CHARACTERIZATION OF HOLLOW PARTICULATE AND GRADED COMPOSITES USING ULTRASONIC TECHNIQUE

An experimental study has been conducted to characterize hollow particulate composites (syntactic foams) using ultrasonic pulse echo techniques. Materials tested for this study consisted of low viscosity epoxy matrix with embeded soda-limeborosilicate glass micro-balloons of different volume fractions. Three sizes of microballoons ranging from 30-65 microns were tested. Measurements of longitudinal and shear wave speed and attenuation of ultrasonic wave in syntactic foams were taken. These wave speed values were further utilized to calculate the various moduli of the material. After understanding the behavior of syntactic foams for low volume fractions, functionally graded materials (FGM) with linear variation of increasing volume fraction were manufactured and studied. Further quasi-static compression and low velocity impacts were also performed to better understand the static and absorption behavior of both syntactic foams and FGM materials. It was found that larger microballoon size had higher attenuation values but not necessarily higher wave speeds in syntactic foams. Matrix absorption was the main attenuation parameter. Ultrasonic tests on FGMs suggest higher degree of interaction due to the impedance mismatch between each layer. Lower volume fractions had higher compressive strength than higher volume fractions. This knowledge is important in understanding the bond strength between the particulates and the epoxy matrix. The peak stress in impact loading decreased with increasing volume fraction and was highest for the smallest size microballoon. Peak load of smallest microballoon size FGM was higher than plain syntactic foam of similar density. ACKNOWLEDGMENTS I would like to thank my advisor Dr. Carl-Ernst Rousseau for his constant support and guidance during the course of my work. I would also like to thank Department of Homeland Security for providing the funding for my research. I am also thankful to Mr. Tom Nelligan of Olympus NDT for his technical expertise and guidance. I would also like to thank Dr. Shukla for making laboratory equipment available for my research. I would also like to thank the Faculty and Staff in the Department of Mechanical, Industrial and Systems Engineering for their help and encouragement throughout my study. I would also like to thank my lab mate Gifford Plume for his technical advice and discussions. I am also deeply thankful to Rakshya Shrestha for always being there for me throughout my study. Finally, I am grateful to my parents, sister and close friends for their invaluable support throughout my time at URI.

This study will characterize hollow particulate composites and graded materials using ultrasonic techniques. The study focuses on the influence of volume fraction and micro-balloon size on the ultrasonic properties of these materials.
Attenuation and speed of propagation of ultrasonic waves vary with change in material composition and property and are used for purposes of characterization of materials.
Quasi-static compressive tests and low velocity drop tower tests were also carried out and the results compared for full comprehensive understanding of the overall material behavior.
Measurement of wave speed within the material and attenuation of ultrasonic waves are parameters important to its characterization [1]. Attenuation refers to the energy loss associated with the decrease in the stress wave amplitude due to both scattering and absorption [2]. They include scattering at the hollow glass particulates, interface absorption within the epoxy matrix and reflections of wave from surrounding particulates and its interactions, and other losses. Hence, due to the nature of the dispersive medium a proper understanding of the attenuation and wave speed behavior must be properly achieved.
Non destructive testing (NDT) methods are used extensively to evaluate material properties. They are being used in characterization of core materials used in sandwich composites, aerospace and naval industry. Ultrasonic characterization is a novel technique being used in many structural and civil applications for measurement of structural stability and reliability.
Newer synthetic composites are being evaluated with ultrasonics for faster and more reliable characterization. In this study, the focus will be hollow particulate composite materials which have high strength to weight ratio, corrosion resistance, high bending stiffness, and excellent thermal capabilities due to the high strength of the glass microballoons. Epoxy matrix embedded with these hollow glass microballoons have been coined syntactic foams. Syntactic foams also have a broad range of multi-functionality due to their vibration damping characteristics and can also be fabricated into functionally graded materials. Their main advantage is that they can be designed and fabricated according to the physical and mechanical requirements of the desired application.
Numerous quasi-static tests have been carried out to determine static stiffness and yield strength of these materials [3][4][5]. Recent studies have also shown that wave analysis techniques can be used to determine these dynamic properties [1,[6][7][8].
Nomenclatures for all specimens in this study are given below. An example of the syntactic foam naming is 'K37-40', where K37 identifies the microballoon type and 40 is the volume percentage of microballoon in syntactic foam. For functionally graded materials 'K37-040-5FGM', where K37 is the microballoon type followed by '040' which denotes 40% as the highest volume percentage of the layers and 5FGM stands for five layered functionally graded material. For 'S60/10000' type microballoon 'S60' is used as the nomenclature in this study.

