Materials Science and Engineering C 49 (2015) 727–734
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Compressive evaluation of homogeneous and graded epoxy–glass particulate composites J. Seaglar, C.-E. Rousseau ⁎ Department of Mechanical, Industrial & Systems Engineering, University of Rhode Island, Kingston, RI 02881, USA
a r t i c l e
i n f o
Article history: Received 23 July 2014 Received in revised form 31 December 2014 Accepted 21 January 2015 Available online 22 January 2015 Keyword: Impact SHPB Compression FGM
a b s t r a c t The propagation of stress waves in epoxy–glass particulate composites and graded materials was studied experimentally. Materials tested in this study consisted of an epoxy matrix with various concentrations of spherical glass particles having a mean diameter of 42 μm. Plate impact experiments were performed using a gas gun. Embedded within the specimens were manganin stress gauges used to record propagating compressive longitudinal stress waves through the material. High strain rate experiments using a Split Hopkinson Pressure Bar (SHPB) apparatus were also performed to evaluate the dynamic strength of the specimens, while quasi-static compression tests were undertaken to characterize their quasi-static behavior. Ultrasonic wave speed measurements were carried-out in order to obtain additional material properties and characterize the gradation in functionally graded materials (FGM). It was found that low volume fractions of particles are detrimental to the performance of the material under impact loading, while concentrations in the range of about 30 to 45% by volume exhibit characteristics of higher degrees of scattering. This suggests that materials in this latter range would be more effective in the thwarting of destructive shock waves than the homogeneous matrix material. Impact testing of FGM specimens suggests that impact loading on the stiff (high volume fraction) face results in much higher levels of scattering. Therefore, such materials would be effective for use in light weight armor or as shielding materials due to their effective attenuation of mechanical impulses. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The study of the damage behavior of particulate composites has traditionally focussed on quasi-static loading. For example, Bazhenov [1] explored the quasi-static response of regular arrays of rigid particles in an elasto-plastic matrix, in which damage failure was related to particle/matrix debonding. That work revealed that the deformation behavior of the composite depended on the relation between the matrix strength and yield stress. Numerically, Garishin and Moshev [2,3] explored the quasi-static response of high volume fraction particulate composites, using a discrete structural model. Early dynamic research includes Herrmann's description of the Hugoniot curve in a ductile powder composite of porous aluminum and iron [4]. This was followed by the formulation of a stress wave propagation model in composite materials. In that work, Barker idealized composites as consisting of a system of periodically alternating materials, where the interaction between the successive layers of the resulting complex laminate would represent the scattering effect thought to be present within more general composites [5]. A similar approach was adopted by Oved et al. [6]. This simplistic, but appealing ⁎ Corresponding author at: 92 Upper College Rd., University of Rhode Island, Kingston, RI 02881, USA. E-mail address: [email protected] (C.-E. Rousseau).
http://dx.doi.org/10.1016/j.msec.2015.01.068 0928-4931/© 2015 Elsevier B.V. All rights reserved.
model was preserved as an experimentally ideal set up by Zhuang et al. [7], who, with the aid of internally positioned gauges, tracked a propagating shock wave at two discrete points located at the interfaces between alternating layers of aluminum and polycarbonate. Related experiments on laminated and fibrous composites include the works of Richardson and Wisheart [8], Cantwell and Morton [9], Aslan et al. [10], and Hebert et al. [11]. The bulk of the experimental work dedicated to particulate composites has focussed mainly on their fracture properties [12–16]. However, few attempts have been made to quantify the amplitude of compressive wave propagation in heterogeneous material, and much remains to be clarified concerning that process. In the above-quoted works, the phenomenon of geometric dispersion of elastic waves has received limited attention. The idea of geometric dispersion has guided this study into investigating the basic physical principles governing the propagation of elastic longitudinal stress waves in non-homogeneous particulate composites and graded materials. In particular, emphasis is placed on distinguishing material characteristics that can inherently thwart the evolution of a destructive shock wave. One of the primary mechanisms thought to impede of stress wave propagation is the phenomenon of scattering. Despite numerous analytical studies, the exact mechanism of scattering is not fully understood. Further, there is a lack of experimental data concerning particulate graded materials. This study is an experimental investigation of the propagation of stress waves in various
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concentrations of epoxy-glass particle composites and graded materials. In addition to impact experiments, both high strain rate and quasi-static compression experiments were performed in order to fully characterize the properties of the materials involved. Ultrasonic wave speed measurements were also performed and analyzed to obtain additional information on the inherent properties of the materials. The use of projectile impact conducted in order to investigate the propagation of stress waves through a material has been used extensively in previous studies [17–20]. The components necessary to perform impact experiments and gather data, such as gas guns, stress gauges, piezoresistive pulse power supplies, and velocity–interferometry systems have been well documented and are readily available. The data analyses performed for such experiments have been presented based on wave propagation theory and experimental correlations in [21–27]. The majority of experimental results obtained in the present study rely on data gathered from projectile impact, using stress gauge data to characterize the evolution of stress waves in the material. Additional relevant characteristic material data were obtained by means of Split Hopkinson Pressure Bars (SHPB) and ultrasonic pulser/receivers, resulting respectively in measurements of dynamic material strength at various strain rates, and longitudinal wave speed within the material [28–32]. The following sections present the procedures used to prepare the materials used in the study and a description of the experimental methods. The Experimental results section presents the relevant data gathered, which is followed by an associated discussion and some concluding remarks. 2. Materials The specimens used in this study were fabricated with an epoxy thermoset matrix mixture. Different variations of these materials were created, ranging from an indigenous material (no added particulates) to mixtures that included glass particles, and functionally graded materials. The following is an overview of the methods used to prepare and cast each specific type of material. 