1. Introduction

In advanced engineering applications, such as in the aerospace and transportation industries, composite materials have been widely used due to their advantages such as high stiffness, high strength, low weight and resistance to corrosion. However, most composite materials exhibit brittle behavior under static loading or fatigue conditions. Fractures from matrix cracking or from delamination with potential fragment debris under impact loading have been a significant concern for aerospace structure applications [1–3]. In general, it has been found that the strength of composite materials will degrade when subjected to a low-velocity impact in a manner that may not be outwardly visible to the naked eyes. Therefore, many studies have used modeling and computational simulation to predict how impacts on composite materials can affect stress, energy, and displacement [4–6]. To evaluate the influence of a high-velocity ballistic impact behavior on a composite material, the relationship between mechanical properties, kinetic energy, and residual velocity were investigated [7–9]. We found that velocity measurements, which range from 100m/s to 2km/s during an impact event, are of particular importance when studying laminate composite material fractures.

For measurements from impacts or shockwaves, the velocity interferometer system for any reflector (VISAR) [10] arrangement is usually utilized with normal or angled probes to detect the velocity component. The major limitation of a VISAR is that the fringe constant is determined by an etalon delay. Therefore, some research directions have shifted towards using a photonic Doppler velocimetry (PDV) [11] configuration which is characterized as possessing a fast response time, a high dynamic range for large intensity fluctuations, is compact in size, and is of low cost. Mixing the individual signals of a Doppler reflection light and reference light, the resulting beat frequency of the heterodyne PDV signal can be analyzed using short-time Fourier transform (STFT) techniques. Pressure shear plate impact (PSPI) examinations have been studied using PDV-based configurations by several others. Kettenbeil et al. [12] presented a heterodyne transverse velocimetry with two different interferometry schemes which enabled accurate measurements of a low-velocity pressure-shear plate impact. Mallick et al. [13] used a dual beam configuration to fulfill the simultaneous detection of both normal and transverse particle velocities on the specimens with surface treatment. Johnson et al.[14] explored different surface process methods to enhance surface transverse velocity measurements. Zuanetti et al. [15] combined a normal displacement interferometer (NDI) and a transverse displacement interferometer (TDI) into one compact PDV configuration to detect the particle motion in shock waves. Several laser-driven flyer measurements and material welding studies were also conducted using PDV. Bowden et al. [16] tried to optimize the laser-driven flyer design based on PDV measurements. Dlott et al. [17–19] worked on a series of experiments using a high-speed laser-driven flyer plate. Wang et al. [20] used a laser-driven flyer to perform material welding and spalling. Kucera et al. [21] determined the acceleration during an explosive welding process using PDV. Andriyash et al. [22] applied PDV to characterize the ejecta from shock-loaded samples.

In our study, we adopted a PDV configuration to simulate and measure the velocity history of fragment debris when a laminate composite material undergoes a rapid impact. In order to realize the flexibility for dynamic evaluation under different momentum conditions, the laminate design with a tunnel structure for the fragment generator (FG) was used as a sample case. The fragment generator demonstrated the advantages of a controllable fragment size, a controllable applied voltage, and a geometrically confined space within the tunnel structure for the ejecting fragment.

