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Polymer bonded explosives (PBXs) with reduced thermal stress and sensitivity by thermal conductivity enhancement with graphene nanoplatelets
Composites Science and Technology 131 (2016) 22e31
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Composites Science and Technology journal homepage: http://www.elsevier.com/locate/compscitech
Polymer bonded explosives (PBXs) with reduced thermal stress and sensitivity by thermal conductivity enhancement with graphene nanoplatelets Guansong He*, Zhijian Yang, Xiaoyu Zhou, Jianhu Zhang, Liping Pan, Shijun Liu Institute of Chemical Material, CAEP, Mianyang, 621900, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 February 2016 Received in revised form 16 May 2016 Accepted 18 May 2016 Available online 20 May 2016
The two-dimensional (2D) graphene nanoplatelets (GNPs) were adopted to enhance the thermal conductivity of PBX. The results indicated that, the thermal conductivity of PBX was only slightly improved with very low GNP loading (0.05 wt% and 0.15 wt%). However, a remarkable enhanced effect was observed at a relatively high GNP loading (0.5 wt% and 1 wt%). The thermal conductivity of PBX had a nonlinear dependence on the GNPs loading. The nonlinear dependence of the thermal conductivity on GNPs content was fitted by an analytical model which incorporated all the effects. And the thermal conduction mechanism of GNPs based composite could change from series thermal structure to parallel thermal structure with the GNP loading increasing. Additionally, the calculated thermal shock resistance and thermal stress distribution of PBX was both enhanced with the GNP loading. Finally, the sensitivity of sensitive hexanitrohexaazaisowurtzitane (CL-20) based PBX composition could be improved by GNPs due to enhanced thermal conductivity. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Polymer-matrix composites (PMCs) Thermal properties Modelling
1. Introduction Polymer Bonded Explosives (PBX), which refer to a particle filled composite consisting of 90e95% weight of powerful explosive crystals held together by a small percentage polymer binder of 5e10% weight, are being extensively used in a variety of conventional and nuclear defense munitions [1e3]. As an important part in weapon system, PBX will be subjected to the complicated thermal physical environment during long-term storage, transportation, and usage process [4]. Moreover, after experienced rapid high-low temperature changes and broad temperature range, the heat in PBX cannot be quickly transferred due to the low thermal conductivity property of explosive crystal and polymer binder (less than 0.5 W m1 K1), resulting in a significant inhomogeneous temperature distribution and gradient. Then the generated severe thermal stress can cause cracking or damage of PBX with a low strength and toughness and further harm the security and reliability of the weapon system [5,6]. Therefore, as a key route to reduce thermal stress and enhance the thermal environment adaptability of PBX, improving the thermal conductivity is
* Corresponding author. E-mail address: [email protected] (G. He). http://dx.doi.org/10.1016/j.compscitech.2016.05.009 0266-3538/© 2016 Elsevier Ltd. All rights reserved.
becoming an urgent problem to be solved [7]. Generally, the thermal conductivity of polymer composites has been effectively enhanced by the addition of thermally conductive fillers. Among these fillers, Carbon-based nanofillers appear to be the best promising fillers, coupling ultrahigh thermal conductivity, lightweight and high aspect ratio [8]. For example, carbon nanotubes (CNTs) considerably improved the heat transport in polymer composites as a result of their one-dimensional (1D) structure, high thermal conductivity and high aspect ratio [9,10]. Recently, graphene has attracted a considerable amount of interest due to its extraordinary electrical, thermal, and mechanical properties [11,12]. As two-dimensional lattice of sp2-bonded carbon that is just one atomic layer thick, it exhibits remarkably high thermal conductivity and has been experimental established as the highest thermal conductivity material ever measured (~3000 W/mK) [13]. Some theoretical descriptions of thermal transport in graphene revealed that thermal conductivity of graphene was actually phonon-based, since the analyzed graphene samples’ dimensions exceeded average free path of phonons (800 nm), and its electronic-based thermal conductivity represented less than 1% of the total thermal conductivity at room temperature [14,15]. Comprised of few graphene layer Gn, where n represents the layer number, the graphene nanoplates (GNPs), show promise for
G. He et al. / Composites Science and Technology 131 (2016) 22e31
application as nanofiller materials in polymer composites due to their high aspect ratio, unique two-dimensional plane nanostructure, and low manufacturing cost [16e18]. In general, the high contact area between polymer and planar GNPs can provide a 2-D path for phonon transport and maximize heat flow from polymer matrix to GNPs. And GNPs rigidity allows for better preservation of their high aspect ratio in comparison with the more flexible CNTs [19]. Thus, polymer-GNPs can be expected to exhibit better reinforcement of thermal conductivity than carbon nanotubes (CNTs) in polymer composites [20]. Many experimental studies have shown that the addition of a small amount of GNPs in polymer could result in a substantially large enhancement of the effective thermal conductivity and this enhancement was nonlinear with GNP loading [21e23]. The nonlinear dependence originated from the interaction among GNPs in matrix [24]. The application of graphene in energetic materials has been previously involved by some workers. The obtained results revealed that graphene could improve the burning rate and mechanical properties of propellant, as well as the release rate of energy [25]. On the other hand, the properties of thermal stability and sensitivity were very important for PBX formulations [26]. And the effect of carbon nanomaterials on the performances of energetic compositions has been well-summarized in the review literature of Yan [27]. It has been shown that the use of carbon nanomaterials in energetic compositions could greatly improve their combustion performances, thermal stability and sensitivity. Especially for the mechanical sensitivity, there are