curvature (last row of table 3) remains constant to within approximately

25 percent while the radius is varied as shown. This result Is in

contrast with the transducer output, which has a much stronger dependence

on Imparted radius (rows 3 and 4).

With due consideration given to possible inadequacies In the theory used

to obtain the Interface pressure, it appears that the transducer ouptut

for the geometries tested follows rather closely the Interface pressure,

which is very sensitive to the impactor geometry. Other measurables,

such as the impactor/carriage acceleration, are not so closely related

to the interface pressure. The remarks above, of course, underscore the

need for a pressure transducer at each point of interest in a crash study.

4.2.2 Spherical Curvature Imparted to Transducer - Table 4 compares the

results of drop-tests performed with a flat and with a spherical impactor

on a polymer transducer with negligible mismatch of its component sections.

This transducer also had much greater piezoelectric activity than the

transducer used in obtaining the data in figure 9 and table 3. The

transducer mounting conditions and drop height are the same as those

given as part of the preceding discussion of table 3. Because the voltage output rather than the charge output was measured in this case, the

outputs in table 4 are expressed in volts.

The last row of table 4 shows calculated sensitivities for the flat and

curved impactors to be in agreement within 7 percent. This agreement

suggests that the measured significant difference in output between the

flat and curved case (row 2) reflects the difference in interface pressure

in the two cases and not effects associated with Imparting double curvature.
-19-

The exploration of a range of imparted spherical curvature was left for

future study.

There is a problem in performing tests with much greater spherical curvature, which is that wrinkling of the surface of the transducer occurs,

particularly around the edges. Such wrinkling was found to occur with

2.5-cm (1-in) radius ball-impactors. Since the theory developed in this

report assumes that the shppe imparted to the transducer is the shape of

the impactor, the theory is applicable only for moderate imparted

spherical curvature.

5. SUMMARY AND RECOMMENDATIONS

A polymer-sheet pressure transducer, operated in the thickness-compression

mode, has been developed for impact interface-pressure measurements. The

selected design is of bilaminate construction. Two piezoelectric polymer

elements are bonded high side to high side in such a manner that the inner

faces in mutual contact form a common positive electrode and the outer

faces form a negative shield electrode. To make electrical connection to

the transducer element, the positive electrode is connected to the center

conductor of a coaxial cable and the shield electrode is connected to the

cable shield, which is normally grounded. This construction is appropriate

for the very high source resistance of the transducer, in that it provides

electrical screening of the sensitive part of the source circuit while

permitting connection to a single-ended signal line compatible with the

input circuitry of commercially available high-input-impedance amplifiers.

As the two transducer elements are mechanically in series by virtue of the

bilaminate construction, but electrically in parallel, the charge outputs

of the component elements add, but the voltage outputs do not.

5.1 Transducer Sensitivity

The sensitivity of the polymer transducer to pressure satisfies the sponsor's

requirements

The piezoelectric constant d33 has been increased from about 5 pC/N (22 pC/lbf)

to about 15 pC/N (22 pC/lbf) by means of improved poling techniques. This

increase, translated into transducer pressure sensitivity, represents an improvement from 1.5 to 4.3 yV/Pa (10 to 30 mV/psi) for 25-ym-thick PVF2.

5.2 Transducer Frequency Response

The frequency response of the transducer also satisfies the requirements given

by the sponsor for the intended interface-pressure measurements. The lowfrequency roll -off point is set by the anplifier to be around 1 Hz, while the

high-frequency response should be primarily limited only by the thicknessresonance frequency, which is estimated to be a few megahertz. Deviations

from a flat response in the range of pressures of interest for crash studies

are expected only if imperfections in the transducer piezoelectric material
-20-

or transducer construction introduce lower frequency resonances or lower

the thickness-resonance frequency, or if the transducer is tested or used

in a manner which excites modes other than the thickness-compression mode.

5.3 Test Methods for Measuring Transducer Output

Two basic test methods for measuring transducer output have been developed.

