A comparison of the ballistic performance of shear thickening fluids based on particle strength and volume fraction

Accepted Manuscript A Comparison of the Ballistic Performance of Shear Thickening Fluids based on Particle Strength and Volume Fraction Oren E. Petel, Simon Ouellet, Jason Loiseau, David L. Frost, Andrew J. Higgins PII:

S0734-743X(15)00120-7

DOI:

10.1016/j.ijimpeng.2015.06.004

Reference:

IE 2523

To appear in:

International Journal of Impact Engineering

Received Date: 10 October 2014 Revised Date:

13 May 2015

Accepted Date: 5 June 2015

Please cite this article as: Petel OE, Ouellet S, Loiseau J, Frost DL, Higgins AJ, A Comparison of the Ballistic Performance of Shear Thickening Fluids based on Particle Strength and Volume Fraction, International Journal of Impact Engineering (2015), doi: 10.1016/j.ijimpeng.2015.06.004. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Article Title: “A Comparison of the Ballistic Performance of Shear Thickening Fluids based on Particle  Strength and Volume Fraction”  Authors: Oren E. Petel1, Simon Ouellet2, Jason Loiseau3, David L. Frost3, and Andrew J. Higgins3 

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Affiliations:  1

 Carleton University, Department of Mechanical and Aerospace Engineering, Ottawa, ON, K1S 5B6,  Canada 

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Defence Research and Development Canada Valcartier, Québec, QC, G3J 1X5, Canada 

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 McGill University, Department of Mechanical Engineering, Montreal, QC, H3A 0C3, Canada 

 

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Highlights

Analytical scaling techniques are used to model the penetration events. Evidence of dynamic material strength is shown in several of the suspensions. Ballistic resistance is shown to be strongly influenced by particle strength. Particle strength is shown to only become a factor at elevated volume fractions. Strength effects are shown to diminish significantly at higher impact velocities.

All correspondences should be addressed to: 

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Oren E. Petel  Assistant Professor, Carleton University   Mechanical and Aerospace Engineering  1125 Colonel By Drive, ME 3230C  Ottawa, ON, K1S 5B6  Tel: +1 (613) 520‐2600 x2059  Fax: +1 (613) 520‐5715  E‐mail: [email protected]   

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A Comparison of the Ballistic Performance of Shear Thickening Fluids based on Particle Strength and Volume Fraction Oren E. Petela,∗, Simon Ouelletb , Jason Loiseauc , David L. Frostc , Andrew J. Higginsc a Carleton

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University, Department of Mechanical and Aerospace Engineering, Ottawa, ON, K1S 5B6, Canada b Defence Research and Development Canada Valcartier, Qu´ ebec, QC, G3J 1X5, Canada c McGill University, Department of Mechanical Engineering, Montreal, QC, H3A 0C3, Canada

Abstract

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The ballistic response of suspensions of solid particles (cornstarch, silicon carbide, and silicon dioxide) in a liquid (ethylene glycol) is experimentally investigated. Some of the suspensions are at sufficient volume fraction to exhibit shear-thickening behavior, while the others are Newtonian or mildly shear-thinning. The response of neat (liquid) ethylene glycol is also studied. Capsules containing the suspensions are impacted with a chisel-nosed fragment-simulating projectiles at velocities between 200 and 700 m/s. The residual projectile velocity upon exit from the capsule is measured via direct videography. The results are analyzed using a number of different energy-based and momentum-based penetration models. A momentum-based model that normalizes the effect of the density of the suspension is seen to perform the best in terms of collapsing the results onto a single curve for the liquid and non-shear thickening suspensions. Only shear thickening suspensions with particles having sufficient strength (SiO2 and SiC) show significant deviation from hydrodynamic-dominated response, resulting in significant velocity decrements in the projectile attributable to the shear strength of the suspensions. These shear strength effects diminish as the projectile velocity increases, suggesting that the strength of the solid material in the interparticle contacts is overcome by the impact-generated stresses. Keywords: Shear thickening fluid, Ballistic impact, Residual velocity, Penetration model, Material strength 1. Introduction

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There has been considerable interest in the potential ballistic applications of shear thickening fluids (STFs), spanning several decades of experimental research [1–5]. STFs have desirable properties that enable a stimulus-responsive transition from a fluid to solid-like material behaviour [6– 30 10], facilitating their effective integration as interstitial additives to ballistic fabrics, providing a flexible soft armour solution [2]. The response of shear thickening (dense particle) suspensions under high-strain-rate transient loading has shown evidence of a strong influence from the material 35 properties of their suspended solid particle sub-phase [11– 13]. Understanding the role of particle material properties on the penetration response of shear thickening fluids may provide some insights into improving the performance of these fluid-impregnated soft-armour systems. 40 Early investigations into the ballistic response of silicabased shear thickening fluids demonstrated that these dense particle suspensions were quite effective at stopping standard lead projectiles, due to their ability to deform the lead projectile on impact [1, 14]; however, the same fluid sys- 45 tems were ineffective against both steel-core and copperjacketed lead rounds [1]. It should be noted that the .22author Email address: [email protected] (Oren E. Petel)

∗ Corresponding

Preprint submitted to International Journal of Impact Engineering

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caliber lead rounds had a significantly lower muzzle velocity than the .30-caliber armour-piercing steel-core and copper-jacketed lead rounds studied. In more recent work, shear thickening fluids were suggested as interstitial fluids that could be embedded within ballistic fabrics [2], demonstrating effective performance in single-ply configurations against a steel fragment simulating projectile (FSP). The effective performance of these hybrid armours in single-ply configurations has been confirmed in subsequent studies involving steel projectiles [3, 4]. In multi-ply configurations of fabric armours, the benefit of STF-impregnation is less obvious as their performance is not particularly noteworthy. In experiments involving steel projectiles and multi-ply STF-impregnated fabrics, Tan et al. [3] found that integrating STFs has no appreciable effect on their ballistic limit for a 6-ply configuration. When the increased areal density of the impregnated fabrics are considered, these results suggest a loss of performance for multiple fabric layers, which are investigated at higher penetrator velocities [3]. Park et al [15] also investigated multiple-layer panels of STFimpregnated fabrics, finding that the integration of the fluids increased the performance of the fabrics against standard jacketed lead projectiles, however in a subsequent paper the same authors determined that these panels had a loss of performance against steel projectiles at impact velocities above 300 m/s [5]. Interestingly, this loss of May 13, 2015

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Figure 1: Schematic of an STF suspension (a) in equilibrium prior to ballistic penetration and (b) a broken-out section view of the projectile penetrating the suspension and the related mesostructural changes to the particle distribution. (c) Top and side views of a chisel-nosed FSP. The hatched region on the top view schematic represents the cross-sectional area of the flat nose of the FSP.

