Development of a PVDF Pressure Gauge for Blast Loading Measurement

  • M. Arrigoni
  • F. Bauer
  • S. Kerampran
  • J. Le Clanche
  • M. Monloubou
Original Paper


We investigate the development of a sensor for dynamic pressure measurement. The sensor relies on a Bauer shock gauge of 25-μm thin Polyvinylidene fluoride (PVDF) film [AIP Conf. Proc 706:1121–1124, [21]. These gauges unfortunately require some skills to be integrated in an acquisition chain and the obtained results are strongly “experiment dependent.” In the presented work, the classical Bauer gauge has been adapted: the reproducible PVDF film is poled at high voltage, in electrical symmetrical response and reproducibility. The sensitive area is a 3 × 3 mm square. The gauge has been electrically shielded and overlaid with a heat conductive material. A 5-m long coaxial wire connects the gauge to a charge amplifier, allowing its connection to a deported oscilloscope. The output electrical charge of the PVDF gauge has been correlated with the pressure measured by calibrated PCB® sensors. Measured pressures are validated by an analytical approach and numerical simulations of the flow in the shock tube. A calibration curve can be deduced for pressures below 10 bar, values which are often met in blast loading situations. This customizable sensor is hence suitable and easy to use to measure the blast-reflected pressure on a flat material.


Shock tube Blast PVDF Pressure Sensor Measurement 


Explosions have become a major threat in occidental nations. Among these risks, accidental explosions within industrial plants [1] as well as improvised explosive devices against critical infrastructures [2] are the most deadly. In addition, to cause death and injuries of people in a large perimeter, they engender important mechanical loadings and damage surrounding structures. These effects are still not easy to predict by numerical modeling due to the size of the areas of interest, the complexity of structures, and the multiphysic aspects of the phenomena involved in explosions. In order to design infrastructures able to sustain the effects of explosions, it becomes then necessary to know more about explosive effects on reduced-scale geometry for a variety of scenario. Unified Facilities Criteria (UFC) [3] has been proposed by engineers and scientists [4, 5] but they are limited to simplified cases of buildings and explosive charges. A reliable approach would consist in using reduced-scale experiments but they require relevant blast measurement methods in order to reproduce a representative loading in terms of overpressure and impulse. A traditional approach consists in using piezoelectric sensors in flush mount in a pencil – or perch – to measure the time resolved measurement of the pressure profile of the incident blast wave, at full and reduced scale. Another approach consists in measuring reflection coefficient on a solid wall at reduced scale with the intention of having a trustable equivalent loading at full scale [6]. Among limitations encountered by experimenters performing full-scale and reduced-scale blast measurements, the inability to reduce the size of the active surface of the sensor, with respect to the curvature of the blast front, induces discrepancy. Another technical problem is to cope with the positioning of a matrix of sensors on a wall; it requires accurate drills for flush mounting on the model.

In order to overcome these difficulties, the work tackled in this study deals with the lab design of an easy-to-use blast sensor for the time-resolved measurement of the blast-reflected overpressure on a rigid wall. This sensor can be stuck and does not require any drilling of the model. So it can be considered as a low-cost acquisition and implementation solution, for reflected pressure measurement. The active surface can be as small as 1 mm2 and is adapted for small curvature of blast waves. This feature is especially convenient in small-scale experiments. Moreover, the bandwidth of the PVDF gauge is higher than 100 MHz while conventional piezoelectric sensors based on crystals offer less than 500 kHz. PVDF shock gauges are however very dependent of the experimental setup and must be physically and electrically implemented with care. This article shows an illustrative example of results that can be obtained by the use of these gauges. The gauge design relies on the use of ferroelectric polymers and is presented in “Ferroelectric Polymers.” The gauge has been tested in laboratory conditions in a shock tube at ENSTA Bretagne, which is presented in “Experimental Setup: Shock Tube.” Results are compared with a PCB® 113B21 sensor and shown in “Experimental Results.” A discussion about accuracy and reproducibility follows in “Discussion” before the conclusion.