many carbon nanomaterials and their derivatives capable of decreasing the sensitivity of energetic materials by suppressing of hotspot formation. For example, the mechanical sensitivities of 3-CL-20/glue could be reduced with the incorporation of graphite and graphene oxide in PBX formulations [28]. In this study, the two-dimensional GNPs will be used in PBX to improve the low thermal conductivity. As one of the most important systems which may have potential military applications, the 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)-based PBX was adopted. The thermal conductivity was measured at the broad temperature range of 20 Ce90 C. Moreover, the nonlinear dependence of thermal conductivity of PBX on GNPs content was fitted by an analytical model. The thermal shock resistance (TSR) of PBX modified by GNPs was evaluated based on the experimental mechanical and thermal conductivity data. Meanwhile, the temperature and thermal stress distribution of TATB based PBX formulations during thermal impact process were simulated by the finite element software ANSYS. At last, to found the relationship between the sensitivity and thermal conductivity, a certain sensitive CL-20 based PBX composition was selected to further study the effect of GNPs on mechanical sensitivity. 2. Experimental section 2.1. Materials TATB (particle size about 17 mm) was provided by Institute of Chemical Materials, CAEP, China. CL-20 was provided by Liaoning Qingyang Chemical Industry Co., Ltd. and purified by solvent/nonsolvent (ethyl acetate/toluene) recrystallization before use. The polymer binder used in TATB-based PBX formulas was a copolymer of chlorotrifluoroethylene (CTFE) and vinylidene fluoride (VDF) provided by Zhonghao Chenguang Chemical Industry Co., Ltd. China, the chemical structure of which was e[(eCF2eCH2e)1e(eCF2eCFCle)4]ne. The raw materials of GNPs with 5 mme10 mm in width and 4 nme20 nm in thickness that were obtained from Beijing DK Nano Technology Co., Ltd. China. The layer number of graphene n was less than 30. And the morphology of
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GNPs used is shown in Fig. 1. 2.2. Sample preparation All TATB-based PBXs formulations included 5 wt% polymer binders. PBX formulations with 0%, 0.05%, 0.15%, 0.5% and 1% GNPs by weight were labelled as PBX-0, PBX-0.05, PBX-0.15, PBX-0.5, and PBX-1, respectively. Molding powder was produced by a conventional water suspension method, in which the TATB crystals agglomerated as they were coated with the binder dissolved in an organic mixed solvent. This process was detailed described in the previous study [29]. Then the obtained molding powders were carefully dried in a vacuum oven at 60 C for 12 h to eliminate the moisture. Afterwards, the molding powder products were pressed in a mould with a desired geometry under 120 C and 400 MPa, and then transformed into explosive pellet for the final thermal conductivity and mechanical tests. 2.3. Thermal conductivity measurements The thermal conductivity measurements were conducted with a LFA 447 Nanoflash™ laser thermal conductivity apparatus. The specimen dimensions were 12.7 mm 2 mm (diameter thickness). A graphite coating layer was applied to the pellet materials before testing. The measurements were performed at the temperature of 20 Ce90 C. 2.4. Mechanical property measurement The tensile mechanical properties of PBX modified by GNPs were obtained through the quasi-static Brazilian test, an efficient way to characterize mechanical properties of brittle PBX. The Brazilian tests of the PBX pellets, with dimension of f20 mm 6 mm (diameter height), were performed using an Instron 5582 machine (Canton, MA, USA) at the room temperature of 23 C. The details of testing process were described previously [30]. The crosshead speed was set at 0.5 mm/min. At least three specimens of each PBX formulation were tested, and the average values were calculated. 2.5. Scanning electron microscopy (SEM) The morphology of GNPs and GNPs/fluoropolymer composites were observed by a field emission-scanning electron microscope (FE-SEM, Hitachi Se4700I, German) with an accelerating potential of 15.0e19.0 kV. 2.6. Thermal behavior analysis The thermogravimetric analysis (TGA) -differential scanning calorimeter (DSC) test was recorded on a METTLER TOLEDO TGA/ DSC 2 instrument from 25 C to 700 C under nitrogen (40 ml/min) atmosphere with a heating rate of 10 C/min. 2.7. Sensitivity test The impact sensitivity test was conducted with a WL-1 type impact sensitivity instrument according to GJB-772A-97 standard method 601.2. The test conditions are: drop weight, 2 kg; sample mass, 30 mg. The impact sensitivity of each test sample was expressed by the drop height of 50% explosion probability (H50). The friction sensitivity test was determined on a WM-1 type friction sensitivity instrument according to GJB-772A-97 standard method 602.1. The test conditions were: relative pressure, 3.92 MPa; sample mass: 30 mg, pendulum weight: 1.5 Kg;
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G. He et al. / Composites Science and Technology 131 (2016) 22e31
Fig. 1. SEM image of an individual GNP.
pendulum angle: 90 . The fraction sensitivity of each test sample was expressed by explosion probability (P). The detailed process was described in the previous literature [31].
3. Results and discussion 3.1. Morphology and characterization The distribution morphologies of GNPs in polymer binder for different PBX formulations are shown in Fig. 2. For PBX-0.05, the 2D platelet-like GNPs were well-distributed in polymer matrix. However, the content of GNPs was so low that no GNPs could connect each other. With the GNPs amount increased to 0.15 wt%, the high aspect ratio and contact area of GNP with matrix facilitated the approaching of adjacent GNPs. Then, with the GNPs amount further increased to 0.5 wt%, some GNPs began to connect with the adjacent GNPs, thereby causing the partially formation of the thermal conductivity path. Finally, with regard to PBX-1, the sufficient amount of GNPs could contribute to the effective inter-connectivity between GNPs and result in the effective of thermal conductivity network as illustrated in Fig. 2d.
Fig. 3. Plots of thermal conductivity versus temperature for different PBX formulations based on TATB.
Fig. 2. Distribution morphologies of GNPs in polymer binder for PBX formulations based on TATB: (a) PBX-0.05, (b) PBX-0.15, (c) PBX-0.5, (d) PBX-1.