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performance closely matches the projectile velocities investigated by Tan et al. [3] in their 6-ply armour configurations. The conclusion that may be drawn from these two studies appears to be consistent with early research by Gates [1] suggesting that silica-based shear thickening fluids were not effective against steel projectiles, despite an apparent effectiveness against lead projectiles. Considering that lead is more easily deformed than steel, it has been suggested that these observations are due to the fact that the dynamic material strength of the STF exceeds that of the lead [1]. Although the majority of published work has focused on the integration of silica-based shear thickening fluids, perhaps silica is not the optimal particle material for STF ballistic applications [16], given the material properties of silica. The conceptual inspiration behind the impregnation of ballistic fabrics with shear thickening fluids has traditionally focused on their rheological behaviour [2]. In this light, the particle sub-phase variations within many studies have focused on particle shape morphology and volume fractions rather than the particle material properties themselves, with much of the cited literature using silica particles in their STFs. Recent rheological evidence suggests that force transfer within the suspended particle sub-phase of a shear thickening fluid is integral to the discontinuous shear thickening response itself [17, 18], particularly the observation of a shear stress maximum, which relates to the particle interactions. The coupling between the amplitude of normal and shear stresses within STFs presents a strong argument for this force transfer mecha-110 nism [17, 19]. Low-velocity impact experiments involving STFs provide further evidence of interparticle interactions dominating the dynamic response of these fluids [20–23]. At elevated strain rates that replicate ballistic conditions, dynamic characterizations of dense particle suspen-115 sions found similar evidence that stress transfer was heavily influenced by particle contacts. Using a modified splitHopkinson pressure bar, Lim et al. [12, 24] observed that the squeeze flow response of a dense particle suspension was primarily dominated by the modulus of the suspended120 particles. Using a plate impact technique, the dynamic material strength of a compacted dense silicon carbide suspension (48% volume fraction) was measured to be on the order of 500 MPa [11], evidence that stress transfer in the compacted suspension is supported through particle inter-125 actions [25]. These plate impact experiments on silicon carbide suspensions led to a hypothesis of a compressiondriven dynamic jamming in contrast with the shear-driven thickening within the particle sub-phase of the suspensions [13]. These observations illustrate the need to in-130 vestigate variations in the material properties of the subphase in order to improve the ballistic performance of STF impregnated fabrics. An investigation into the performance of single-ply fabrics impregnated with STFs containing two different par-135 ticle materials, polymethylmethacrylate or silica, demonstrated that the particle strength of the solid sub-phase

had a significant influence on the ballistic limits of the fabrics [4]. This study also investigated the effect of fluid impregnation, demonstrating that the performance of STFimpregnated fabrics was either identical to or slightly poorer than dry particle impregnation of the fabrics, for the same particle materials. Given the importance of the particle sub-phase on the dynamic response of dense suspensions, both in dynamic characterization and ballistic experiments, the relationship between the ballistic performance of an STF and the material of the particles used deserves further investigation. The penetration of a shear thickening fluid by a projectile is shown schematically in Figure 1, illustrating how the expected development of interparticle contacts may result in a strong influence from particle material strength. A preliminary investigation of ballistic penetration through shear thickening fluid capsules demonstrated that there was a definite relationship between the strength of the suspended particles and the resistance to penetration of that suspension [16]. In the present study, this comparison will be extended to include a broader set of suspensions that are investigated in multiple target capsule sizes. In the present study, we investigate the response of suspensions with varying volume fractions and particle sub-phase materials to impact, extending our preliminary dataset [16]. The residual velocity data that we generated is used to investigate scaling laws that provide useful tools for evaluating the penetration resistance of the fluids. Using these scaled parameters, we investigate the response of the fluids and the influence of the particles on

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the dynamic behaviour that we observed. Comparisons are made to analytical plug formation models of hydrodynamic (no material strength) behaviour to highlight the effects of material strength on the response of the suspensions, accounting for the inertially-dominated penetration response of the suspensions. As suggested by the comparison of the ballistic performance of STFs against lead and steel projectiles [1, 5], improvements to the performance of STFs requires a further characterization of the role of particle strength in their resistance to penetration at high impact velocities. 2. Experimental Details

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The investigations of the present study involved several fluid mixtures, the proportions of which are given in Table 1. The components of these mixtures included liquid ethylene glycol, silica (Fiber Optic Center, monodisperse spheres, d = 1 µm), α-silicon carbide (Washington Mills, irregular morphology, dmean = 5 µm), and cornstarch (Fleichmann, dmean = 10 µm). Scanning Electron Microscope (SEM) images of these particles are shown in Figure 2. Three particle materials were used in this series of experiments, chosen for their different material properties, which are summarized in Table 2. The silica particles used in the present study had a nano-porous structure, as noted by the manufacturer, consisting of voids that were inaccessible to the liquid ethylene glycol. This void fraction resulted in a wetted bulk particle density of approximately 1.85 g/cm3 based on our estimates, effectively containing a 16% gas-filled void fraction. This bulk particle density estimate is consistent with the wetted bulk density of silica particles used in previous experiments involving silica-based STFs [2]. The gas-filled void fraction would have an adverse effect on the strength of the silica particles in comparison to the values listed in Table 2, although this effect was not independently determined or estimated in the present study.

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2.1. Rheological Behaviour of the Mixtures

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Rheological measurements were performed in a Couette geometry using an MCR 502 Rheometer (Anton-Paar) at a controlled temperature of 23 ◦ C. The steady shear viscosity is shown in Figure 3 as a function of steady shear rate for the various mixtures given in Table 1. From these results there are a number of trends that are noticeable among the mixtures being investigated, which reflects the choice of the mixture variations for the present study. These material and volume fraction variations within the chosen mixtures are able to provide insight into the dynamic response of these multiphase mixtures. All of the fluids were prepared with a common suspending medium of liquid ethylene glycol, which was also investigated in its neat form. Ethylene glycol was chosen as the suspending medium due to its compatibility with silicon carbide, enabling us to prepare a wide variety of

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(c) Figure 2: SEM images of the (a) cornstarch, (b) silica, and (c) silicon carbide particles.