Ferroelectric Polymers


Among ferroelectric polymers, PVDF and its copolymers with 20 to 50 mol% trifluoroethylene (TrFE) are known to exhibit scientifically interesting and technologically important electrical properties due to their polar structure [7, 8]. Nylon has been reported to exhibit similar properties [9]. The crystal structures of PVDF leading to these properties are summarized in Fig. 1, which shows the conformations of the alpha, beta, and delta phases.
Fig. 1

Schematic of three typical molecular conformations (all-trans, TGTG’, and T3GT3G’) of PVDF-based ferroelectric polymer (the gray atoms without any symbol are carbon)

As indicated in Fig. 1, PVDF is a partially crystalline linear polymer, whose carbon backbone is composed of the monomer [–CH2–CF2–], and has two dipole moments, one associated with the CF2 and the other with CH2. The crystal structures are critically dependent on the mechanical processes used in sample preparation. Melt cast films have the helical alpha form in which the conformation is transgauch (TGTG) and the chains are packed in an antipolar unit cell. By stretching, the alpha phase transforms to the beta phase in which the conformation is an all-trans (TT) planar zigzag arrangement with the dipole moments perpendicular to the chain axis. This beta form exhibits reversible, spontaneous polarization and is therefore the most useful ferroelectric phase. Under appropriate electrical poling, PVDF and its copolymers in the ferroelectric phase exhibit well-defined remanent polarization [10, 11, 12].

The beta phase is typically achieved from uniaxially or biaxially stretched films which typically range in thickness from 100 to 3 μm. The highest quality material is obtained with biaxial stretching with thicknesses of about 25 μm and recently with one-dimensional stretching of 18 μm.

The earliest electrical and most widely available process applied to pole PVDF films is the room temperature “Corona poling” method which can produce large area films for nominal applications which do not require high electrical quality. In such a large volume production method, quality and reproducibility are not desired.

For application and material studies requiring high quality and reproducibility, individual samples must be produced with well-defined electrical properties in a process which can control amplitude, duration, and history of the electric field. With control of electrical field applied to an individual sample, electrical displacement, displacement current, remanent polarization, and homogeneity of polarization can be controlled. Further, with appropriate attention of the history of each sample, space charge in the samples can be eliminated [13]. With the Bauer cyclic poling process, reproducible remanent polarizations as large as 9 μC cm−2 are routinely achieved in commercial processes. Because electric fields as high as 5 MV cm−1 are utilized, inferior film is eliminated in the process.

A typical sample response in the cyclic poling process is shown in Fig. 2. In Fig. 2, both polarization and displacement are shown at various stages of the process. Starting at low electric fields, the sample is cycled through many “loops” until a consistent behavior is indicated. Higher applied fields are then utilized until the desired stable polarization is achieved. A higher degree of reproducibility is achieved when the maximum displacement current at the coercive field is stabilized.
Fig. 2

Example of a PVDF hysteresis curve. Induction (orange curve), polarization (blue line), and polarization current (green curve) as a function of the electric field. The value of the remnant polarization P R is at the intersection of the curves D (E) and P (E). When D = P = 0, it is easily to determine the coercive field E c

Each sample produced in this process is characterized with an individual poling history with well-defined electrical properties which can be reproduced at will.

Sensor Design

Five sensors have been elaborated from a Bauer shock gauge (Fig. 3) manufactured by AIFP [14] from a reproducible PVDF film poled at high voltage, following same instructions, by different operators (MSc students). The measurement of polarization has been enhanced in precision, and in electrical symmetrical response and reproducibility. The sensitive area is a 3 × 3 mm square. The gauge has been sandwiched between an insulator electrically shielded and overlaid with a heat conductive material. The gauge has been extended to 180 mm and used with adhesive, allowing its insertion in a closed shock tube, stuck on the inner flat end.
Fig. 3

Physical specification of a 25-μm thick Bauer shock gauge

Experimental Setup: Shock Tube

General Considerations

The first use of a shock tube is attributed to French researcher Paul Vieille while he was studying combustion and detonation in tubes in 1899 [15]. The shock tube was sparingly used for almost 50 years. The growing interest for the flow of fast-moving gas and gas phase combustion reactions brought it to the attention of scientists in the 1940s. The first research paper making use of shock tube was published by the Royal Society and authored by Payman and Shepherd in 1946 [16]. In the late 1950s, shock tubes were successfully employed at several universities and government laboratories in the USA, Russia, Canada, and the UK. Since then, the shock tube has remained a staple in the field of experimental aerodynamics.