We first looked into the background of composite material fracture issues as well as the systems related to velocity measurements. In order to assist with fracture behavior analysis especially for velocity data history of an ejecting fragment accelerating from at rest, a measurement system with a velocity range from a low velocity to a high velocity was developed. In a traditional PDV system, a focus lens is generally used and is suitable for taking measurements in restricted regions such as shockwaves. However, in the case of ejecting fragments, the movement range of a target is large and the focusing requirement is thus an issue during returning light collection which can cause interference phase distortion. The focus aberration effects of laser pulses have been explored by Sun et al. [23]. Furthermore, the collected light presents a large intensity fluctuation during the fragment debris as it flies along the cone-shaped projection beam of a focus lens. We thus replaced the probe with a collimated lens ensuring that the undistorted reflection light can be collected at a lower intensity fluctuation during the long-range flight path of the fragment. An iris was placed between the probe and the specimen simultaneously to confine the laser projection area and to block uninterested backscattering light from the specimen regions other than the specific fragment debris within the tunnel structure. At the same time, the tunnel structure served as the ejection trajectory confinement space and the space region of interest (ROI) in this study. With the integration of a collimated probe, an iris, and a tunnel structure, this arrangement led to an improved PDV configuration whose purpose was to detect fragment debris (see Fig. 1). A continuous wavelet transform (CWT) was adopted to analyze the collected heterodyne signals imbedded with the velocity history information and to generate the time-frequency mapping, namely the scalogram. We proposed a velocity line tracing algorithm (VLTA) based on an image processing method to analyze the scalogram and to produce the quantized velocity curve. The experimental and simulation results are presented herein. The experimental work with the buzzer as specimens were conducted first under different operating frequencies in order to validate the measurement system. To correctly analyze the fragment signals, a three-dimensional (3D) FG morphology was measured using a confocal microscope and was examined with the scalogram. The spectra distribution was then compared with a course of events during an impact. The simulated heterodyne signal was analyzed and compared to reflection light intensity data and vibration motion to support our spectra distribution findings. Finally, experimental results using the FGs demonstrated the effectiveness and innovation of our modified PDV configuration.

 

Fig. 1. Experimental configuration and the cross-section of the fragment generator. Configuration can be divided into three major parts: fiber-optics components, FG specimen, and signal acquisition equipment. The velocity history of the fragment debris flying within the tunnel structure of the FG was a major target of interest.

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2. Principles and methods

2.1 Configuration

Our PDV system was built using fiber components which exhibit low transmission loss and at a relatively low cost due to a well-developed telecommunications industry which offers low cost commercially available components. The configuration scheme is shown in Fig. 1. A single wavelength fiber laser (Koheras BASIK C15) from NKT Photonics was used as the measurement light source with a 1550nm wavelength, 10mW output power, and a 15kHz narrow linewidth. To aid with the alignment procedure, a 633nm HeNe laser was used as the laser source each time at the beginning of a new measurement. The laser source was manually switched to the 1550nm laser after the alignment was completed (To clarify, the two lasers are never turned on at the same time). Between each optical component, a 1550nm single-mode fiber (Thorlabs SM1550G80) with FC/APC connector was used for the light transmission. With the convenience of a fiber circulator, the optical transmission efficiency was successful in guiding the light from Port 1 to exit through Port 2 and then guiding the light from Port 2 to exit through Port 3. This circulator (Thorlabs 6015-3-APC) was connected between the laser source, the optical probe, and the photodetector. A collimated optical probe (LPC-04-1550-9/125-S-3.8-18AS-60-3A-1-1) from OZ Optics was used both to project light onto the fragment debris and to collect the Doppler-shifted scattering light. Due to a possible mismatch interface between the probe and its connected fiber, a certain fraction (−60dBm) of the reflection light was introduced as a non-Doppler-shifted reference signal for interference. The specimen was our FG designed laminated structure. The detailed description of the FG structure is shown in Section 3.2. After the electrical launch, a piece of the fragment debris was ejected and it flew through the tunnel structure into the ROI space. An iris was placed between the probe and the specimen to enhance the signal-to-noise ratio (SNR) by controlling the spot size and by blocking unwanted scattering light. The iris size was changed to fit the requirement of the different fragment sizes. A camera was placed between the probe and the specimen to ensure the laser spot aimed correctly at the position between the copper bridge where the fragment debris ejected. With an attempt to optimize both the collection light intensity and field of view of the monitoring camera, a camera was placed 30 degrees from the probe pointing direction and the iris was placed as close as possible to the specimen. A Doppler-shifted reflection signal was collected with the same probe that transmitted the non-Doppler-shifted reference signal through the circulator. The introduced heterodyne signal was detected with an InGaAs photodetector (Thorlabs DET08CFC/M) which had a 5GHz bandwidth. Finally, the signal was digitized using an oscilloscope (Tektronix DPO7354C) with a 3.5GHz bandwidth and a 40GHz sampling rate. The data processing and analysis were performed using MATLAB 2016. The simulation for the reflection light evaluation was performed using LightTools 8.2.0.

