The SHPB system (Figure 2) was driven by a compressed air vessel connected with a solenoid switch valve to one end of the steel barrel having convex-end solid cylindrical striker. The overall system consists of an incident bar, a transmission bar, momentum bar and a momentum-trap made of white putty clay packed in a robust steel frame. The bars and the striker are made from 19 mm diameter (0.75 inch) Aluminum bars [43] .

Two sets of 350 Ω strain gages were attached at a distance away from the specimen on the incident and transmitted bars allowing the strain gages to capture the initiation of the incident, reflected and transmitted pulses distinctly (Figure 2). Each set consists of two gages located diametrically opposite side of the bar and connected in series to compensate the bending effect of the bars and measure only axial strain of the bars. A digital oscilloscope of 1.25 GS sampling rate, connected to strain gages through a Wheatstone bridge and a signal conditioner, records the corresponding voltage-time history during the test event.

The Brazilian disk test method [39] is an efficient indirect approach for obtaining the tensile strength of high- stiffness low-strength brittle materials. It assumes a state of plane stress in the disk due to the application of diametrically opposite loading on the disk specimen [39] [40] . The tensile stress [39] -[41] induced at the center of the specimen along the transverse diameter of the disk specimen has been analytically and experimentally determined as, where, is the applied compressive load, is the diameter of the specimen,

is the specimen thickness.

Conventional Brazilian disk method proposes flat-end anvils for loading the circular disk specimen. The disadvantage of this approach is a large stress concentration at the loading lines along the thickness of the specimen. Hence, in most of the cases premature failure occurs close to the loading lines [45] . Two controlled loading approaches have been tried in this investigation. The geometry of the disk specimen was modified in the first attempt. The diametrically opposite loading lines along the thickness of the specimen were made flat [46] for about angle subtended at the center of the specimen to decentralize the stress concentration at the loading point and hence the relation of induced tensile stress with applied compressive load was modified based on the subtended angle by the flat-ends. The disadvantage of this approach is that the specimens rupture at the edges of the flat-ends, instead of at the center of the specimen. It was observed that the flatness and parallelism of the flat ends are crucial for the success. High precision in specimen preparation is required for this approach and achieving that level of geometric accuracy is practically difficult in case of quasi-brittle materials.

The second approach eliminates all these complexities by modifying the flat-end of anvil to circular concave ends [45] . Also the concave ends hold the disk specimen more securely than flat-ends in horizontal SHPB testing. The stress concentration is optimally reduced with failure of the disk specimen initiating at the disk-center and propagating along the compressive loading axis, thus ensuring a valid indirect tensile test (Figure 3).

The incident and transmission bars were threaded in and coupled with respective concave-end fixtures. The disk specimen was diametrically held in between the larger diameter concaved surfaces of the loading fixtures.

A fundamental requirement for the validation of the Brazilian disk test method is that the initiation of specimen failure should occur at the center of the specimen and propagates through the diameter along the compressive loading axis [39] . At high strain rate loading, the failure occurs within micro- to milli-second depending on the brittleness of the material. Human eye is able to persistently and distinguishably observe only such dynamic events that takes more than 40 milli-seconds [47] and even cannot record this event; hence a high-speed camera is essential in this validation process. A sample specimen of 19 mm (0.75 inch) diameter was tested at 10 psi reservoir pressure to ensure the recording of the diametrical fracture phenomena according to the scope of the high-speed camera (Hadland HPV-2 Shimadzu). The camera was operated at 250,000 fps. The dynamic event was captured in 102 image-frames with 1 ms exposure. The specimen expanded along the transverse diameter and the failure occurred through the diameter along the compressive loading axis (Figure 4) within 48 to 52 ms. The fracture initiated at the center of the specimen and propagated through the diameter along the loading axis towards the points of loading. The maximum expansion occurred along transverse diameter of the specimen, which validated the experimental setup for characterizing the tensile properties of the materials under compressive diametrical loading.

The striker bar was launched by elevated air pressure, resulting in a one-dimensional incident stress wave in incident bar. The strains (and) developed in the incident bar due to the consequent incident and reflected

stress waves were measured by the strain gages mounted on the incident bar and similarly the strain developed on the transmission bar due to the transmitted stress wave (subscript) measured by the strain gages mounted on the transmission bar. The forces on the two ends of the specimen along the SHPB loading axis [48] were estimated by the following equation:

where is elastic modulus of the bar material, is the cross-sectional area of the bar and denotes strain. The average of the end forces were considered for estimating the average dynamic tensile stress induced at the center of the Brazilian disk specimen along the orthogonal diameter of the loading axis using Equation (2) according to the circular disk theory [39] -[41] .

where, , and, are the diameter and the thickness of the disk specimen.