A shock tube is an experimental device used to generate a reproducible calibrated shock wave. In its simplest form, it consists of a long tube of constant internal circular or rectangular cross section. It is divided by a diaphragm which separates the high-pressure driver section from the low pressure driven or test section. The tube is usually closed at both ends, although the test section can be left opened if needed. The material of the diaphragm and its thickness are deduced from the desired pressure ratio between the sections. The events taking place during a shock tube experiment are illustrated in a wave diagram and space diagram respectively in Figs. 4 and 5. The initial states of the driver and test sections are respectively denoted 4 and 1. At t = 0, the diaphragm is abruptly ruptured (more on this in the practical aspects section), triggering the following events:
  • Compression waves propagate in the driven (or test) section, and rapidly coalesce to form a steady shock front. This shock wave separates states 1 and 2.

  • Simultaneously, an expansion fan propagates upstream in the driver section, between states 3 and 4.

  • A contact surface is transported by the gas flow behind the shock wave. Initially located at the position of the diaphragm, this discontinuity separates the driver and driven gas (states 2 and 3). Given the briefness of the experiment, molecular diffusion across the contact surface is assumed to be negligible.

Fig. 4

Shock tube wave diagram

Fig. 5

Main variable profiles at a given time

Assuming the tube is closed at both ends, the shock wave and expansion fan are reflected at the ends of the tube and propagate toward one another. Waves continue to propagate back and forth and intersect until the medium is eventually at rest. The time available for measurement is actually much shorter than the whole phenomenon.

Analytical Description

In order to solve the shock tube problem, some basic notions of gas dynamics are required and can be found in [17, 18, 19, 20]. Some summarized results can be found in this part, considering only the ideal one-dimensional case with two types of discontinuity: contact surfaces (fixed) and shock fronts (supersonic). For both discontinuities, the thermodynamic states of gas obey to Rankine-Hugoniot equations describing the conservation of mass, momentum, and energy across a discontinuity for an ideal gas.

In Fig. 6, subscripts 1 and 2 respectively denote the upstream and downstream states and v is the specific volume, a is the sound velocity, and the Mach number \( {M}_1=\frac{W_1}{a_1} \) expressed from the flow velocity with respect to the wave front w = u−V s . Subscript 4 stands for the flow velocity, assuming the gas is initially at rest (u1 = 0). Knowing the initial state (subscript 1) and the shock wave velocity, the shocked state can therefore readily be determined.
Fig. 6

Incident shock wave (laboratory-fixed coordinates)

It is also noticeable that states 2 and 3 are in mechanical equilibrium (they share the same pressure), although this does not hold from a thermodynamical point of view (different temperatures, entropies, etc.). This fact is actually important in the following analytical study of the shock tube. The contact surface can be considered as a virtual piston moving at a constant speed, supporting the shock wave and generating the expansion fan.

The properties of the shock wave generated by the rupture of the diaphragm can be determined in two ways, essentially relying on the same reasoning. The data of the problem are the initial pressures p, sound velocities a, and heat capacity ratios γ in both sections of the tube (states 1 and 4). The flow is assumed to be inviscid and one-dimensional.

The first way to proceed consists in expressing the pressures reached behind the shock wave p2 and behind the rarefaction wave p3 with Relations (1) and (3):
$$ {p}_2=\frac{2{\gamma}_1{M}_1^2-{\gamma}_1+1}{\left({\gamma}_1+1\right)}{p}_1 $$
$$ \frac{u_2}{a_1}=\frac{2}{\gamma_1+1}\left({M}_1-\frac{1}{M_1}\right) $$
$$ {p}_3={\left(1-\frac{\gamma_4-1}{2}\frac{u_3}{a_4}\right)}^{\raisebox{1ex}{$2{\gamma}_4$}\!\left/ \!\raisebox{-1ex}{${\gamma}_4-1$}\right.}{p}_4 $$
Taking into account the fact that p2 = p3 and u2 = u3, the following relation can be obtained (4):
$$ \frac{p_4}{p_1}=\frac{2{\gamma}_1{M}_1^2-{\gamma}_1+1}{\gamma_1+1}\frac{1}{{\left[1-\frac{\gamma_4-1}{\gamma_1+1}\frac{a_1}{a_4}\left({M}_1-\frac{1}{M_1}\right)\right]}^{\raisebox{1ex}{$2{\gamma}_4$}\!\left/ \!\raisebox{-1ex}{${\gamma}_4-1$}\right.}} $$

