The variance on the shock response of a carbon fibre composite due to the orientation of the weave

The variance on the shock response of a carbon fibre composite due to the orientation of the weave J Mater Sci (2018) 53:11415–11425 COMPOSITES Composites The variance on the shock response of a carbon fibre composite due to the orientation of the weave 1, 1 1 2 2 3 D. C. Wood *, G. J. Appleby-Thomas , A. Hameed , N. R. Barnes , A. Hughes , and P. J. Hazell Centre for Defence Engineering, Cranfield University, Defence Academy of the UK, Shrivenham SN6 8LA, UK AWE, Aldermaston, Reading RG7 4PR, UK School of Engineering and Information Technology, The University of New South Wales, UNSW Canberra, PO Box 7916, Canberra, BC 2610, Australia Received: 20 February 2018 ABSTRACT Accepted: 9 May 2018 Three different orientations of a tape-wrapped carbon fibre composite with Published online: phenolic resin matrix (abbreviated to TWCP) have been investigated under one- 22 May 2018 dimensional shock loading. This has been achieved via a single-stage gas gun, with manganin gauges as the diagnostic tool. The orientations of TWCP studied The Author(s) 2018 in this paper were 25,45 and 90, with respect to the impact face. The shock response of these orientations, for this material, has been obtained (the Hugoniot equation of state). These results have been contrasted with previously reported literature data for the same material at different orientations (0 and 20). It was found that orientation had minimal effect on the behaviour of this composite under shock. The exception to this was the 90 orientation which exhibited an -1 elastic precursor at particle velocities of less than 0.65 mm ls ; where the shock velocity was equivalent to the elastic sound speed of the material. matrix) [4, 5], configuration of the layered structure Introduction [6], thickness of the composite sample [7, 8] and the orientation of constituent layer [9–11] which is the Composites have a high strength to weight ratio focus of this paper. making them ideal candidates for multiple applica- To understand the behaviour of shocked materials, tions in a wide range of industries, for example the five parameters are needed. These parameters are aerospace industry [1–3]. Due to these numerous shock velocity U , particle velocity u , density q, industries and therefore applications, a wide range of S p pressure P and internal energy E. With any two of conditions may be experienced such as shock these five parameters obtained, the materials shock loading. response can be fully described using the Rankine– When looking at the shock response of composite materials, a multitude of different configurations can Hugoniot equations [12] (which are based on princi- alter the observed behaviour. These can include ples of conservation of mass, momentum and constituents used (such as fibre ratio, type of fibre or energy). The two parameters directly measured in Address correspondence to E-mail: d.wood@cranfield.ac.uk https://doi.org/10.1007/s10853-018-2431-0 J Mater Sci (2018) 53:11415–11425 this study were U and r , with a third parameter u orientation of the fibre weave with respect to the S x p found using the impedance matching technique [12]. shock front in a carbon fibre composite. Further to these parameters, density was calculated Many authors have investigated the effect that from the Rankine–Hugoniot jump equations (with orientation has on the shock response of composites; the inverse of density giving the volume, V). This however, they tend to focus on the orientations par- allowed the Hugoniot in both the U –u and pres- allel and perpendicular to the shock front, a good S p sure–volume planes to be ascertained. overview on the shock response of composites is In the U –u plane, the Hugoniot relationship tends given by Ref. [18]. S p to be linear in nature for most materials, following One study that investigated a wide range of ori- the form shown in Eq. (1). Nonlinear behaviour in the entations and its affect on the shock profile was the U –u Hugoniot plane has been observed with some work of Bordzilovsky et al. [10]. In this paper, an S p materials such as polymers [13–15], including the aramid fibre composite with an epoxy resin matrix matrix material of TWCP investigated here [16]. For material was investigated. A single set of experi- Eq. (1), c is the Hugoniot intercept at the ground mental conditions was picked, utilising TNT to state which tends to be comparable to c (the bulk impart a shock into the sample, such that any dif- sound velocity of the material, given by Eq. 5); while ference in the shock profile was due to the orientation S is the slope of the Hugoniot. of the aramid fibre weave. The angles of the fibre weave investigated were 5,15,45 and 90, with U ¼ c þ Su ð1Þ S 0 p respect to the direction of shock wave. An elastic The hydrodynamic pressure of a material (P , also precursor was noted at the orientations of 5 and 15 referred to as the Hugoniot pressure) is given by before finally smearing and disappearing at 90. Eq. (2) and is typically represented in the pressure– Millett et al. [9] investigated the effect that orien- particle velocity plane. This equation may be adjus- tation of a carbon fibre weave had on the resultant ted for use in the pressure–volume plane with this shock profile. In this study, two orientations of fibre form given in Eq. (3), where q is the initial density weaves were investigated; one where the fibre weave and V along with V are the volume at the Hugoniot was orientated parallel to the shock front, with the pressure and initial state, respectively. other fibre weave orientated perpendicular to the P ¼ q U u ð2Þ shock front. To impart the shock wave, aluminium or H S p copper flyers were used at velocities between 200 and 2 -1 P ¼ q U 1  ð3Þ 1125 m s . It was found that when the fibre weave 0 S was parallel to the shock front the carbon fibre The Hugoniot pressure and deviatoric (maximum composite behaved more like a monolithic material; shear stress s, derived from the Cauchy stress tensor with the exception of very small oscillations on the [17]) elements of stress are linked by Eq. (4). This plateau of the trace. These were attributed to shock relation implies that if the longitudinal stress equals wave interactions between the fibres and matrix the hydrodynamic pressure then there will be little to within the sample material. However, when the fibre no strength effect in the material. weave was orientated perpendicular to the shock front, a ramped elastic portion was seen with an r ¼ P þ s ð4Þ -1 x H approximate velocity of 7 mm ls , before the main shock front overtook the elastic portion. This beha- Due to the number of different constituents and viour was explained as an elastic wave travelling arrangements, a wide range of composite systems are down the fibres ahead of the main shock front. commercially available. This adjustment in the com- Despite this behaviour, both Hugoniots in the U –u S p posite material due to a change in constituents can plane were found to be linear in nature, with signif- greatly alter the material response especially in the icant deviation at lower particle velocities before shock regime. This adjustment could be a change in convergence was observed at elevated particle fibres, matrix or of the volume fraction of the mate- velocities. rial, for example. For the purposes of this investiga- Hazell et al. [7] also investigated a carbon fibre tion, the property under consideration was the composite, where the weave was orientated perpen- dicular to the shock front. The main focus of this J Mater Sci (2018) 53:11415–11425 11417 paper was the effect of thickness on the shock was noted. Within the data, there was no indication response of this composite. The four thicknesses used of any elastic behaviour, as noted in composites were 1.52, 3.00, 6.05 and 9.06 mm. As observed in the studied by Bordzilovsky et al. [10], Millett et al. [9] study by Millett et al. [9], an initial ramped portion and Hazell et al. [7]. due to an elastic precursor through the fibres was In this paper, the previous work conducted by seen. As the thickness of the composite was Wood et al. [20] and Burrell et al. [1] will be built increased, the initial ramped portion of the trace upon and expanded to include more orientations. became more pronounced, as did the magnitude of The orientations that will be investigated here are 25, pressure of this initial ramped portion. 