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ACCEPTED MANUSCRIPT Table 1: Summary of the mixture compositions investigated in the present study.

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2.2. Mixture Preparation The test mixtures were prepared by gradually introducing the particles into the ethylene glycol using a con-245 ventional blender, followed by a vortex mixer for a period of 24 hours to ensure a proper dispersion of the particles. The mixtures were prepared in 250 mL batches which were cross-blended in an effort to reduce potential batch to batch variability in the results. Prior to transferring250 the test mixtures into the test capsules, the mixtures were placed on the vortex mixer for a minimum of 10 minutes to ensure sufficient dispersion of the particles. Particle settling was not a concern since experiments were conducted promptly, within 5-10 minutes, following the filling of the test capsules.

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STF No Yes No No N/A Yes Yes

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Solid Volume Fraction (%) n/a 54.0 21.5 41.0 48.0 61.5 47.6 13.9

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suspensions. Three shear thickening mixtures were evaluated, two were silica-based (61 SiO2 and 61 Mix) and the third was cornstarch-based (54 CS). These mixtures were chosen to identify particle strength effects, particularly the comparison of the two silica-based STFs. These two STFs were prepared with a constant volume fraction of particles, but the 61 Mix STF saw 22.6% of its silica volume fraction replaced by silicon carbide particles. Note that a 61% volume faction of SiC was not possible to prepare, due to the SiC particle morphology resulting in a packed bed at volume fractions below this value. Thus, it was only possible to replace some of the silica in the 61 SiO2 , resulting in what we term “61 Mix”. The rheological behaviour of these two mixtures exhibit a similar critical strain rate, however the 61 SiO2 mixture exhibited a sharper increase in the response of its viscosity to shear. The 21 SiC mixture was investigated because it could provide a direct density comparison to the 61 SiO2 mixture, but it has a shear thinning response that appears to plateau to a Newtonian behaviour at higher strain rates. This behaviour provides a sharp contrast to the shear thickening response of the 61 SiO2 . The 41 SiC and 48 SiC are both shear thin235 ning fluids in the range of strain rates measured, although the 48 SiC mixture testing exceeded the torque limitations of the equipment and could not be tested in an adequate range of strain rates. The 41 SiC mixture provides a dense (shear thinning) suspension for comparison to the response 240 of the fluids with Newtonian or shear thickening behaviour.

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Solid Mass Fraction (%) n/a 62.0 44.2 66.8 72.7 72.5 50.2 25.5

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Particle Material n/a Cornstarch Silicon Carbide Silicon Carbide Silicon Carbide Silicon Dioxide Silicon Dioxide Silicon Carbide

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2.3. Cornstarch-based Mixture The experiments involving the mixture of cornstarch and ethylene glycol (54 CS) were more complex due to a suspected aerobic reaction that would cause the mixture to solidify in open containers within several minutes. Samples of this mixture were prepared in small batches immediately prior to experiments, which may have resulted in some batch to batch variability between the samples tested, however this was not quantified. The test capsules had O-ring seals on both faces, which reduced the rate of this reaction once the capsules were properly sealed. Immediately following each experiment with this mixture, one of the investigators examined the state of the sample remaining in the test capsule for evidence of solidification. If there was any evidence of a reaction having taken place, the data were discarded and the experiment was repeated. This complication may have led to some variability in the results of the experiments. 2.4. Ballistic Testing Methodology The penetration resistance of the target specimens was investigated through the capacity of the targets to decelerate a 17 grain (1.1 g) chisel-nosed mild steel NATOstandard FSP (see Figure 1c). The experiments were con-

ACCEPTED MANUSCRIPT Table 2: Summary of the bulk-material properties for the solid materials used in the present study.

Material Cornstarch Silicon Dioxide (amorph.) Silicon Carbide

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ducted with a smooth-bore single-stage gas gun that had an upper velocity limit of 700 m/s. A schematic of the configuration of the experiment, which was similar to that used by Nam et al. [28], is shown in Figure 4a. The incident and residual velocities of the FSP were measured with a Photron SA5 high-speed camera at 20,000 fps. A set of sample images showing the FSP entering and exiting a test capsule is shown in Figure 4b and 4c. In order to avoid measurement errors due to optical distortion, a ruler was photographed along the FSP path prior to each experiment, providing an accurate set of fiducial markers for a given experiment. In order to minimize yaw of the FSP emerging from the smooth-bore gun barrel, the test capsules were placed in close proximity of the muzzle (within 5 cm). Two steel test capsule designs were used to contain the fluid test samples in the present study with dimensions given in Table 3. Both of the capsules used identical 0.1 mm thick Mylar diaphragms seated on O-rings (2 mm diameter) to contain the fluid samples. The Mylar diaphragms were supported by outer flanges that compressed the O-rings to provide the seal. These diaphragms were found to have a negligible influence on the residual velocity measurements, which was verified by measuring the residual velocity of FSP penetrations through an empty capsule. 3. Experimental Results

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Figure 4: (a) Schematic of the experimental configuration showing the FSP, test capsule assembly, and the camera viewing angle. Photographs of an experiment in which the FSP is (b) entering and (c) exiting test capsule #2.

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Data from perforation and penetration experiments are typically presented in terms of the incident and residual velocities of the projectiles, which provides an effective means of comparing the performance of target materials [29, 30]. The residual velocity data from the present 310 study involving all seven mixtures listed in Table 1 are plotted in Figure 5. Each sub-figure contains the data for a single mixture in multiple capsules. The complete dataset from the present study is tabulated in Appendix A for reference. 315 Figure 5 shows the residual velocity of the projectile upon exit from the capsule as a function of its initial velocity. The diagonal line (slope = 1) indicates no deceleration of the projectile through the capsule. All of the materials resulted in some projectile deceleration. The liquid EG 320 resulted in the least velocity decrement, while the 61 SiO2 and the 61 Mix resulted in the greatest decrements, results which are consistent across all of the capsules tested. The 61 Mix was able to completely arrest the FSP up to an

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Hardness (GPa) Not Available 8.3 30.8

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Young’s Modulus (GPa) 4.9 69.3 454.7

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Density (g/cm3 ) 1.55 2.20 3.22