2.2 Photonic Doppler velocimetry (PDV)

During the process of taking the PDV measurements, a laser light was illuminated onto the moving object and the reflection light was collected with the same probe. Mixing the individual signals of the Doppler reflection light and reference light, the time-dependent heterodyne beat signal intensity I(t) was produced and then recorded as:

2.3 Continuous wavelet transform (CWT)

Within the PDV configuration, the heterodyne signal was embedded with time-varying velocity information and recorded as a beat signal. It required a time-frequency analysis method such as a STFT or CWT to resolve and localize the spectra distribution temporally. The STFT provided a mathematical approach that mapped the frequency information sequentially with a pre-defined window function designed according to the specific frequency range of interest. However, a computation process can be time-consuming and can also result in vague transformations for signals of widespread frequency content with a fixed window function. Kettenbeil et al.[12] previously indicated that an inadequate window size can lead to a higher frequency uncertainty when using a STFT. On the other hand, a CWT method possesses both a versatile frequency localization accuracy and a higher computation efficiency for its waveform flexibility and for its multi-scaling ability which enables a mother wavelet selection and daughter wavelet generation. Liu et al.[24] previously showed that a velocity change resolving capability of CWT when compared with a STFT. The transformation coefficient X_w can be acquired by CWT where the mathematical function can be expressed as the following equation:

The time-frequency analysis was conducted using a MATLAB cwt function with analytic generalized Morse wavelets, morse, which is suitable for analyzing signals with time-varying amplitudes and frequencies.

2.4 Velocity line tracing algorithm

The overall product obtained after the time-frequency analysis was a three-dimensional datum consisting of variables such as time, frequency, and transformation products in a magnitude which is usually presented graphically as a spectrogram for STFT or a scalogram for CWT. In the scalograms presented in this study, the frequency dimension was converted into a velocity scale using a wavelength relationship as described in Eq. 4. Due to the laminated structure of the adopted FG, the resulting scalograms were imbedded with a complex spectrum content which made the peak-finding algorithm unsuitable for FG scalogram analysis. Therefore, we proposed a velocity line tracing algorithm (VLTA) based on image processing methods to produce a quantized velocity profile analyzing the FG scalograms. Figure 2 shows the scheme of the VLTA processing flow. Since the signal-to-noise ratio (SNR) can be found in the observed magnitude differences according to the frequency range or the velocity region in the scalogram, the scalogram was binarized separately with two different magnitude thresholds for low velocity, denoted as thr_LV, and threshold for high velocity, denoted as thr_HV. The two resulting binary maps were acquired after the division with the velocity edge. The pre-set values of thr_LV, thr_HV, and velocity edge were defined empirically according to the SNR distribution of the input scalograms. The union of the two binary maps gave the resulting complete binary map a rough and noisy texture. The procedures of the morphological operation and rupture elimination were performed to retrieve the interested spectral domain. In the morphological operation procedure, the open operation divided the unrelated small ruptures. The close operation linked the disconnected surroundings of the major domain together. The void textures of the major domain introduced after close operation were filled using a padding operation. In the procedure of the rupture elimination, a connected component algorithm was used to label all the isolated domains. Using area sorting, the major domain with the largest area was obtained. Then, the surrounding line of the major domain was obtained using an edge detection algorithm.

 

Fig. 2. Flowchart of a velocity line tracing algorithm. The scalogram was binarized with two magnitude thresholds and a velocity edge to give a complete binary map. The morphological operations were used to retouch the rough and noisy textures of the complete binary map. The rupture elimination procedure was used to retrieve the interested spectral domain and the corresponding edge line from the retouched binary map. The velocity profile was acquired after tailoring the details of the edge line.