45 and 90 with the orientation referring to the angle Multiple diagnostic techniques were used by Wil- between the shock front and the fibre weave. These lows et al. [19] to investigate the shock response of a data will then be compared to previous work in the carbon fibre composite using the plate impact tech- literature (specifically Refs. [1, 20]), to see the effect nique. By employing both VISAR and manganin that orientation has on the shock response of this stress gauges, on ring up and ring down experiments TWCP material. the shock profile was investigated. It was concluded, via the use of a computational model that fibre ori- entation was unimportant above a particle velocity Experimental technique -1 value of approximately 1000 m s . This supports the The plate impact technique was used to induce a one- work conducted by Millett et al. [9], who observed dimensional shock wave into the TWCP samples. To Hugoniot convergence with their composite at higher achieve this, a single-stage gas gun with a 5-m-long particle velocities. barrel and 50-mm bore was used to accelerate flyer In this study, a tape-wrapped carbon fibre com- plates (attached to sabots for stability) into the tar- posite with a phenolic resin (abbreviated to TWCP) gets. The flyer plates used in these experiments were will be investigated. This material has been studied aluminium or copper (either 5 or 10 mm thick) due to previously by Wood et al. [20] and Burrell et al. [1]at their well characterised behaviour while under shock orientations of 0 and 20, respectively. These orien- [21]. Velocity measurements were obtained via a tations were with respect to the impact surface of the series of sequential infrared transmitters and recei- sample. vers. This experimental setup is shown simplistically Wood et al. [20] investigated a TWCP composite in Fig. 1. One-dimensionality is assured by careful where the fibre weave was arranged parallel to the machining of all components within the targets such shock front. As was observed by Millett et al. [9]on that all parallel surfaces to the shock front are flat and their carbon fibre composite, the 0 weave orientation parallel to tolerances of ± 10 lm. To confirm the behaved monolithically, with the exception of noted accuracy of the gas gun with relation to the target, tilt oscillations on the plateau of the experimental gauge pins experiments are performed before and after shot traces. These oscillations were found to be due to the programs. The maximum misalignment of the cov- thickness of the fibre weave and the shock interac- erplate surface to flyerplate surface within this pro- tions between the carbon fibre weave and the matrix gram of work was found to be 1.9 mrad. material. It was noted in this study that convergence To investigate the effect that orientation has on the between the TWCP and the phenolic resin matrix shock response of composites manganin pressure material occurred above a particle velocity of -1 gauges were used to monitor the transit of the shock 0.8 mm ls . profile. Manganin is used as it is largely unaffected The shock response of a TWCP composite, with the by the temperature increase associated with a shock weave orientated at 20 to the impact face was wave, and as such the output is the pressure of the investigated by Burrell et al. [1]. Unlike the one material (assuming hydrodynamic behaviour). The investigated by Wood et al. [20] and in this study, the gauges employed within these experiments were TWCP material investigated by Burrell et al. had a manufactured by Vishay Micro-measurements with different compositional makeup, as noted by the the product designation being LM-SS-125CH-048, difference in the initial density. The shock response with an active manganin grid element of 3.18 by was compared to previously obtained data for 4.45 mm for a total active area of 14.15 mm . When a TWCP, where good agreement between the data sets J Mater Sci (2018) 53:11415–11425 Velocity TWCP 50 μm Mylar® Measurement 50 μm Mylar® Sample System Coverplate PMMA (Al or Cu) Backing Manganin Sabot/Flyer Pressure Gauges Figure 1 General experimental setup, with typical target configuration. pressure is applied to the gauge a proportional the discrepancy between the densities in Table 1. For change in resistance is noted, which by using the all orientations of this TWCP material, ultrasonic calibration method of Rosenberg et al. [22] can be measurements have been obtained using 1 MHz calculated. quartz transducers and a Panametrics 5077PR pulse Figure 1 shows a simplified target setup arrange- receiver. Pulse-echo mode was used to obtain longi- ment. One thing to note is the inclusion of 50 lmof tudinal sound speed (cL), with the shear sound speed Mylar which is used as both electrical and physical (cS) found using transmit–receive configuration, with protection of the gauges. All matching surfaces of the the bulk sound speed found via Eq. (5). Table 1 components were joined together with a slow curing shows the key elastic properties for TWCP, c , c , c L S B TM epoxy resin Locite 0151 HYSOL Epoxi-Patch .In and v (Poisson’s ratio) for all of the orientations these experiments, all samples were of dimensions 60 investigated here, as well as previous work by Burrell by 60 by 8 mm. et al. [1] and Wood et al. [20]. Poisson’s ratio is given by Eq. (6) and is based on the sound speed of the materials, which leads to the discrepancy in Table 1 Material properties caused by the anisotropy of the composite. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 For the material investigated here, the carbon fibres c ¼ c  c ð5Þ L S are woven into a two-dimensional fabric (plain weave), which are stacked upon one another, before 0:5 being impregnated by the phenolic resin (Durite SC- v ¼ ð6Þ 1008 previously investigated by Wood et al. [16]). It is 1:0 these weaves that are orientated with respect to the Using micrographs, the volume fraction of the shock front. Density measurements were conducted TWCP composite was calculated as previously con- using a Micrometrics AccuPyc 1330 gas pycnometer -3 ducted in the work by Wood et al. [20]. This tech- which gave a value of 1.46 g cm for all of the ori- nique led to a volume fraction of 54 ± 4% for all the entations of TWCP. The orientation investigated by orientations investigated in this study, with the fibre Burrell et al. [1] had a slightly higher density at -3 weave being between 300 and 600 lm. 1.48 g cm due to manufacturing techniques, hence J Mater Sci (2018) 53:11415–11425 11419 Table 1 Key elastic -3 -1 -1 -1 Cloth angle () q gcm ) c (mm ls ) c (mm ls ) c (mm ls ) v 0( L S B properties of TWCP for all of the orientations 0 [20] 1.46 ± 0.01 3.61 ± 0.02 2.00 ± 0.02 2.78 ± 0.03 0.28 20 [1] 1.48 ± 0.01 3.63 ± 0.03 0.99 ± 0.03 3.45 ± 0.04 0.46 25 1.46 ± 0.01 3.55 ± 0.02 1.00 ± 0.02 3.36 ± 0.03 0.46 45 1.46 ± 0.01 3.47 ± 0.02 1.04 ± 0.02 3.26 ± 0.03 0.45 90 1.46 ± 0.01 4.20 ± 0.02 2.01 ± 0.02 3.50 ± 0.03 0.35 With the manganin gauge diagnostic, an average Results and discussion shock response of the composite would be obtained. Typical experimental data traces for the 90 TWCP This is due to the dimensions of the gauge (men- orientation are shown in Figs. 2 and 3. Typical shock tioned in ‘‘Experimental technique’’ section) when traces such as the one shown in Fig. 2 follow the same compared to the dimensions of the fibre weave. For basic form, with subtleties dependent on the material the worst case scenario of a weave thickness of being investigated. Initially a sharp rise is seen on 600 lm there are between 5.3 and 7.4 layers across the both the front and rear gauge traces (assuming no active grid element depending on orientation with precursor wave was seen, as observed in Fig. 3)on respect to each other, with the best case scenario the order of 70 ns for this experiment, with this value being 10.6–14.8 layers across the active manganin due to the thicker than normal insulation/protection gauge (for a 300 lm fibre weave). Because of the layer (50 lm instead of 25 lm of Mylar ) being averaging effect of the gauge, the shock response of employed. After this rise, a plateau of 3 ls on the the composite behaves more like a isotropic material, front gauge is present, and 1.5 ls on the rear gauge, this behaviour noted previously by Hazell et al. [7] which corresponds to the longitudinal stress and Millett et al. [9]. As such, isotropic equations observed by the gauge. After this plateau gauge have been employed on this anisotropic material due death is seen, where no more information from the to the relative size of the active gauge element and the composite layers. With a diagnostic that has experiment is attainable. higher spatial resolution such as Het-V or VISAR, From Fig. 2, with the experimental setup employed which monitors over a potentially very small area, (shown in Fig. 1) the stress and shock velocity can be issues may arise, as it would be possible to focus on directly ascertained, via use of the manganin gauges. either the fibres/weave or the matrix independently. To calculate the value of U the time (Dt in Fig. 2)is used with the known thickness of the sample and Mylar used. Shock velocity is simply then the 6.0 4.0 5.0 3.0 4.0 3.0 2.0 2.0 1.0 Front Gauge 1.0 Δt Front Gauge Back Gauge Back Gauge 0.0 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Time (μs) Time (μs) Figure 2 Typical gauge for the 90 TWCP orientation where no Figure 3 A representative trace for the 90 TWCP orientation elastic precursor behaviour was observed. Experimental condi- displaying the elastic precursor. Impact conditions were a 10 mm -1 -1 tions employed a 10 mm Cu flyer impacting at 890 m s . Cu flyer travelling at a velocity of 600 m s . Longitudinal Stress (GPa) Longitudinal Stress(GPa) J Mater Sci (2018) 53:11415–11425 distance between the gauges, divided by the time it angle according to Eq. (1) to be ascertained (Eqs. 8, takes the shock wave to interact with each gauge (Dt). 9, 10, as well as collated together in Table 6). Stress is obtained from the gauges after the raw Precursor waves were seen with the 90 TWCP data are interpreted according to the calibration by orientation, as seen in Fig. 3. It should be noted that Rosenberg et al. [22]. Due to the difference in impe- the drop seen on the rear gauge is due to crosstalk of dance between the target and PMMA backing plate the gauges and occurs at the death of the front gauge. the rear gauge pressure is adjusted according to Precursor wave behaviour has been noted in multiple Eq. (7). The rear gauge pressure would be the one composites including aramid fibre [10], Dyneema associated with the target and not the PMMA backing [24], glass fibre [11] and carbon fibre [7, 9]. This material [23] as given by the current experimental behaviour on the composite investigated here was setup would give with no adjustment. only observed on experiments below a certain parti- cle velocity, and will be discussed later in more 1 Z þ Z Sample Backing r ¼ r ð7Þ Sample Rear Gauge depth. 