This equation can be solved numerically to determine M1 and, using the Rankin-Hugoniot relations, the remaining shock properties.

The other way to proceed is to plot the shock polar with respect to state 1 and the rarefaction polar with respect to state 4. Since both waves lead to the same pressure and velocity, the intersection of the two polar gives states 2 and 3. Here again, determining the properties of the shock wave is quite straightforward.

When a normal steady shock waves impinges on a motionless wall (Fig. 7), the state of the gas behind the reflected shock (subscript 2′) wave can be determined from the Mach number of the incident wave \( \left({M}_1=\frac{W_1}{a_1}\right) \) by using Relation (5).
$$ \frac{p_{2\prime }}{p_2}=\frac{\left(3\gamma -1\right)\frac{p_2}{p_1}-\left(\gamma -1\right)}{\left(\gamma -1\right)\frac{p_2}{p_1}-\left(\gamma +1\right)} $$
Fig. 7

Incident and reflected shock wave (laboratory-fixed coordinates)

Shock Tube Facility at ENSTA Bretagne

The shock tube at ENSTA Bretagne is a 92-cm-long driver section and 3.72-m driven section, having a 8 × 8cm cross section (Fig. 8). These two sections are separated by a calibrated Mylar® membrane that bursts when the hydrostatic absolute pressure inside the driver section exceeds p4 = 6.2 ± 0.1 bar. The room temperature was 293 K, the driven pressure p1 is 1 bar, and the heat capacity ratio γ is 1.4. Under these considerations, the Mach number M1 is 1.46 and the reflected pressure p2′ is 4.96 bar (absolute). Calculations can be checked with the WiSTL applet available on line [20].
Fig. 8

End of the shock tube showing windows, led, sensors positions, and conditioners

The end of the driven section is equipped with large windows for visualization and instrumented with two PCB® 113B21 sensors coupled to a charge conditioner (Figs. 8 and 9). The PCB® 113B21 SN no. 28292 is 5 cm in front of the tube end in flush mount while the PCB® 113B21 SN no. 28293 is placed face to the stream, on the tube led. Charge conditioners are connected to a Tektronix TDS 2024 oscilloscope with a 100-kS/s acquisition rate. The acquisition chain is triggered on the rising front of PCB SN no. 28293 sensor.
Fig. 9

Schematic view of sensors implementation in the led at the end of the shock tube

Two PVDF gauges among the five manufactured were stuck next to the PCB® 113B21 SN no. 28293 so that they can measure the reflected pressure (Fig. 10). One of the two PVDF gauges is noted PVDF_Y (manufactured by Yulrick) and remains for all shots while the second PVDF sensor is alternatively taken among the fourth PVDF sensors left. Coaxial wires of 5 m long connect the PVDF gauges to Kistler® 5011 charge amplifiers. These charge amplifiers are set to 15.7 pC/N, according to Bauer [21], with an output range of 10 N/V.
Fig. 10

Example of time-resolved signals given by PVDF and PCB® sensors for shot no. 11

Twenty-five shots have been carried out. The first nine showed parasites. After having grounded the gauges in a suitable way and eliminated parasites, shot nos. 10 to 24 are considered. For each shot, PVDF and PCB sensor signals are recorded and compared to each other. Shot nos. 10 to 20 show the reproducibility of the signal on PVDF_Y. They also allow the calibration of PVDF_Y from a statistical point of view by comparison with the calibrated PCB SN no. 28293. The alternate use of the second PVDF sensor shows the difference of calibration within a set of sensors from the same process, assembled by different operators but without repeated measurements.