2.1. Preparation of virgin epoxy The epoxy used in all the castings is an Epo-Thin™ resin and hardener, manufactured by Buehler, Ltd. It is a low-viscosity thermoset with a nominal curing time of 18 h at room temperature. The resin is a bisphenol-A type epoxy resin. The hardener's primary ingredient is a polyoxyalkylamine blend. The density of the mixed epoxy is given by the manufacturer as 1147 kg/m3 and was also confirmed experimentally. 2.2. Preparation of homogeneous particulate materials The procedure used for producing castings containing micro-scale glass particles was identical to that used for the virgin epoxy specimens. Spherical soda-lime glass beads, manufactured by the Mo-Sci Corporation, were used. The primary ingredient of these particles is silica (SiO2), with a concentration of 72.5% by weight. The specific gravity of the particles is given by the manufacturer as 2.5, and the mean diameter as 42 μm. The nature of this study called for various concentrations of these particles to be mixed with the epoxy prior to casting. The concentrations used for casting were chosen incrementally to be 2, 10, 20, 30, and 40 g of glass per 17 g of epoxy (17 g was the nominal weight of epoxy used to fill a single casting cup, composed of 12.5 g of resin and 4.5 g of hardener). Knowing the densities of the glass particles and the epoxy, it is straightforward to obtain the volume fractions for each respective concentration. These were approximately 5, 21, 35, 45, and 52%, respectively. 2.3. Preparation of functionally graded specimens Functionally graded material (FGM) castings were produced by combining virgin epoxy with glass particles. This consisted of 12.1 g of
resin, 4.3 g of hardener, and 38.6 g of glass particles. In the absence of further mixing, the glass particles, which were initially uniformly distributed in the epoxy, gradually settled toward the bottom of the mold, concurrently with the hardening processed triggered by the thermosetting reaction. As a result, the bulk of the glass particles settled at the bottom due to gravity. However, a substantial number of particles remained suspended at various intermediate heights, resulting in specimens exhibiting smooth property gradations with vertical distance. More details on the gradation of these specimens can be found in the Experimental results section, which presents data from ultrasonic measurements. 2.4. Predicted and measured specimen densities The theoretical density of each glass–epoxy composite specimen was evaluated using the rule of mixtures. The given specific gravity of the glass particles was 2.5. The density of the epoxy was given by the manufacturer as 1147 kg/m3. The rule of mixtures, as it applies to the current specimens, can be formulated as: ρmix ¼ ρglass V f −glass þ ρepoxy 1–V f −glass ;
ð1Þ
where Vf-glass is the volume fraction of glass, and ρmix, ρglass and ρepoxy are the densities of the composite mixture, the glass particles, and the epoxy matrix, respectively. For each volume fraction, individual specimens were weighed, their volume measured, and the associated measured density was obtained. Differences between theoretical and measured densities increased with increasing volume fractions of the glass particles in the matrix. The presence of air voids is noted to be exacerbated by the accumulation of glass beads in the castings, and was identified as a primary contributor to this variance. The weight and density of the constituents, and the measured and theoretical volumes of the composites were used to approximate the volume of air in each specimen. This volume of air was then divided by the measured volume to calculate the percentage of air by volume in each specimen. Table 1 summarizes these evaluations and shows that the maximum air volume fraction is 4.1% for the specimens measured. 3. Methods of evaluation 3.1. Impact testing The primary focus of this study was to investigate the behavior of cast epoxy materials subjected to impact loading. Following methods established by other researchers [1,2,4,17–20], an experimental procedure and setup were designed, which is shown in Fig. 1. To achieve planar plate impact, a 19 mm (0.75 in.) diameter polycarbonate impactor was machined to a thickness of 3.18 mm (0.125 in.). In order to accelerate the impactor to the desired impact speeds of approximately 300 m/s, a single stage helium-powered gas gun with a 2.1 m (7.0 ft) long, 2.54 cm (1.00 in.) diameter barrel was used. The impactor was appended to the front face of a 2.53 cm (0.995 in.) diameter, 2.54 long Table 1 Density and air void data for epoxy–glass specimens. Specimen
Vf glass (%)
Theoretical density (kg/m3)
Measured density (kg/m3)
Volume of air (cc)
Percent air by volume
0g 2g 10 g 20 g 30 g 40 g
0 5 21 35 45 52
1147 1216 1435 1621 1752 1849
1160 1204 1420 1591 1713 1773
0 0.0608 0.0607 0.1114 0.1354 0.2475
0 1.003 1.014 1.846 2.251 4.101
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Fig. 1. Gas gun impact test setup.
(1.00 in.) Teflon sabot. The use of the sabot prevented damage to the impactor during firing, and enhanced its stability. The various specimens were placed at the exit of the gun barrel for impact. In order to capture the stress waves propagating through the specimens, manganin stress gauges (manufactured by Dynasen, Inc. and Vishay Micro-Measurements) were embedded within the specimens. The gauges were used in concert with a piezoresistive pulse power supply, a four-channel digital oscilloscope, and a light emitter/ detector (photodetector). The entire impact event is captured and recorded for later analysis. For cases where virgin and non-graded homogeneous specimens were being probed, these specimens were subdivided into three distinct layers to allow the embedding of stress gauges at two intermediate locations. Fig. 2 shows the configuration of a typical non-graded specimen, where the 7.62 mm (0.300 in.) top layer corresponds to the face that is subjected to impact. Having two gauges at discreet locations within the specimen provides information as to how the stress wave changed throughout its propagation. For functionally graded specimens, the front (impacted) layer was graded, while the back layer was selected to have a glass volume fraction that matched that of the graded layer at the interface. In order to compare performance of these materials under impact, one specimen was chosen to have the stiff (high volume fraction) face subjected to impact, while for the other case, the compliant (low volume fraction) face was subjected to impact. Fig. 3 illustrates the case corresponding to the former. In order to perform a test, the specimen was first placed in the designated specimen holder, at a distance of 30 cm (12 in.) from the end of the gun barrel. The alignment of the gun and the specimen was finetuned in order to maximize the instances of fully planar impact. All data acquisition devices were inspected and set to ensure that the
whole impact event would be captured. The gas gun was then pressurized to 2.07 MPa (300 psi) and discharged, thus releasing the impactor and sabot assembly at speeds of 300 m/s. Upon completion of each test, debris were collected and labeled for post-mortem analysis. Data from the photodetector was used to calculate the projectile velocity, using the interruption time of the light beam. The manganin gauge data established the basis for subsequent stress wave analyses, using procedures outlined in the Dynasen pulse power supply manual [27] to convert the voltage data as acquired by the manganin gauges into units of stress.
Fig. 2. Specimen configuration and stress gauge locations.
Fig. 3. Schematic of functionally graded specimens.