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initial velocity of nearly 300 m/s. This velocity, at which a material in a given capsule will completely stop the projectile, is subsequently referred to as the “ballistic limit” (or Vbl ). The ballistic limit of our materials can be determined from the residual velocity plots in Figure 5, where they are simplistically determined as the horizontal axis intercepts of the data based on extrapolation. The estimated values of the ballistic limits for several of the suspensions are presented in Table 4. The residual velocity plots and ballistic limit estimates illustrate a trend of performance among the mixtures. A comparison of the dilute silicon carbide suspensions (21 SiC) and the cornstarch-based STF (54 CS) shows that particle volume fraction is an important parameter to consider. Despite the higher density and particle strength of the silicon carbide suspension, the cornstarch suspension outperforms this silicon carbide suspension at lower impact velocities, leading to a higher ballistic limit. Although in a comparison of mixtures with identical volume fractions, 61 SiO2 and 61 Mix, their performance appears to be dominated by the particle strength of the suspended particle sub-phase [16]. This simple comparison

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(g) Figure 5: The residual velocity plots for the penetration of a standard 17 grain (1.1 g) FSP are presented for each mixture (a) EG, (b) 21 SiC, (c) 41 SiC, (d) 48 SiC, (e) 54 CS, (f) 61 SiO2 , and (g) 61 Mix.

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4. Analysis of Residual Velocity Data using Energy Approaches

Ballistic penetration data can be presented in multiple375 forms scaled against material or performance parameters that provide some insight into the penetration mechanics involved in an experiment on ductile materials. One manner of presenting residual velocity data involves normalizing all velocities by the ballistic limit of the target380 material [30]. The rationale behind this scaling approach is derived from considering a simple energy balance from two impact scenarios, a complete perforation of the target and the critical scenario of an impact at the ballistic limit, where the residual velocity is zero. These two cases are385 described by the equations,

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where Mfsp is the mass of the fragment simulating projectile, W is the work involved in the perforation process, and Vi , Vr , and Vbl are the incident, residual, and ballistic limit velocity of the projectile, respectively. Combining395 these equations to remove the work term results in the expression,  2  2 Vi Vr − =1 (2) Vbl Vbl 400

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fails to account for the inertial response of the fluids, which365 may provide further insight into the comparative response of the fluids. The following analysis will use various scaling techniques based on simple penetration models to develop finer comparison tools through which the performance of 370 these fluids can be discussed.

1 1 Mfsp Vi2 = Mfsp Vr2 + W 2 2 1 Mfsp Vbl2 = W 2 345

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the ballistic limit term which is used to normalize both axes. For flat-nosed projectiles, the normalized residual velocity plot results in a series of curves that depend simply on the target thickness and density, due to the formation of a plug in front of the projectile. Since plug formation results in a transfer of kinetic energy to the plug, the residual velocity of the projectile will be lower than in a perforation process. In a scenario where the projectile is perforating a fluid, the influence of an effective plug formation is not obvious, so normalizing the residual velocity plots for the data from the different fluids could provide some insight into the penetration mechanics at play. For example, comparing the normalized residual velocity data from the different capsule sizes will show the influence of the ejecta kinetic energy on the penetration. Using the values for the ballistic limits given in Table 4, the residual velocity data were normalized for several of the mixtures, the results of which are shown in Figure 6. Estimating the ballistic limit from extrapolations of the residual velocity data was sufficiently accurate for the current purpose, since both axes are scaled simultaneously. These plots are not overly sensitive to the possible errors in choosing an appropriate ballistic limit. This normalized residual velocity data does not collapse onto a single curve, as would have been expected for a pure perforation process, evidence that the ejecta associated with the penetration of the FSP through the mixtures is significant and must be taken into account in the models. The ejecta field is clearly seen in Figure 4. Using image processing ejecta analysis techniques, the ejecta from these experiments have been analyzed to discuss the role of interparticle friction within the fluids [32], however this analysis technique is unable to resolve the exact magnitude of kinetic energy contained within the ejecta field. The expression for residual velocity in equation 2 can be rederived to account for the ejecta contribution, however, for simplicity, we will model the complex fluid ejecta field as a generalized solid plug of material. This plug formation model assumes that the impact and penetration process is perfectly plastic, resulting in final plug velocities that are identical to the final velocities of the projectile. Although perfect plug formation may not seem to be representative of the true ejecta field seen in Figure 4c, the model is assumed to be representative of the ejecta field at the first instant following penetration, rather than the later times seen in Figure 4c. If we assume a perfect plug is formed ahead of the FSP moving at the same velocity as the projectile [30], the appropriate energy conservation equations for the complete penetration and critical pene-

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Table 4: Summary of the (estimated) ballistic limits for the different mixtures and capsules.

Previous research has shown that normalizing both axes of the residual velocity plot by the ballistic limit of a ductile target material causes perforation data from different materials and thicknesses to collapse onto a single curve described by equation 2 [31]. Notice that equation 2 con-405 tains no material or projectile specific information, such as material strength, which is all effectively integrated into 7

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The expressions for the mass of the projectile and the plug can be rearranged into a more useful form, considering that the effective plug cross-sectional area describ465 ing the ejecta mass may differ from that of the projectile. Since the plug model is an idealization of the true ejecta field, the relative cross-sectional areas provide some flexibility to the model. Therefore, equation 4 may be written in the form, 470 v ! u     2 u Vi Vr 1 = ·t −1 (5) Vbl 1+β Vbl β=

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where Ar is the cross-sectional area ratio between the plug formed and the projected area of the FSP, L is the axial length, ρ is the density, and the subscripts “fsp” and p refer to the projectile and plug, respectively. Note that480 when Ar is equal to unity, the plug will have the same diameter as the FSP. The relationship between the incident and residual velocities predicted by equation 5 is compared to the experimental data in Figure 6 for two different area ratios. The485 solid lines in this figure represent the analytical model assuming a common diameter between the plug and FSP (Ar = 1). This area ratio appears to significantly overestimate the kinetic energy associated with the ejecta (i.e., residual velocities are under-predicted), resulting in poor490 agreement between the model and experiment. The dashdot lines represent an area ratio that is based on the actual area ratio of the flat nose of the FSP to its diametric crosssectional area. Since the mixtures are fluids and the projectile has a495 flat nose, assuming a perfect plug at the same diameter as the FSP body over-predicts the resistance encountered in the penetration process. One interpretation of this discrepancy is that less ejecta is seen experimentally than