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Since the collected signal of a fragment debris was composed of several events, the traced velocity was divided into an expansion stage, a low velocity stage, and a flight stage. The abnormal textures of the traced velocity line were tailored separately according to the event stages with physical meaning. Due to the extremely short duration of the whole fragment launch event, the spectrum magnitude below 15m/s was at times unobtainable and was more likely to be affected by an edge effect [25] with CWT. At the expansion stage, an extrapolation procedure was performed to complete the velocity profile from at rest. The slope of the velocity profile during the expansion stage was used for the linear extrapolation. At the flight stage, the corresponding scalogram region displayed a comb-like texture which was caused by a waveform flaw of the collected heterodyne signal due to data acquisition limitations of the voltage dynamic range. A detailed description about the scalogram texture with waveform of the heterodyne signal is in Section 3.4.1. Using image processing methods, it was possible to reconnect the comb-like texture and make the VLTA more immune to intensity fluctuations and data acquisition issues. Finally, the velocity profile of interest was ready for comparison after adopting a Gaussian smoothing filter to iron out the profile discontinuity produced during image processing. The spatial velocity profile was then easily calculated by integrating the temporal velocity profile.

3. Results and discussions

3.1 System validation

Before the FG launch tests, the validation experiments were conducted using a buzzer operated at different sinusoidal frequencies, and where the exerted frequency was denoted as f_ex. Using a simple harmonic motion, a single point position on the buzzer was expressed as Eq. (5) with vibrational amplitude A and structure constant k related to the structure design and to the material properties. The velocity at the corresponding point shown by Eq. (6) had a maximum velocity v_max with a value of 2πkAf_ex. Substituting the maximum velocity into Eq. (3), the relationship between the exerted frequency and maximum beat frequency f_b,max can be written as Eq. (7). The vibrational amplitudes were measured using an advanced vibrometer/interferometer device (AVID) [26] (see Fig. 3(a)). With exerted frequencies at 10Hz, 50Hz, and 100Hz, we obtained vibrational amplitudes of 1.30µm, 1.26µm, and 1.15µm, respectively. The structure constant k of 3.8, was calculated using a time-frequency analysis result with a 10Hz exerted frequency. Substituting the structure constant and the measured vibrational amplitudes into Eq. (7), the resulting maximum beat frequencies of 399Hz, 1947Hz, 3545Hz were obtained and the measured maximum beat frequencies were 400Hz, 2000Hz, and 3400Hz, respectively. Hence, the beat frequencies measured by this system was validated with an average error of 2.39%. Figure 3(b) shows the heterodyne signal and the corresponding spectrum of the buzzer operated at 50 Hz. Figure 4(a-c) shows the heterodyne signals and their corresponding scalograms of the buzzer when operated at 10Hz, 50Hz, and 100Hz, respectively.

 

Fig. 3. Buzzer signals: (a) vibrational waveform of buzzer triggered under operating frequencies at 10Hz, 50Hz, and 100Hz, with vibrational amplitudes of 1.30µm, 1.26µm, and 1.15µm, respectively, and (b) heterodyne signal of buzzer and its corresponding spectrum.

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Fig. 4. Scalograms of the buzzer triggered under operating frequencies at 10Hz, 50Hz, and 100Hz. (The observed maximum beat frequencies were 400Hz, 2000Hz, and 3400Hz.)