3.2. SHPB testing To further characterize the dynamic behavior of the epoxy–glass composites, high strain rate compression tests were performed using a Split–Hopkinson Pressure Bar. The experiments were conducted with specimens having 0, 21, 35, 45, and 52% volume fraction of glass sphere in the matrix. The specimens were first machined from castings by using a combination of turning and facing processes to obtain the dimensions of 9.53 mm (0.375 in.) diameter and 6.35 mm (0.250 in.) thickness. Aluminum bars of 12.7 mm (0.500 in.) diameter were used
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for incident and transmitter bars. The striker bar was powered by a pressurized gas mechanism. A total of four strain gauges were mounted on the bars, two on the incident bar and two on the transmitter bar. The gauges were connected to a data acquisition unit that contained both strain gauge amplifiers and transducers, connected to a computer for data recording. The equation relating the strain history from the transmitter bar to the stress in the specimen is:
these discrete locations along the height of the specimen (parallel to the direction of gradation). This resulted in different wave speed readings at each location, which was characteristic of the gradation of glass particles through the height of the specimen. 4. Experimental results 4.1. Ultrasonic evaluation
A σ ðt Þ ¼ Eb b εT ðt Þ A
ð2Þ
where Eb and Ab are the Young's modulus and cross-sectional area of the bar, respectively. εT (t) is the average value of the two strain gauges on the transmitter bar. A is the cross-sectional area of the specimen [22]. Tests at pressures of 69 kPa (10 psi), 140 kPa (20 psi), and 280 kPa (40 psi) were conducted by sandwiching the specimens between the incident and transmitter bars, the surfaces of which were lubricated slightly in order to prevent localized Poisson's effects from manifesting within the specimen. The test data was then transferred from the data acquisition unit to another computer workstation for analysis. The strain rates for the above-mentioned pressures were 800 s−1, 1700 s−1, and 2900 s−1, respectively. 3.3. Quasi-static compression testing In order to gather information on the compressive strength of the materials subjected to quasi-static loading, compression tests were done, based on ASTM D 695-85 Standards [33]. The tests were done using an Instron 5582 testing apparatus with cylindrical plate fixtures and a load/ extension transducer designed for compression tests. The specimens were machined from castings by using turning and facing to achieve the dimensions of 6.35 mm (0.250 in.) diameter and 12.7 mm (0.500 in.) height, conforming to the height to diameter ratio of 2:1 prescribed by the ASTM standards. Two samples were tested for each concentration of glass particles, at a loading rate of 1.3 mm/min. In most cases, the tests were conducted until complete fracture was observed, although the decision to stop the tests was based on observation of the real-time load-extension graphs. As a result, not all tests display complete fracture. Upon completion of the tests, the loadextension data was exported and analyzed. 3.4. Ultrasonic testing Measurements using an ultrasonic pulser/receiver were conducted to investigate the wave speeds of the materials of interest and characterize the degree of gradation of the FGM specimens. A PanametricsNDT Model 5058PR with an attached 5.72 mm (0.225 in.) throughtransmission sensor was used for this purpose. Machined 7.62 mm (0.300 in.) thick samples of the cast materials were used. The wave speed was calculated by measuring the time interval for the peak of the first pulse to reflect back to the transducer. Since the distance traveled is twice the thickness, this calculation is very straightforward and produces accurate results. For FGM specimens, a 12.7 mm (0.500 in.) thick section was machined along the direction of gradation. Tick marks were placed every 1.59 mm (0.0625 in.) on the specimens and ultrasonic readings taken
Table 2 shows the wave speeds for homogeneous epoxy–glass specimens as measured with the ultrasonic pulser/receiver. Ultrasonic measurements were also conducted on machined FGM specimens in order to measure the wave speed at various locations and determine their gradation. The volume fraction of glass particles at each location was then computed using data from Table 2 and is plotted in Fig. 4. The volume fraction is shown as a function of the distance from pure epoxy, which is situated at the top of the specimen, where it is completely devoid of glass particles. 4.2. Results of impact evaluation Multiple experiments were performed for each concentration of glass particles in the epoxy matrix. Data for the six concentrations of glass particles (0, 5, 21, 35, 45, and 52% volume fraction) as well as an FGM impact test are presented here. A typical test of each glass concentration is shown. These results depict representative experiments characterized by planar, central impact, exhibiting strong gauge signals, and devoid of any anomalies. Fig. 5(a)–(f) shows the front and back gauge stress data for each type of epoxy–glass particle composite specimen tested. The time scale corresponds to the elapsed time from the moment the photodetector was triggered. Table 3 is a summary of the results for non-graded specimens. “Impact velocity [interruption time]” refers to the projectile velocity calculated using photodetector interruption time and projectile length. “Impact velocity [delay time]” refers the projectile velocity calculated using an alternative method involving the time delay between the triggering of the photodetector and the arrival of the stress pulse at the front stress gauge. This method takes into account the time for the projectile to travel to the impact surface of the specimen, and the time for the stress wave to reach the front gauge (different for every specimen due to varying wave speeds). “Ultrasonic wave velocity” is the wave velocity measured using the ultrasonic pulser/receiver, whereas “calculated wave velocity” is the approximate experimental wave speed obtained by measuring the time interval between the arrival of the stress pulse at the front gauge and
Table 2 Ultrasonic wave speed measurements for epoxy–glass specimens. Specimen
Vf % glass
wt.% glass
Wave speed (m/s)
0g 2g 10 g 20 g 30 g 40 g
0 5 21 35 45 52
0 10.53 37.04 54.05 63.83 70.18
2675 2609 2802 3022 3172 3350
Fig. 4. FGM gradation.
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Fig. 5. Stress gauge data: (a) 0%, (b) 5%, (c) 21%, (d) 35%, (e) 45%, (f) 52% Vf.
its arrival at the back gauge. “Front” and “back gauge rise time” are the periods of time necessary for the front and back gauge signals to reach an initial peak value. Finally, “attenuation” is representative of the percent difference in magnitude of the initial peak stress of the back gauge relative to the front gauge. The symbol “***” indicates cases where the specific data could not be evaluated for the particular test instance.
Fig. 6 shows rise time data for the front gauge signal. An initial decrease in rise time with increasing particulate volume fraction is followed by a monotonic increase, indicative of scattering. Fig. 7 presents a plot of the stress wave attenuation for each type of specimen tested. An initial decrease can be observed for the 5% volume fraction specimen, again followed by a monotonic increase in attenuation to a value of about twice that of the virgin epoxy specimen.