The first method uses a mechanical press for static calibration of transducer output under conditions approximating uniaxial compression. The

second method uses a drop- test machine for measurement of transducer output

under conditions in which pressure and flexure are simultaneously applied.

Because of time limitations, only the effects of imparting single curvature

to the transducer at impact have been studied in detail.

The results of drop-tests with cylindrical impactors of various radii of

curvature Indicate that membrane stresses can Introduce significant contributions to transducer output mixed with the output resulting from applied

pressure. However, these results also Indicate that If lubrication Is

used to reduce frictional forces between transducer and the compliant body

to which it is attached, extraneous outputs arising from membrane stresses

may be held to acceptably low levels in all but extreme cases.

5.4 Recommendations for Further Work

The following recommendations are presented for future work:

(1) The effects of spherical curvature imparted to the transducer during

impact should be investigated experimentally and theoretically with and

without lubrication. The imposition of spherical curvature to a nominally

flat transducer results unavoidably in the generation of a membrane stress

distribution, which will be specific to each impact. For this reason, it

should be advisable to explore a range of experimental conditions closely

simulating particular classes of conditions expected during motor-vehicle

crashes.

(2) The effects of transducer size should be investigated. Theoretical

considerations indicate that the effects of bending, both with single and

spherical curvature, will become less important as the size of the transducer

is reduced.

(3) Compound piezoelectric-element designs should be explored such as a transducer with two separate concentric sensitive areas. In the form of a central dot and an annul us surrounding the dot. The separate sections of

such transducers would have different sensitivities to bending and should

allow estimates to be made of the accuracy of the pressure measurements

in the presence of bending stresses.

(4) An evaluation of the polymer pressure transducer should be made for

applications involving fluid pressures, to permit measurements such as intracranial fluid pressure measurements during impact.
-21-

6. REFERENCES

[1] Cohen, J., and Edelman, S,, Piezoelectric Effect of Oriented Polyvinylchloride and Polyvinyl fluoride, J. Appl . Phys. 4^, 3072-3074 (July 1971).

[2] Contracts FH-11-72888 and DOT-HS-031 -2-382.

[3] Contract DOT-HS-024-2-490.

[4] Berlincourt, D.A., Curran, D.R., and Jaffe, H., Piezoelectric and

Piezomagnetic Materials and Their Function in Transducers, Book,

Physical Acoustics, Vol. 1, Part a., Ed. W.P. Mason, pp. 169-270

(Academic Press, New York, NY, 1964).

[5] Fukada, E., and Takashita, S., Piezoelectric Effect in Polarized

Poly (vinyli dene Fluoride), Japan, J. Appl. Phys. 8_, p. 960 (1969).

[6] Kawai , H., The Piezoelectricity of Poly(vinylidene Fluoride), Japan,

J. Appl. Phys. 8, pp. 975-976 (1969).

[7] Hayakawa, R., and Wada, Y., Piezoelectricity and Related Properties of

Polymer Films, Book, Advances in Polymer Science, Vol. 11, Ed. H.J. Cantow,

et al^ pp. 1-55 (Springer-Verlag, New York, NY, 1973).

[8] Nakamura, K. , and Wada, Y., Piezoelectricity, Pyroelectricity , and the

Electrostriction Constant of Poly (vinyl idene Fluoride), J. Polymer Sci.

A-2, 9, pp. 161-173 (1971).

USCOMM-NBS-DC
-22-

Table 1

Drop Masses for 2.5-kg Carriage

Impactor Impactor Total Mass Dropped

Identification Geometry (kg)

A Flat 2.562

B Spherical, with radius of 2.592

curvature of 25 cm. This

impactor was furnished with

the drop-tester.

C Cylindrical , with radius of 2.53G

curvature of 2.5 cm (1.0 in).

D Cylindrical, with radius of 2.336

curvature of 1.25 cm (0.50 in).