Review of Literature
Ultrasonic wave measurements were introduced in mid 1950s. Hirone and Kamigaki [9] calculated the attenuation coefficient of aluminum using ultrasonic waves at a frequency of 2 to 25 MHz. Attenuation coefficients showed a strong dependence on the grain size of the material and frequency.
Further theoretical work was also being conducted evaluating the scattering of plane longitudinal wave by spherical obstacles by Ying and Truell [10]. They discussed three types of obstacles: an isotropically elastic sphere, a spherical cavity, and a rigid sphere for Rayleigh scattering.
Datta [11] further studied the scattering of plane longitudinal waves by a distribution of elastic ellipsoidal inclusions. Using a self consistent approximation and assuming distribution of scatterer centers as a random homogenous function of position, approximate wave speeds are derived for certain orientations. Various theories and application of wave propagation and scattering are discussed by A.
Wave propagation on random particulate composites was studied by Beltzer,  [7] takes into account the effect of particle size, porosity and radius ratio while measuring the ultrasonic attenuation of syntactic foams at low volume fractions.
Attenuation losses by absorption, scattering and resonance are integrated into the model. For a frequency of 1 MHz and volume fractions up to 30% good correlation between the experimental and theoretical results were obtained.
Mylavarapu and Woldesenbet [1] also studied the effects of volume fraction of solid sphere in epoxy matrix and the ultrasonic wave attenuation, wave speeds and dynamic Young's modulus were calculated. In the case of solid spheres, particulate composites showed higher attenuation than syntactic foams of similar sphere size due to internal resonance of solid glass spheres. They also showed that the wave speeds of solid particulate composites were also higher than the syntactic foams. Ultrasonic properties of polyester/fly ash composites were also studied by Rohatgi,Matsunaga,and Gupta [32]. Ultrasonic measurements were used to calculate various material properties such as shear modulus, Young's modulus and bulk modulus. Attention was given to decrease in attenuation with increasing volume fractions of fly ash microballoons. It was seen that the velocity of ultrasound was faster in fly ash microballoons than in the polyester matrix.
Characterization of materials is incomplete without material stress strain behaviors. There have been many studies related to the compressive behaviors of syntactic foams and solid particulate composites [33][34][35][36][37][38][39]. Gupta,Woldesenbet and Jerro [33] studied the effects of microballoon radius ratio on the compressive properties of syntactic foams. They noticed that the compressive strength and modulus of syntactic foams increase with a decrease in the microballoon radius. Gupta,Woldesenbet,and Mensah [34] also conducted compressive tests on syntactic foams of different radius ratios and found similar results. They found that orientation during compression affected the peak stress obtained. Tensile properties of vinyl ester microballoon syntactic foams were tested by Gupta,Ye and Porfiri [35]. It was found that the tensile modulus was 15-30% higher than the compressive modulus for same type of syntactic foams. This was due to particle-matrix interfacial debonding and the possibility of particle fracture under compressive loading conditions. Further tests on layered syntactic foams were conducted by Gupta and Ricci [36]. They introduced functionally graded syntactic foams not based on volume fraction but on microballoon wall thickness variation along the length. Syntactic foam behaviors were studied at higher strain rates of 1s -1 to 1000s -1 [40][41][42][43][44][45]. Hsiao and Daniel [40] studied the strain rate on the compressive and shear behavior of carbon epoxy composite materials. They showed that for cross ply laminates the dynamic stress strain curve stiffened with increasing strain rate. The shear stress-strain behavior also showed that the plateau region of stress increased with increasing strain rate. Low velocity impacts on nanoparticulate syntactic foams were also performed by Woldesenbet [41]. Here nanoclay is mixed with low density syntactic foams and it was observed that at 1% nanoclay volume fraction peak load and highest initiation energy was obtained. Also microcracks were being contained by the stiffer nanoclay particulates in forming major cracks. Li and Jones [42] did similar low velocity impacts on rubberized syntactic foams. The results showed that rubberized syntactic foams were able to absorb higher amount of energy with very little loss in strength. SEM pictures showed that several mechanisms were activated to collaboratively absorb impact energy, including microballoon crushing, interfacial debonding, matrix microcracking, and fiber pull-out; the rubber layer and the microfibers prevented the microcracks from propagating into macroscopic damage by means of rubber pinning and fiber bridge-over mechanisms [42].
Higher strain rate impacts were performed by using split Hopkinson Pressure Bar to obtain the dynamic compressive behavior of syntactic foams. Song,Chen and Frew [43] assessed that the compressive strength of epoxy syntactic foams increased with strain rate up to a transition strain rate between 550-1030s -1 .Woldesetbet and Peter [44] also studied the effects of volume fraction of syntactic foams on the strain rate properties. The results showed that there is a decrease in compressive strength and modulus for increasing volume fraction. For high strain rates of 800s -1 , there was a large decline in strength and modulus for up to 10-20% volume fraction followed by steady decline. Temperature effects on the dynamic compressive behavior were also studied by Song,Chen,Yanagita,and Frew [45]. Environmental temperature had a significant effect, i.e. with decreasing temperature, the foam initially hardens but then softens when below a transitional temperature. Based on the experimental data collected a model taking into account temperature and strain effects was developed and tested.
Hence even with the immense research in the field of strain rate testing on syntactic foams, there has not been much work that can be found for attenuation and wave speed of syntactic foams and FGMs. Not all sizes of microballoons have been tested for ultrasonic attenuation and wave speed measurements. There is also a lack of literature on the volume fraction FGMs material properties and layering effects. This study will focus on first developing a clear relationship of attenuation and wave speed behavior of syntactic foams with 3 different types of microballoons. This knowledge will be utilized in making FGMs of different sized microballoons and characterizing them using ultrasonic techniques. Effect of radius ratio and volume fraction of syntactic foams on ultrasonic and compressive behaviors will also be studied. Future work will involve relating ultrasonic attenuation to stress wave attenuation from destructive impact testing. under the brand name 'Scotchlite Glass Bubbles-General Purpose Series' [1]. The details about the microballoons are provided in Table 1.
Radius ratio is defined as the ratio of inner and outer radius of the sphere and represents the hollowness of the sphere. The spheres have different radius ratio and size leading to difference in density and void content in epoxy syntactic foam. As the radius ratio and particle size increases the density of the syntactic foam for the same volume fraction decreases. The density of the syntactic foams also decreases with increase in volume fraction due to increasing voids inside the matrix.