G. He et al. / Composites Science and Technology 131 (2016) 22e31
3.2. Thermal conductivity of PBX The thermal conductivities of all PBX formulations at the temperature range of 20 Ce90 C are shown in Fig. 3. It was found that, at each temperature, the neat PBX had a lowest thermal conductivity of 0.5 W/mK, revealing a bad thermal conductivity property. After the addition of CNTs, the thermal conductivity of composite was enhanced, because the thermal conductivity of GNPs was much higher than that of neat PBX. And the enhanced effect was more pronounced with the GNPs loading increasing, especially for the GNPs filled composites with 0.5 wt% and 1 wt% loadings. The thermally conductive coefficient of PBX filled by GNPs was greatly improved to 2.799 W/mK (60 C) with 1 wt% loading, 5.4 times higher than that of neat PBX (0.522 W/mK, 60 C). Actually, a substantially large enhancement of effective thermal conductivity was achieved by only very small addition of GNPs in PBX. This enhanced effect was much higher than those obtained by other thermal conductivity fillers in our previous studies [7,32]. The planar structure of GNPs can provide a 2D path for phonon transport, and GNP ultrahigh surface area allows a large surface contact area with polymer binder, resulting in effective enhancement of the composite thermal conductivity. As could be seen in Fig. 3, while with a very small amount addition of GNPs (0.05 wt% and 0.15 wt %), there was smaller increment for the thermal conductivities of the GNPs/PBX composites only from 0.5 W/mK to 0.7 W/mK. This was ascribed to that the badly insufficient amount of GNPs could not contribute to the effective inter-connectivity between GNPs, as illustrated in Fig. 4a and Fig. 4b. Thereby, without effective thermal conductivity path, the GNP-matrix interfacial thermal resistance would greatly restrict the heat transmission, resulting in a relatively low thermal conductivity. However, with further increasing the GNPs loading to 0.5 wt%, the thermal conductivities of the GNPs/PBX composites were obviously improved to approximate 0.7 W/mK. From Figs. 2c and 4c, at 0.5 wt % loading, some effective inter-connectivity between GNPs was found, causing the partially formation of the thermal conductivity path which could largely contributed to the heat transfer. Next, with the GNPs loading finally increased to 1 wt%, more GNPs began to touch each other. Then the criss-cross distribution of thermal conductivity path was transformed into a highly effective thermal conductivity network (shown in Figs. 2d and 4d). Consequently, the thermal conductivity of the GNPs/PBX composites was largely enhanced. In general, enhanced thermal conductivity of GNPs based PBX composites was attributed to the following factors: i) from Fig. 4e, the GNPs were only distributed in the polymer binder, which totally held a small weight percentage of 5%. Therefore, the GNP concentration in network-like binder was much higher than that in PBX. ii) GNPs rigidity allows for better preservation of their high aspect ratio and contact area, which were very useful for bridging adjacent 2D-nanoplatelets and provide paths for the heat flow bypassing the polymer matrix. On the other hand, the junctions between the 2D GNPs could decrease the thermal interface resistance of heat flow. In addition, from Fig. 3, for a given GNP loading, the thermal conductivity of composite had a nonlinear dependence on the testing temperature. For most PBX formulations, the thermal conductivity exhibited a somewhat drop in the temperature domain from 20 C to 40 C. This was due to the fact that the thermal conductivities of both the TATB (shown in Fig. 7a) and graphene nanoplatelets decreased with temperature [33], while the thermal conductivity of polymer binder almost did not change at the range of 20 Ce40 C. However, with the temperature continued to increased (from 50 C to 70 C), the thermal conductivity manifested an increased trend, especially for PBX with 1 wt% loading of GNPs. At this temperature range, the glass transition of polymer
25
binder just occurred [7], i.e. the molecular chain segments began to move, which was contributed to the phonon transport in the binder. Hence the thermal conductivity of polymer binder increased at the temperature range of 50 Ce70 C. Consequently, the thermal conductivity of composite increased. And for PBX with 1 wt% loading of GNPs, the increase trend was more significant. Perhaps, at this process, some new thermal conductive network formed during the rearrangement of GNPs mainly induced by the different volume expansion between conductive fillers and the matrix during heating. Finally, with further increasing temperature from 70 C to 90 C, the thermal conductivity decreased again. Besides the thermal conductivities of TATB and GNPs further decreased, the intersheet average distance between the GNPs increased as the result of the difference in the thermal expansion of polymer binder and conductive fillers, which would harm the thermal conductive network in PBX, causing the thermal conductivity decreased at high temperature. 3.3. Theoretical study of the thermal conductivity Although the thermal conductivity behavior of PBX with GNPs has been adequately discussed above, the theoretical analysis of the thermal transport behavior of these composites was rather limited. Recently, a theoretical model, which was proposed by Chu [34] and had well described the effective thermal conductivity of graphenebased composites, would be firstly adopted to describe the thermal conductivity of PBX filled by GNPs with different loadings. By taking into account all the effects of the thermal conductivity anisotropy, aspect ratio, concentration, interfacial thermal resistance, and interaction among GNPs, the theoretical description for the thermal conductivity GNP-based composites was ultimately given as:
Ke 2=3½f 1=pa þ1 ¼ Km HðpÞ þ 1=ðKx =Km 1Þ
(1)
where Km is the thermal conductivity of the matrix, Ke is the thermal conductivity of the GNP-based composites, f denotes the volume fraction of the GNPs, a is a critical conductivity exponent involving structural information and depending on the intrinsic conductivity of the filler and/or of the contacts between them, and thus is taken as a fitting parameter. L and c are the length and thickness of the GNP, respectively. H(p) is well-known geometrical factors dependent on the aspect ratio, p ¼ L/c, and given by Ref. [35]:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ln p þ p2 1 p 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 HðpÞ ¼ 3ffi p 1 p2 1
(2)
The comparison between theoretical calculations and experimental data for PBX with GNPs at 20 C is shown in Fig. 5, while the data and theoretical calculations at 30 C 90 C was shown in Fig. 5 inset. As seen, Equation (1) could provide the best fit for the measured experimental data and well described the nonlinear thermal conductivity behavior with GNPs content. The fitted parameter a was in the range of 1/2-2, which brought into correspondence with the reported results for the GNP based composites [34]. More importantly, it was interesting to note that, the nonlinear thermal conductivity behavior of GNP based PBX had already occurred at such low GNP volume fractions (0%e8%), with the conductivity-volume fraction curve exhibiting upward-convex dependence. By comparison, only at relatively high volume fractions, obvious upward-convex dependence could be observed for GNP based polymer composites. The nonlinear dependence was related to the different GNP interaction patterns at various GNP
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G. He et al. / Composites Science and Technology 131 (2016) 22e31
Fig. 4. Schematic diagrams of the percolation network: (a) PBX-0.05, (b) PBX-0.15, (c) PBX-0.5, (d) PBX-1, (e) microstructural representation of PBX.