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3.2 Specimens

In order to compare composite rupture conditions with various sizes or kinetic energies, an FG was designed using a laminated structure comprised mainly of four layers from bottom to top sequentially: a base layer, copper bridge, fragment layer, and tunnel layer. The cross-sectional structure of the FG is shown in Fig. 1. Polyimide (PI) was chosen to be the material for both the fragment layer and tunnel layer. When we applied the set voltage in the order of kV on the copper bridge, the arcing effect raised the temperature of the gas in the void rapidly which caused volume expansion to provide the kinetic energy to the intermediate fragment layer. The fragment debris cut along and ejected through the tunnel structure of the tunnel layer. The FG topological morphology before and after electrical launch was observed using an optical microscope (OM) and a confocal microscope (CM) as shown in Fig. 5. The cutting diameter provided the expected fragment size, and the circular opening of the tunnel layer provided the function to confine the flight trajectory of the fragment debris as shown in Fig. 5(a, b). Also, a slight mis-alignment of the center position between the copper bridge, the cutting diameter, and the tunnel diameter was observed. It should be noted that the overall pattern positioning during specimen fabrication determined how close the tunneling diameter matched the fragment cutting diameter. The size of the fragment debris was observed to be roughly equal to the cutting diameter (see Fig. 5(c)). Although the fragment debris was not in a perfectly circular shape cutting along the cutting diameter, only one major fragment debris was expected to be produced in an FG launch. During the detachment, some residual polyimide of the ripped-out structure was observed in the CM image (see Fig. 5(d)).

 

Fig. 5. Topological morphology of fragment generator: (a) OM (optical microscope) image before launch, (b) CM (confocal microscope) image before launch, (c) OM after launch, and (d) the CM image after launch.

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3.3 Expected Fragment Generator Spectrum

Due to the laminated structure of the FG, a complicated sequence of events occurred during the processing of the fragment generation and where the entire velocity history information was embedded in the heterodyne signal. Although the velocity history of a single piece of fragment debris within the ROI space of the tunnel structure was our major concern, the unwanted scattering light from the PI residuals, the copper bridge, and the base layer were also inevitably collected. Therefore, the spectra distribution was of importance since it showed the stages during a fragment ejection process. A scalogram analyzed from an actual experimental heterodyne signal processed with CWT is shown in Fig. 6. The distribution was divided over five regions: a) when a high voltage was applied to the copper bridge, the gas within the void became heated which provided the kinetic energy needed to push the whole structure outward; thus a rapid velocity acceleration process can be observed first in the region of the thermal expansion; b) with continued thermal expansion until the mechanical limit of the polyimide was reached, the fragment layer was cut along the cutting diameter of the fragment layer and the central piece was ripped into a fragment debris which detached from the surface; the detached fragment was observed to accelerate for a short time by the remaining expansion gas until the maximum velocity was reached and the intensity faded away during the fragment flight; c) when the fragment was ripped out from the intermediate layer, a ring of polyimide residues was formed along the cutting edge which continued to bounce after fragment detachment; d) by absorbing the main portion of the kinetic energy provided by the copper bridge arcing, the copper bridge rapidly accelerated to its resonance frequency and the energy was consumed with its vibration motion; due to the bigger size and heavier mass of the copper bridge, the structure resonance frequency was located below the range of the fragment flight and residue bouncing; and e) the spectra of the low frequency came from either the FG holder or was introduced due to the edge effect with wavelet transformation.

 

Fig. 6. Expected spectra distribution of the fragment generator.

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3.4 Simulation

3.4.1 Reflection intensity

In order to simulate the heterodyne signal closer to a practical situation and to examine the effects of different iris sizes, the reflection light intensity was evaluated using LightTools. The exploded drawing of the simulated configuration is shown in Fig. 7(a) with the assembly drawing shown in Fig. 7(b). The incident collimated light coming from the lens was projected onto the FG or onto the fragment debris in two separate cases to collect their individual reflection light. The different beam diameters were restricted by the iris with different opening sizes. Polyimide was chosen as the material for the tunnel layer and fragment layer. The geometrical parameters of the tunnel diameter and the cutting diameter were set at 1.2mm and 1mm, respectively. The material properties were defined as simple scattering for the Lambertian model with the polyimide layer and copper bridge, and the reflection/transmission ratios were set at 1/99 and 90/10, respectively. In our simulation, a 50/50 beam splitter was placed between the lens and iris with the two receivers at the sides for intensity detection of the incident light and reflection light. A trace amount was set at 10 million rays and the mesh number of each receiver was set to be 51 × 51. Figure 8 shows the simulation results. Due to the small size of the fragment and to the poor reflection of the polyimide material, the obtained major intensity was controlled by the illuminated area of the substrate (mainly by the copper bridge) which occupied the usable dynamic range of the oscilloscope and decreased the signal-to-noise (SNR) simultaneously. With the addition of the iris in the configuration, the substrate reflection intensity was effectively reduced (see Fig. 8(a)). With the iris size decreasing until the fragment size was reached, the fragment reflection intensity remained nearly unchanged. In order to collect the highest quantity of light intensity with a high SNR, the recommended iris size was found to be between 2mm to 5mm according to the result shown in Fig. 8(b). During the fragment detaching flight, a rotational motion was inevitable but showed no observable impact on the obtained intensity due to the scattering surface (see Fig. 8(c)).