2 Z Backing The experimental data for the 90 TWCP weave Particle velocity for these experiments is obtained orientation is collated and shown in Table 2 with from the impedance match technique described by corresponding impact conditions. Meyers [12]. This allow the experimental data to be This is plotted graphically in Fig. 4 for both the calculated (as shown in Tables 2, 3, 4, 5), the Hugo- Hugoniot in the U –u and pressure–unitless volume S p niots in the U –u and pressure–unitless V plane S p plane. Included on this graph is data from the liter- (Figs. 4, 6, 8, 9, 10) allow the equation of state for each ature of other previously studied orientation of the Table 2 Experimental results for the TWCP with the cloth angled perpendicular to the shock front -1 -1 -1 3 -1 Velocity (m s ) Flyer thickness/material (mm) U (mm ls ) u (mm ls ) Volume (cm g ) r (GPa) S p x 355 10 aluminium 4.17 0.24 0.64 1.43 530 10 copper 4.15 0.45 0.61 2.73 600 10 copper 4.13 0.51 0.60 3.21 690 10 copper 4.08 0.59 0.59 3.70 835 10 copper 4.31 0.71 0.57 4.05 890 10 copper 4.40 0.76 0.57 4.76 1015 5 copper 4.39 0.87 0.55 5.61 Table 3 Experimental results for the elastic precursor -1 F F -1 -1 Impact velocity (m s ) Flyer thickness/materials (mm) Dx (mm) Dt (ls) U /c (mm ls ) u (mm ls ) S L p 530 10 copper 8.00 1.27 6.30 0.42 600 10 copper 8.00 1.31 6.12 0.48 690 10 copper 7.98 1.66 4.80 0.58 Table 4 Experimental results for the TWCP with the cloth angled 45 to the shock front -1 -1 -1 3 -1 Velocity (m s ) Flyer thickness/material (mm) U (mm ls ) u (mm ls ) Volume (cm g ) r (GPa) S p x 350 10 aluminium 3.87 0.25 0.64 1.40 540 10 aluminium 3.78 0.39 0.61 2.11 550 10 aluminium 3.82 0.39 0.61 2.17 675 10 copper 4.03 0.58 0.59 3.42 700 10 copper 4.04 0.60 0.58 3.73 840 10 copper 4.34 0.72 0.57 4.51 985 5 copper 4.41 0.84 0.56 5.51 J Mater Sci (2018) 53:11415–11425 11421 Table 5 Experimental results for the TWCP with the cloth angled 25 to the shock front -1 -1 -1 3 -1 Velocity (m s ) Flyer thickness/material (mm) U (mm ls ) u (mm ls ) Volume (cm g ) r (GPa) S p x 330 10 aluminium 3.80 0.23 0.64 1.30 350 10 aluminium 3.86 0.25 0.64 1.51 400 10 aluminium 3.54 0.29 0.63 1.62 440 10 aluminium 3.54 0.32 0.62 1.78 510 10 copper 3.89 0.44 0.61 2.60 535 10 aluminium 3.48 0.39 0.61 2.21 600 10 copper 3.93 0.52 0.59 3.08 690 10 copper 3.88 0.60 0.58 3.74 820 10 copper 3.74 0.71 0.55 4.36 1155 5 copper 4.34 0.99 0.53 6.79 8.0 5.0 4.5 90 Degree Experimental Data 7.0 4.0 90 Degree Hugoniot 6.0 3.5 U = 3.46 + 1.15u S p 2 0 Degree Hugoniot (Wood et al.) U = 4.2 R = 0.78 5.0 3.0 2 R = 0.80 20 Degree Hugoniot (Burrell et al.) 4.0 2.5 90 Degree Experimental Data 2.0 3.0 90 Degree Hugoniot 1.5 2.0 1.0 0 Degree Hugoniot (Wood et al.) 1.0 0.5 20 Degree Hugoniot (Burrell et al.) 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Particle Velocity (mm/ s) Unitless Volume Figure 4 Hugoniot in the shock velocity–particle velocity (left) and pressure–unitless volume (right) plane for the 90 orientation of the composite TWCP. Table 6 Hugoniot equations TWCP orientation Equation for each orientation of TWCP investigated here as well as the -1 90 elastic U = 4.20; for u less than 0.65 mm ls S p ones investigated by Wood -1 90 plastic U = 3.46 ? 1.15u ; for up between 0.65 and 0.9 mm ls S p et al. [20] and Burrell et al. [1] 45 U = 3.44 ? 1.12u S p 25 U = 3.45 ? 0.73u S p 0 [20] U = 3.69 ? 0.59u S p 20 [1] U = 3.74 ? 0.57u S p same composite [1, 20]. Considering first the shock traditional shock response is observed. The equation velocity–particle velocity plane, it can be seen that the for both of these regions is shown in Eq. (8). There is 90 orientation has more complex shock behaviour little scatter of the experimental data from the line of 2 2 when compared to the more monolithic behaviour best fits as shown by the R values, with a R value of exhibited by both the 0 [20] and 20 [1] orientations. 0.80 for the initial response and 0.78 for the more The Hugoniot for the 90 TWCP orientation has two standard shock response. distinct regions, an initial response where the elastic 4:20; u \0:65 mm ls U ¼ ð8Þ wave dominates the material behaviour, and a sec- 1 3:46 þ 1:15u ; 0:65\u [ 0:9mm ls p p ond region above a particle velocity value of -1 approximately 0.65 mm ls where a more Shock Velocity (mm/ s) Longitudinal Stress (GPa) J Mater Sci (2018) 53:11415–11425 5.0 Figure 4 also shows the Hugoniot for the 90 Front Gauge TWCP orientation in the pressure–volume plane. For Back Gauge 4.0 comparative purposes a unitless volume is employed (primarily for comparison between this composition 3.0 of TWCP and the one investigated by Burrell et al. Ref. [1], due to the different density). Due to the ini- 2.0 tial elastic behaviour of the Hugoniot in the U –u S p plane for the 90 orientation, elastic behaviour is also 1.0 seen in the pressure–volume plane. No substantial deviation was noted between the experimental data 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 and the Hugoniot (Eq. 8) for the 90 orientations of Time (μs) the TWCP material. As such, no strengthening was seen with the 90 experimental data, which had Figure 5 A gauge trace for a 10 mm Cu flyer impacting at -1 700 m s for the 45 TWCP orientation. previously been seen with the 0 TWCP orientation investigated by Wood et al. [20]. gradient than the Hugoniot observed for the 0 ori- As mentioned earlier an elastic precursor was entation of TWCP (obtained from Ref. [20]), but the observed on the traces in the elastic region, e.g. Fig. 3. gradient is close to what is observed for the shock Elastic precursors such as this have been seen in portion of the 90 orientation (as shown in Eq. 8). A carbon fibre composites previously investigated by small amount of scatter is noted in the data, signified Hazell et al. [7] and Millett et al. [9], as well as other by the R value of 0.85. composites such as the aramid fibre composite investigated by Bordzilovsky et al. [10]. U ¼ 3:44 þ 1:12u ð9Þ S p Table 3 shows all of the experimental data which For the pressure–unitless volume plane no relate to the elastic precursor for the TWCP material strengthening effects were seen between the Hugo- with regard to the 90 orientation. This table includes niot and the experimental data. Deviation was the velocity of the precursor wave, ascertained from observed with the 90 TWCP orientation as noted the time between the rise on the front gauge and the between this orientation (45) and the ones investi- start of the precursor on the rear gauge. As the par- gated previously (0 by Wood et at. [20], and the 20 ticle velocity of the associated shock wave increased, orientation investigated by Burrell et al. [1]). the velocity of the elastic precursor wave decreased, Figure 7 shows the manganin gauge trace for the with the precursor wave disappearing completely 25 orientated TWCP sample. As seen with the 45 -1 between 0.59 and 0.71 mm ls . This range agrees orientation no elastic precursor wave were observed, with the elastic to shock wave transition observed in as noted with the 90 orientated TWCP sample. The the Hugoniot in the U –u plane (Fig. 9). This would S p trace follows the behaviour noted with the other likely mean that the most probable value that this orientations including sharp rises and plateaus. The transition occurs at a particle velocity of experimental data for the 25 TWCP orientation -1 0.65 mm ls ; however, due to the lack of experi- shown in Table 5. mental data in this region this cannot be definitively The data for the 25 TWCP orientation are plotted proven. in U –u and pressure–unitless volume plane in S p Figure 5 shows a typical trace obtained for the 45 Fig. 8, with the calculated Hugoniot in Eq. (10). It orientated TWCP sample. Unlike the low velocity 90 should be noted, however, that the scatter on this experiments no precursor wave was observed. The data is large, compared with the other orientations as other typical trace behaviour was observed such as, demonstrated by the low R value of 0.49. This scatter sharp rises and plateaus. The experimental data for is also observed in the pressure–unitless volume the 45 TWCP orientation are shown in Table 4, with plane as well. While the other orientations agreed the data plotted graphically in the U –u and pres- S p well with the Hugoniot in this plane, clear deviation sure–unitless volume plane in Fig. 6. is observed on the highest pressure compared to the The Hugoniot for the TWCP orientated at 45 is Hugoniot. This would normally imply a strengthen- given in Eq. (9). It can be seen that it has a steeper ing effect. However, with the scatter on the Longitudinal Stress (GPa) J Mater Sci (2018) 53:11415–11425 11423 5.0 7.0 4.5 45 Degree Experimental Data 6.0 4.0 45 Degree Hugoniot 5.0 3.5 0 Degree Hugoniot (Wood et al.) 3.0 U = 3.44 + 1.12u S p 4.0 R = 0.85 20 Degree Hugoniot (Burrell et al.) 2.5 3.0 45 Degree Experimental Data 2.0 45 Degree Hugoniot 1.5 2.0 1.0 0 Degree Hugoniot (Wood et al.) 1.0 0.5 20 Degree Hugoniot (Burrell et al.) 