14
30 50 70 90
(Ke-Km)/Km
10
=1.83 =1.77 =1.74 =1.77
40 C, =1.78 60 C, =1.73 80 C, =1.73
(K -K )/K
12
C, C, C, C,
8 6
f (vol.%)
4 o
20 C, =1.81
2 0 0
2
4
6
8
10
12
14
f (vol.%) Fig. 5. Model predictions of the effective thermal conductivity of PBXs based on TATB as a function of GNP loading (fg) compared with the experimental data.
concentrations. The upward-convex trend might imply that the GNP began to contact each other, contributing to the formation of the corresponding thermally conductive paths. That was to say, for PBX, the percolation effect, which was related to the thermally conductive network, was more easily to happen at a low volume fraction of GNP. And this was to a great extent decided by the special structure of GNP based PBX, shown in Fig. 4e. Therefore, the theoretical study could help in further designs of GNP composites with optimal or desired thermal conductivity. On the other hand, as a particle highly filled polymer composite, PBX is comprised of explosive crystals as the fillers suspended in a polymeric binder. For the PBX modified by GNPs, there were two kinds of fillers including explosive crystals and GNPs distributed in the polymer binder matrix. In our previous study [7], the prediction the thermal conductivity of this three-phase polymer composites had been successfully described by using Agari model [36], which was very helpful for understanding the effects of contact of fillers with each other or the formation of thermal conductivity pathway on the thermal behavior of GNP based PBX. In this work, the thermal conductivity of PBX modified by GNPs was firstly described by Agari model. According to this model, the thermal conductivity
G. He et al. / Composites Science and Technology 131 (2016) 22e31
27
of polymer composites would be estimated in parallel and series conductions, shown in Fig. 6. In the parallel conduction, thermal conductivity of the composite would be the highest in the event that all fillers were gathered to form a conductive block and another block of polymer was arranged in parallel in the direction of thermal flux. And for the series conduction, thermal conductivity was the lowest in the case where these blocks were arranged in a series in the direction of thermal flux. Thermal conductivities of polymer composites in the parallel and series conductions could be estimated, respectively, by the following equations: Parallel conduction:
Twophase lc ¼ Vf 1 lf1 þ
1 Vf 1 lp
Threephase lc ¼ Vf1 lf 1 þ Vf 2 lf2 þ
1 Vf1 Vf2 lp
(3)
(4)
Series conduction:
. i Twophase lc ¼ 1=½Vf 1 lf1 þ 1 Vf 1 =lp
Fig. 6. Thermal conductivity model for polymer based composites: (a) parallel model of two-phase system, (b) series model of two-phase system, (c) parallel model of three-phase system, (d) series model of three-phase system.
(5)
. . i Threephase lc ¼ 1=½ Vf1 lf 1 þ Vf 2 lf 2 þ 1 Vf1 Vf 2 =lp
Fig. 7. Comparison of the experimental data and fitting results by Agari model for the PBXs based on TATB.
(6)
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G. He et al. / Composites Science and Technology 131 (2016) 22e31 Table 1 Mechanical test results for the PBXs based on TATB.
Fig. 8. Variation trends of experimental thermal conductivity data and fitting results for the PBXs based on TATB.
Where lc is the thermal conductivity of composite, Vf1 and Vf2 are the weight fractions of filler phases 1 and 2 in the composite, lf1 and lf2 are the thermal conductivity of two corresponding filler phases 1 and 2, respectively. lp is the thermal conductivity of the polymer. The calculated thermal conductivity values by parallel (upper value) and series (lower value) conduction based on the volume fraction and thermal conductivity of individual component, as well as the experimental data, are shown in Fig. 7. As could be seen from Fig. 7a, the thermal conductivities of TATB and polymer binder were both very low, especially for polymer binder with a thermal conductivity of only 0.2 W/mK. With regard to the fitting results, the thermal conductivity of PBX-0 was intervenient between TATB and polymer binder and close to the fitting results by series model. After the introduction of GNPs, which had an intrinsic thermal conductivity up to 3000 W/mK, the thermal conductivity of PBX was significantly enhanced. According to the fitting results listed from Fig. 7c to f, all the thermal conductivities of GNPs based PBX were between the values calculated by series model and parallel model. Moreover, with the GNPs loading increasing, the thermal conductivity was gradually approaching parallel value, indicating that the thermal conduction mechanism gradually
Fig. 9. Brazilian stressestrain curves of PBXs based on TATB.
Sample
Fracture strength (MPa)
PBX-0 PBX-0.05 PBX-0.15 PBX-0.5 PBX-1
5.63 6.57 6.47 6.46 6.53
± ± ± ± ±
0.03 0.05 0.06 0.06 0.13
Fracture strain (102) 0.16 0.24 0.23 0.23 0.22
± ± ± ± ±
0.01 0.01 0.01 0.01 0.01
Modulus (GPa) 7.11 8.36 8.67 8.51 8.80
± ± ± ± ±
0.15 0.20 0.42 0.40 0.85
changed from series model to partial parallel model. This phenomenon was related to the formation of some thermal conductive paths due to the contact of GNPs with each other at a relatively high loading. To better observe the change trend of experimental data and fitting results with the content of GNPs, the obtained results of 20 C are displayed in Fig. 8. It could be found that the thermal conductivity fitted by parallel model was obviously higher than that fitted by series model, and had a linear increase until 2700 W/ mK with the concentration of GNPs. However, the thermal conductivity fitted by series model just had a nonlinear increase at the range of 0.5e3.0 W/mK with the content of GNPs increasing. Furthermore, the experimental thermal conductivity data and calculated values by Equation (1) had a nonlinear upward-convex dependence on the GNP loading, and gradually deviated away from the series model values more and more. Therefore, the thermal conduction mechanism of GNPs based composite could change from series thermal structure to parallel thermal structure with the GNP loading increasing.