 

Fig. 7. Simulated system configuration: (a) exploded drawing and (b) assembly drawing with light tracing.

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Fig. 8. Reflection light intensity simulation: (a) light intensity of projection light, substrate reflection, and fragment reflection, (b) intensity ratio with different iris sizes, and (c) reflection intensity of fragments considered with rotational motion.

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3.4.2 Simulated heterodyne signal

Based on the proposed scalogram distribution described in Section 3.3, three simplified velocity profiles for the fragment, polyimide residue, and substrate were assumed in the heterodyne signal simulation with the time-averaged modulation intensity calculated from the reflection intensity simulation. The smooth and distinct scalogram texture shown in Fig. 9(a) does not match the results of the experimental heterodyne signal since the object vibration during motion was ignored in the first case of the simulation. From a more practical viewpoint, a more realistic scalogram was simulated with residue velocity and substrate velocity in addition to a slight fraction of the vibration motion (see Fig. 9(b)). In the experimental scalogram of the FG, the comb-like texture (see the region (b) in Fig. 6) of the fragment spectra can be explained by the restriction of the oscilloscope dynamic range. As shown in the zoom-in profile of Fig. 9(c), the simulated heterodyne signal was composed of two frequencies. The high frequency corresponded to the fragment while the low frequency corresponded to the substrate. As the fragment signal showed relatively weak intensity, a higher voltage gain on the oscilloscope can be used to amplify the collected signal. However, the substrate reflection light intensity, which presents a major attribution of the received intensity, was also amplified at the same time. Due to the voltage detection range limitation of the oscilloscope, the voltage dynamic range was mainly occupied by the substrate intensity which introduced a cut-off phenomenon in the waveform. The fragment signal with high frequency was then found to increase and decrease with the substrate signal at low frequency. As a result, the fragment signal near the cut-off region was lost and the resulting comb-like texture scalogram shown in Fig. 9(c) was observed.

 

Fig. 9. Simulated heterodyne signals: (a) simulated velocity without vibration, (b) simulated velocity with vibration, and (c) cut-off heterodyne waveform restricted by dynamic range and the scalogram with tattered texture.

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3.5 Uncertainty analysis

With an ejecting fragment debris serving as the measurement target, the uncertainty and the potential error was mainly contributed by the laser quality, the sensitivity direction, the dynamic motion, and the signal analysis method. According to the specifications, a 15kHz linewidth of an adopted 1550nm laser corresponds to a 120 attometer (10⁻⁹ nm) spectral deviation. Due to an extremely short duration (within 1µs) of an FG launch process, the laser center frequency was expected to be sufficiently stable over the whole duration. With a sampling rate up to 40GHz used during the data acquisition, the time scale of the scalogram was obtained with high precision. Therefore, the influences related to laser quality and data localization including the center wavelength, the spectral deviation, the center frequency localization, and the temporal position localization have little impact on the velocity information.