A pulse shaper was employed to achieve dynamic force balance in the specimen during the experiment. In a traditional SHPB test, the incident wave with rectangular stress-pulse may initiate undesired damage to the specimen upon impact before achieving stress equilibrium. If forces on both sides of the specimen are not the same during test event, the test cannot be considered as valid [49] . A polyurea disk, 0.313 inch in diameter and 0.003 inch in thickness, was used for shaping the incident wave from a rectangular to a trapezoidal wave (Figure 5(a)). This rubbery pulse shaper ramped the incident pulse such that the tensile stresses induced in the disk specimen achieved an equilibrium state before diametrical splitting of the specimen occurred. Figure 5(b) shows the pulses on both ends of the specimen obtained in a typical test. The dynamic force on the end of the specimen towards incident bar is proportional to the sum of the incident and reflected stress waves, and the dynamic force on the other end of the specimen towards transmission bar is proportional to the transmitted stress wave. It can be seen from Figure 5(b) that the dynamic pulses responsible for these two forces on both sides of the specimen remained almost identical during the whole dynamic loading period. The inertial effects were thus eliminated due to the absence of global force difference in the specimen. Hence, the static equilibrium analysis is valid [41] for this test method.

The diametrical transverse strain of the disk specimen was measured using a Laser Occluding Expansion Gage. LOEG works on the principle of occluding a thin parallel sheet of laser passing over the deforming specimen under dynamic loading [42] [50] . The full-field potential output due to the non-occluded laser was recorded as the base-line potential for a measurement. Any occlusion of laser due to the presence and subsequent deformation of the specimen across the path of laser sheet was depicted as the drop of potential. The specimen-strain was directly predicted from the ratio of the increment of drop of potential during specimen deformation to the initial drop of potential due to the placement of the specimen across the path of laser sheet.

A comparative study was performed through installing a strain gage (EA-06-062DN-350) on the disk specimen and obtaining indirect tensile strain simultaneously using LOEG setup and on-specimen strain gage (Figures 6(a)-(c)). The single strain gage was mounted on one side of the disk specimen and connected in quarter bridge

circuit through digital strain indicator system (Model P-3500 from Vishay Measurements Group). The dynamic data was transmitted to oscilloscope and stored in memory card. This dynamic response was plotted as the indirect tensile strain-time history of the disk specimen. Simultaneously LOEG setup provided comparative strain response to the same oscilloscope. In this comparative investigation, a similar strain-time history was obtained from both the strain-gage and LOEG responses (Figure 6(e)); thus validated the application of LOEG for indirect tensile strain measurement.

Quasi-static indirect tensile experiments were conducted on EnduraTec, a pneumatically driven materials test system (Figure 7(a)) for evaluating the strain-rate effects over a broad range of loading. An interface load cell was used to measure the axial load. The disk specimen was mounted diametrically within the same concave end fixtures for obtaining identical boundary condition applied in SHPB tests. LOEG unit was oriented transversely with respect to the loading axis for measuring the induced transverse tensile strain in disk specimen.

Quasi-static indirect tensile experiments were conducted on EnduraTec, a pneumatically driven materials test

system (Figure 7(a)) for evaluating the strain-rate effects over a broad range of loading. An interface load cell was used to measure the axial load. The disk specimen was mounted diametrically within the same concave end fixtures for obtaining identical boundary condition applied in SHPB tests. LOEG unit was oriented transversely with respect to the loading axis for measuring the induced transverse tensile strain in disk specimen. Five different DERAKANE 510A-40 vinyl ester thermoset nanocomposite panels [20] were considered for the dynamic indirect tensile characterization. The brominated bisphenol-A based vinyl ester consists of 38 weight % styrene, added with Butanone peroxide, N,N-Dimethylaniline, Cobalt Naphthenate and 2-4-Pentanedione additives to impart maximum fire retardance, chemical resistance and toughness. Pure brominated vinyl ester polymer (VE) was reinforced with 1.25 weight % and 2.5 weight % exfoliated graphite nanoplatelates (1.25xGnP+VE and 2.5xGnP+VE respectively) in two different batches. One of the reinforced nanocomposite batches was toughened with 10 weight % almost unreactive liquid carboxyl terminated butadiene nitrile (CTBN) rubber (1.25xGnP+CTBN+VE and 2.5xGnP+CTBN+VE). The nanoplatelets were exfoliated and homogeneously dispersed in polymer matrix by applying sonication technique. The solution of vinyl ester resin with nanoreinforcement and toughening agent was poured into a mold, kept at room temperature for 30 minutes and then post cured at 80˚C for 3 hours [32] .