3.4. Thermal shock resistance of PBX As an important property of PBX to resist severe thermal stress generated due to rapid temperature changes, the thermal shock resistance (TSR) was evaluated based on the experimental mechanical and thermal conductivity data measured for neat PBX and modified PBX. On the basis of the thermoelastic theories, by incorporating the effect of mechanical strength, thermal expansion and thermal conductivity, the theory of thermal shock resistance focusing attention on the initiation of fracture resulted from thermal stresses was presented by Kingery [37], who defined a parameter R0 for describing the thermal shock resistance of brittle materials, this parameter was represented as:
Fig. 10. Thermal shock resistance (TSR) of PBX formulations based on TATB.
G. He et al. / Composites Science and Technology 131 (2016) 22e31
R0 ¼
sð1 nÞk Ea
(7)
Where s is the mechanical strength; E is the Young’s modulus; a is the linear expansion coefficient; n is the Poisson’s ratio; and k is the thermal conductivity. The mechanical properties obtained by quasi-static Brazilian test are listed in Fig. 9 and Table 1. It was found that the strength, fracture strain and modulus were all obviously increased with the addition of GNPs, indicating that the PBX could be both reinforced and toughened by the incorporation of GNPs. Then, the calculated TSR values according to Equation (7) were displayed in Fig. 10. As could be seen, similar to the change trend of thermal conductivity, the TSR of PBX was enhanced after the addition of GNPs. And the enhanced effect was more pronounced with the GNPs loading increasing. The results showed a
29
pronounced maximum of TSR ¼ 24.41 W/m at a GNP loading of 1 wt%, about 343% higher than that of neat PBX. Thus the GNP filler demonstrated a severely enhanced effect on the thermal shock resistance through the high efficient thermal conductivity and mechanical property enhancement. 3.5. Numerical simulation on thermal impact of PBX Based on a two dimensional axis symmetric model, the temperature field and thermal stress field of TATB based PBX formulations during thermal impact process were simulated by the finite element software ANSYS. The details of calculation model and process for the thermal conductivity and thermal stress could be found in our previous literature [5]. And the obtained temperature and stress distribution results of low temperature impact test from 60 C to 20 C were shown in Fig. 11. The temperature distributions were all calculated at the case that the temperature difference was maximum for each formula. From Fig. 11, in the PBX cylinder, the maximum temperature appeared at the center while the minimum temperature appeared at the edge of end face. And the maximum temperature gradient appeared at the middle of side face. With the thermal conductivity of PBX increasing, the maximum temperature difference decreased in the low temperature impact process, due to the fact that the heat could be quickly transferred with the thermal conductivity increasing. Moreover, the maximum stress distribution occurred when the temperature difference became largest. In the impact process, the surface of PBX cylinder was subjected to tensile stress, and the center was subjected to compressive stress. By comparison, the tensile stress could more easily cause the damage of PBX, as the tensile strength of PBX was very low. From the right section of Fig. 11, the maximum tensile stress appeared at the middle of side face significantly decreased with the thermal conductivity of PBX increasing. Therefore, the enhanced thermal conductivity was contributed to reduce thermal stress in the PBX when faced rapid temperature changes. 3.6. Thermal stability of PBX The effect of GNPs on the thermal stability of TATB based PBX was evaluated by a TGA/DSC instrument. The obtained curves are displayed in Fig. 12 (the inset shows DSC curves). It could be found that the GNPs had nearly no effect on the thermal behavior of PBX. The decomposition temperature of TATB had very little change with the addition of GNPs. This phenomenon was due to the fact that
Fig. 11. Contour of temperature distribution (left) and major principal stress distribution (right) of PBX cylinder based on TATB in low temperature impact test: (a) PBX-0, (b) PBX-0.5, (c) PBX-1.
Fig. 12. TGA/DSC curves of PBX formulations based on TATB.
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G. He et al. / Composites Science and Technology 131 (2016) 22e31
Fig. 13. The relationship between sensitivity and thermal conductivity for CL-20 formula: (a) impact sensitivity, (b) friction sensitivity.
GNPs were distributed only in polymer binder (as shown in Fig. 4e), and thus could not have an interaction with the explosive. However, as one of the most thermally stable insensitive explosive, TATB and TATB based PBX have no urgent demand to improve thermal stability. 3.7. Mechanical sensitivity of PBX In this work a CL-20 based PBX formula has been selected to study the effect of enhanced thermal conductivity by GNPs on the mechanical (impact and friction) sensitivity, as TATB-based PBX is so insensitive that the mechanical sensitivity is usually zero. The impact sensitivity and friction sensitivity of CL-20 based formulas were tested, and the relationships between mechanical sensitivity and thermal conductivity were displayed in Fig. 13. Both the impact and friction sensitivity decreased significantly with the relative thermal conductivity of CL-20 based PBX increasing. The high thermal conductivity is contributed to heat transfer in the PBX during stimuli. Therefore, the probability of hot-spot generation (heat localization) was decreased. And this is consistent with most research results and sensitivity decreased mechanism in the review literature [27]. 4. Conclusion In summary, the low thermal conductivity of PBX was enhanced by incorporation of the 2D GNPs. The experimental results revealed that the thermal conductivity of PBX was nonlinearly increased with the GNP loading increasing, due to the formation of highly effective thermal network. And by incorporating all the effects of GNP parameters, the nonlinear dependence of the thermal conductivity on GNPs content was well fitted by an analytical model. The following conclusions could be drawn: (1) With the low GNPs loadings of 0.05 wt% and 0.15 wt%, the thermal conductivity of PBX was only slightly enhanced. However, the enhanced effect was more pronounced with the GNPs loading increased to 0.5 wt% and 1 wt%, ascribed to the fact that interactions between GNPs could lead to the formation of a more efficient thermal conductivity percolating network. (2) The nonlinear dependence of thermal conductivity of PBX on GNPs content has been successfully described by a theoretical model. And the effective thermal network could change the thermal conduction mechanism from series thermal structure to parallel thermal structure. Through the evaluation of the thermal shock resistance (TSR), the GNP filler demonstrated a strong enhanced effect on the thermal shock resistance and largely surpassed the performance of neat