Syntactic Foams
Appropriate amounts of resin and hardener were poured according to the manufacturers specifications. The epoxy was mixed in the ratio of 73.5% resin and 26.4% hardener.
First, hardener was poured in a heat resistant paper cup and weighed in a OHAUS Scout Pro digital scale with an accuracy and maximum weight limit of 0.1g and 400g, respectively. The required amount of resin was poured into the cup which was tilted at a 45 degree angle and gently stirred using a wooden stirrer. After 5 minutes of stirring, the cup is left alone at room temperature for another 5 minutes to reduce the amount of air bubbles formed during stirring.
The cup is then placed back into the scale and a known mass of microballoons is added to the mixture. It is stirred again slowly until all the clumps of microballoons have been dispersed evenly in the mixture. It is then cast into 1.5" (38.1 mm) inner diameter and 1" (25.4 mm) inner height plastic cylindrical casting cups (manufactured by Beuhler, ID 20-9181). These cups have been coated with release agent (Beuhler ID 20-8185-016), 5 minutes prior to pouring the mixture so that the epoxy will not bond to the walls upon hardening.
After pouring the mixture into the cup it is taken to a vacuum chamber and kept at a vacuum pressure of 30 torr (0.58 psi) for 10 minutes to remove air bubbles. It is then gently stirred and set to cure for 24 hours at room temperature although a set time of 9 hrs is specified by manufacturer. Due to the microballoons having lower density than the surrounding epoxy, it rises up through the mixture during the vacuuming process. Hence the mixture is gently stirred again before setting it for cure.
After curing the sample is extracted from the casting cup and machined to the required size for testing.

Functionally Graded Syntactic Foams (FGMs)
The cast is assembled and labeled with a marks for each layer as shown in After the cast has been placed, the first layer from the bottom is filled with of virgin epoxy and left to cure for 1 hour. After another hour 10% volume fraction syntactic foam mixture is poured on top of the first layer until it reaches the location designated for the bottom of 3 rd layer. Here no adhesive is added as the bond between the layers is assumed to be stronger and a more linear variation of the gradation is obtained. This process continues with increasing volume fraction upto a 40% volume fraction at the top of the cast. The top layer has slightly larger thickness so that it is easier to machine to the required dimension for testing. The same process is followed for making 0-30% FGM.

Volume Fraction and Density Calculation
In order to characterize the volume fractions and the required mass of microballoons in the syntactic foam, Equation 1 was used. Volume fractions ranging from 5-40 % were calculated in this analysis. Table 2 shows the syntactic foam composition by mass for one casting cup.   Figure 2. Results of density calculation of FGMs are shown in Figure 3 and Figure   4. As shown in Figure 2, the measured density decreases with increasing volume fraction. Also from Figure 3   The values of density are higher for the FGMs 0-30% than the FGMs 0-40% because with increasing layer of higher volume fraction, more voids are created and hence it lowers the overall density of the FGM. It is assumed for all analysis that, the volume fraction of natural voids, formed during the mixing and curing process is negligible and occupies 0 to 4% with the latter value being for higher volume fractions.