E Cylindrical, with radius of 2.382

curvature of 0.62 cm (0.25 in).
-23-

Table 2

Six-Trial Pressure Sensitivity, d33, of 20 Transducers

as Measured with the Mechanical Press Apparatus

Mean (pC/N) Sample Standard

Deviation (pC/N)

5.2 0.1

5.3 nU.I1 5 4 n 1 5 6

15 1 U . J

20.6 0.5

22.8 0.6

23.5 1.1

24.5 2.1

25.2 0.4

25.3 1 .2

26.1 0.4

26.3 0.6

26.5 0.9

26.6 1.1

27.0 0.8

27.2 0.7

27.7 0.6

28.2 0.5

28.9 0.8
-24-

Table 3

DROP TEST CONDITIONS AND DATA FOR SINGLE POLYMER PRESSURE TRANSDUCER

EVALUATED WITH ONE FLAT AND TWO CYLINDRICAL IMPACTORS

Quantity

Peak Acceleration {g^)

Force

Transducer Output (pC) side 1 side 2

Peak Penetration (cm)

(in]

Striker Length (cm)

[in]

2 Footprint Area (cm J

. [in2]

Average Pressure over Footprint Area (kPa)

[psi]

Calculated Pressure at Center

of Footprint (kPa)

[p^i]

Calculated Pressure Sensitivity

side 1 (with negative tension

contribution) (pC/Pa)

[pC/psi]

side 2 (with positive tension

contribution) (pC/Pa)

[pC/psi]

average of sides 1 & 2 (with no tension contribution)pc/Pa) 5.31x10

[pC/psi] [3.66]

-4

6.82x10

[4.70]

-4

Impactor Used

Flat Cylindrical

Kduius ^.04 cm Kaoius \ ,c7 cm [1.00 in] [0.500 in]

63.4 62.0

2.26 1.57 1.42

[509] [354] ^ [319]

157 290 340

230 670 1010

0.472 0.762 0.838

[0.186] [0.300] [0.330]

8.89 8.81

[3.50] [3.47]

62.1 24.6 15.2

[9.62] [3.807] [2.354]

365 640 917

[53. OJ [92.8] [133]

365 705 926

[53.0] [102] [134]

4.29x10" 4.11x10"^ 3.67x10"^

[2.96] [2.83] [2.53]

6.31x10' 9.49x10"^ 1.09x10"'^

[4.35] [6.54] [7.53]

7.25x10

[5.00]

-4

English unit equivalents are given in brackets.
-25-

Table 4

DROP-TEST CONDITIONS AND DATA FOR SINGLE POLYMER PRESSURE TRANSDUCER

EVALUATED WITH FLAT AND SPHERICAL IMPACTORS

Nominal drop height - 25 cm [10 in]

Nominal dropped mass - 2.3 kg

Gage capacitance - 913 pF

Cable capacitance - 132 pF

Impactor Used

Flat

Quantity

Peak Force (kN) 2.26

[Ibsf]* [508]

Peak ^age Output (V) 0.861

Peak Penetration (cm) 0.447

[in] [0.176]

2

Footprint Area (cm ) 62.1

[in2] [9.62]

Average Pressure over Entire

Footprint Area (kPa) 364

[psi] [52.8]

Calculated Pressure at

Center of Footprint

(kPa) 364

[psi] [52.8]

Calculated Voltage Pres- sure Sensitivity

(mV/Pa)_ 2.36x10

[mV/psi] [16.3]

Calculated Charge Pres- sure Sensitivity

(pC/Pa) 2.47x10

[pC/psi] [17.0]

-3

-3

Spherical

(with nominal radius of

curvature of 23 cm [9

2.26

[508]

1.46

0.579

[0.228]

62.1

[9.62]

364

[52.8]

583

[84.6]

2.51x10"

[17.3]

2.62x10

[18.1]

-3

*English unit equivalents are given in brackets.
-26-

Figure 1: Steps in polymer pressure transducer construction. At THE top is the MASK USED TO DEFINE THE AREAS OF THE POLYMER SHEET THAT ARE COATED WITH ALUMINUM IN THE VACUUM EVAPORATOR TO FORM NINE POSITIVE ELECTRODES.