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assumed in an ideal plug scenario. If we consider that the main resistance to penetration is due to the high pressure generated on the face of the projectile, we can make a simplifying assumption regarding the penetration process. We can assume that the plug formed by the projectile will have a cross-sectional area equivalent to the area of the flat portion of the nose on the FSP (see hatched region in Figure 1c). This shape factor assumes that the portion of the mixture participating in the deceleration of the FSP is primarily located in a region defined by the path of the flat nose region of the FSP, accounting for the divergence of material around the projectile tip. The area ratio of the flat nose region to the diametric area is defined by the expression,

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Momentum approaches may prove more useful in terms of investigating the role of material strength in the ballistic performance of the mixtures since momentum variations can be directly correlated to resistive stresses integrated through the material thickness. A model that enables a comparison of the penetration response of the mixtures, isolating the purely hydrodynamic response (i.e., no material strength) expected from an inertially-dominated penetration process, could provide insight into the dynamic resistance of the fluids. To understand the role of material strength in the penetration process, a simple analytic model that focuses on conserving linear momentum between the projectile and ejecta can provide a useful basis of discussion. For this model, we start by assuming that the target material has no material strength (the hydrodynamic limit) and that an ideal plastic plug is formed within the fluid target. Therefore, our momentum model is adequately described by the equation, ρfsp · Lfsp · Vi = (ρfsp · Lfsp + ρp · Lp · Ar ) · Vr

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The benefit of the normalization of the velocities in equation 8 is that this normalized decrease in the velocity of the projectile is independent of the incident velocity, depending only on the density of the fluid for a given projectile and target geometry. The result is that any deviation from this behaviour would be attributable primarily to the555 material strength of the target material. Figure 7, which plots the normalized decrease in projectile velocity against its incident velocity, shows that this behaviour is observed experimentally for some of the mixtures tested, particularly the ethylene glycol and dilute 21 SiC suspension (see560 Movie S1 available as supplementary material). The remainder of the mixtures deviate from this hydrodynamic behaviour at low incident projectile velocities, but converge to an incident velocity independent behaviour at higher incident velocities, which could signify565 the effect of a loss of dynamic material strength at higher impact velocities. This change in response at higher impact velocities is apparent in Movies S2, S3, and S4 available as supplementary materials for samples of 54 CS, 61 SiO2 , and 61 Mix, respectively. The final offset between570 the hydrodynamic prediction for the mixture and the converging trend of the experimental data could be directly indicative of the dynamic material strength of the mixtures. For example, a comparison of the behaviour of the 21 SiC and 61 SiO2 mixtures (Figure 8) is the most effective illus-575 tration of the effect that high particle volume fraction has

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on the dynamic strength of the mixtures during a penetration event (see Movie S5 available as supplementary material for a side-by-side comparison). Although both of these mixtures have the same bulk density, the high volume fraction of silica particles in the 61 SiO2 gives this mixture a measurable strength that increases penetration resistance in comparison to the inertial responses of the dilute silicon carbide mixture (21 SiC). While it is tempting to attribute the difference in the dynamic response of these density-matched mixtures directly to their respective rheological responses (see Figure 3), one must be careful not to erroneously extrapolate material behaviours across strain rates and dynamic ranges. Although the 21 SiC mixture is shear thinning, while the 61 SiO2 mixture is shear thickening, the ballistic response is strongly linked to the volume fraction and material strength of the particle sub-phase. The link between the rheological response and ballistic response of our mixtures may be partially correlational, but this link is not causal. Rheological behaviour in itself is not a predictor of superior ballistic response in the fluids tested. For example, the rheological behaviours of 61 SiO2 to 61 Mix are practically identical, however their ballistic response is not. These mixtures have a similar volume frac-

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tion of particles suspended and both have a similar critical shear rate, however the 61 SiO2 mixture has a more sharply discontinuous shear thickening response (see Figure 3), which may lead an observer to posit that this mixture should have superior resistance to penetration. Based on the results in Figure 7, the opposite is true; the 61 Mix mixture provides superior penetration resistance, having a higher ballistic limit and larger offset between its experimental and predicted inertial response. This suggests that particle strength may be of greater importance to penetration resistance than the nature of the rheological behaviour of the mixture. Consider that the 61 Mix is proportionally similar to the 61 SiO2 mixture, only with 22.6% of the silica replaced by an equivalent volume fraction of silicon carbide. This replacement results in an increase in the bulk mixture density, however the increase in the apparent dynamic strength of the mixture that is seen experimentally is disproportionate to this inertial effect. The irrelevance of rheological response to ballistic performance is most striking for the cornstarch-based STF, which clearly performs poorly despite a discontinuous shear thickening response, further illustrating the importance of particle strength. To demonstrate these points further, the three different shear thickening fluids that were tested in the present study, each containing a different particle material, should be compared. A comparison of the penetration resistance results of the various STFs for each capsule is shown in Figure 9 with the hydrodynamic model predictions (equation 8) for reference. When making a direct comparison between the penetration results for these fluids, it is important to keep in mind that three mixtures have different densities. Using this representation of the data, the important comparison to make is the relative offsets of each fluid to its own expected hydrodynamic response. This offset is an effective measure of the influence from dynamic material strength, which can be seen to increase with the strength of the particle materials in the mixtures. The results demonstrate that the material strength of the suspended particle sub-phase is an important factor in its ballistic resistance. While particle strength is an important factor in determining the ballistic response of the mixtures, particle strength alone is not a predictor of penetration resistance. For instance, considering the results of the mixtures containing only silicon carbide particles shows the influence of volume fraction (Figure 10). The volume fractions of these mixtures varied from 21.5-48% and the experimental results for these mixtures did not deviate significantly from their predicted hydrodynamic response. Although the densest of these suspensions had a significant volume fraction of particles at 48%, these particles were not likely driven into extensive contact, limiting the influence of the particle strength on the penetration process. Previously, under plate loading, the densest of these mixtures (48 SiC) was shown to stiffen under an analogous compression-induced thickening mechanism [11, 13], which

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led us to initially hypothesize that there would be extensive particle contacts and a strong particle influence on the ballistic response of these mixtures. The results illustrate690 that away from the nose of the projectile, the mixture was most likely not seeing the pressure levels (2-4 GPa) required to drive the particles into sufficient contact. This may be due to the expansion of material around the nose of the projectile that would limit the extent of the high695 pressure region away from the nose. Clearly, the effect of particle material strength cannot be discussed in the absence of considering the role of particle volume fraction on the ballistic resistance of these mixtures, a role which cannot be understated. Particle strength only be-700 comes an important factor in the resistance to penetration when enough particles are present, forcing the interparticle contacts to directly participate. For instance, if we compare the penetration resistance of the 41 SiC and the 61 Mix mixtures (Figures 7c and 7g respectively), although705 the 41 SiC mixture has a significantly higher density and overall particle strength, it offers poorer resistance to penetration, illustrating the dynamic strength seen in the high volume fraction 61 Mix suspension.