PBX at a loading of 1 wt%. Moreover, the numerical simulation on thermal impact of PBX demonstrated that the enhanced thermal conductivity could reduce thermal stress in the PBX when faced rapid temperature changes. (3) The mechanical (impact and friction) sensitivity of sensitive CL-20 based formula significantly decreased with the relative thermal conductivity enhanced by GNP filler. Acknowledgments The authors are grateful to the National Natural Science Foundation of China (11502245, 11502248, 11402238) and the Science and Technology Fund of CAEP (2014B0302037) for financial support of this work. References [1] P.J. Rae, S.J.P. Palmer, H.T. Goldrein, J.E. Field, A.L. Lewis, Quasi-static studies of the deformation and failure of PBX 9501, Proc. R. Soc. Lond. Ser. A 458 (2025) (2002) 2227e2242. [2] P. Chen, H. Xie, F. Huang, T. Huang, Y. Ding, Deformation and failure of polymer bonded explosives under diametric compression test, Polym. Test. 25 (3) (2006) 333e341. [3] Z. Qiao, J. Shen, J. Wang, B. Huang, Z. Yang, G. Yang, K. Zhang, Fast deflagration to detonation transition of energetic material based on a quasi-core/shell structured nanothermite composite, Compos Sci. Technol. 107 (1) (2015) 113e119. [4] Z. Liu, H. Xie, K. Li, P. Chen, F. Huang, Fracture behavior of PBX simulation subject to combined thermal and mechanical loads, Polym. Test. 28 (6) (2009) 627e635. [5] X. Wei, S. Wu, X. Tang, Numerical simulation and experimental study on thermal damage of HMX based polymer bonded explosive, Chin. J. Explos. Propellants 37 (4) (2014) 9e13. [6] C.R. Siviour, M.J. Gifford, S.M. Walley, W.G. Proud, J.E. Field, Particle size effects on the mechanical properties of a polymer bonded explosive, J. Mater. Sci. 39 (4) (2004) 1255e1258. [7] C. Lin, G. He, J. Liu, L. Pan, S. Liu, Construction and thermal properties of nanostructured polymer bonded explosives with graphene, RSC Adv. 5 (119) (2015) 98514e98521. [8] Z. Han, A. Fina, Thermal conductivity of carbon nanotubes and their polymer nanocomposites: a review, Prog. Polym. Sci. 36 (7) (2011) 914e944. [9] E.T. Thostenson, C. Li, T.W. Chou, Nanocomposites in context, Compos. Sci. Technol. 65 (3e4) (2005) 491e516. [10] C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube, Nano Lett. 5 (9) (2005) 1842e1846. [11] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless dirac fermions in graphene, Nature 438 (7065) (2005) 197e200. [12] A.A. Balandin, S. Ghosh, W.Z. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C.N. Lau, Superior thermal conductivity of single-layer graphene, Nano Lett. 8 (3) (2008) 902e907. [13] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (5887) (2008) 385e388. [14] S.K. Ja cimovski, M. Bukurov, J.P. Setraj ci c, D.I. Rakovi c, Phonon thermal conductivity of graphene, Superlattice Microst. 88 (1) (2015) 330e337. [15] D.L. Nika, E.P. Pokatilov, A.A. Balandin, Theoretical description of thermal transport in graphene: the issues of phonon cut-off frequencies and
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Contents lists available at ScienceDirect
Composites Science and Technology journal homepage: http://www.elsevier.com/locate/compscitech
Polymer bonded explosives (PBXs) with reduced thermal stress and sensitivity by thermal conductivity enhancement with graphene nanoplatelets Guansong He*, Zhijian Yang, Xiaoyu Zhou, Jianhu Zhang, Liping Pan, Shijun Liu Institute of Chemical Material, CAEP, Mianyang, 621900, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 February 2016 Received in revised form 16 May 2016 Accepted 18 May 2016 Available online 20 May 2016
The two-dimensional (2D) graphene nanoplatelets (GNPs) were adopted to enhance the thermal conductivity of PBX. The results indicated that, the thermal conductivity of PBX was only slightly improved with very low GNP loading (0.05 wt% and 0.15 wt%). However, a remarkable enhanced effect was observed at a relatively high GNP loading (0.5 wt% and 1 wt%). The thermal conductivity of PBX had a nonlinear dependence on the GNPs loading. The nonlinear dependence of the thermal conductivity on GNPs content was fitted by an analytical model which incorporated all the effects. And the thermal conduction mechanism of GNPs based composite could change from series thermal structure to parallel thermal structure with the GNP loading increasing. Additionally, the calculated thermal shock resistance and thermal stress distribution of PBX was both enhanced with the GNP loading. Finally, the sensitivity of sensitive hexanitrohexaazaisowurtzitane (CL-20) based PBX composition could be improved by GNPs due to enhanced thermal conductivity. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Polymer-matrix composites (PMCs) Thermal properties Modelling
1. Introduction Polymer Bonded Explosives (PBX), which refer to a particle filled composite consisting of 90e95% weight of powerful explosive crystals held together by a small percentage polymer binder of 5e10% weight, are being extensively used in a variety of conventional and nuclear defense munitions [1e3]. As an important part in weapon system, PBX will be subjected to the complicated thermal physical environment during long-term storage, transportation, and usage process [4]. Moreover, after experienced rapid high-low temperature changes and broad temperature range, the heat in PBX cannot be quickly transferred due to the low thermal conductivity property of explosive crystal and polymer binder (less than 0.5 W m1 K1), resulting in a significant inhomogeneous temperature distribution and gradient. Then the generated severe thermal stress can cause cracking or damage of PBX with a low strength and toughness and further harm the security and reliability of the weapon system [5,6]. Therefore, as a key route to reduce thermal stress and enhance the thermal environment adaptability of PBX, improving the thermal conductivity is
* Corresponding author. E-mail address: [email protected] (G. He). http://dx.doi.org/10.1016/j.compscitech.2016.05.009 0266-3538/© 2016 Elsevier Ltd. All rights reserved.