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Particle Velocity (mm/ s) Unitless Volume Figure 6 Hugoniot in the U –u (left) and P–V (right) plane for the 45 orientation of TWCP. S p 3.0 to assume that this scatter is caused by the orientation of the fibre weave within this composite, i.e. the interaction between the fibre weave and matrix material and the shock front, as the other orientation 2.0 have less scatter associated with them as shown by their higher R values. U ¼ 3:45 þ 0:73u ð10Þ 1.0 S p Front Gauge When the Hugoniots of the three investigated ori- Back Gauge entations (25,45 and 90, with the equations are 0.0 given collated in Table 6) are contrasted in the U –u S p 0.0 1.0 2.0 3.0 4.0 5.0 6.0 plane (Fig. 9) and pressure–unitless volume plane Time (μs) (Fig. 10), the experimental results are comparable. Figure 7 Representative gauge trace for the 25 TWCP orienta- The exception to this behaviour is the 90 experi- -1 tion, impacted at 510 m s with a 10 mm Cu flyer. mental data, which is due to the elastic precursor -1 dominance at particle velocities below 0.65 mm ls . experimental data, how statistically realistic this The scatter observed within the experimental data is conclusion is, is questionable. The experimental data most notable with the 25 TWCP orientation. Due to for this orientation agree closer to the 0 and 20 this scatter within the experimental data, conver- orientations previously investigated by Wood et al. gence of the individual Hugoniot of each orientation [20] and Burrell et al. [1], respectively. It is reasonable 5.0 8.0 4.5 25 Degree Experimental Data 7.0 4.0 25 Degree Hugoniot 6.0 3.5 0 Degree Hugoniot (Wood et al.) 5.0 3.0 U = 3.45 + 0.73u S p 2 20 Degree Hugoniot (Burrell et al.) 2.5 R = 0.49 4.0 25 Degree Experimental Data 2.0 3.0 25 Degree Hugoniot 1.5 2.0 1.0 0 Degree Hugoniot (Wood et al.) 1.0 0.5 20 Degree Hugoniot (Burrell et al.) 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Particle Velocity (mm/ s) Unitless Volume Figure 8 Hugoniot in the U –u (left) and P–V (right) plane for the 25 orientation for the composite TWCP. S p Shock Velocity (mm/ s) Shock Velocity (mm/ s) Longitudinal Stress (GPa) LongitudinalStress (GPa) Longitudinal Stress (GPa) J Mater Sci (2018) 53:11415–11425 5.0 Conclusion 4.5 4.0 The shock response of three different orientations of a 3.5 tape-wrapped carbon fibre composite with phenolic 3.0 resin matrix has been investigated. This has been 2.5 achieved by using the plate impact technique via a 25 Degree Hugoniot 2.0 single-stage gas gun, with manganin pressure gauges 45 Degree Hugoniot 1.5 as a diagnostic technique. The orientations of the 90 Degree Hugoniot 1.0 fibre weave studied here were 25,45 and 90 with 0 Degree Hugoniot (Wood et al.) 0.5 respect to the impact face. These data have been 20 Degree Hugoniot (Burrell et al.) 0.0 contrasted with the previously obtained data for 0.0 0.2 0.4 0.6 0.8 1.0 1.2 other TWCP orientations by Wood et al. [20] and Particle Velocity (mm/ s) Burrell et al. [1], who used a different composition Figure 9 Hugoniot in the U –u plane, for all of the investigated within their TWCP material, as well as fibre weave S p orientations as well as the literature data for Wood et al. [20] and orientation. When all of the orientations are com- Burrell et al. [1]. pared to one another, little difference was observed with the exception of the 90 TWCP orientation. This was due to elastic behaviour below a particle velocity -1 8.0 value of 0.65 mm ls . Also noted within the data set 25 Degree Hugoniot 7.0 was an amount of scatter present, especially with the 45 Degree Hugoniot 25 TWCP orientation. This is most likely induced by 6.0 90 Degree Hugoniot the differing constituents within the composite, 5.0 0 Degree Hugoniot (Wood et al.) leading to a more dispersed and complex wave pro- 4.0 20 Degree Hugoniot (Burrell et al.) file. This therefore means that other properties such 3.0 as strength, ablation etc. may be considered for the materials application. 2.0 1.0 0.0 Acknowledgements 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Unitless Volume The authors would like to acknowledge the support of the Institute of Shock Physics and AWE. Lockheed- Figure 10 Hugoniot in the pressure–volume plane, for all of the investigated orientations as well as the literature data for Wood Martin Insys is also thanked for supplying the et al. [20] and Burrell et al. [1]. experimental samples. In addition, we would also like to thank Mr. Andrew Roberts for technical help in carrying out the experiments. British Crown did not occur as previously observed with the 0 Copyright MOD/2018. TWCP orientation and the phenolic resin matrix material investigated by Wood et al. [20]. With the Open Access This article is distributed under the associated error bars taken into account the majority terms of the Creative Commons Attribution 4.0 of the data is broadly similar to the orientations of International License (http://creativecommons.org/ TWCP previously investigated by Wood et al. [20] licenses/by/4.0/), which permits unrestricted use, and Burrell et al. [1]. Therefore, the Hugoniot for the distribution, and reproduction in any medium, pro- 0 TWCP material can be used as an approximation vided you give appropriate credit to the original for the shock response of this material. The caveat is author(s) and the source, provide a link to the Crea- that the initial shock response of the 90 orientation is tive Commons license, and indicate if changes were elastic in nature has to be taken into account. Due to made. this relative insensitivity of the orientation with regard to the shock response of TWCP; other factors such as ablation, strength etc. can be considered for the materials application. Longitudinal Stress (GPa) Shock Velocity (mm/ s) J Mater Sci (2018) 53:11415–11425 11425 [12] Meyers MA (1994) Elastic waves. In: Meyers MA (ed) References Dynamic behavior of materials, p 55. Wiley, New York. [1] Burrell RH, Barnes NR, Keightley PT et al (2009) The https://doi.org/10.1007/s11340-012-9598-0 response of a carbon fibre-phenolic resin composite to one- [13] Barker LM, Hollenbach RE (1970) Shock-wave studies of dimensional shock loading. In: 16th APS topical conference PMMA, fused silica, and sapphire. J Appl Phys on shock compression of condensed matter 41:4208–4226. https://doi.org/10.1063/1.1658439 [2] Windhorst T, Blount G (1997) Carbon–carbon composites: a [14] Carter WJ, Marsh SP (1995) Hugoniot equation of state of summary of recent developments and applications. Mater polymers Des 18:11–15. https://doi.org/10.1016/S0261- [15] Shepherd CJ, Appleby-Thomas GJ, Wilgeroth JM et al 3069(97)00024-1 (2011) On the response of ballistic soap to one-dimensional [3] Wicklein M, Ryan S, White DM, Clegg RA (2008) Hyper- shock loading. Int J Impact Eng 38:981–988. https://doi.org/ velocity impact on CFRP: testing, material modelling, and 10.1016/j.ijimpeng.2011.07.003 numerical simulation. Int J Impact Eng 35:1861–1869. [16] Wood DC, Hazell PJ, Appleby-Thomas GJ, Barnes NR https://doi.org/10.1016/j.ijimpeng.2008.07.015 (2011) Shock behaviour of a phenolic resin. J Mater Sci [4] Millett JCF, Bourne NK, Deas D (2005) The equation of 46:5991–5999. https://doi.org/10.1007/s10853-011-5560-2 state of two alumina-filled epoxy resins. J Phys D Appl Phys [17] Davison L (2008) Fundamentals of shock wave propagation 38:930–934. https://doi.org/10.1088/0022-3727/38/6/023 in solids. Springer, Berlin [5] Dattelbaum DM, Coe JD, Rigg PA et al (2014) Shockwave [18] Appleby-Thomas GJ, Hazell PJ (2012) The impact of response of two carbon fiber–polymer composites to structural composite materials. Part 2: hypervelocity impact 50 GPa. J Appl Phys 116:194308. https://doi.org/10.1063/1. and shock. J Strain Anal Eng Des 47:406–418. https://doi. org/10.1177/0309324712448299 [6] Oved Y, Luttwak GE, Rosenberg Z (1978) Shock wave [19] Willows M, Tsembelis K, Proud WG, Church PD (2007) propagation in layered composites. J Compos Mater. https:// Shock characterisation of a carbon fibre composite. In: 15th doi.org/10.1177/002199837801200107 APS topical conference on shock compression of condensed [7] Hazell PJ, Stennett C, Cooper G (2009) The effect of spec- matter. Poster presentation only imen thickness on the shock propagation along the in-fibre [20] Wood DC, Appleby-Thomas GJ, Hazell PJ, Barnes NR direction of an aerospace-grade CFRP laminate. Compos (2012) Shock propagation in a tape wrapped carbon fibre Part A Appl Sci Manuf 40:204–209. https://doi.org/10.1016/ composite. Compos Part A Appl Sci Manuf 43:1550–1560. j.compositesa.2008.11.002 https://doi.org/10.1016/j.compositesa.2012.04.013 [8] Tsai L, Prakash V, Rajendran AM, Dandekar DP (2007) [21] Marsh SP (1980) LASL shock hugoniot data. Los Alamos Structure of shock waves in glass fiber reinforced polymer Ser Dyn Mater Prop, p 150. ISBN 0-520-04008-2 matrix composites. Appl Phys Lett 90:061909. https://doi. [22] Rosenberg Z, Yaziv D, Partom Y (1980) Calibration of foil- org/10.1063/1.2435340 like manganin gauges in planar shock wave experiments. [9] Millett JCF, Bourne NK, Meziere YJE et al (2007) The effect J Appl Phys 51:3702–3705. https://doi.org/10.1063/1. of orientation on the shock response of a carbon fibre–epoxy composite. Compos Sci Technol 67:3253–3260. https://doi. [23] Appleby-Thomas GJ, Hazell PJ, Stennett C (2009) The org/10.1016/j.compscitech.2007.03.034 variation in lateral and longitudinal stress gauge response [10] Bordzilovsky SA, Karakhanov SM, Merzhievsky LA (1998) within an RTM 6 epoxy resin under one-dimensional shock Shock response of a unidirectional composite at various loading. J Mater Sci 44:6187–6198. https://doi.org/10.1007/ orientation of fibers. In: 10th APS topical conference on s10853-009-3859-z shock compression of condensed matter, pp 545–548 [24] Hazell PJ, Appleby-Thomas GJ, Trinquant X, Chapman DJ [11] Millett JCF, Meziere YJE, Bourne NK (2007) The response (2011) In-fiber shock propagation in Dyneema . J Appl to shock loading of a glass–fibre–epoxy composite: effects of Phys 110:043504. https://doi.org/10.1063/1.3622294 fibre orientation to the loading axis. J Phys D Appl Phys 40:5358–5365. https://doi.org/10.1088/0022-3727/40/17/ http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Materials Science Springer Journals