Ultrasonic Testing
The main focus of this study was to characterize the syntactic foams according to ultrasonic wave speed and attenuation. All specimen faces were sandpapered to make the surfaces smooth for ultrasonic testing. Description of the experimental setup, equipments used, instrumentation, test procedure and data analysis for the ultrasonic tests are given below. Figure 5 gives the overall view of the experimental setup used for immersion testing.

Figure 5. Ultrasonic Immersion Testing Setup
Here the pulser/receiver instrument generates short, large amplitude electric pulses that are converted into short ultrasonic pulses that are applied to the ultrasonic transducer. The pulses cause the piezo-electric crystals to vibrate and thus produce an ultrasonic wave.
The wave from the transducer travels through the specimen and the voltage signals from the reflected waves at the back surface of the specimen are detected, amplified and measured in the oscilloscope. The reflection happens at the back surface and the front surface due to the large impedance mismatch between the solid specimen and water (couplant). Both surfaces of the specimen are exposed to water for uniform coupling which reduces the sensitivity variations of the received signal for immersion transducers. A thick, sticky and highly viscous PANAMETRICS couplant SWC was used for shear wave contact transducers for shear wave testing as shear waves does not propagate in liquids.

Transducers
Ultrasonic tests were carried out with both immersion and contact type transducers. The transducers used for the test were of the frequency 1 MHz for immersion and 2.25 MHz for shear wave contact testing. Higher frequency immersion transducers from 2.25 to 5 MHz were neglected for the test due to the high attenuation and inconsistent results. All samples were tested using pulse-echo method to determine the response to ultrasonic waves.
The longitudinal wave attenuation and wave speed were evaluated using the ultrasonic immersion transducer as shown in Figure 6. The shear wave speed was measured using the contact transducer as shown in Figure 7. testing. An average of 16 values was taken for each waveform passing through a point in the oscilloscope. The gain was set such that at least 2 back reflections were seen during the event. All tests were carried in water and of a room temperature of 23 degree Celsius. Calibration of the transducers was done for materials with known wave speeds (aluminum and polycarbonate) before each test to ensure the correctness of the experimental results.

Pulser/Reciever
The pulser/receiver unit for all the ultrasonic testing was the PANAMETRICS 5058 -PR as shown in Figure 8. It was designed specifically for a pulse-echo or through transmission testing modes but only the former was used here. It has a capability of excitation voltages of up to 900 V. It has up to 80 dB of attenuation and 60 dB of gain for signals entering the receiver unit. The high voltage pulser and high gain receiver make it ideal for testing composites. Signals received by the receiver unit are transmitted to the oscilloscope for further processing.

Digital Oscilloscope
A Tektronix TDS 3014B Four Channel Color Digital phosphor oscilloscope capable of 10000 sample points per second was used as shown in Figure 9. The BNC end of the coaxial cable was attached to the Rf connecter of the pulser/amplifier. The scale on the oscilloscope was 4 μs/div on the X axis and 1 Volt/div on the Y axis. The data was saved in a 3.5" (88.9 mm) floppy disc and transferred to the computer for further analysis.

Tank and Accessories
The immersion tank is made up of 0.5" (12.7 mm) thick polycarbonate sheets.
The stand is stainless steel and the specimen and transducer holders were made with T-6061 grade aluminum. It was chosen as it was easily machinable and non-corrosive.
Rubber gaskets were inserted in between the insertion of transducers to allow for proper parallel alignment with the specimen and loss of signal from contact with the aluminum periphery. A level was used to check the alignment before experimentation.
The coaxial cable of 50 ohm impedance with a BNC to waterproof UHF (up to 50m) was used for the immersion testing. The shear wave testing was conducted with a 50 ohm coaxial cables with BNC to microdot connecters.

Test Procedure
Immersion Testing 1. Fill the tank with water up to 7.5" (190.5 mm) depth and water temperature of 23º C.
2. Connect the BNC Cable output to the receiver and the UHF output to the transducer.
3. Connect the BNC cable from the sync out from pulser/receiver to the oscilloscope Channel 2.
4. Connect the BNC cable from the RF output of the pulser/receiver to the oscilloscope Channel 1 as shown in Figure 10.

Figure 10. Cable connection of Pulser/Reciever and oscilloscope
5. Turn on Oscilloscope and set the Y axis as 1volts/div, X axis to 4μs/div and from the 'Acquire Menu' select mode and set to 16 point averaging.
6. Set the Pulser/Receiver settings to repetition rate of 500 Hz, damping to 200Ω, pulse height to 200 volts, mode to pulse echo transmission, attenuation to 0 dB, gain to 40 dB, HP filter to 1 MHz, LP filter to out.
7. After machining to the required dimensions, the prepared specimen's center was located and 0.5" (12.7 mm) circle was drawn around it with a circular ruler as shown in Figure 11. The required measurement of height of specimen was measured from the center of the circle with a micrometer with 0.0001" (0.00254 mm) precision.