Table 3 Epoxy–glass composite impact test results. Test
Volume fraction (%)
Impact velocity [interruption time] (m/s)
Impact velocity [delay time] (m/s)
Ultrasonic wave velocity (m/s)
Calculated wave velocity (m/s)
Front gauge rise time (μs)
Back gauge rise time (μs)
Attenuation (%)
0g 2g 10 g 20 g 30 g 40 g
0 5 21 35 45 52
354 358 351 267 270 248
320 374 335 304 259 259
2675 2609 2802 3022 3172 3350
2700 3000 2900 3100 3000 3300
0.52 0.40 0.48 0.60 0.70 ***
0.40 0.28 0.36 0.36 0.38 ***
23.1 9.4 18.4 31.9 41.7 ***
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Fig. 6. Rise time.
Fig. 8. Normalized particle velocity comparison.
The particle velocity for each type of specimen was computed by using the front gauge data and the expression: σ ðt Þ ¼ ρ c V p ðt Þ;
ð3Þ
which comes from one-dimensional wave theory. Vp (t) is the particle velocity history, and ρ and c are the material density and wave speed, respectively. The particle velocities were normalized with respect to the impact velocity Vi, which is an average of the two impact velocity values “impact velocity [interruption time]” and “Impact velocity [delay time]” listed in Table 3. Fig. 8 is a plot of this data. The time scale has been adjusted so that t = 0 μs corresponds to the moment of impact. The particle velocity varies from a normalized value of 0.3 in. the virgin specimen to a narrow range between 0.35 and 0.40 in. the specimens with 5, 21, and 35% volume fractions. A dramatic decrease in particle velocity can be seen for the high volume fraction specimens (45% and 52%). Also, the rate of increase of the curves of high volume fraction specimens is not as steep as lower volume fraction specimens, which is indicative of more gradual particle acceleration. Two FGM specimens were tested under impact, one having a low volume fraction of glass particles at the impact face, and another with a high volume fraction at the impact face. Stress gauge data for the two tests was normalized with respect to the initial peak stress of each gauge for comparison purposes. This was done because the rise time of the stress pulse rather than the absolute magnitude of stress was of interest. Fig. 9 shows a plot of the normalized stress for the two FGM specimens tested. The rise time for the high volume fraction on
Fig. 7. Stress wave attenuation.
impact face specimen is almost twice that of the specimen impacted on the compliant face.
4.3. SHPB evaluation Tests at three different pressures were conducted using the SHPB apparatus. These three pressures (480, 960, and 1920 Pa) correspond to average strain rates of 800 s−1, 1700 s−1, and 2900 s−1, respectively. Table 4 shows dynamic material strength results for all tests done using the SHPB. Fig. 10 is a comparison plot of this data. For a strain rate of 800 s−1, the strength did not change significantly for the various concentrations of glass, although an initially slight decrease was observed for the 21% volume fraction specimen. The 1700 s−1 strain rate test showed that the strength for virgin specimens was approximately twice that as for the low strain rate test. An initial increase for intermediate volume fraction specimens was followed by a slight decrease for the 52% volume fraction specimen. The 2900 s− 1 test shows even more drastic increases in strength for higher concentrations of glass particles. The SHPB experiments clearly exhibit strain rate dependency. It is, therefore expected that quasi-static values for the compressive strength of these composites will reside below those quoted above. This is indeed the case. Two samples of each epoxy–glass particle composite specimen were tested under quasi-static compression conditions. This is also shown in Fig. 10, where the average ultimate compressive strength is half that of the SHPB experiments conducted at 800 s−1. Compressive
Fig. 9. Normalized FGM impact comparison.
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Table 4 SHPB test results. Specimen
% Vf
Maximum strength (MPa)
10 psi (strain rate = 800/s) 0g 10 g 20 g 30 g 40 g
0 21 35 45 52
239 223 224 230 233
20 psi (strain rate = 1700/s) 0g 10 g 20 g 30 g 40 g
0 21 35 45 52
434 442 470 474 469
40 psi (strain rate = 3900/s) 0g 10 g 20 g 30 g 40 g
0 21 35 45 52
573 585 679 704 800
strength in these composites shows a slight monotonic increase with increasing volume fraction of glass in the epoxy matrix. Fig. 11 shows the specimen strain at the point of ultimate stress for each specimen type, which is representative of the brittleness of the material. A decreasing trend is observed, which is indicative of the increasing degree of brittleness of the specimens with increasing volume fraction. The 45% volume fraction specimen appears to be more brittle than expected, which may be due to imperfections generated during the fabrication of this specific composite. 5. Concluding remarks Quasi-static and dynamic compressive experiments brought to light the strain rate dependence of epoxy-based composites. At low strain rates, no significant variation in material strength can be observed. At relatively high strain rate, on the other hand, the strength of high volume fraction specimens was noted to be about 1.5 times that of the virgin material. This suggests that materials with particulate inclusions may be advantageous over homogeneous materials under high strain rate loading. From impact test data, the normalized rise time was observed to be slowest for a glass particle volume fraction of 45%. Lower volume fraction specimens actually displayed swifter rise times than the virgin epoxy specimens, suggesting that effective scattering did not initiate
Fig. 10. SHPB experiments describing the variation in dynamic strength of composites with increasing volume fraction. The experiments were conducted at strain rate values of 800, 1700, and 2900/s. comparative quasi-static values are presented.
Fig. 11. Strain at ultimate stress.
at low volume fractions of particulates. Similar conclusions can be drawn from normalized particle velocity calculations. The particle velocities were observed to decrease significantly at higher particle concentrations (45 and 52% volume fraction). Lower particle velocity in conjunction with longer particle accelerations suggests a milder stress environment and thus more effective thwarting of damaging stress waves within the material. The stress wave attenuation data, as measured by comparing the magnitude of the stress signal from the front gauge to the back gauge shows an initial decrease in attenuation compared to virgin epoxy at low concentrations of particles, followed by a monotonic increase to about 42% attenuation at a volume fraction of 45%. The general trend in the data from all tests performed suggests that a low volume fraction (Vf = 5%) is actually detrimental to the material, both under quasi-static and dynamic conditions. Beneficial material characteristics are generally not observed until a volume fraction of about 30%. Thus, the most effective range of volume fraction of particulates for thwarting propagating stress waves is between about 30 and 45%. Although certain characteristics of 52% Vf materials were even more desirable, the behavior of the material under impact loading as well as its very brittle nature suggest that at such higher volume fraction levels, a detrimental outcome might be expected.