Considering the normal velocity interferometer (NVI), the collected PDV signal was expected to contain only the velocity information normal to the specimen surface. However, the collected light was usually in a scattering manner in real cases of object velocity measurements. The scattering light implied that the light traveled in a wide range of directions, which can result in estimation errors related to angle fractions. Compared to a case where a focus lens is used, the use of a collimated lens can inherently reduce the uncertainty caused by angle fractions with a lower acceptance angle. On the other hand, the receiving angle of the scattering light is inversely proportional to the distance between the iris and the specimen. Utilizing an iris between the collimated lens provided the benefit of reducing the reflection light from uninterested regions by controlling the beam size as well as allowing only the collimated fraction within the scattering light to pass through. Therefore, the uncertainty related to the probing and collection directions was minimized by the well-defined sensitivity direction with the collimated lens and utilized iris. Although the optimization on power efficiency was further achieved with a collimated lens of a specific numerical aperture (NA), the arrangement of a collimated lens with a slightly bigger beam size with an additional iris provided it with inherent advantages such as beam size control, blocking scattering light from other regions, and giving it a well-defined sensitivity of direction.

The dynamic motion of a tiny ejecting fragment debris in free space included varying the flying angle and rotation during flight which can lead to some uncertainty in velocity detection. The varying flying angle can cause serious velocity underestimation since only the velocity information in the sensitivity direction can be detected. With the tunnel structure design of an FG, the fragment ejection trajectory can be well constrained. The following uncertainty estimation was made based on the FG geometrical parameters of a 1000µm tunnel diameter, a 150µm tunnel depth, a 700µm fragment diameter, a 100µm fragment thickness, and a 100µm transverse gap between the fragment and tunnel wall. Just considering only directional deviation, the largest flight deviation angle from the normal axis was estimated to be 33 degrees which implied that the maximum velocity was under estimated by 16.1%. The rotation motion increased the velocity content which broadened the spectrum distribution slightly, but the rotation motion had little effect on the central velocity of the mass point. However, the rotation motion geometrically increased the transverse gap by 42µm which increased the maximum velocity to be under estimated from 16.1% to 27.4%. Such uncertainty related to the dynamic motion can be further improved with a tunnel diameter closer to the cutting diameter. However, such improvement relies on more delicate FG fabrication techniques.

Analyzing the heterodyne signal using a CWT, the time-frequency mapping of the scalogram was obtained. We developed a VLTA method to analyze a scalogram and to retrieve the velocity profile of a fragment debris. Due to the short duration of the fragment launch event, the spectrum magnitude below 15m/s was unobtainable by the CWT, and we thus used a linear extrapolation procedure to complete the velocity profile from its at rest point. The extrapolation procedure played an insignificant role when the spatial distance of the trajectory was compared. However, the temporal comparison can introduce some uncertainty due to the amount of the extrapolation time (5ns on the average).

3.6 Experimental results

In order to evaluate the velocity profile of the ejected fragments, the FGs with the same model were used with different applied voltages exerted on the copper bridge, which applied different amounts of kinetic energy to the fragment debris. For the data collection parameter set-up, the sampling rate was set to 40GHz and the voltage gain was fixed at 10mV/div with an AC coupling mode. In the FG measurements with tunnel size of 1mm, an iris size of 2mm was chosen to ensure complete information of the fragment was collected with better signal-to-noise ratio. With applied voltages of 1.5kV, 2.5kV, 3.0kV, 3.5kV, and 4.0kV, all the fragment ejection durations were within 1µs. The collected heterodyne signal of the 1.5kV electrically-launched FG and its spectrum is shown in Fig. 10(a) with the corresponding scalogram shown in Fig. 10(b). A great improvement on the signal-to-noise ratio was observed when comparing the results of the non-iris configurations (see Fig. 10(c)) to the iris configurations (see Fig. 10(d)). With the iris configurations, the substrate reflection was suppressed, reducing the noise over the whole scalogram ranging from a low frequency to the high frequency. The noisy spectra surrounding the main signal domain was thus eliminated. At the same time, a higher voltage gain was further set in an AC coupling mode since the unimportant reflected light other than the fragment scattering was blocked. Hence, the SNR over the high frequency region was enhanced (see Fig. 10(d)).

 

Fig. 10. Experimental signals of fragment ejection under different applied voltages: (a) heterodyne signal with applied voltage of 1.5kV, (b) corresponding scalogram of 1.5kV applied voltage signal, and (c & d) scalograms of 4.0kV applied voltage signal under different data collection parameters and utilized iris.