becoming an urgent problem to be solved [7]. Generally, the thermal conductivity of polymer composites has been effectively enhanced by the addition of thermally conductive fillers. Among these fillers, Carbon-based nanofillers appear to be the best promising fillers, coupling ultrahigh thermal conductivity, lightweight and high aspect ratio [8]. For example, carbon nanotubes (CNTs) considerably improved the heat transport in polymer composites as a result of their one-dimensional (1D) structure, high thermal conductivity and high aspect ratio [9,10]. Recently, graphene has attracted a considerable amount of interest due to its extraordinary electrical, thermal, and mechanical properties [11,12]. As two-dimensional lattice of sp2-bonded carbon that is just one atomic layer thick, it exhibits remarkably high thermal conductivity and has been experimental established as the highest thermal conductivity material ever measured (~3000 W/mK) [13]. Some theoretical descriptions of thermal transport in graphene revealed that thermal conductivity of graphene was actually phonon-based, since the analyzed graphene samples’ dimensions exceeded average free path of phonons (800 nm), and its electronic-based thermal conductivity represented less than 1% of the total thermal conductivity at room temperature [14,15]. Comprised of few graphene layer Gn, where n represents the layer number, the graphene nanoplates (GNPs), show promise for
G. He et al. / Composites Science and Technology 131 (2016) 22e31
application as nanofiller materials in polymer composites due to their high aspect ratio, unique two-dimensional plane nanostructure, and low manufacturing cost [16e18]. In general, the high contact area between polymer and planar GNPs can provide a 2-D path for phonon transport and maximize heat flow from polymer matrix to GNPs. And GNPs rigidity allows for better preservation of their high aspect ratio in comparison with the more flexible CNTs [19]. Thus, polymer-GNPs can be expected to exhibit better reinforcement of thermal conductivity than carbon nanotubes (CNTs) in polymer composites [20]. Many experimental studies have shown that the addition of a small amount of GNPs in polymer could result in a substantially large enhancement of the effective thermal conductivity and this enhancement was nonlinear with GNP loading [21e23]. The nonlinear dependence originated from the interaction among GNPs in matrix [24]. The application of graphene in energetic materials has been previously involved by some workers. The obtained results revealed that graphene could improve the burning rate and mechanical properties of propellant, as well as the release rate of energy [25]. On the other hand, the properties of thermal stability and sensitivity were very important for PBX formulations [26]. And the effect of carbon nanomaterials on the performances of energetic compositions has been well-summarized in the review literature of Yan [27]. It has been shown that the use of carbon nanomaterials in energetic compositions could greatly improve their combustion performances, thermal stability and sensitivity. Especially for the mechanical sensitivity, there are many carbon nanomaterials and their derivatives capable of decreasing the sensitivity of energetic materials by suppressing of hotspot formation. For example, the mechanical sensitivities of 3-CL-20/glue could be reduced with the incorporation of graphite and graphene oxide in PBX formulations [28]. In this study, the two-dimensional GNPs will be used in PBX to improve the low thermal conductivity. As one of the most important systems which may have potential military applications, the 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)-based PBX was adopted. The thermal conductivity was measured at the broad temperature range of 20 Ce90 C. Moreover, the nonlinear dependence of thermal conductivity of PBX on GNPs content was fitted by an analytical model. The thermal shock resistance (TSR) of PBX modified by GNPs was evaluated based on the experimental mechanical and thermal conductivity data. Meanwhile, the temperature and thermal stress distribution of TATB based PBX formulations during thermal impact process were simulated by the finite element software ANSYS. At last, to found the relationship between the sensitivity and thermal conductivity, a certain sensitive CL-20 based PBX composition was selected to further study the effect of GNPs on mechanical sensitivity. 2. Experimental section 2.1. Materials TATB (particle size about 17 mm) was provided by Institute of Chemical Materials, CAEP, China. CL-20 was provided by Liaoning Qingyang Chemical Industry Co., Ltd. and purified by solvent/nonsolvent (ethyl acetate/toluene) recrystallization before use. The polymer binder used in TATB-based PBX formulas was a copolymer of chlorotrifluoroethylene (CTFE) and vinylidene fluoride (VDF) provided by Zhonghao Chenguang Chemical Industry Co., Ltd. China, the chemical structure of which was e[(eCF2eCH2e)1e(eCF2eCFCle)4]ne. The raw materials of GNPs with 5 mme10 mm in width and 4 nme20 nm in thickness that were obtained from Beijing DK Nano Technology Co., Ltd. China. The layer number of graphene n was less than 30. And the morphology of
23
GNPs used is shown in Fig. 1. 2.2. Sample preparation All TATB-based PBXs formulations included 5 wt% polymer binders. PBX formulations with 0%, 0.05%, 0.15%, 0.5% and 1% GNPs by weight were labelled as PBX-0, PBX-0.05, PBX-0.15, PBX-0.5, and PBX-1, respectively. Molding powder was produced by a conventional water suspension method, in which the TATB crystals agglomerated as they were coated with the binder dissolved in an organic mixed solvent. This process was detailed described in the previous study [29]. Then the obtained molding powders were carefully dried in a vacuum oven at 60 C for 12 h to eliminate the moisture. Afterwards, the molding powder products were pressed in a mould with a desired geometry under 120 C and 400 MPa, and then transformed into explosive pellet for the final thermal conductivity and mechanical tests. 2.3. Thermal conductivity measurements The thermal conductivity measurements were conducted with a LFA 447 Nanoflash™ laser thermal conductivity apparatus. The specimen dimensions were 12.7 mm 2 mm (diameter thickness). A graphite coating layer was applied to the pellet materials before testing. The measurements were performed at the temperature of 20 Ce90 C. 2.4. Mechanical property measurement The tensile mechanical properties of PBX modified by GNPs were obtained through the quasi-static Brazilian test, an efficient way to characterize mechanical properties of brittle PBX. The Brazilian tests of the PBX pellets, with dimension of f20 mm 6 mm (diameter height), were performed using an Instron 5582 machine (Canton, MA, USA) at the room temperature of 23 C. The details of testing process were described previously [30]. The crosshead speed was set at 0.5 mm/min. At least three specimens of each PBX formulation were tested, and the average values were calculated. 2.5. Scanning electron microscopy (SEM) The morphology of GNPs and GNPs/fluoropolymer composites were observed by a field emission-scanning electron microscope (FE-SEM, Hitachi Se4700I, German) with an accelerating potential of 15.0e19.0 kV. 2.6. Thermal behavior analysis The thermogravimetric analysis (TGA) -differential scanning calorimeter (DSC) test was recorded on a METTLER TOLEDO TGA/ DSC 2 instrument from 25 C to 700 C under nitrogen (40 ml/min) atmosphere with a heating rate of 10 C/min. 2.7. Sensitivity test The impact sensitivity test was conducted with a WL-1 type impact sensitivity instrument according to GJB-772A-97 standard method 601.2. The test conditions are: drop weight, 2 kg; sample mass, 30 mg. The impact sensitivity of each test sample was expressed by the drop height of 50% explosion probability (H50). The friction sensitivity test was determined on a WM-1 type friction sensitivity instrument according to GJB-772A-97 standard method 602.1. The test conditions were: relative pressure, 3.92 MPa; sample mass: 30 mg, pendulum weight: 1.5 Kg;
24
G. He et al. / Composites Science and Technology 131 (2016) 22e31
Fig. 1. SEM image of an individual GNP.