The variance on the shock response of a carbon fibre composite due to the orientation of the weave

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Abstract

J Mater Sci (2018) 53:11415–11425 COMPOSITES Composites The variance on the shock response of a carbon fibre composite due to the orientation of the weave 1, 1 1 2 2 3 D. C. Wood *, G. J. Appleby-Thomas , A. Hameed , N. R. Barnes , A. Hughes , and P. J. Hazell Centre for Defence Engineering, Cranfield University, Defence Academy of the UK, Shrivenham SN6 8LA, UK AWE, Aldermaston, Reading RG7 4PR, UK School of Engineering and Information Technology, The University of New South Wales, UNSW Canberra, PO Box 7916, Canberra, BC 2610, Australia Received: 20 February 2018 ABSTRACT Accepted: 9 May 2018 Three different orientations of a tape-wrapped carbon fibre composite with Published online: phenolic resin matrix (abbreviated to TWCP) have been investigated under one- 22 May 2018 dimensional shock loading. This has been achieved via a single-stage gas gun, with manganin gauges as the diagnostic tool. The orientations of TWCP studied The Author(s) 2018 in this paper were 25,45 and 90, with respect to the impact face. The shock response of these orientations, for this material, has been obtained (the Hugoniot equation of state). These results have been contrasted with previously reported literature data for the same material at different orientations (0 and 20). It was found that orientation had minimal effect on the behaviour of this composite under shock. The exception to this was the 90 orientation which exhibited an -1 elastic precursor at particle velocities of less than 0.65 mm ls ; where the shock velocity was equivalent to the elastic sound speed of the material. matrix) [4, 5], configuration of the layered structure Introduction [6], thickness of the composite sample [7, 8] and the orientation of constituent layer [9–11] which is the Composites have a high strength to weight ratio focus of this paper. making them ideal candidates for multiple applica- To understand the behaviour of shocked materials, tions in a wide range of industries, for example the five parameters are needed. These parameters are aerospace industry [1–3]. Due to these numerous shock velocity U , particle velocity u , density q, industries and therefore applications, a wide range of S p pressure P and internal energy E. With any two of conditions may be experienced such as shock these five parameters obtained, the materials shock loading. response can be fully described using the Rankine– When looking at the shock response of composite materials, a multitude of different configurations can Hugoniot equations [12] (which are based on princi- alter the observed behaviour. These can include ples of conservation of mass, momentum and constituents used (such as fibre ratio, type of fibre or energy). The two parameters directly measured in Address correspondence to E-mail: d.wood@cranfield.ac.uk https://doi.org/10.1007/s10853-018-2431-0 J Mater Sci (2018) 53:11415–11425 this study were U and r , with a third parameter u orientation of the fibre weave with respect to the S x p found using the impedance matching technique [12]. shock front in a carbon fibre composite. Further to these parameters, density was calculated Many authors have investigated the effect that from the Rankine–Hugoniot jump equations (with orientation has on the shock response of composites; the inverse of density giving the volume, V). This however, they tend to focus on the orientations par- allowed the Hugoniot in both the U –u and pres- allel and perpendicular to the shock front, a good S p sure–volume planes to be ascertained. overview on the shock response of composites is In the U –u plane, the Hugoniot relationship tends given by Ref. [18]. S p to be linear in nature for most materials, following One study that investigated a wide range of ori- the form shown in Eq. (1). Nonlinear behaviour in the entations and its affect on the shock profile was the U –u Hugoniot plane has been observed with some work of Bordzilovsky et al. [10]. In this paper, an S p materials such as polymers [13–15], including the aramid fibre composite with an epoxy resin matrix matrix material of TWCP investigated here [16]. For material was investigated. A single set of experi- Eq. (1), c is the Hugoniot intercept at the ground mental conditions was picked, utilising TNT to state which tends to be comparable to c (the bulk impart a shock into the sample, such that any dif- sound velocity of the material, given by Eq. 5); while ference in the shock profile was due to the orientation S is the slope of the Hugoniot. of the aramid fibre weave. The angles of the fibre weave investigated were 5,15,45 and 90, with U ¼ c þ Su ð1Þ S 0 p respect to the direction of shock wave. An elastic The hydrodynamic pressure of a material (P , also precursor was noted at the orientations of 5 and 15 referred to as the Hugoniot pressure) is given by before finally smearing and disappearing at 90. Eq. (2) and is typically represented in the pressure– Millett et al. [9] investigated the effect that orien- particle velocity plane. This equation may be adjus- tation of a carbon fibre weave had on the resultant ted for use in the pressure–volume plane with this shock profile. In this study, two orientations of fibre form given in Eq. (3), where q is the initial density weaves were investigated; one where the fibre weave and V along with V are the volume at the Hugoniot was orientated parallel to the shock front, with the pressure and initial state, respectively. other fibre weave orientated perpendicular to the P ¼ q U u ð2Þ shock front. To impart the shock wave, aluminium or H S p copper flyers were used at velocities between 200 and 2 -1 P ¼ q U 1  ð3Þ 1125 m s . It was found that when the fibre weave 0 S was parallel to the shock front the carbon fibre The Hugoniot pressure and deviatoric (maximum composite behaved more like a monolithic material; shear stress s, derived from the Cauchy stress tensor with the exception of very small oscillations on the [17]) elements of stress are linked by Eq. (4). This plateau of the trace. These were attributed to shock relation implies that if the longitudinal stress equals wave interactions between the fibres and matrix the hydrodynamic pressure then there will be little to within the sample material. However, when the fibre no strength effect in the material. weave was orientated perpendicular to the shock front, a ramped elastic portion was seen with an r ¼ P þ s ð4Þ -1 x H approximate velocity of 7 mm ls , before the main shock front overtook the elastic portion. This beha- Due to the number of different constituents and viour was explained as an elastic wave travelling arrangements, a wide range of composite systems are down the fibres ahead of the main shock front. commercially available. This adjustment in the com- Despite this behaviour, both Hugoniots in the U –u S p posite material due to a change in constituents can plane were found to be linear in nature, with signif- greatly alter the material response especially in the icant deviation at lower particle velocities before shock regime. This adjustment could be a change in convergence was observed at elevated particle fibres, matrix or of the volume fraction of the mate- velocities. rial, for example. For the purposes of this investiga- Hazell et al. [7] also investigated a carbon fibre tion, the property under consideration was the composite, where the weave was orientated perpen- dicular to the shock front. The main focus of this J Mater Sci (2018) 53:11415–11425 11417 paper was the effect of thickness on the shock was noted. Within the data, there was no indication response of this composite. The four thicknesses used of any elastic behaviour, as noted in composites were 1.52, 3.00, 6.05 and 9.06 mm. As observed in the studied by Bordzilovsky et al. [10], Millett et al. [9] study by Millett et al. [9], an initial ramped portion and Hazell et al. [7]. due to an elastic precursor through the fibres was In this paper, the previous work conducted by seen. As the thickness of the composite was Wood et al. [20] and Burrell et al. [1] will be built increased, the initial ramped portion of the trace upon and expanded to include more orientations. became more pronounced, as did the magnitude of The orientations that will be investigated here are 25, pressure of this initial ramped portion. 