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Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec
Compressive evaluation of homogeneous and graded epoxy–glass particulate composites J. Seaglar, C.-E. Rousseau ⁎ Department of Mechanical, Industrial & Systems Engineering, University of Rhode Island, Kingston, RI 02881, USA
a r t i c l e
i n f o
Article history: Received 23 July 2014 Received in revised form 31 December 2014 Accepted 21 January 2015 Available online 22 January 2015 Keyword: Impact SHPB Compression FGM
a b s t r a c t The propagation of stress waves in epoxy–glass particulate composites and graded materials was studied experimentally. Materials tested in this study consisted of an epoxy matrix with various concentrations of spherical glass particles having a mean diameter of 42 μm. Plate impact experiments were performed using a gas gun. Embedded within the specimens were manganin stress gauges used to record propagating compressive longitudinal stress waves through the material. High strain rate experiments using a Split Hopkinson Pressure Bar (SHPB) apparatus were also performed to evaluate the dynamic strength of the specimens, while quasi-static compression tests were undertaken to characterize their quasi-static behavior. Ultrasonic wave speed measurements were carried-out in order to obtain additional material properties and characterize the gradation in functionally graded materials (FGM). It was found that low volume fractions of particles are detrimental to the performance of the material under impact loading, while concentrations in the range of about 30 to 45% by volume exhibit characteristics of higher degrees of scattering. This suggests that materials in this latter range would be more effective in the thwarting of destructive shock waves than the homogeneous matrix material. Impact testing of FGM specimens suggests that impact loading on the stiff (high volume fraction) face results in much higher levels of scattering. Therefore, such materials would be effective for use in light weight armor or as shielding materials due to their effective attenuation of mechanical impulses. © 2015 Elsevier B.V. All rights reserved.
1. Introduction The study of the damage behavior of particulate composites has traditionally focussed on quasi-static loading. For example, Bazhenov [1] explored the quasi-static response of regular arrays of rigid particles in an elasto-plastic matrix, in which damage failure was related to particle/matrix debonding. That work revealed that the deformation behavior of the composite depended on the relation between the matrix strength and yield stress. Numerically, Garishin and Moshev [2,3] explored the quasi-static response of high volume fraction particulate composites, using a discrete structural model. Early dynamic research includes Herrmann's description of the Hugoniot curve in a ductile powder composite of porous aluminum and iron [4]. This was followed by the formulation of a stress wave propagation model in composite materials. In that work, Barker idealized composites as consisting of a system of periodically alternating materials, where the interaction between the successive layers of the resulting complex laminate would represent the scattering effect thought to be present within more general composites [5]. A similar approach was adopted by Oved et al. [6]. This simplistic, but appealing ⁎ Corresponding author at: 92 Upper College Rd., University of Rhode Island, Kingston, RI 02881, USA. E-mail address: [email protected] (C.-E. Rousseau).
http://dx.doi.org/10.1016/j.msec.2015.01.068 0928-4931/© 2015 Elsevier B.V. All rights reserved.
model was preserved as an experimentally ideal set up by Zhuang et al. [7], who, with the aid of internally positioned gauges, tracked a propagating shock wave at two discrete points located at the interfaces between alternating layers of aluminum and polycarbonate. Related experiments on laminated and fibrous composites include the works of Richardson and Wisheart [8], Cantwell and Morton [9], Aslan et al. [10], and Hebert et al. [11]. The bulk of the experimental work dedicated to particulate composites has focussed mainly on their fracture properties [12–16]. However, few attempts have been made to quantify the amplitude of compressive wave propagation in heterogeneous material, and much remains to be clarified concerning that process. In the above-quoted works, the phenomenon of geometric dispersion of elastic waves has received limited attention. The idea of geometric dispersion has guided this study into investigating the basic physical principles governing the propagation of elastic longitudinal stress waves in non-homogeneous particulate composites and graded materials. In particular, emphasis is placed on distinguishing material characteristics that can inherently thwart the evolution of a destructive shock wave. One of the primary mechanisms thought to impede of stress wave propagation is the phenomenon of scattering. Despite numerous analytical studies, the exact mechanism of scattering is not fully understood. Further, there is a lack of experimental data concerning particulate graded materials. This study is an experimental investigation of the propagation of stress waves in various
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concentrations of epoxy-glass particle composites and graded materials. In addition to impact experiments, both high strain rate and quasi-static compression experiments were performed in order to fully characterize the properties of the materials involved. Ultrasonic wave speed measurements were also performed and analyzed to obtain additional information on the inherent properties of the materials. The use of projectile impact conducted in order to investigate the propagation of stress waves through a material has been used extensively in previous studies [17–20]. The components necessary to perform impact experiments and gather data, such as gas guns, stress gauges, piezoresistive pulse power supplies, and velocity–interferometry systems have been well documented and are readily available. The data analyses performed for such experiments have been presented based on wave propagation theory and experimental correlations in [21–27]. The majority of experimental results obtained in the present study rely on data gathered from projectile impact, using stress gauge data to characterize the evolution of stress waves in the material. Additional relevant characteristic material data were obtained by means of Split Hopkinson Pressure Bars (SHPB) and ultrasonic pulser/receivers, resulting respectively in measurements of dynamic material strength at various strain rates, and longitudinal wave speed within the material [28–32]. The following sections present the procedures used to prepare the materials used in the study and a description of the experimental methods. The Experimental results section presents the relevant data gathered, which is followed by an associated discussion and some concluding remarks. 2. Materials The specimens used in this study were fabricated with an epoxy thermoset matrix mixture. Different variations of these materials were created, ranging from an indigenous material (no added particulates) to mixtures that included glass particles, and functionally graded materials. The following is an overview of the methods used to prepare and cast each specific type of material. 