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where K will have a value of unity in the hydrodynamic limit. The experimental data are plotted in terms of this K parameter in Figure 11. This format of the data provides the clearest indication of the response of the mixtures in comparison to their predicted inertially-dominated hydrodynamic response. The K parameter is independent of the target thickness, allowing us to make a direct comparison of the entire dataset, combining data from all of the capsules (Figure 11h). The data for several mixtures collapse fairly consistently when plotted in terms of this parameter. The response of the ethylene glycol is consistently below a K value of unity, which is seemingly odd considering that it is the only fluid that should have a perfectly hydrodynamic response and these lower values mean that ethylene glycol provided a resistance that was worse than its density would suggest. Our interpretation of this result was that there may have been some cavitation of the ethylene glycol near the projectile, reducing its ability to resist penetration. The addition of the silicon carbide particles in the dilute 21 SiC may have contributed to suppressing this behaviour during the penetration process. While there is clearly some scatter in the data, shown in Figure 11, three mixtures show a consistent deviation from the model that is interpreted as evidence of dynamic material strength influencing the penetration process. These three mixtures in order of increasing K offset were 48 SiC, 61 SiO2 , and 61 Mix. Note that the STF involving cornstarch showed no evidence of influence from material strength at the higher impact velocities. The dense silicon carbide mixture (48 SiC), did show evidence of material strength, although it was outperformed by the 61 SiO2 mixture, which had a more significant K offset. In other words, once inertial effects due to the higher density of the silicon carbide mixture are removed from the comparison, the silica-based mixture, although involving a weaker particle material, exhibited a stronger dynamic response due to the higher volume fraction of particles in the mixture. Finally, once the volume fractions are held constant and inertial effects removed, the addition of small amounts of silicon carbide at a high volume fraction (61 Mix) does lead to an increase in the dynamic strength of the mixtures as described earlier based on the normalized decrease in projectile velocity. The K offset penetration performance parameter, which accounts for the inertial effects of the

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suspensions, is shown as a function of increasing particle material strength in Figure 12. This plot only includes data recorded for incident impact velocities above 400 m/s, which allows the plot to focus on the strength limits for the suspensions under impact. 770 6. Discussion

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The influence of interparticle friction on the rheological response of dense suspensions has been given closer775 consideration in recent work [17, 18]. Recognizing that shear thickening can result from suspended particles being driven into direct contact, combined with the elevated stresses associated with ballistic impacts, then it is reasonable to associate the penetration resistance of the sus-780 pensions with the need to continually deform particle microstructures that form during impact. As the projectile penetrates the fluids, force carrying interparticle networks will need to deform to allow the projectile to penetrate. This deformation can take any possible number of785 forms, from simply elastic deformations that enable relative motion of the particles to plastic deformation or fracture of the particles. This is consistent with previous research on high-strain-rate loading of dense saturated sand beds, which can undergo grain crushing relating to interparticle contact, despite the presence of the interstitial fluid [33, 34]. However, if the particles are not ini-790 tially present with a sufficient concentration, they will not form particle contact networks and the influence of particle strength in penetration becomes irrelevant. Although the strength of the particle sub-phase is contributing to resisting the penetration of the projectile in795 the dense suspensions, the influence of this particle strength

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is clearly reduced at higher impact velocities. This is seen from the plots of the K parameter as well as the normalized velocity decrease, Figures 9 and 8, respectively. It should be noted that in both cases, at higher impact velocities, the influence of the particle strength on the ballistic resistance is diminishing as the inertial response of the mixtures begins to dominate. This is evident from the convergence of the data in the plots comparing the silica-based STF to the dilute silicon carbide suspension (Figure 8). The diminishing influence of the particle strength provides further evidence that the particles are likely deforming under ballistic loading. This developing picture of the role of the solid subphase within the suspensions is consistent with the previous ballistic studies comparing wetted and dry particle integration into ballistic fabrics, which showed that both impregnation techniques were comparably effective and that the ballistic performance scaled with the particle material strength [4]. Computational studies of ballistic impact on STF-impregnated Kevlar has estimated that the mean stress at the point of impact is on the order of gigapascals [35], while force chains between particles can witness stress fluctuations that deviate upward from the mean stress by an order of magnitude [36]. Therefore, it is reasonable to estimate that some particles will deform and may even fracture during the penetration process. Several recent studies on packed beds of granular material have shown the propensity of these saturated granular beds to undergo particle fracture and deformation from impact loading at similar pressures [37, 38]. If we consider that the particles within the suspensions will undergo relative motion due to the impact, then there is an opportunity for mesostructural reorganization in the form of significant interparticle contact networks. The penetration of the projectile would then be limited by its ability to destroy the force chains that were formed, making the strength of the suspended particles a key parameter in the dynamic response of a suspension, provided that there was a sufficient concentration of particles to begin with. Under typical low-strain-rate loading conditions, where particle crushing is unlikely, the particle contact networks can be disrupted through rotational and translational mechanisms. At the high strain rates associated with a ballistic impact, particle chains can also be disrupted through localized particle deformations.

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7. Conclusions The ballistic responses of six different particle suspensions in liquid ethylene glycol and the neat liquid alone have been quantified by measuring the residual velocity of the projectile upon exiting containers of the suspensions or liquid. The results were consistent when using different capsule sizes. A penetration model based on momentum conservation that normalized the effect of the density of the suspensions has been shown to be superior to

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The authors thank Jacques Blais of DRDC Valcartier for his assistance in conducting the experiments. The au-880 thors appreciate the efforts of Bradley Marr in carrying out the experimental trials. The authors are grateful to Charles Dubois, Cameron Munro, and Behnam Ashrafi for their assistance in obtaining the rheological data for885 the fluids. This work was conducted with the support of Hamid Bennadi of Stedfast Ltd., Natural Science and Engineering Research Council of Canada, and the Department of National Defence under Project No. DNDPJ890 385687-09. OE Petel would like to acknowledge funding support from the NSERC Discovery Grant program RGPIN-2014-06295. 895