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The velocity profiles were retrieved from the scalograms using our proposed VLTA (see Fig. 11(a)). The velocity profiles were grouped into two separate categories. In a low voltage excitation case below 3.0kV, the velocity profiles showed an inverse-S curve. The intermediate fragment layer was pushed outward by the thermal expanded gas. Until the expansion reached the mechanical limit of the polyimide, a resulting horizontal line of constant-velocity was observed between 20ns to 28ns. After that, the fragment debris was ripped out from the fragment layer and continued to accelerate by the remaining expanded gas. On the other hand, the exponential rising velocity profiles were observed for the high voltage excitation cases. Since a much higher kinetic energy was provided for the cases with the higher applied voltage, the fragment debris was ripped out directly over the mechanical limit and no obvious constant-velocity profile was observed.

 

Fig. 11. Quantitative experimental results: (a) velocity profiles of different applied voltages, (b) comparison of acceleration time (orange bars indicate the extrapolation time from rest, blue bars indicate the acceleration time including extrapolation time), and (c) comparison of tunnel-end velocity

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In order to compare the fragment velocity after detachment more quantitively, the characteristic indexes were compared from two aspects: the acceleration time and the tunnel-end velocity. The required time for the fragment to accelerate to a velocity of 1000m/s from at rest was set as the standard for the definition of acceleration time. We then defined the tunnel-end velocity as an end-value of the measured velocity profile within and at the end of the tunnel structure. Our results showed that the acceleration time was shortened when a higher voltage was applied (see Fig. 11(b)). However, the extrapolation time (orange bars in Fig. 11(b)) accounted for 12% to 30% of the amount in the acceleration time which can introduce uncertain estimation errors. Therefore, the comparison with acceleration time should be taken with a conservative attitude. On the other hand, a comparison with a tunnel-end velocity shows a more revealing trend as shown in Fig. 11(c). We found that with a higher exerted voltage on the copper bridge, the tunnel-end velocity increased proportionally. With a 3.5GHz bandwidth oscilloscope and a 5GHz bandwidth photodetector, the system bandwidth was conservatively estimated to be 2.87GHz, which indicated that a velocity up to at least 2217m/s can be measured. As the frequency response of the overall velocity did not suddenly drop to zero with a frequency higher than 2.87GHz, the higher velocity was still detectable if the resulting scalogram resulted in a good signal-to-noise ratio of the high frequency region. Therefore, a reasonable maximum tunnel-end velocity up to 3053m/s was observed in our FG tests.

4. Conclusions

In this research, we devised a modified PDV configuration with an aim to measure ejecting fragment debris. In the validation experiment using a buzzer, the average error was found to be 2.39%. A collimated lens was used in our configuration for alignment convenience and to allow for high signal-to-noise ratio measurements over long distances. We utilized an iris to provide the flexibility to change the illumination region depending on different specimen sizes. We found that by adopting an iris in the configuration, it can improve the signal-to-noise ratio. The combination of a collimated lens along with an iris can improve the sensitivity direction. A fragment generator with a laminate structure made of polyimide and copper bridge layers was designed to give flexibility to control fragment sizes and to control the voltage applied. The tunnel structure of the fragment generator provided a good motion trajectory confinement space. Based on the procedure of a time-frequency analysis with continuous wavelet transform (CWT) and our proposed velocity line tracing algorithm (VLTA), the velocity profiles under different applied voltages were successfully obtained. The spectra distribution based on a course of events during an impact was compared with a fracture morphology measured with an optical microscope and a confocal microscope. The observed tunnel-end velocity of the detached fragment was proportional to the applied voltage exerted on a copper bridge with the same geometric design of a fragment generator. With an applied voltage of 4.0kV, the maximum tunnel-end velocity of 3053m/s was measured. For further advanced study on fracture behaviors, the fragment layer can be replaced with different composite materials of specific sizes and different applied voltages.