2.1. Preparation of virgin epoxy The epoxy used in all the castings is an Epo-Thin™ resin and hardener, manufactured by Buehler, Ltd. It is a low-viscosity thermoset with a nominal curing time of 18 h at room temperature. The resin is a bisphenol-A type epoxy resin. The hardener's primary ingredient is a polyoxyalkylamine blend. The density of the mixed epoxy is given by the manufacturer as 1147 kg/m3 and was also confirmed experimentally. 2.2. Preparation of homogeneous particulate materials The procedure used for producing castings containing micro-scale glass particles was identical to that used for the virgin epoxy specimens. Spherical soda-lime glass beads, manufactured by the Mo-Sci Corporation, were used. The primary ingredient of these particles is silica (SiO2), with a concentration of 72.5% by weight. The specific gravity of the particles is given by the manufacturer as 2.5, and the mean diameter as 42 μm. The nature of this study called for various concentrations of these particles to be mixed with the epoxy prior to casting. The concentrations used for casting were chosen incrementally to be 2, 10, 20, 30, and 40 g of glass per 17 g of epoxy (17 g was the nominal weight of epoxy used to fill a single casting cup, composed of 12.5 g of resin and 4.5 g of hardener). Knowing the densities of the glass particles and the epoxy, it is straightforward to obtain the volume fractions for each respective concentration. These were approximately 5, 21, 35, 45, and 52%, respectively. 2.3. Preparation of functionally graded specimens Functionally graded material (FGM) castings were produced by combining virgin epoxy with glass particles. This consisted of 12.1 g of
resin, 4.3 g of hardener, and 38.6 g of glass particles. In the absence of further mixing, the glass particles, which were initially uniformly distributed in the epoxy, gradually settled toward the bottom of the mold, concurrently with the hardening processed triggered by the thermosetting reaction. As a result, the bulk of the glass particles settled at the bottom due to gravity. However, a substantial number of particles remained suspended at various intermediate heights, resulting in specimens exhibiting smooth property gradations with vertical distance. More details on the gradation of these specimens can be found in the Experimental results section, which presents data from ultrasonic measurements. 2.4. Predicted and measured specimen densities The theoretical density of each glass–epoxy composite specimen was evaluated using the rule of mixtures. The given specific gravity of the glass particles was 2.5. The density of the epoxy was given by the manufacturer as 1147 kg/m3. The rule of mixtures, as it applies to the current specimens, can be formulated as: ρmix ¼ ρglass V f −glass þ ρepoxy 1–V f −glass ;
ð1Þ
where Vf-glass is the volume fraction of glass, and ρmix, ρglass and ρepoxy are the densities of the composite mixture, the glass particles, and the epoxy matrix, respectively. For each volume fraction, individual specimens were weighed, their volume measured, and the associated measured density was obtained. Differences between theoretical and measured densities increased with increasing volume fractions of the glass particles in the matrix. The presence of air voids is noted to be exacerbated by the accumulation of glass beads in the castings, and was identified as a primary contributor to this variance. The weight and density of the constituents, and the measured and theoretical volumes of the composites were used to approximate the volume of air in each specimen. This volume of air was then divided by the measured volume to calculate the percentage of air by volume in each specimen. Table 1 summarizes these evaluations and shows that the maximum air volume fraction is 4.1% for the specimens measured. 3. Methods of evaluation 3.1. Impact testing The primary focus of this study was to investigate the behavior of cast epoxy materials subjected to impact loading. Following methods established by other researchers [1,2,4,17–20], an experimental procedure and setup were designed, which is shown in Fig. 1. To achieve planar plate impact, a 19 mm (0.75 in.) diameter polycarbonate impactor was machined to a thickness of 3.18 mm (0.125 in.). In order to accelerate the impactor to the desired impact speeds of approximately 300 m/s, a single stage helium-powered gas gun with a 2.1 m (7.0 ft) long, 2.54 cm (1.00 in.) diameter barrel was used. The impactor was appended to the front face of a 2.53 cm (0.995 in.) diameter, 2.54 long Table 1 Density and air void data for epoxy–glass specimens. Specimen
Vf glass (%)
Theoretical density (kg/m3)
Measured density (kg/m3)
Volume of air (cc)
Percent air by volume
0g 2g 10 g 20 g 30 g 40 g
0 5 21 35 45 52
1147 1216 1435 1621 1752 1849
1160 1204 1420 1591 1713 1773
0 0.0608 0.0607 0.1114 0.1354 0.2475
0 1.003 1.014 1.846 2.251 4.101
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Fig. 1. Gas gun impact test setup.
(1.00 in.) Teflon sabot. The use of the sabot prevented damage to the impactor during firing, and enhanced its stability. The various specimens were placed at the exit of the gun barrel for impact. In order to capture the stress waves propagating through the specimens, manganin stress gauges (manufactured by Dynasen, Inc. and Vishay Micro-Measurements) were embedded within the specimens. The gauges were used in concert with a piezoresistive pulse power supply, a four-channel digital oscilloscope, and a light emitter/ detector (photodetector). The entire impact event is captured and recorded for later analysis. For cases where virgin and non-graded homogeneous specimens were being probed, these specimens were subdivided into three distinct layers to allow the embedding of stress gauges at two intermediate locations. Fig. 2 shows the configuration of a typical non-graded specimen, where the 7.62 mm (0.300 in.) top layer corresponds to the face that is subjected to impact. Having two gauges at discreet locations within the specimen provides information as to how the stress wave changed throughout its propagation. For functionally graded specimens, the front (impacted) layer was graded, while the back layer was selected to have a glass volume fraction that matched that of the graded layer at the interface. In order to compare performance of these materials under impact, one specimen was chosen to have the stiff (high volume fraction) face subjected to impact, while for the other case, the compliant (low volume fraction) face was subjected to impact. Fig. 3 illustrates the case corresponding to the former. In order to perform a test, the specimen was first placed in the designated specimen holder, at a distance of 30 cm (12 in.) from the end of the gun barrel. The alignment of the gun and the specimen was finetuned in order to maximize the instances of fully planar impact. All data acquisition devices were inspected and set to ensure that the
whole impact event would be captured. The gas gun was then pressurized to 2.07 MPa (300 psi) and discharged, thus releasing the impactor and sabot assembly at speeds of 300 m/s. Upon completion of each test, debris were collected and labeled for post-mortem analysis. Data from the photodetector was used to calculate the projectile velocity, using the interruption time of the light beam. The manganin gauge data established the basis for subsequent stress wave analyses, using procedures outlined in the Dynasen pulse power supply manual [27] to convert the voltage data as acquired by the manganin gauges into units of stress.
Fig. 2. Specimen configuration and stress gauge locations.
Fig. 3. Schematic of functionally graded specimens.