Figure 11. Circular Ruler Marking
8. It is then placed on the specimen holder and tightened with the help of 3 soft tip set screws at 120 degrees angle around the periphery as seen in Figure 12.
The specimen holder is then slid on the stand until it reaches the tip of the transducer.
9. The specimen holder screw was tightened at the end of clamp. Alignment of the circle of specimen to the tip of transducer was done by slightly pressing the specimen against the transducer bottom with a flat plate. The soft tip screws were loosened and slight adjustments were made. They were tightened again, ensuring the transducer and the circle drawn on the specimen were vertically aligned. 11. The whole setup was immersed in water and the pulser/amplifier turned on.
12. Disturbances in water were allowed to subside and the data was recorded by the oscilloscope.
13. The specimen was removed steps 7-12 were, again, repeated. 8. Turn on the pulser/receiver and save the data in oscilloscope.

Compression Testing
For further characterization of syntactic foams and graded materials, quasistatic tests were conducted using ASTM D 695-63T Standards [1]. The tests were conducted in an Instron 5582 machine with a loading speed of 1.3mm/min. The force measuring range of the load cell is from 0-100 kN which is applicable for this study.
The tests were conducted until total fracture of the specimens, as seen from the realtime load extension graphs on the computer connected to the Instron machine. The data was obtained from the load transducers attached to the Instron head. After completion of the experiment, the data was analyzed and plotted to evaluate true stress-strain plots. Specimens were coated on the top and bottom surface with a thin layer of lubricant for better contact between machine head and specimen. Before running the tests, a compliance test at 0.01in/min (0.254 mm/min) with no sample was conducted for calibration of the initial adjustments of machine head. Figure 13 shows the Instron testing machine used for quasi static testing.

Drop Tower Impact Machine
A Dynatup 9210 drop tower assembly was used for low velocity impact at 3 m/s impact velocity as shown in Figure 14. The impact data which includes the load, energy, displacement, velocities with respect to time is obtained by the data acquisition software connected to the drop tower assembly. The system is capable of producing impact velocities up to 5m/s depending upon the weight and height input into the system. Various types of strikers can be adjusted into the tup which records data up to maximum load of 10,000lb (44.48 kN).
The sampling rate of the system is up to 4.1 MHz. The system was modified to allow for the implementation of a fixed back support fixture outside the drop tower enclosure. The impact test was performed until the bottom of the cross head reaches the stop blocks.
First the drop height was that would result in an impact velocity of 3m/s must be determined. The mass of the system was first calculated. It included the total mass of crosshead, weights, tup, tup bolts, striker, reaction plate and bolts. Table 3 shows all the components of mass being applied to the system. imparted to the specimen. The impact energy for the analysis was determined by, E = mgh [2] Where m is the total mass of the drop weight, g is the acceleration due to gravity and h is the height from which the mass was dropped.
Also verification of the impact velocity obtained from machine was checked against velocity determined by When checking the velocity of impact, first the striker bar is lowered until it just touches the specimen. Then the velocity sensor is adjusted so that the bottom edge 35 of the detector aligns with the bottom edge of the flag. This is the point from which the height is calculated for testing. A number of velocity tests are performed before each set of experiment. A quoted calibration factor was input for the tup for correct data acquisition. The input variables are listed in Table 4. The duration of data collection was set at 20 ms at a sampling rate of 409.6 kHz to allow ample time of data recording during the impact event. The impact time was between 0.5 to 6ms.

Ultrasonic Testing of Syntactic Foams
In a transducer there are many waves that emanate from the piezo-electric and it is called near field zone. This beam spreads out and a far field zone of intense uniform field develops at a certain distance from transducer field. This far field zone is the ultrasonic longitudinal wave travelling through a medium. For our ultrasonic testing we utilize the propagation of this longitudinal wave using the C scan method.
In a typical C-scan ultrasonic pulse echo technique acoustic impedance plays a major role in analyzing the wave data. Acoustic impedance (Z) of a material is defined as [1,2]: Where ρ is the density of the material and v is the sound velocity. At the boundary between two materials lies the acoustic interface where, due to different acoustic impedance of the two materials, a wave travelling from one media to another is partially transmitted and partially reflected as shown in Figure 15. According to Non-Destructive Testing (NDT) [3] the reflection coefficient (R) is calculated by: T =1-R [6] Where T is the transmission coefficient. The amount of energy reflected depends upon the difference in acoustic impedances at the boundary. The higher the difference in acoustic impedances, the higher will the value of the reflection coefficient be. Hence this property determines the wave energy being reflected from the interface boundary.