Shot nos. 15 and 16 have not been considered since there was an obstacle introduced in the driven section behind the sensors.

Experimental Results

After each shot, pressure signals are compared to each other. Figure 10 illustrates an example of results obtained by considering calibration coefficients given for PCB® sensors, and a fitting calibration coefficient for PVDF sensors so that they match data recorded by the calibrated PCB® sensors. Several methods have been used to determine this calibration coefficient and will be discussed.

First observations show that all sensors exhibit the same rising front at the trigger time. Differences, if there are some, cannot be observed because of the limited bandwidth of the Kistler charge amplifier (max 150 kHz). They detect the arrival of the shock front at the end of the tube that corresponds to state 2′ described in “Analytical Description.” The overpressure of the shock reflected is around 4 bar, with respect to a 0 baseline (relative), which conforms to the 5 bar absolute, as predicted by the analytical approach in “Experimental Setup: Shock Tube.” After the first plateau, a progressive release diminishes the overpressure from 4 bar down to almost 0. Afterwards, a succession of triangular-like peaks is visible. It corresponds to the back and forth of waves in the tube and each peak corresponds to the waves going back and forth in the tube. The triangular temporal pressure profile is due to the hydrodynamic decay: the release fan of state 3 is reflected at the opposite end of the tube in the driver section and propagates backward the shock front. The sound speed in state 2 is higher than that in state 1 and there is in addition a flow speed; thus, release waves propagating behind the shock will catch it up and diminish its amplitude.

Figure 10 also shows that PCB SN no. 28292 signal is a bit different than the others because it is a bit backwards to the end of the tube, not at the same location as the other sensors. Peaks are visible at each rising front on PVDF signals. PVDF signals are noisier than PCB ones because the vertical scale of the scope was 200 mV/division in 8 bits, which was not optimal for the PVDF signal amplitude (about 1/8 of the full vertical scale). A first calibration coefficient has been determined by considering it as being the ratio of the average voltage of the plateau for the PCB SN no. 28293 divided by the average pressure signal of the plateau for the sensor PVDF_Y. The plateau is the region described as state 2 in “General Considerations” and is defined between 0.48 and 3.68 ms. The calibration coefficient of the PCB SN no. 28293 has been established by the manufacturer and is 3.753 mV/kPa. This calibration method allows determining a calibration coefficient of PVDF_Y of 10.1 V/bar. Using this calibration factor for both PVDF sensors, it can be seen in Fig. 10 that PVDF and PCB SN no. 28293 signals are in good agreement and in amplitude as well as in chronology. PVDF signals exhibit a periodic structure on the release phase, hardly visible in Fig. 12. This corresponds to back and forth of the acoustic waves in the tube led thickness on which the PVDF gauge is stuck. Although this periodic structure is not very important, it could be suppressed by using a backing material that matches the PVDF acoustic impedance.


Signals recorded for all shots, excluding shot nos. 15 to 17, were implemented in the same Fig. 11 for sensor PCB SN no. 28293 and in Fig. 11 for sensor PVDF_Y. They show a fairly good reproducibility. By using the calibration coefficient described in paragraph 4, it can be seen that PVDF signals for sensor PVDF_Y are also reproducible but with a higher variability (Fig. 12). On average on all available shots, the calibration factor based on the ratio of the average maximum on the plateau is 9.96 bar/V with a standard deviation of 0.76.
Fig. 11

Pressure signals measured by the PCB SN no. 28293 sensor at the end of the shock tube

Fig. 12

Pressure signals measured by the PVDF_Y sensor at the end of the shock tube

Fig. 13

Comparison of averaged signals on available shots for PCB SN no. 29293 (full) and PVDF_Y (dashed)

Fig. 14

Relative difference in percentage between averaged PVDF_Y and PCB SN no. 28293

Two other calibration methods have been considered. The first one is based on the minimization of the sum of absolute difference of both signals for each shot. The second is the least square method. Calibration coefficient for the three presented methods and for each shots are given in Table 1. All methods seem to be in agreement and give a calibration factor around 10 bar/V for PVDF_Y. The average plateau ratio method results in the lowest standard deviation while the minimization of the sum of absolute differences gives the highest one. For all methods, shot no. 13 leads to the highest calibration factor (12% above average) and shot no. 17 gives the lowest one (12% below average). No obvious explanations have been found and we suggest that it may be due to the non-reproducibility of the burst of the Mylar® membrane during the shot.
Table 1

Calibration factors given by the three methods

Shot no.