3.2. SHPB testing To further characterize the dynamic behavior of the epoxy–glass composites, high strain rate compression tests were performed using a Split–Hopkinson Pressure Bar. The experiments were conducted with specimens having 0, 21, 35, 45, and 52% volume fraction of glass sphere in the matrix. The specimens were first machined from castings by using a combination of turning and facing processes to obtain the dimensions of 9.53 mm (0.375 in.) diameter and 6.35 mm (0.250 in.) thickness. Aluminum bars of 12.7 mm (0.500 in.) diameter were used
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for incident and transmitter bars. The striker bar was powered by a pressurized gas mechanism. A total of four strain gauges were mounted on the bars, two on the incident bar and two on the transmitter bar. The gauges were connected to a data acquisition unit that contained both strain gauge amplifiers and transducers, connected to a computer for data recording. The equation relating the strain history from the transmitter bar to the stress in the specimen is:
these discrete locations along the height of the specimen (parallel to the direction of gradation). This resulted in different wave speed readings at each location, which was characteristic of the gradation of glass particles through the height of the specimen. 4. Experimental results 4.1. Ultrasonic evaluation
A σ ðt Þ ¼ Eb b εT ðt Þ A
ð2Þ
where Eb and Ab are the Young's modulus and cross-sectional area of the bar, respectively. εT (t) is the average value of the two strain gauges on the transmitter bar. A is the cross-sectional area of the specimen [22]. Tests at pressures of 69 kPa (10 psi), 140 kPa (20 psi), and 280 kPa (40 psi) were conducted by sandwiching the specimens between the incident and transmitter bars, the surfaces of which were lubricated slightly in order to prevent localized Poisson's effects from manifesting within the specimen. The test data was then transferred from the data acquisition unit to another computer workstation for analysis. The strain rates for the above-mentioned pressures were 800 s−1, 1700 s−1, and 2900 s−1, respectively. 3.3. Quasi-static compression testing In order to gather information on the compressive strength of the materials subjected to quasi-static loading, compression tests were done, based on ASTM D 695-85 Standards [33]. The tests were done using an Instron 5582 testing apparatus with cylindrical plate fixtures and a load/ extension transducer designed for compression tests. The specimens were machined from castings by using turning and facing to achieve the dimensions of 6.35 mm (0.250 in.) diameter and 12.7 mm (0.500 in.) height, conforming to the height to diameter ratio of 2:1 prescribed by the ASTM standards. Two samples were tested for each concentration of glass particles, at a loading rate of 1.3 mm/min. In most cases, the tests were conducted until complete fracture was observed, although the decision to stop the tests was based on observation of the real-time load-extension graphs. As a result, not all tests display complete fracture. Upon completion of the tests, the loadextension data was exported and analyzed. 3.4. Ultrasonic testing Measurements using an ultrasonic pulser/receiver were conducted to investigate the wave speeds of the materials of interest and characterize the degree of gradation of the FGM specimens. A PanametricsNDT Model 5058PR with an attached 5.72 mm (0.225 in.) throughtransmission sensor was used for this purpose. Machined 7.62 mm (0.300 in.) thick samples of the cast materials were used. The wave speed was calculated by measuring the time interval for the peak of the first pulse to reflect back to the transducer. Since the distance traveled is twice the thickness, this calculation is very straightforward and produces accurate results. For FGM specimens, a 12.7 mm (0.500 in.) thick section was machined along the direction of gradation. Tick marks were placed every 1.59 mm (0.0625 in.) on the specimens and ultrasonic readings taken
Table 2 shows the wave speeds for homogeneous epoxy–glass specimens as measured with the ultrasonic pulser/receiver. Ultrasonic measurements were also conducted on machined FGM specimens in order to measure the wave speed at various locations and determine their gradation. The volume fraction of glass particles at each location was then computed using data from Table 2 and is plotted in Fig. 4. The volume fraction is shown as a function of the distance from pure epoxy, which is situated at the top of the specimen, where it is completely devoid of glass particles. 4.2. Results of impact evaluation Multiple experiments were performed for each concentration of glass particles in the epoxy matrix. Data for the six concentrations of glass particles (0, 5, 21, 35, 45, and 52% volume fraction) as well as an FGM impact test are presented here. A typical test of each glass concentration is shown. These results depict representative experiments characterized by planar, central impact, exhibiting strong gauge signals, and devoid of any anomalies. Fig. 5(a)–(f) shows the front and back gauge stress data for each type of epoxy–glass particle composite specimen tested. The time scale corresponds to the elapsed time from the moment the photodetector was triggered. Table 3 is a summary of the results for non-graded specimens. “Impact velocity [interruption time]” refers to the projectile velocity calculated using photodetector interruption time and projectile length. “Impact velocity [delay time]” refers the projectile velocity calculated using an alternative method involving the time delay between the triggering of the photodetector and the arrival of the stress pulse at the front stress gauge. This method takes into account the time for the projectile to travel to the impact surface of the specimen, and the time for the stress wave to reach the front gauge (different for every specimen due to varying wave speeds). “Ultrasonic wave velocity” is the wave velocity measured using the ultrasonic pulser/receiver, whereas “calculated wave velocity” is the approximate experimental wave speed obtained by measuring the time interval between the arrival of the stress pulse at the front gauge and
Table 2 Ultrasonic wave speed measurements for epoxy–glass specimens. Specimen
Vf % glass
wt.% glass
Wave speed (m/s)
0g 2g 10 g 20 g 30 g 40 g
0 5 21 35 45 52
0 10.53 37.04 54.05 63.83 70.18
2675 2609 2802 3022 3172 3350
Fig. 4. FGM gradation.
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Fig. 5. Stress gauge data: (a) 0%, (b) 5%, (c) 21%, (d) 35%, (e) 45%, (f) 52% Vf.
its arrival at the back gauge. “Front” and “back gauge rise time” are the periods of time necessary for the front and back gauge signals to reach an initial peak value. Finally, “attenuation” is representative of the percent difference in magnitude of the initial peak stress of the back gauge relative to the front gauge. The symbol “***” indicates cases where the specific data could not be evaluated for the particular test instance.
Fig. 6 shows rise time data for the front gauge signal. An initial decrease in rise time with increasing particulate volume fraction is followed by a monotonic increase, indicative of scattering. Fig. 7 presents a plot of the stress wave attenuation for each type of specimen tested. An initial decrease can be observed for the 5% volume fraction specimen, again followed by a monotonic increase in attenuation to a value of about twice that of the virgin epoxy specimen.