Figure 15. View of reflected and transmitted wave at interface boundary
A typical ultrasonic wave form obtained for the syntactic foams is shown in Figure 16. The peaks corresponding to the back wall reflection of the specimen can be clearly seen from Figure 16. The location in the time axis and the corresponding amplitude is noted for the first two back wall reflections to calculate the longitudinal wave speed and attenuation in the specimen. The third back wall reflection was omitted because it could not be detected in all samples. ASTM E664 -93 is used to calculate the apparent attenuation [4].  Where A m and A n = amplitude of m th and n th back reflections (n>m) and t = specimen thickness.
Attenuation of an ultrasonic wave here is compared with a previously determined theoretical model for low volume fractions. The model, developed by Mylavarapu and Woldesenbet [5] is based on ultrasonic attenuation by scattering and absorption of spherical elastic microballoons taking into account the matrix attenuation. Their model takes into account the effect of particle size, porosity and radius ratio. Attenuation coefficient according to model proposed by Mylavarapu and Woldesenbet is calculated by Equation 8 [5].
Where ν is the Poisson ratio, E is the Young's Modulus and G is the shear modulus.
Specimens' sizes for all syntactic foam testing were 0.5" (12.7 mm) thickness and 1.5" (38.1 mm) diameter. Five specimens were tested per volume fraction for all syntactic foams. The water path between the transducer and the specimen was 26.5 mm.

Attenuation results
Attenuation coefficient for pure epoxy was 0.434 dB/mm. All errors are calculated by taking the change from the mean value, the maximum and minimum from the five samples. Some examples of wave reflections obtained from the syntactic foams are shown in Figures 17-19. and Table 5, attenuation is highest for the largest size micro-balloon (K1) and lowest for smallest size microballoon S60. It increases for increasing volume fractions for K1 and decreases for K37 and S60 size microballoons.

Figure 20. Attenuation coefficient calculated from syntactic foams
In syntactic foam composites, wave propagation behavior, such as scattering at inclusions governs the elastic properties obtained by ultrasonic testing and are determined by the ratio of wavelength to particle size [6]. The range of the wavelength to particle size ratio was between 35-92 at 1 MHz as shown in Table 6. Hence, the ultrasonic wave will pass through clusters rather than millions of particles that are present in the composite. Therefore, scattering of ultrasonic wave does not occur at each and every particle-particle interface rather than between clusters of particles [6].
Due to the ratio being smaller for K1 size sphere than the S60 and K37, there is more probability of wave-particle interaction to occur hence a case for increase in wave attenuation. Due to the larger voids and smaller wall thickness, K1 size microballoon interacts with the plane longitudinal wave causing more scattering and absorption. It can further be noted that as the radius ratio decreases the material becomes more elastic, the absorption cross-section becomes zero and does not contribute to wave decay [7]. Hence the attenuation of K37 microballoon is higher than S60 due to larger voids for the same volume fraction and higher density. Longitudinal wave speeds of syntactic foams are shown in Figure 21. It can be seen that the wave speed increases with volume fraction for S60 and K37 type syntactic foams whereas it decreases for K1 type syntactic foams. Because of the larger voids and smaller wall thickness, K1 size microballoons interact with the plane longitudinal wave causing more scattering and absorption. The longitudinal velocity also decreases with increasing volume fraction due to more wave interaction with microballoons as shown in Figure 21. An increase in wave speed is the result of the wave travelling faster in the microballoon of smaller sizes S60 and K37 than the epoxy matrix hence less interaction with the surrounding particles and less scattering.
Average longitudinal wave speed values were calculated from 5 samples for each type of syntactic foam.
All longitudinal wave speed values for the syntactic foams with S60 and K37 were higher than pure epoxy longitudinal wave speed which was 2526 m/s. The small drop in wave speed for K37 at 20% volume fraction was negligible and could be due to properties of wave propagation not varying for low volume fractions in the range of 10-20%.

Poisson Ratio
Density (kg/m^3) particle ratio and higher speed than epoxy matrix. There is also a variation due to the assumption that the 'planar wave' of the ultrasonic beam propagates and comes back through the specimen of thickness 'l' without alteration [5].

Ultrasonic Characterization of Graded Materials
Graded specimens as shown in Figure 24 were tested with ultrasonic immersion pulse echo testing. The specimen was 1.  to the non-graded syntactic foams were obtained as seen in Figure 28. Graded syntactic foams with overall attenuation are presented in Table 8. The attenuation for FGMs were calculated from the front wall reflection and the 4th back reflection as shown in Figure 25. It can also be seen that the K1 FGMs had the highest attenution among the FGMs.