Nanocomposite disk specimens with a diameter of 12.7 mm (0.5 inch) were machined using carbide tipped tool in CNC machine from 101.4 mm × 101.4 mm (12 inch × 12 inch) molded panels with thickness of 10 mm (0.4 inch). The diameter of specimen was decided based on the dynamic pulse duration through the diameter of the specimen. The pulse-wave needs to reverberate more than three times before failure initiation to ensure dynamic stress equilibrium in the specimen. The pulse speed in the specimen was predicted based on quasi-static properties (Table 1) that were obtained [34] according to ASTM 638-08 [51] using typical dog-bone specimen geometry.

The quasi-static (0.015 mm/s displacement controlled at 0.001 s⁻¹ strain rate) indirect tensile response shows a detrimental effect of the inclusion of xGnP and CTBN to pristine vinyl ester (Table 2). The pure vinyl ester specimens (Figure 7(b)) showed ductile deformation response beyond the load cell limit (10 kN). Hence, the conventional Brazilian disk test method, which is appropriate for brittle materials, could not capture the true behavior of pure vinyl ester under quasi-static loading due to its ductility. It is, therefore, recognized that the modulus, strength and failure strain data for pure vinyl ester as reported in Table 2 are not meaningful. However, addition of xGnP and CTBN makes the vinyl ester polymer more brittle (Figure 7(c)) and thus suitable for this indirect experimental method. The quasi-static indirect tensile response (Table 2) agrees reasonably with previous investigations performed [34] according to ASTM 638-08 [51] , using dog-bone specimen geometry (Table 1).

The quasi-static indirect tensile stress-strain history for pure vinyl ester, xGnP reinforced and CTBN toughened samples is shown in Figure 10. As mentioned earlier, stress-strain plots for only the pure vinyl ester

specimens have been terminated due to load cell capacity before the specimen failure occurs, whereas all reinforced samples failed within the load cell range.

It can be observed in Figure 10(ii) that tensile strength of pure vinyl ester is reduced by the addition of xGnP reinforcement (Figure 10(ii-a)), and even with CTBN toughening (Figure 10(ii-b)).

Energy absorbing capacity (Figure 10(iii)) is similarly affected by the addition of xGnP (Figure 10(iii-a)). The addition of CTBN did not improve the energy absorbing capacity (Figure 10(iii-b)) of pure vinyl ester, however, a marginal enhancement (Figure 10(iii-b)) can be observed when compared to only xGnP reinforced (i.e., without CTBN, Figure 10(iii-a)) nanocomposites.

Figure 11 summarizes the indirect tensile high-strain rate response of xGnP reinforced and with additional CTBN toughened vinyl ester nanocomposites at strain-rate of 1000 s-1 from SHPB tests. All of the nanoreinforced specimens including pure vinyl ester failed in a brittle manner under dynamic tensile loading (Figure 11(i)).

It can be observed that the tensile strength of pure vinyl ester remains unchanged with xGnP reinforcement (Figure 11(ii-a)). Addition of CTBN toughening to the 1.25 wt % xGnP reinforced nanocomposites showed a marginal improvement (Figure 11(ii-b)). The energy absorbing capacity of pure vinyl ester is improved with xGnP (Figure 11(iii-a)) reinforcement. However, this improvement is reduced about 50% by further CTBN toughening to the xGnP reinforced nanocomposites (Figure 11(iii-b)).

Comparative observation of Figure 10 and Figure 11 shows the strain-rate dependency of tensile strength and energy absorbing capacity of these candidate materials. As noted earlier, during quasi-static tests pure vinyl ester did not fail within maximum load limit of the load cell used, deforming elliptically in a ductile manner (Figure 7(b) and Figure 10(i)). However, it failed in a brittle fashion at much lesser strain (Figure 11(i)) under the high-strain rate SHPB loading. This ductile-to-brittle transition may be due to the significant influence of strain-rate effect. These nanocomposites can be considered as thermo-viscoelastic under high-strain rate loading in Hopkinson bar experiments, and the time-temperature superposition principle would be applicable for characterizing their response. A higher strain rate would correspond to a shorter loading time, equivalent to lower temperatures [14] causing the ductile-to-brittle transition of the specimen. This phenomenon has been further explained by the authors applying a technique of measuring fractal parameters of the fractured surfaces on the same candidate materials [38] .

About 25% increment in tensile strength is observed at high-strain rate loading (Figure 11(ii)) with respect to the quasi-static response (Figure 10(ii)). The energy absorption capacity of pure vinyl ester is adversely affected under high-strain rate loading, whereas it is improved with the addition of xGnP reinforcement (Figure 10(iii-a) and Figure 11(iii-a)). However, additional CTBN toughening agent could not contribute towards increasing the energy absorbing capacity (Figure 10(iii-b) and Figure 11(iii-b)).