45 and 90 with the orientation referring to the angle Multiple diagnostic techniques were used by Wil- between the shock front and the fibre weave. These lows et al. [19] to investigate the shock response of a data will then be compared to previous work in the carbon fibre composite using the plate impact tech- literature (specifically Refs. [1, 20]), to see the effect nique. By employing both VISAR and manganin that orientation has on the shock response of this stress gauges, on ring up and ring down experiments TWCP material. the shock profile was investigated. It was concluded, via the use of a computational model that fibre ori- entation was unimportant above a particle velocity Experimental technique -1 value of approximately 1000 m s . This supports the The plate impact technique was used to induce a one- work conducted by Millett et al. [9], who observed dimensional shock wave into the TWCP samples. To Hugoniot convergence with their composite at higher achieve this, a single-stage gas gun with a 5-m-long particle velocities. barrel and 50-mm bore was used to accelerate flyer In this study, a tape-wrapped carbon fibre com- plates (attached to sabots for stability) into the tar- posite with a phenolic resin (abbreviated to TWCP) gets. The flyer plates used in these experiments were will be investigated. This material has been studied aluminium or copper (either 5 or 10 mm thick) due to previously by Wood et al. [20] and Burrell et al. [1]at their well characterised behaviour while under shock orientations of 0 and 20, respectively. These orien- [21]. Velocity measurements were obtained via a tations were with respect to the impact surface of the series of sequential infrared transmitters and recei- sample. vers. This experimental setup is shown simplistically Wood et al. [20] investigated a TWCP composite in Fig. 1. One-dimensionality is assured by careful where the fibre weave was arranged parallel to the machining of all components within the targets such shock front. As was observed by Millett et al. [9]on that all parallel surfaces to the shock front are flat and their carbon fibre composite, the 0 weave orientation parallel to tolerances of ± 10 lm. To confirm the behaved monolithically, with the exception of noted accuracy of the gas gun with relation to the target, tilt oscillations on the plateau of the experimental gauge pins experiments are performed before and after shot traces. These oscillations were found to be due to the programs. The maximum misalignment of the cov- thickness of the fibre weave and the shock interac- erplate surface to flyerplate surface within this pro- tions between the carbon fibre weave and the matrix gram of work was found to be 1.9 mrad. material. It was noted in this study that convergence To investigate the effect that orientation has on the between the TWCP and the phenolic resin matrix shock response of composites manganin pressure material occurred above a particle velocity of -1 gauges were used to monitor the transit of the shock 0.8 mm ls . profile. Manganin is used as it is largely unaffected The shock response of a TWCP composite, with the by the temperature increase associated with a shock weave orientated at 20 to the impact face was wave, and as such the output is the pressure of the investigated by Burrell et al. [1]. Unlike the one material (assuming hydrodynamic behaviour). The investigated by Wood et al. [20] and in this study, the gauges employed within these experiments were TWCP material investigated by Burrell et al. had a manufactured by Vishay Micro-measurements with different compositional makeup, as noted by the the product designation being LM-SS-125CH-048, difference in the initial density. The shock response with an active manganin grid element of 3.18 by was compared to previously obtained data for 4.45 mm for a total active area of 14.15 mm . When a TWCP, where good agreement between the data sets J Mater Sci (2018) 53:11415–11425 Velocity TWCP 50 μm Mylar® Measurement 50 μm Mylar® Sample System Coverplate PMMA (Al or Cu) Backing Manganin Sabot/Flyer Pressure Gauges Figure 1 General experimental setup, with typical target configuration. pressure is applied to the gauge a proportional the discrepancy between the densities in Table 1. For change in resistance is noted, which by using the all orientations of this TWCP material, ultrasonic calibration method of Rosenberg et al. [22] can be measurements have been obtained using 1 MHz calculated. quartz transducers and a Panametrics 5077PR pulse Figure 1 shows a simplified target setup arrange- receiver. Pulse-echo mode was used to obtain longi- ment. One thing to note is the inclusion of 50 lmof tudinal sound speed (cL), with the shear sound speed Mylar which is used as both electrical and physical (cS) found using transmit–receive configuration, with protection of the gauges. All matching surfaces of the the bulk sound speed found via Eq. (5). Table 1 components were joined together with a slow curing shows the key elastic properties for TWCP, c , c , c L S B TM epoxy resin Locite 0151 HYSOL Epoxi-Patch .In and v (Poisson’s ratio) for all of the orientations these experiments, all samples were of dimensions 60 investigated here, as well as previous work by Burrell by 60 by 8 mm. et al. [1] and Wood et al. [20]. Poisson’s ratio is given by Eq. (6) and is based on the sound speed of the materials, which leads to the discrepancy in Table 1 Material properties caused by the anisotropy of the composite. rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 For the material investigated here, the carbon fibres c ¼ c  c ð5Þ L S are woven into a two-dimensional fabric (plain weave), which are stacked upon one another, before 0:5 being impregnated by the phenolic resin (Durite SC- v ¼ ð6Þ 1008 previously investigated by Wood et al. [16]). It is 1:0 these weaves that are orientated with respect to the Using micrographs, the volume fraction of the shock front. Density measurements were conducted TWCP composite was calculated as previously con- using a Micrometrics AccuPyc 1330 gas pycnometer -3 ducted in the work by Wood et al. [20]. This tech- which gave a value of 1.46 g cm for all of the ori- nique led to a volume fraction of 54 ± 4% for all the entations of TWCP. The orientation investigated by orientations investigated in this study, with the fibre Burrell et al. [1] had a slightly higher density at -3 weave being between 300 and 600 lm. 1.48 g cm due to manufacturing techniques, hence J Mater Sci (2018) 53:11415–11425 11419 Table 1 Key elastic -3 -1 -1 -1 Cloth angle () q gcm ) c (mm ls ) c (mm ls ) c (mm ls ) v 0( L S B properties of TWCP for all of the orientations 0 [20] 1.46 ± 0.01 3.61 ± 0.02 2.00 ± 0.02 2.78 ± 0.03 0.28 20 [1] 1.48 ± 0.01 3.63 ± 0.03 0.99 ± 0.03 3.45 ± 0.04 0.46 25 1.46 ± 0.01 3.55 ± 0.02 1.00 ± 0.02 3.36 ± 0.03 0.46 45 1.46 ± 0.01 3.47 ± 0.02 1.04 ± 0.02 3.26 ± 0.03 0.45 90 1.46 ± 0.01 4.20 ± 0.02 2.01 ± 0.02 3.50 ± 0.03 0.35 With the manganin gauge diagnostic, an average Results and discussion shock response of the composite would be obtained. Typical experimental data traces for the 90 TWCP This is due to the dimensions of the gauge (men- orientation are shown in Figs. 2 and 3. Typical shock tioned in ‘‘Experimental technique’’ section) when traces such as the one shown in Fig. 2 follow the same compared to the dimensions of the fibre weave. For basic form, with subtleties dependent on the material the worst case scenario of a weave thickness of being investigated. Initially a sharp rise is seen on 600 lm there are between 5.3 and 7.4 layers across the both the front and rear gauge traces (assuming no active grid element depending on orientation with precursor wave was seen, as observed in Fig. 3)on respect to each other, with the best case scenario the order of 70 ns for this experiment, with this value being 10.6–14.8 layers across the active manganin due to the thicker than normal insulation/protection gauge (for a 300 lm fibre weave). Because of the layer (50 lm instead of 25 lm of Mylar ) being averaging effect of the gauge, the shock response of employed. After this rise, a plateau of 3 ls on the the composite behaves more like a isotropic material, front gauge is present, and 1.5 ls on the rear gauge, this behaviour noted previously by Hazell et al. [7] which corresponds to the longitudinal stress and Millett et al. [9]. As such, isotropic equations observed by the gauge. After this plateau gauge have been employed on this anisotropic material due death is seen, where no more information from the to the relative size of the active gauge element and the composite layers. With a diagnostic that has experiment is attainable. higher spatial resolution such as Het-V or VISAR, From Fig. 2, with the experimental setup employed which monitors over a potentially very small area, (shown in Fig. 1) the stress and shock velocity can be issues may arise, as it would be possible to focus on directly ascertained, via use of the manganin gauges. either the fibres/weave or the matrix independently. To calculate the value of U the time (Dt in Fig. 2)is used with the known thickness of the sample and Mylar used. Shock velocity is simply then the 6.0 4.0 5.0 3.0 4.0 3.0 2.0 2.0 1.0 Front Gauge 1.0 Δt Front Gauge Back Gauge Back Gauge 0.0 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 Time (μs) Time (μs) Figure 2 Typical gauge for the 90 TWCP orientation where no Figure 3 A representative trace for the 90 TWCP orientation elastic precursor behaviour was observed. Experimental condi- displaying the elastic precursor. Impact conditions were a 10 mm -1 -1 tions employed a 10 mm Cu flyer impacting at 890 m s . Cu flyer travelling at a velocity of 600 m s . Longitudinal Stress (GPa) Longitudinal Stress(GPa) J Mater Sci (2018) 53:11415–11425 distance between the gauges, divided by the time it angle according to Eq. (1) to be ascertained (Eqs. 8, takes the shock wave to interact with each gauge (Dt). 9, 10, as well as collated together in Table 6). Stress is obtained from the gauges after the raw Precursor waves were seen with the 90 TWCP data are interpreted according to the calibration by orientation, as seen in Fig. 3. It should be noted that Rosenberg et al. [22]. Due to the difference in impe- the drop seen on the rear gauge is due to crosstalk of dance between the target and PMMA backing plate the gauges and occurs at the death of the front gauge. the rear gauge pressure is adjusted according to Precursor wave behaviour has been noted in multiple Eq. (7). The rear gauge pressure would be the one composites including aramid fibre [10], Dyneema associated with the target and not the PMMA backing [24], glass fibre [11] and carbon fibre [7, 9]. This material [23] as given by the current experimental behaviour on the composite investigated here was setup would give with no adjustment. only observed on experiments below a certain parti- cle velocity, and will be discussed later in more 1 Z þ Z Sample Backing r ¼ r ð7Þ Sample Rear Gauge depth. 