Syntactic Foams
The compressive modulus is measured by the slope of the initial linear portion of the stress strain curve. The compressive strength is the first peak in the stress strain curve. It is similar to the curves obtained by [8]. The linear portion is up to the elastic limit after which plastic deformation occurs. After reaching the peak stress the stress drops and nearly becomes constant. This region is called the plateau region or densification region. In this stage the microballoons are crushed and the open space is occupied by the debris are matrix material while getting compressed [8]. Cracks start to appear at the ultimate compressive strength value. For our analysis, only the linear portion up to the peak stress was studied.    Fracture accompanied by cracks formation along the direction of load was seen as shown in Figure 32. It can be seen that fewer cracks were formed for the 10% volume fraction than 40% volume fractions. Also there was more barreling effect seen for the lower volume fraction foams as the load was applied. This can be attributed by greater bonding and interfacial strength between the epoxy and microballoons at lower volume fractions.

Figure 32. Cracks formation on K1-40 (left) and K1-10 (right) type syntactic foams
Further absorption energy (toughness) was calculated for each type of syntactic foams by calculating the area under the stress strain curve. Absorption energy curves for all types of syntactic foams tested are shown in Figure 33. Absorption was calculated until the second peak stress in the stress strain graphs for all the materials. It can be seen that with the increase of volume fraction the material loses its toughness for all syntactic foams.

Functionally Graded Materials
Functionally graded syntactic foams with increasing volume fractions with the orientation were manufactured as shown in Figure 34. The volume fraction range was 0-40% with five layers of gradation. Each layer was 0.2" (5.1 mm) thick. The color of the layers turns from transparent green to opaque white with the addition of layers.

Figure 34. FGM 0-40% specimens for compression testing
The stress strain curves for the FGM specimens are shown in Figure 35. The curves represent an average of 6 samples for each microballoon type. Curves similar to those of the syntactic foams are observed for the graded specimens with S60 having the highest yield strength and modulus from all the 3 foams, as shown in Table 10.
Compressive modulus and yield values are between the ranges obtained for syntactic foams of 0-40%.   Figure 36, shows a sample of K37-040-5FGM after compression testing.
Barreling effect was seen in all specimens and cracks initiated at the stiffer side i.e. the 40% side of the specimens. The cracks ran along the middle of the specimen edge in the vertical direction parallel to the applied load.

Figure 36. Graded K37 specimen with cracks after compression testing
Values of compressive modulus and yield strength all were lower than the syntactic foam values for similar densities. This is attributed to the weaker interfacial bonds between layers compared to the more uniform bond in syntactic foams between particulates and epoxy. The absorption of FGM specimens were calculated from the stress strain curves. Figure 37 shows

Low Velocity Impacts
Low velocity impacts are the most common type of impacts experienced by materials. Collision occurring during parking, or dropping of a hammer are examples of such instances. During the events a small indentation may mark the outside while significant damage occurs internally. This could cause the load bearing capacity of a structure to reduce significantly and failure to occur soon afterwards. Hence low velocity impacts must be studied for these syntactic foams.
Six samples of syntactic foams and FGM (0-40%) 5 layered specimens were tested during this study. The load/energy vs. the time was recorded for the contact loading time as shown in Figure 38. It shows the load that is exerted on the sample while the tup assembly is in contact with the specimen during impact. The energy corresponding to the maximum load during impact is known as initiation energy. It is the energy that is absorbed by the material before failure. It can also be defined as the strain energy transferred elastically by the target [9]. The propagation energy is defined as the difference between the Maximum Energy and the Initiation energy. It includes all the energy absorption of the specimen during failure. Crushing of microballoons and crack formation are all accounted for in Propagation Energy. An ideal system for highest energy absorption prior to failure would consist of high Initiation Energy but absorption after failure to have high Propagation energy. Impact velocity of 3m/s was chosen for analysis for all tests. The dip in the energy curve after reaching maximum energy is due to impactor being pushed back by the specimen after reaching maximum deflection. Due to force acting in the negative direction, the impact force does negative work on the specimen and a portion of strain energy is transferred back to the impactor hence a decline in total energy.