The HAND HOLDS A POLYMER SHEET WITH POSITIVE ELECTRODES

DEPOSITED. At the BOTTOM IS A POLYMER SHEET WITH POSItive electrodes and a single common negative electrode.

The negative electrode faces up. The procedure used

TO BOND together TWO SHEETS WITH ELECTRODES TO FORM

NINE BILAMINATE TRANSDUCER ACTIVE .ELEMENTS IS DESCRIBED

IN THE TEXT. UnDER THE HAND ON THE LEFT IS A BILAMINATE

TRANSDUCER WITH A LEAD WIRE ATTACHED TO THE TWO POSITIVE

ELECTRODES. In THE MIDDLE, THE TRANSDUCER HAS A MINIATURE COAXIAL CONNECTOR ATTACHED. At THE RIGHT IS A FINISHED TRANSDUCER.
-27-

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-28-

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a; CO o LU

Li- Q. LU O

_1 GO

CM

(3U| indinO 39dVH3

LUo CO

q; CO O LU

LU <

< <X

CO o

=> LU

CO s: LU LU > X

CO

O

LU

Qc: o

< \ I- c_)Q. <

C5

IXJ

CD

LO

CO< oo
-29-
-30-
-31-

0 20 40

TIME (ms]

Figure 6: Proximity sensor output (V) as a function of time

(upper panel) and ACCELEROMETER output (V) AS A function of time (lower panel) for 2,5-kg (5.5-lb

mass) mass carriage with flat impactor at 13-cm

(5 in) drop height. Recorded traces are shown,

At the right of the upper panel is a calibration

scale for the separation between target and

proximity sensor (cm).
-32-

DROP HEIGHT (in)

5 10

"1

\—rn

\—

—170

B

5 10 15 20 25

DROP HEIGHT (cm)

Figure 7: Peak accelerometer output (V) as a function of drop

HEIGHT (cm and IN) FOR FIVE IMPACTORS/ A-E. ImPACTORS

are identified in the caption of figure 5 and in table 1. The carriage mass was 2,5 kg (5.5 lb mass); a flatsurfaced HALF-SINE PAD WAS USED ON THE ANVIL, AS DESCRIBED

IN THE TEXT, A CALIBRATION SCALE IN UNITS OF PEAK ACCELERATION (^p) FOR THE ACCELEROMETER OUTPUT IS GIVEN AT THE

RIGHT,
-33-

DROP HEIGHT (in)

0 5 10

DROP HEIGHT (cm)

Figure 8; Penetration depth (cm and in) as a function of drop

HEIGHT (cm and IN) FOR FIVE IMPACTORS/ A-E. ImPACTORS

are IDENTIFIED IN THE CAPTION OF FIGURE 5 AND IN TABLE 1. The CARRIAGE MASS WAS 2,5 KG (5.5 LB MASS);

A FLAT-SURFACED HALF-SINE PAD WAS USED ON THE ANVIL/

AS DESCRIBED IN THE TEXT.
-34-

INVERSE RADIUS OF CURVATURE (in 'j

0 1 2 3 4 S

INVERSE RADIUS OF CURVATURE (cm")

Figure 9: Peak polymer pressure transducer outpuT/ curves Ql,

Q2, AND Q (nC); absolute magnitude of peak ACCELERATION/ CURVE y {g^)i AND PEAK PENETRATION DEPTH/