2 Z Backing The experimental data for the 90 TWCP weave Particle velocity for these experiments is obtained orientation is collated and shown in Table 2 with from the impedance match technique described by corresponding impact conditions. Meyers [12]. This allow the experimental data to be This is plotted graphically in Fig. 4 for both the calculated (as shown in Tables 2, 3, 4, 5), the Hugo- Hugoniot in the U –u and pressure–unitless volume S p niots in the U –u and pressure–unitless V plane S p plane. Included on this graph is data from the liter- (Figs. 4, 6, 8, 9, 10) allow the equation of state for each ature of other previously studied orientation of the Table 2 Experimental results for the TWCP with the cloth angled perpendicular to the shock front -1 -1 -1 3 -1 Velocity (m s ) Flyer thickness/material (mm) U (mm ls ) u (mm ls ) Volume (cm g ) r (GPa) S p x 355 10 aluminium 4.17 0.24 0.64 1.43 530 10 copper 4.15 0.45 0.61 2.73 600 10 copper 4.13 0.51 0.60 3.21 690 10 copper 4.08 0.59 0.59 3.70 835 10 copper 4.31 0.71 0.57 4.05 890 10 copper 4.40 0.76 0.57 4.76 1015 5 copper 4.39 0.87 0.55 5.61 Table 3 Experimental results for the elastic precursor -1 F F -1 -1 Impact velocity (m s ) Flyer thickness/materials (mm) Dx (mm) Dt (ls) U /c (mm ls ) u (mm ls ) S L p 530 10 copper 8.00 1.27 6.30 0.42 600 10 copper 8.00 1.31 6.12 0.48 690 10 copper 7.98 1.66 4.80 0.58 Table 4 Experimental results for the TWCP with the cloth angled 45 to the shock front -1 -1 -1 3 -1 Velocity (m s ) Flyer thickness/material (mm) U (mm ls ) u (mm ls ) Volume (cm g ) r (GPa) S p x 350 10 aluminium 3.87 0.25 0.64 1.40 540 10 aluminium 3.78 0.39 0.61 2.11 550 10 aluminium 3.82 0.39 0.61 2.17 675 10 copper 4.03 0.58 0.59 3.42 700 10 copper 4.04 0.60 0.58 3.73 840 10 copper 4.34 0.72 0.57 4.51 985 5 copper 4.41 0.84 0.56 5.51 J Mater Sci (2018) 53:11415–11425 11421 Table 5 Experimental results for the TWCP with the cloth angled 25 to the shock front -1 -1 -1 3 -1 Velocity (m s ) Flyer thickness/material (mm) U (mm ls ) u (mm ls ) Volume (cm g ) r (GPa) S p x 330 10 aluminium 3.80 0.23 0.64 1.30 350 10 aluminium 3.86 0.25 0.64 1.51 400 10 aluminium 3.54 0.29 0.63 1.62 440 10 aluminium 3.54 0.32 0.62 1.78 510 10 copper 3.89 0.44 0.61 2.60 535 10 aluminium 3.48 0.39 0.61 2.21 600 10 copper 3.93 0.52 0.59 3.08 690 10 copper 3.88 0.60 0.58 3.74 820 10 copper 3.74 0.71 0.55 4.36 1155 5 copper 4.34 0.99 0.53 6.79 8.0 5.0 4.5 90 Degree Experimental Data 7.0 4.0 90 Degree Hugoniot 6.0 3.5 U = 3.46 + 1.15u S p 2 0 Degree Hugoniot (Wood et al.) U = 4.2 R = 0.78 5.0 3.0 2 R = 0.80 20 Degree Hugoniot (Burrell et al.) 4.0 2.5 90 Degree Experimental Data 2.0 3.0 90 Degree Hugoniot 1.5 2.0 1.0 0 Degree Hugoniot (Wood et al.) 1.0 0.5 20 Degree Hugoniot (Burrell et al.) 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Particle Velocity (mm/ s) Unitless Volume Figure 4 Hugoniot in the shock velocity–particle velocity (left) and pressure–unitless volume (right) plane for the 90 orientation of the composite TWCP. Table 6 Hugoniot equations TWCP orientation Equation for each orientation of TWCP investigated here as well as the -1 90 elastic U = 4.20; for u less than 0.65 mm ls S p ones investigated by Wood -1 90 plastic U = 3.46 ? 1.15u ; for up between 0.65 and 0.9 mm ls S p et al. [20] and Burrell et al. [1] 45 U = 3.44 ? 1.12u S p 25 U = 3.45 ? 0.73u S p 0 [20] U = 3.69 ? 0.59u S p 20 [1] U = 3.74 ? 0.57u S p same composite [1, 20]. Considering first the shock traditional shock response is observed. The equation velocity–particle velocity plane, it can be seen that the for both of these regions is shown in Eq. (8). There is 90 orientation has more complex shock behaviour little scatter of the experimental data from the line of 2 2 when compared to the more monolithic behaviour best fits as shown by the R values, with a R value of exhibited by both the 0 [20] and 20 [1] orientations. 0.80 for the initial response and 0.78 for the more The Hugoniot for the 90 TWCP orientation has two standard shock response. distinct regions, an initial response where the elastic 4:20; u \0:65 mm ls U ¼ ð8Þ wave dominates the material behaviour, and a sec- 1 3:46 þ 1:15u ; 0:65\u [ 0:9mm ls p p ond region above a particle velocity value of -1 approximately 0.65 mm ls where a more Shock Velocity (mm/ s) Longitudinal Stress (GPa) J Mater Sci (2018) 53:11415–11425 5.0 Figure 4 also shows the Hugoniot for the 90 Front Gauge TWCP orientation in the pressure–volume plane. For Back Gauge 4.0 comparative purposes a unitless volume is employed (primarily for comparison between this composition 3.0 of TWCP and the one investigated by Burrell et al. Ref. [1], due to the different density). Due to the ini- 2.0 tial elastic behaviour of the Hugoniot in the U –u S p plane for the 90 orientation, elastic behaviour is also 1.0 seen in the pressure–volume plane. No substantial deviation was noted between the experimental data 0.0 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 and the Hugoniot (Eq. 8) for the 90 orientations of Time (μs) the TWCP material. As such, no strengthening was seen with the 90 experimental data, which had Figure 5 A gauge trace for a 10 mm Cu flyer impacting at -1 700 m s for the 45 TWCP orientation. previously been seen with the 0 TWCP orientation investigated by Wood et al. [20]. gradient than the Hugoniot observed for the 0 ori- As mentioned earlier an elastic precursor was entation of TWCP (obtained from Ref. [20]), but the observed on the traces in the elastic region, e.g. Fig. 3. gradient is close to what is observed for the shock Elastic precursors such as this have been seen in portion of the 90 orientation (as shown in Eq. 8). A carbon fibre composites previously investigated by small amount of scatter is noted in the data, signified Hazell et al. [7] and Millett et al. [9], as well as other by the R value of 0.85. composites such as the aramid fibre composite investigated by Bordzilovsky et al. [10]. U ¼ 3:44 þ 1:12u ð9Þ S p Table 3 shows all of the experimental data which For the pressure–unitless volume plane no relate to the elastic precursor for the TWCP material strengthening effects were seen between the Hugo- with regard to the 90 orientation. This table includes niot and the experimental data. Deviation was the velocity of the precursor wave, ascertained from observed with the 90 TWCP orientation as noted the time between the rise on the front gauge and the between this orientation (45) and the ones investi- start of the precursor on the rear gauge. As the par- gated previously (0 by Wood et at. [20], and the 20 ticle velocity of the associated shock wave increased, orientation investigated by Burrell et al. [1]). the velocity of the elastic precursor wave decreased, Figure 7 shows the manganin gauge trace for the with the precursor wave disappearing completely 25 orientated TWCP sample. As seen with the 45 -1 between 0.59 and 0.71 mm ls . This range agrees orientation no elastic precursor wave were observed, with the elastic to shock wave transition observed in as noted with the 90 orientated TWCP sample. The the Hugoniot in the U –u plane (Fig. 9). This would S p trace follows the behaviour noted with the other likely mean that the most probable value that this orientations including sharp rises and plateaus. The transition occurs at a particle velocity of experimental data for the 25 TWCP orientation -1 0.65 mm ls ; however, due to the lack of experi- shown in Table 5. mental data in this region this cannot be definitively The data for the 25 TWCP orientation are plotted proven. in U –u and pressure–unitless volume plane in S p Figure 5 shows a typical trace obtained for the 45 Fig. 8, with the calculated Hugoniot in Eq. (10). It orientated TWCP sample. Unlike the low velocity 90 should be noted, however, that the scatter on this experiments no precursor wave was observed. The data is large, compared with the other orientations as other typical trace behaviour was observed such as, demonstrated by the low R value of 0.49. This scatter sharp rises and plateaus. The experimental data for is also observed in the pressure–unitless volume the 45 TWCP orientation are shown in Table 4, with plane as well. While the other orientations agreed the data plotted graphically in the U –u and pres- S p well with the Hugoniot in this plane, clear deviation sure–unitless volume plane in Fig. 6. is observed on the highest pressure compared to the The Hugoniot for the TWCP orientated at 45 is Hugoniot. This would normally imply a strengthen- given in Eq. (9). It can be seen that it has a steeper ing effect. However, with the scatter on the Longitudinal Stress (GPa) J Mater Sci (2018) 53:11415–11425 11423 5.0 7.0 4.5 45 Degree Experimental Data 6.0 4.0 45 Degree Hugoniot 5.0 3.5 0 Degree Hugoniot (Wood et al.) 3.0 U = 3.44 + 1.12u S p 4.0 R = 0.85 20 Degree Hugoniot (Burrell et al.) 2.5 3.0 45 Degree Experimental Data 2.0 45 Degree Hugoniot 1.5 2.0 1.0 0 Degree Hugoniot (Wood et al.) 1.0 0.5 20 Degree Hugoniot (Burrell et al.) 