References

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[1] L. E. Gates Jr., Evaluation and development of fluid armor systems, Air Force Materials Laboratory AFML-TR-68-362 (1968).900 [2] Y. S. Lee, E. D. Wetzel, N. J. Wagner, The ballistic impact characteristics of Kevlar woven fabrics impregnated with a colloidal shear thickening fluid, Journal of Materials Science 38 (13) (2003) 2825. [3] V. B. C. Tan, T. E. Tay, W. K. Teo, Strengthening fabric armour905 with silica colloidal suspensions, International Journal of Solids and Structures 42 (5-6) (2005) 1561–1576. [4] D. P. Kalman, R. L. Merrill, N. J. Wagner, E. D. Wetzel, Effect of particle hardness on the penetration behavior of fabrics intercalated with dry particles and concentrated particle-fluid 910 suspensions, Applied Materials & Interfaces 1 (11) (2009) 2602– 2612. [5] J. L. Park, B. I. Yoon, J. G. Paik, T. J. Kang, Ballistic performance of p-aramid fabrics impregnated with shear thickening fluid; part ii effect of fabric count and shot location, Textile 915 Research Journal 82 (6) (2012) 542–557. [6] R. L. Hoffman, Discontinuous and dilatant viscosity behavior in concentrated suspensions. i. observations of a flow instability, Transactions of the Society of Rheology 16 (1972) 155–173. [7] J. F. Brady, G. Bossis, The rheology of concentrated suspen920 sions of spheres in simple shear flow by numerical simulation, Journal of Fluid Mechanics 155 (1985) 105–129. [8] H. A. Barnes, Shear-thickening (“dilatancy”) in suspensions of nonaggregating solid particles dispersed in Newtonian liquids, Journal of Rheology 33 (2) (1989) 329–366.

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[9] M. E. Cates, J. P. Wittmer, J. P. Bouchard, P. Claudin, Jamming, force chains, and fragile matter, Physical Review Letters 81 (1998) 1841–1844. [10] A. J. Liu, S. R. Nagel, The jamming transition and the marginally jammed solid, Annual Review of Condensed Matter Physics 1 (2010) 347. [11] O. E. Petel, A. J. Higgins, Shock wave propagation in dense particle suspensions, Journal of Applied Physics 108 (2010) 114918. [12] A. Lim, S. Lopatnikov, N. Wagner, J. W. Gillespie, An experimental investigation into the kinematics of a concentrated hardsphere colloidal suspension during Hopkinson bar evaluation at high stresses, Journal of Non-Newtonian Fluid Mechanics 165 (2010) 1342–1350. [13] O. E. Petel, D. L. Frost, A. J. Higgins, S. Ouellet, Formation of a disordered solid via a shock-induced transition in a dense particle suspension, Physical Review E 85 (2012) 021401. [14] L. E. Gates Jr., Flexible protective armour material and method of making same, U.S. Patent No. 3,649,426 (14 March 1972.). [15] J. L. Park, B. I. Yoon, J. G. Paik, T. J. Kang, Ballistic performance of p-aramid fabrics impregnated with shear thickening fluid; part i effect of laminating sequence, Textile Research Journal 82 (6) (2012) 527–542. [16] O. E. Petel, S. Ouellet, J. Loiseau, B. J. Marr, D. L. Frost, A. J. Higgins, The effect of particle strength on the ballistic resistance of shear thickening fluids, Applied Physics Letters 102 (2013) 064103. [17] E. Brown, H. M. Jaeger, The role of dilation and confining stresses in shear thickening of dense suspensions, Journal of Rheology 56 (2012) 875–923. [18] E. Brown, H. M. Jaeger, Shear thickening in concentrated suspensions: phenomenology, mechanisms and relations to jamming, Reports on Progress in Physics 77 (2014) 046602. [19] D. Lootens, H. Van Damme, P. H´ ebraud, Giant stress fluctuations at the jamming transition, Physical Review Letters 90 (17) (2003) 178301. [20] S. R. Waitukaitis, H. M. Jaeger, Impact-activated solidification of dense suspensions via dynamic jamming fronts, Nature 487 (2012) 205–209. [21] S. R. Waitukaitis, L. K. Roth, V. Vitelli, H. M. Jaeger, Dynamic jamming fronts, Europhysics Letter 102 (2013) 44001. [22] M. Roch´ e, E. Myftiu, M. C. Johnston, P. Kim, H. A. Stone, Dynamic fracture of nonglassy suspensions, Physical Review Letters 110 (2013) 148304. [23] S. Mukhopadhyay, B. Allen, E. Brown, A shear thickening transition in concentrated suspensions under impact, arXiv:1407.0719. [24] A. S. Lim, S. L. Lopatnikov, N. J. Wagner, J. W. Gillespie Jr., Investigating the transient response of a shear thickening fluid using the split Hopkinson pressure bar technique, Rheologica Acta 49 (2010) 879–890. [25] O. E. Petel, D. L. Frost, A. J. Higgins, S. Ouellet, Lateral stress measurements in dense suspensions, AIP Conference Proceedings 1426 (1) (2012) 1495–1498. [26] S. R. Waitukaitis, Impact-activated solidification of cornstarch and water suspensions, Ph.D. Thesis - The University of Chicago, 2013. [27] G. M. Pharr, Measurement of mechanical properties by ultralow load indentation, Materials Science and Engineering A 253 (1998) 151–159. [28] C. H. Nam, M. J. Decker, C. J. Halbach, E. D. Wetzel, N. J. Wagner, Ballistic and rheological properties of stfs reinforced by short discontinuous fibers, Proceedings of SAMPE: New Horizons for Materials and Processing Technologies (2005). [29] R. L. Jameson, J. S. Williams, Velocity losses of cylindrical steel projectiles perforating mild-steel plates, Ballistics Research Laboratory Report No. 1019 (1957). [30] R. F. Recht, T. W. Ipson, Ballistic perforation dynamics, Journal of Applied Mechanics 30 (1963) 384–390. [31] Z. Rosenberg, E. Dekel, On the deep penetration and plate perforation by rigid projectiles, International Journal of Solids and Structures 46 (2009) 4169–4180.