CURVE d (cm) as FUNCTIONS OF INVERSE IMPARTED RADIUS

OF CURVATURE (cm) / FOR CYLINDRICAL CURVATURE. ThE

CURVES HAVE BEEN FITTED BY EYE TO THE EXPERIMENTAL

POINTS SHOWN. Ql REPRESENTS TRANSDUCER OUTPUT WHEN

SIDE 1 IS FACING UPWARDS/ Q2 REPRESENTS TRANSDUCER

OUTPUT WHEN SIDE 2 IS FACING UPWARDS, AND Q.IS THE

AVERAGE OF Ql AND Q2 . ThE DATA REFER TO A SPECIFIC

TRANSDUCER TESTED WITH SPECIFIC DROP-TEST CONDITIONS/

AS DESCRIBED IN 4.2.1.
FIv3ijR[ 13: Impact geometry for (a) flat impactor, (b) spherical

IMPACTOR, AND (c) CYLINDRICAL IMPACTOR, ThE MEANING

OF THE LABELS IS DESCRIBED IN THE TEXT,
-36-

INVERSE IMPARTED RADIUS OF CURVATURE (in

8x10

100 52

50

</9

INVERSE MPARTED RADIUS OF CURVATURE (cnf^)

FIGURE 11: Peak impact pressure (Pa and psi) as a function of the

INVERSE imparted RADIUS OF CURVATURE (CM"1 AND IN'l),

OF THE CYLINDRICAL IMPACTOR, FOR THREE DROP HEIGHTS.

The CURVES were plotted from calculated values, as DESCRIBED IN THE TEXT, CURVE A IS FOR A DROP HEIGHT

OF 5.2 cf", (2.0 in); B, 12.7 cm (5.0 in); and C, 25.4 cm

(10.0 in). Constant d/R contours (lines of constant

PENETRATION DEPTH/RADIUS OF CURVATURE) ARE ALSO SHOWN.
HSS.114A (REV. 7-73)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBSIR 75-740

2, Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Piezoelectric Polymer Transducer for Impact Pressure

Measurement

5. Publication Date July 1975

6. Performing Organization Code

7. AUTHOR(S)

Aime S. DeReggi

B. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 4253560

11. Contract/Grant No. DOT-HS-4-00835

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Office of Vehicle Safety Research and Development

National Highway Traffic Safety Administration

Department of Transportation

400 Seventh Street, SW, Washington, D.C. 20590

13. Type of Report & Period Covered

12/15/73-12/31/74

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most si^ificant information. If document includes a significant

bibliography or literature survey, mention it here.) Described are development efforts relating to the design, construction, and

calibration of a piezoelectric polymer transducer for the recording of pressure

transients developed over the interface between two bodies as a result of impact.

A bilaminate design was selected which uses electrically poled sheets of 25-ym

poly(vinylidene fluoride) as the active material. The intended primary response

of the transducer is to compression in the thickness direction, which is produced

by either hydrostatic or normal pressure; the transducer was also found to respond

to extension in the membrane direction. Individual-sheet activity in the thicknesscompression mode is approximately 15 pC/N, resulting in a bilaminate transducer

pressure response of 4.5 yV/Pa(30 mV/psi). Instructions for poling sheets and for

constructing transducers are given in detail. Static and dynamic methods for characterizing transducer output are described. In particular, in order to simulate

field conditions in which the transducer may bend or stretch, or both, during impacts,

a drop-test procedure with curved impactors has been devised and a theoretical analysis (simplified to the extent of considering the membrane-stress contribution

negligible) has been developed to yield the interface pressure.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semico/ons; Cal i brat ion; cons truc t i on ; impact; interface; piezoelectric

polymer; polymer; pressure; pressure transducer; theory; transducer.

18. AVAILABILITY ^Unlimited

I I For Official Distribution. Do Not Release to NTIS

I I Order From Sup. of Doc, U.S. Government Printing Office Washington, D.C. 20402, SD Cat. No. CU

1 ! Order From National Technical Information Service (NTIS)

Springfield, Virginia 22151

19. SECURITY CLASS

(THIS REPORT)

UNCL ASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

37

22. Price

USCOMM-DC 29042-P74