Average plateau ratio (bar/V)

Min. abs. difference (bar/V)

Least square (bar/V)

Tir 11




Tir 12




Tir 13




Tir 14




Tir 17




Tir 18




Tir 19




Tir 20








Std. dev.




A comparison is shown in Fig. 13 between average signals from available shots for PCB SN no. 28293 and PVDF_Y. Some discrepancies remain on the first peak but overshoots have been smoothed by the averaging.

Impulses of the averaged time-resolved pressure signals respectively given by the PCB sensor and the PVDF sensors are calculated by using the Simpson method. Results are respectively 1.824e-7 and 1.967e-7 bar/s, i.e., a relative difference of 7.8% with respect to the PCB sensor, what remains reasonable in an impulse calculation.

Figure 14 shows the relative difference in percentage of PVDF_Y with respect to PCB SN no. 28293. The agreement remains in average on the overall signal less than − 13.5%, that is to say that PVDF_Y signal is slightly higher than PCB SN no. 28293 especially during the first release. Afterwards, the difference is lower, below 8.5% in absolute value, except for front shocks. It has been explained earlier that the impedance mismatch between the tube led and the PVDF can justify the over/undershoot phenomena at the origin of these discrepancies. The lack of vertical resolution could also degrade the results. At last, it is known that PVDF, as a polymer, is more sensitive than quartz (implemented in PCB sensors) to temperature. Under shock and release, temperature changes may result in temporal variations of the calibration coefficient.


A blast sensor based on ferroelectric PVDF material is proposed. It gave some interesting responses for blast experiments and can be easily mounted on a target, even in matrix. Its sensitive surface can be as small as 1 mm2, which is very convenient for small-scale experiments. A 9-mm2 PVDF sensor has been tested in shock tube and shows interesting results compared to what was traditionally utilized in blast experiment, PCB® 113B21 at ENSTA Bretagne. Ten successful shots were conducted, leading to time-resolved overpressure records. Experimental results are in agreement with the shock tube theory; the reflected overpressure obtained is around 4 bar in a reproducible way for an initial loading pressure of 6.2 ± 0.1 bar.

The PVDF sensor has been calibrated with respect to the calibrated PCB sensor, according to three different methods that lead to comparable results. The calibration coefficient obtained with the method of the average plateau ratio gives the lowest standard deviation and a value of 9.96 bar/V. The relative difference between PVDF_Y sensor and the calibrated PCB sensor is lower than 13.5% on average. Highest discrepancies are noted for shock breakouts and are explained by the impedance mismatch between the PVDF sensor and the tube led. Also, some oscillations are visible on the signal given by the PVDF.

As perspectives, extra shots are planned including a polymer backing as a led for the shock tube. Blast-like profiles obtained by shock tube are also a matter of interest and are currently in progress at ENSTA Bretagne. Next experiments will be coupled with high-speed shadowgraph observations in order to check the planarity of the shock front. The testing of smaller PVDF sensors (4 and 1 mm2) is also planned. At last, the influence of the angle of incidence between the shock front and the sensor is also to be investigated.



The authors want to thank the technical staff of ENSTA Bretagne, especially Frédéric Montel. They are also grateful to the European commission who granted the ERASMUS+ program “Greener and Safer Energetic and Balistic Systems.” They are also grateful to Yulric PHILIPPE, Quentin Weisse, Jérémie Tartière, Chanlika Tes, and Manon Es Soussi and MSc students at ENSTA Bretagne who mounted the PVDF gauge under our supervision.


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.ENSTA Bretagne, IRDL FRE CNRS N°3744Brest Cedex 09France
  2. 2.AIFPSaint-LouisFrance

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