Syntactic Foams Low Velocity Impacts
The specimen size was 11.43 mm in diameter and 22.86 mm in height. Figure   39 shows the maximum peak load obtained for all types of syntactic foams. The value is an average of six samples tested for each specimen. It can be clearly seen that the peak load decreases for all type of syntactic foams with increasing volume fraction. It is due to the increase in voids in the material causing the material to weaken. S60 type syntactic foams showed the highest peak load values of all the other type of microballoons. The peak load values follow the trend of smallest size microballoon with highest crush strength having higher load bearing properties similar to quasi static compression testing.  Table 11 can be used to further analyze the absorptive behavior, where initiation and propagation energy are obtained for each type of syntactic foam according to volume fraction. Numerical values for the peak load are also given in Table 11. The highest initiation energy was obtained for pure epoxy which also has the highest peak load, suggesting pure epoxy has higher load bearing capacity at higher strain rates. It can be seen that with increasing volume fractions initiation energy decreased, and that propagation energy increased for all type of syntactic foams. This denotes that the strength of the syntactic foams decreased with the addition of microballoons and better absorption during propagation was seen. The highest propagation energy was seen for the K1 type syntactic foams due to the larger microballoon size and ease of fracture than the other two microballoons. Figure 40 shows an impacted specimen of S60-10 type syntactic foams. It can be seen that there are multiple cracks which have been propagated cracks along the length of specimen. On the other hand, a higher volume fraction specimen such as K1-40 type syntactic foams was crushed as seen in Figure 41.

Funtionally Graded Materials Low Velocity Impacts
Graded specimens of 0-40% FGMs were also tested. The specimen size was 12.7 x 12.7 x 25.4 mm. Initiation and propagation energy of the specimens can be seen from Figure 42. The propagation energy are higher and initiation energy smaller for increasing bubble size of FGMs. This trend is similar to plain syntactic foams.
Lower density layers in the FGMs tend to absorb more energy during failure whereas the higher density layers add strength to the material. It can be seen that the S60 type FGMs showed a higher peak load than the other two FGMs as shown in Figure 43.
S60 FGMs showed higher load bearing capacity for impact loading than plain syntactic foams with similar density as shown in Table 12.   Figure 44 and 45 show the impacted specimens of FGMs. It can bee that failure of S60-040-5FGM are due to crack propagation whereas for K1-040-5FGM the failure is due to total crushing of the microballoons. Also S60-040-5FGM is stiffer than the K1-040-5FGM and hence K1-040-5FGM has higher propagation energy than S60-040-5FGM. 3. Attenuation values ranged from 0.324 to 0.632 dB/mm for all the syntactic foams tested. Attenuation was highest for the K1 type syntactic foams and increased with volume fraction. It suggests that scattering was a dominant factor in controlling the attenuation behaviors of these materials. Attenuation decreased with increasing volume fraction for S60 and K37 because of the increasing speed of the waves and the decreasing interaction with the microballoons. Absorption due to epoxy was also one of the main attenuation parameters. Clusters of particles for smaller size microballoons at higher volume fractions also affected the theoretical [1] and experimental values.
Values of attenuation coefficient predicted by the theoretical model suggests more experimental results on different size microballoons must be obtained and that parameters such as cluster to cluster wave interaction, scattering due to particle to particle interaction, internal losses due to heat, friction must be taken into account in the overall model. 4. Ultrasonic tests on FGMs suggest higher degree of interaction due to the impedance mismatch between each layer. Overall attenuation calculated from the front and 1 st back reflection of the last layer suggest similar trend as syntactic foams with K1 FGMs having higher attenuation than K37 and S60 syntactic foams. Wave speeds were also higher for the smaller size microballoons S60 FGMs than K37 and K1 FGMs.

Compression Tests
1. Increasing of compressive yield strength by lowering the volume fraction of microballoons and by using smaller size microballoons was seen for these tests on syntactic foams as supported by [2]. The values of compressive modulus and compressive yield ranged from 1325-2984 Mpa and 35-90 Mpa respectively. This suggests a wide load range capacity for these syntactic foams.
2. Failure was mainly due to crack propagation after the densification of the syntactic foams during compression. Cracks propagated in the direction of the load. Fewer cracks were observed for lower volume fractions than higher volume fractions. This is due to weaker particle to matrix bond strength since a higher number of microballoons are present with increasing volume fraction.
3. Values of compressive modulus and compressive yield strength were highest for S60 FGMs. This is due to the high crush strength of S60 microballoons.
Barreling effect was seen on all FGMs during compression. Cracks started at the high volume fraction side for all FGMs and ran in the direction of applied load.
4. Values of compressive modulus and yield strength all were lower than those of the syntactic foam for similar densities. This is attributed to the weaker interfacial bonds between layers compared to the more uniform bond in syntactic foams between the particulates and the matrix.

Expansion into solid particulate composites and their behavior to ultrasonic
wave propagation would be beneficial in choosing materials for determining and comparing the results of their wave speed and attenuation to those of syntactic foams.

Better methods of gradation of microballoons could improve properties of
FGMs and reduce the interlayer reflection occurring at each interface for evaluating attenuation coefficient.