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other penetration models (including energy-based methods). The suspensions that exhibited the greatest projec-855 tile deceleration (in excess of what can be attributed to hydrodynamic-dominated behavior) were the suspensions of 61% SiO2 (by volume) and a 61% mix (by volume) of SiO2 and SiC (in a 2:1 mass ratio). A suspension of corn-860 starch, while exhibiting a classical shear-thickening behavior under low shear rates, did not display any enhanced resistance to penetration. The enhanced ballistic protection offered by the 61 SiO2 and 61 Mix diminished as the865 projectile velocity increased, reverting to hydrodynamic behavior at projectile velocities above 500 m/s. The 61% mixtures containing SiC showed enhanced protection at a greater velocity than the 61 SiO2 suspension, suggesting870 that the harder particles were better able to withstand the interparticle stresses occurring upon impact.

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EG EG EG EG EG EG EG 21 SiC 21 SiC 21 SiC 21 SiC 21 SiC 41 SiC 41 SiC 41 SiC 41 SiC 41 SiC 48 SiC 48 SiC 48 SiC 48 SiC 48 SiC 48 SiC 54 CS 54 CS 54 CS 54 CS 54 CS 61 SiO2 61 SiO2 61 SiO2 61 SiO2 61 SiO2 61 Mix 61 Mix 61 Mix 61 Mix 61 Mix

198 311 334 416 404 526 640 201 302 420 539 704 268 314 534 630 695 201 314 412 455 540 704 205 316 407 506 680 202 310 420 538 688 194 310 398 540 700

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Vr (m/s)

Vi − Vr Vi

K

0.379 0.367 0.353 0.389 0.356 0.390 0.391 0.503 0.431 0.481 0.462 0.476 0.627 0.554 0.551 0.521 0.551 0.716 0.592 0.592 0.571 0.578 0.585 0.522 0.579 0.477 0.435 0.462 1.000 0.610 0.530 0.532 0.517 1.000 0.865 0.646 0.567 0.570

0.960 0.929 0.895 0.987 0.934 0.989 0.990 1.053 0.902 1.008 0.968 0.997 1.170 1.035 1.028 0.972 1.029 1.294 1.070 1.069 1.032 1.043 1.057 1.182 1.311 1.080 0.985 1.046 2.095 1.277 1.110 1.114 1.084 1.980 1.703 1.272 1.117 1.123

RI PT

Vi (m/s)

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Mixture

M AN U

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Table .5: Summary of the experimental data with Capsule #1 (small diameter).

TE D

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EP

930

[32] O. E. Petel, J. D. Hogan, An investigation of shear thickening fluids using ejecta analysis techniques, International Journal of Impact Engineering submitted. [33] K. Lee, H. B. Seed, P. Dunlop, Effect of transient loading on the strength of sand, Proceedings of the 7th International Conference on Soil Mechanics and Foundation Engineering 1 (1969) 239–247. [34] M. Omidvar, M. Iskander, S. Bless, Stress-strain behavior of sand at high strain rates, International Journal of Impact Engineering 49 (2012) 192–213. [35] B. Lee, C. Kim, Computational analysis of shear thickening fluid impregnated fabrics subjected to ballistic impacts, Advanced Composite Materials 21 (2012) 177–192. [36] D. W. Howell, R. P. Behringer, C. T. Veje, Fluctuations in granular media, Chaos 9 (1999) 559–572. [37] A. Yoshinaka, F. Zhang, W. Wilson, Effect of shock compression on aluminum particles in condensed media, AIP Conference Proceedings 955 (2007) 1057–1060. [38] B. J. Marr, O. Petel, D. L. Frost, A. J. Higgins, S. Ringuette, Shock-induced deformation in wetted particle beds, Journal of Physics: Conference Series 500 (2014) 112044.

AC C

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123 197 216 254 260 321 390 100 172 218 290 369 100 140 240 302 312 57 128 168 195 228 292 98 133 213 286 366 0 121 198 252 332 0 42 141 234 301

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Vi − Vr Vi

K

EG EG EG EG EG EG 21 SiC 21 SiC 21 SiC 21 SiC 21 SiC 41 SiC 41 SiC 41 SiC 41 SiC 41 SiC 41 SiC 48 SiC 48 SiC 48 SiC 48 SiC 48 SiC 48 SiC 48 SiC 54 CS 54 CS 54 CS 54 CS 54 CS 61 SiO2 61 SiO2 61 SiO2 61 SiO2 61 SiO2 61 Mix 61 Mix 61 Mix 61 Mix 61 Mix

196 315 416 473 562 680 202 311 400 518 651 225 353 434 546 560 707 199 356 565 567 580 686 820 199 306 404 505 693 205 307 405 528 695 204 311 401 518 696

112 181 240 283 326 386 94 141 190 243 300 83 135 182 221 218 266 0 121 210 205 208 239 280 92 126 191 237 354 0 93 150 210 302 0 12 103 171 246

0.429 0.425 0.423 0.402 0.420 0.432 0.535 0.547 0.525 0.531 0.539 0.631 0.616 0.581 0.595 0.611 0.624 1.567 0.660 0.628 0.638 0.642 0.652 0.659 0.537 0.588 0.527 0.531 0.489 1.000 0.697 0.630 0.602 0.566 1.000 0.961 0.743 0.670 0.647

0.955 0.948 0.942 0.895 0.935 0.963 1.003 1.025 0.985 0.996 1.011 1.069 1.044 0.980 1.007 1.034 1.056 1.645 1.086 1.033 1.050 1.056 1.072 1.083 1.082 1.184 1.061 1.068 0.984 1.876 1.308 1.181 1.130 1.061 1.776 1.708 1.320 1.190 1.149

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Table .6: Summary of the experimental data with Capsule #2 (large diameter).

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Captions for the Supplementary Materials  

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The caption associated with MovieS1.mp4  Movie S1. This video compilation shows the penetration of the 21 SiC mixture by a 17 grain FSP at  311 m/s and 651 m/s.   

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    The caption associated with MovieS3.mp4 

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Movie S2. This video compilation shows the penetration of the 54 CS mixture by a 17 grain FSP at  306 m/s and 693 m/s.  

 

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Movie S3. This video compilation shows the penetration of the 61 SiO2 mixture by a 17 grain FSP at  307 m/s and 695 m/s.  

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Movie S4. This video compilation shows the penetration of the 61 Mix mixture by a 17 grain FSP at  311 m/s and 696 m/s.  

The caption associated with MovieS5.mp4  Movie S5. This video compilation shows the penetration of two mixtures having the same density but  different volume fractions, 21 SiC and 61 SiO2, by a 17 grain FSP at 311 m/s and 307 m/s, respectively.   

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