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Particle Velocity (mm/ s) Unitless Volume Figure 6 Hugoniot in the U –u (left) and P–V (right) plane for the 45 orientation of TWCP. S p 3.0 to assume that this scatter is caused by the orientation of the fibre weave within this composite, i.e. the interaction between the fibre weave and matrix material and the shock front, as the other orientation 2.0 have less scatter associated with them as shown by their higher R values. U ¼ 3:45 þ 0:73u ð10Þ 1.0 S p Front Gauge When the Hugoniots of the three investigated ori- Back Gauge entations (25,45 and 90, with the equations are 0.0 given collated in Table 6) are contrasted in the U –u S p 0.0 1.0 2.0 3.0 4.0 5.0 6.0 plane (Fig. 9) and pressure–unitless volume plane Time (μs) (Fig. 10), the experimental results are comparable. Figure 7 Representative gauge trace for the 25 TWCP orienta- The exception to this behaviour is the 90 experi- -1 tion, impacted at 510 m s with a 10 mm Cu flyer. mental data, which is due to the elastic precursor -1 dominance at particle velocities below 0.65 mm ls . experimental data, how statistically realistic this The scatter observed within the experimental data is conclusion is, is questionable. The experimental data most notable with the 25 TWCP orientation. Due to for this orientation agree closer to the 0 and 20 this scatter within the experimental data, conver- orientations previously investigated by Wood et al. gence of the individual Hugoniot of each orientation [20] and Burrell et al. [1], respectively. It is reasonable 5.0 8.0 4.5 25 Degree Experimental Data 7.0 4.0 25 Degree Hugoniot 6.0 3.5 0 Degree Hugoniot (Wood et al.) 5.0 3.0 U = 3.45 + 0.73u S p 2 20 Degree Hugoniot (Burrell et al.) 2.5 R = 0.49 4.0 25 Degree Experimental Data 2.0 3.0 25 Degree Hugoniot 1.5 2.0 1.0 0 Degree Hugoniot (Wood et al.) 1.0 0.5 20 Degree Hugoniot (Burrell et al.) 0.0 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Particle Velocity (mm/ s) Unitless Volume Figure 8 Hugoniot in the U –u (left) and P–V (right) plane for the 25 orientation for the composite TWCP. S p Shock Velocity (mm/ s) Shock Velocity (mm/ s) Longitudinal Stress (GPa) LongitudinalStress (GPa) Longitudinal Stress (GPa) J Mater Sci (2018) 53:11415–11425 5.0 Conclusion 4.5 4.0 The shock response of three different orientations of a 3.5 tape-wrapped carbon fibre composite with phenolic 3.0 resin matrix has been investigated. This has been 2.5 achieved by using the plate impact technique via a 25 Degree Hugoniot 2.0 single-stage gas gun, with manganin pressure gauges 45 Degree Hugoniot 1.5 as a diagnostic technique. The orientations of the 90 Degree Hugoniot 1.0 fibre weave studied here were 25,45 and 90 with 0 Degree Hugoniot (Wood et al.) 0.5 respect to the impact face. These data have been 20 Degree Hugoniot (Burrell et al.) 0.0 contrasted with the previously obtained data for 0.0 0.2 0.4 0.6 0.8 1.0 1.2 other TWCP orientations by Wood et al. [20] and Particle Velocity (mm/ s) Burrell et al. [1], who used a different composition Figure 9 Hugoniot in the U –u plane, for all of the investigated within their TWCP material, as well as fibre weave S p orientations as well as the literature data for Wood et al. [20] and orientation. When all of the orientations are com- Burrell et al. [1]. pared to one another, little difference was observed with the exception of the 90 TWCP orientation. This was due to elastic behaviour below a particle velocity -1 8.0 value of 0.65 mm ls . Also noted within the data set 25 Degree Hugoniot 7.0 was an amount of scatter present, especially with the 45 Degree Hugoniot 25 TWCP orientation. This is most likely induced by 6.0 90 Degree Hugoniot the differing constituents within the composite, 5.0 0 Degree Hugoniot (Wood et al.) leading to a more dispersed and complex wave pro- 4.0 20 Degree Hugoniot (Burrell et al.) file. This therefore means that other properties such 3.0 as strength, ablation etc. may be considered for the materials application. 2.0 1.0 0.0 Acknowledgements 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Unitless Volume The authors would like to acknowledge the support of the Institute of Shock Physics and AWE. Lockheed- Figure 10 Hugoniot in the pressure–volume plane, for all of the investigated orientations as well as the literature data for Wood Martin Insys is also thanked for supplying the et al. [20] and Burrell et al. [1]. experimental samples. In addition, we would also like to thank Mr. Andrew Roberts for technical help in carrying out the experiments. British Crown did not occur as previously observed with the 0 Copyright MOD/2018. TWCP orientation and the phenolic resin matrix material investigated by Wood et al. [20]. With the Open Access This article is distributed under the associated error bars taken into account the majority terms of the Creative Commons Attribution 4.0 of the data is broadly similar to the orientations of International License (http://creativecommons.org/ TWCP previously investigated by Wood et al. [20] licenses/by/4.0/), which permits unrestricted use, and Burrell et al. [1]. Therefore, the Hugoniot for the distribution, and reproduction in any medium, pro- 0 TWCP material can be used as an approximation vided you give appropriate credit to the original for the shock response of this material. The caveat is author(s) and the source, provide a link to the Crea- that the initial shock response of the 90 orientation is tive Commons license, and indicate if changes were elastic in nature has to be taken into account. Due to made. this relative insensitivity of the orientation with regard to the shock response of TWCP; other factors such as ablation, strength etc. can be considered for the materials application. Longitudinal Stress (GPa) Shock Velocity (mm/ s) J Mater Sci (2018) 53:11415–11425 11425 [12] Meyers MA (1994) Elastic waves. In: Meyers MA (ed) References Dynamic behavior of materials, p 55. Wiley, New York. [1] Burrell RH, Barnes NR, Keightley PT et al (2009) The https://doi.org/10.1007/s11340-012-9598-0 response of a carbon fibre-phenolic resin composite to one- [13] Barker LM, Hollenbach RE (1970) Shock-wave studies of dimensional shock loading. In: 16th APS topical conference PMMA, fused silica, and sapphire. J Appl Phys on shock compression of condensed matter 41:4208–4226. https://doi.org/10.1063/1.1658439 [2] Windhorst T, Blount G (1997) Carbon–carbon composites: a [14] Carter WJ, Marsh SP (1995) Hugoniot equation of state of summary of recent developments and applications. Mater polymers Des 18:11–15. https://doi.org/10.1016/S0261- [15] Shepherd CJ, Appleby-Thomas GJ, Wilgeroth JM et al 3069(97)00024-1 (2011) On the response of ballistic soap to one-dimensional [3] Wicklein M, Ryan S, White DM, Clegg RA (2008) Hyper- shock loading. Int J Impact Eng 38:981–988. https://doi.org/ velocity impact on CFRP: testing, material modelling, and 10.1016/j.ijimpeng.2011.07.003 numerical simulation. Int J Impact Eng 35:1861–1869. [16] Wood DC, Hazell PJ, Appleby-Thomas GJ, Barnes NR https://doi.org/10.1016/j.ijimpeng.2008.07.015 (2011) Shock behaviour of a phenolic resin. J Mater Sci [4] Millett JCF, Bourne NK, Deas D (2005) The equation of 46:5991–5999. https://doi.org/10.1007/s10853-011-5560-2 state of two alumina-filled epoxy resins. J Phys D Appl Phys [17] Davison L (2008) Fundamentals of shock wave propagation 38:930–934. https://doi.org/10.1088/0022-3727/38/6/023 in solids. Springer, Berlin [5] Dattelbaum DM, Coe JD, Rigg PA et al (2014) Shockwave [18] Appleby-Thomas GJ, Hazell PJ (2012) The impact of response of two carbon fiber–polymer composites to structural composite materials. Part 2: hypervelocity impact 50 GPa. J Appl Phys 116:194308. https://doi.org/10.1063/1. and shock. J Strain Anal Eng Des 47:406–418. https://doi. org/10.1177/0309324712448299 [6] Oved Y, Luttwak GE, Rosenberg Z (1978) Shock wave [19] Willows M, Tsembelis K, Proud WG, Church PD (2007) propagation in layered composites. J Compos Mater. https:// Shock characterisation of a carbon fibre composite. In: 15th doi.org/10.1177/002199837801200107 APS topical conference on shock compression of condensed [7] Hazell PJ, Stennett C, Cooper G (2009) The effect of spec- matter. Poster presentation only imen thickness on the shock propagation along the in-fibre [20] Wood DC, Appleby-Thomas GJ, Hazell PJ, Barnes NR direction of an aerospace-grade CFRP laminate. Compos (2012) Shock propagation in a tape wrapped carbon fibre Part A Appl Sci Manuf 40:204–209. https://doi.org/10.1016/ composite. Compos Part A Appl Sci Manuf 43:1550–1560. j.compositesa.2008.11.002 https://doi.org/10.1016/j.compositesa.2012.04.013 [8] Tsai L, Prakash V, Rajendran AM, Dandekar DP (2007) [21] Marsh SP (1980) LASL shock hugoniot data. Los Alamos Structure of shock waves in glass fiber reinforced polymer Ser Dyn Mater Prop, p 150. ISBN 0-520-04008-2 matrix composites. Appl Phys Lett 90:061909. https://doi. [22] Rosenberg Z, Yaziv D, Partom Y (1980) Calibration of foil- org/10.1063/1.2435340 like manganin gauges in planar shock wave experiments. [9] Millett JCF, Bourne NK, Meziere YJE et al (2007) The effect J Appl Phys 51:3702–3705. https://doi.org/10.1063/1. of orientation on the shock response of a carbon fibre–epoxy composite. Compos Sci Technol 67:3253–3260. https://doi. [23] Appleby-Thomas GJ, Hazell PJ, Stennett C (2009) The org/10.1016/j.compscitech.2007.03.034 variation in lateral and longitudinal stress gauge response [10] Bordzilovsky SA, Karakhanov SM, Merzhievsky LA (1998) within an RTM 6 epoxy resin under one-dimensional shock Shock response of a unidirectional composite at various loading. J Mater Sci 44:6187–6198. https://doi.org/10.1007/ orientation of fibers. In: 10th APS topical conference on s10853-009-3859-z shock compression of condensed matter, pp 545–548 [24] Hazell PJ, Appleby-Thomas GJ, Trinquant X, Chapman DJ [11] Millett JCF, Meziere YJE, Bourne NK (2007) The response (2011) In-fiber shock propagation in Dyneema . J Appl to shock loading of a glass–fibre–epoxy composite: effects of Phys 110:043504. https://doi.org/10.1063/1.3622294 fibre orientation to the loading axis. J Phys D Appl Phys 40:5358–5365. https://doi.org/10.1088/0022-3727/40/17/

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Journal of Materials ScienceSpringer Journals

Published: May 22, 2018

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