Table 3 Epoxy–glass composite impact test results. Test
Volume fraction (%)
Impact velocity [interruption time] (m/s)
Impact velocity [delay time] (m/s)
Ultrasonic wave velocity (m/s)
Calculated wave velocity (m/s)
Front gauge rise time (μs)
Back gauge rise time (μs)
Attenuation (%)
0g 2g 10 g 20 g 30 g 40 g
0 5 21 35 45 52
354 358 351 267 270 248
320 374 335 304 259 259
2675 2609 2802 3022 3172 3350
2700 3000 2900 3100 3000 3300
0.52 0.40 0.48 0.60 0.70 ***
0.40 0.28 0.36 0.36 0.38 ***
23.1 9.4 18.4 31.9 41.7 ***
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Fig. 6. Rise time.
Fig. 8. Normalized particle velocity comparison.
The particle velocity for each type of specimen was computed by using the front gauge data and the expression: σ ðt Þ ¼ ρ c V p ðt Þ;
ð3Þ
which comes from one-dimensional wave theory. Vp (t) is the particle velocity history, and ρ and c are the material density and wave speed, respectively. The particle velocities were normalized with respect to the impact velocity Vi, which is an average of the two impact velocity values “impact velocity [interruption time]” and “Impact velocity [delay time]” listed in Table 3. Fig. 8 is a plot of this data. The time scale has been adjusted so that t = 0 μs corresponds to the moment of impact. The particle velocity varies from a normalized value of 0.3 in. the virgin specimen to a narrow range between 0.35 and 0.40 in. the specimens with 5, 21, and 35% volume fractions. A dramatic decrease in particle velocity can be seen for the high volume fraction specimens (45% and 52%). Also, the rate of increase of the curves of high volume fraction specimens is not as steep as lower volume fraction specimens, which is indicative of more gradual particle acceleration. Two FGM specimens were tested under impact, one having a low volume fraction of glass particles at the impact face, and another with a high volume fraction at the impact face. Stress gauge data for the two tests was normalized with respect to the initial peak stress of each gauge for comparison purposes. This was done because the rise time of the stress pulse rather than the absolute magnitude of stress was of interest. Fig. 9 shows a plot of the normalized stress for the two FGM specimens tested. The rise time for the high volume fraction on
Fig. 7. Stress wave attenuation.
impact face specimen is almost twice that of the specimen impacted on the compliant face.
4.3. SHPB evaluation Tests at three different pressures were conducted using the SHPB apparatus. These three pressures (480, 960, and 1920 Pa) correspond to average strain rates of 800 s−1, 1700 s−1, and 2900 s−1, respectively. Table 4 shows dynamic material strength results for all tests done using the SHPB. Fig. 10 is a comparison plot of this data. For a strain rate of 800 s−1, the strength did not change significantly for the various concentrations of glass, although an initially slight decrease was observed for the 21% volume fraction specimen. The 1700 s−1 strain rate test showed that the strength for virgin specimens was approximately twice that as for the low strain rate test. An initial increase for intermediate volume fraction specimens was followed by a slight decrease for the 52% volume fraction specimen. The 2900 s− 1 test shows even more drastic increases in strength for higher concentrations of glass particles. The SHPB experiments clearly exhibit strain rate dependency. It is, therefore expected that quasi-static values for the compressive strength of these composites will reside below those quoted above. This is indeed the case. Two samples of each epoxy–glass particle composite specimen were tested under quasi-static compression conditions. This is also shown in Fig. 10, where the average ultimate compressive strength is half that of the SHPB experiments conducted at 800 s−1. Compressive
Fig. 9. Normalized FGM impact comparison.
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Table 4 SHPB test results. Specimen
% Vf
Maximum strength (MPa)
10 psi (strain rate = 800/s) 0g 10 g 20 g 30 g 40 g
0 21 35 45 52
239 223 224 230 233
20 psi (strain rate = 1700/s) 0g 10 g 20 g 30 g 40 g
0 21 35 45 52
434 442 470 474 469
40 psi (strain rate = 3900/s) 0g 10 g 20 g 30 g 40 g
0 21 35 45 52
573 585 679 704 800
strength in these composites shows a slight monotonic increase with increasing volume fraction of glass in the epoxy matrix. Fig. 11 shows the specimen strain at the point of ultimate stress for each specimen type, which is representative of the brittleness of the material. A decreasing trend is observed, which is indicative of the increasing degree of brittleness of the specimens with increasing volume fraction. The 45% volume fraction specimen appears to be more brittle than expected, which may be due to imperfections generated during the fabrication of this specific composite. 5. Concluding remarks Quasi-static and dynamic compressive experiments brought to light the strain rate dependence of epoxy-based composites. At low strain rates, no significant variation in material strength can be observed. At relatively high strain rate, on the other hand, the strength of high volume fraction specimens was noted to be about 1.5 times that of the virgin material. This suggests that materials with particulate inclusions may be advantageous over homogeneous materials under high strain rate loading. From impact test data, the normalized rise time was observed to be slowest for a glass particle volume fraction of 45%. Lower volume fraction specimens actually displayed swifter rise times than the virgin epoxy specimens, suggesting that effective scattering did not initiate
Fig. 10. SHPB experiments describing the variation in dynamic strength of composites with increasing volume fraction. The experiments were conducted at strain rate values of 800, 1700, and 2900/s. comparative quasi-static values are presented.
Fig. 11. Strain at ultimate stress.
at low volume fractions of particulates. Similar conclusions can be drawn from normalized particle velocity calculations. The particle velocities were observed to decrease significantly at higher particle concentrations (45 and 52% volume fraction). Lower particle velocity in conjunction with longer particle accelerations suggests a milder stress environment and thus more effective thwarting of damaging stress waves within the material. The stress wave attenuation data, as measured by comparing the magnitude of the stress signal from the front gauge to the back gauge shows an initial decrease in attenuation compared to virgin epoxy at low concentrations of particles, followed by a monotonic increase to about 42% attenuation at a volume fraction of 45%. The general trend in the data from all tests performed suggests that a low volume fraction (Vf = 5%) is actually detrimental to the material, both under quasi-static and dynamic conditions. Beneficial material characteristics are generally not observed until a volume fraction of about 30%. Thus, the most effective range of volume fraction of particulates for thwarting propagating stress waves is between about 30 and 45%. Although certain characteristics of 52% Vf materials were even more desirable, the behavior of the material under impact loading as well as its very brittle nature suggest that at such higher volume fraction levels, a detrimental outcome might be expected.
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