pendulum angle: 90 . The fraction sensitivity of each test sample was expressed by explosion probability (P). The detailed process was described in the previous literature [31].
3. Results and discussion 3.1. Morphology and characterization The distribution morphologies of GNPs in polymer binder for different PBX formulations are shown in Fig. 2. For PBX-0.05, the 2D platelet-like GNPs were well-distributed in polymer matrix. However, the content of GNPs was so low that no GNPs could connect each other. With the GNPs amount increased to 0.15 wt%, the high aspect ratio and contact area of GNP with matrix facilitated the approaching of adjacent GNPs. Then, with the GNPs amount further increased to 0.5 wt%, some GNPs began to connect with the adjacent GNPs, thereby causing the partially formation of the thermal conductivity path. Finally, with regard to PBX-1, the sufficient amount of GNPs could contribute to the effective inter-connectivity between GNPs and result in the effective of thermal conductivity network as illustrated in Fig. 2d.
Fig. 3. Plots of thermal conductivity versus temperature for different PBX formulations based on TATB.
Fig. 2. Distribution morphologies of GNPs in polymer binder for PBX formulations based on TATB: (a) PBX-0.05, (b) PBX-0.15, (c) PBX-0.5, (d) PBX-1.
G. He et al. / Composites Science and Technology 131 (2016) 22e31
3.2. Thermal conductivity of PBX The thermal conductivities of all PBX formulations at the temperature range of 20 Ce90 C are shown in Fig. 3. It was found that, at each temperature, the neat PBX had a lowest thermal conductivity of 0.5 W/mK, revealing a bad thermal conductivity property. After the addition of CNTs, the thermal conductivity of composite was enhanced, because the thermal conductivity of GNPs was much higher than that of neat PBX. And the enhanced effect was more pronounced with the GNPs loading increasing, especially for the GNPs filled composites with 0.5 wt% and 1 wt% loadings. The thermally conductive coefficient of PBX filled by GNPs was greatly improved to 2.799 W/mK (60 C) with 1 wt% loading, 5.4 times higher than that of neat PBX (0.522 W/mK, 60 C). Actually, a substantially large enhancement of effective thermal conductivity was achieved by only very small addition of GNPs in PBX. This enhanced effect was much higher than those obtained by other thermal conductivity fillers in our previous studies [7,32]. The planar structure of GNPs can provide a 2D path for phonon transport, and GNP ultrahigh surface area allows a large surface contact area with polymer binder, resulting in effective enhancement of the composite thermal conductivity. As could be seen in Fig. 3, while with a very small amount addition of GNPs (0.05 wt% and 0.15 wt %), there was smaller increment for the thermal conductivities of the GNPs/PBX composites only from 0.5 W/mK to 0.7 W/mK. This was ascribed to that the badly insufficient amount of GNPs could not contribute to the effective inter-connectivity between GNPs, as illustrated in Fig. 4a and Fig. 4b. Thereby, without effective thermal conductivity path, the GNP-matrix interfacial thermal resistance would greatly restrict the heat transmission, resulting in a relatively low thermal conductivity. However, with further increasing the GNPs loading to 0.5 wt%, the thermal conductivities of the GNPs/PBX composites were obviously improved to approximate 0.7 W/mK. From Figs. 2c and 4c, at 0.5 wt % loading, some effective inter-connectivity between GNPs was found, causing the partially formation of the thermal conductivity path which could largely contributed to the heat transfer. Next, with the GNPs loading finally increased to 1 wt%, more GNPs began to touch each other. Then the criss-cross distribution of thermal conductivity path was transformed into a highly effective thermal conductivity network (shown in Figs. 2d and 4d). Consequently, the thermal conductivity of the GNPs/PBX composites was largely enhanced. In general, enhanced thermal conductivity of GNPs based PBX composites was attributed to the following factors: i) from Fig. 4e, the GNPs were only distributed in the polymer binder, which totally held a small weight percentage of 5%. Therefore, the GNP concentration in network-like binder was much higher than that in PBX. ii) GNPs rigidity allows for better preservation of their high aspect ratio and contact area, which were very useful for bridging adjacent 2D-nanoplatelets and provide paths for the heat flow bypassing the polymer matrix. On the other hand, the junctions between the 2D GNPs could decrease the thermal interface resistance of heat flow. In addition, from Fig. 3, for a given GNP loading, the thermal conductivity of composite had a nonlinear dependence on the testing temperature. For most PBX formulations, the thermal conductivity exhibited a somewhat drop in the temperature domain from 20 C to 40 C. This was due to the fact that the thermal conductivities of both the TATB (shown in Fig. 7a) and graphene nanoplatelets decreased with temperature [33], while the thermal conductivity of polymer binder almost did not change at the range of 20 Ce40 C. However, with the temperature continued to increased (from 50 C to 70 C), the thermal conductivity manifested an increased trend, especially for PBX with 1 wt% loading of GNPs. At this temperature range, the glass transition of polymer
25
binder just occurred [7], i.e. the molecular chain segments began to move, which was contributed to the phonon transport in the binder. Hence the thermal conductivity of polymer binder increased at the temperature range of 50 Ce70 C. Consequently, the thermal conductivity of composite increased. And for PBX with 1 wt% loading of GNPs, the increase trend was more significant. Perhaps, at this process, some new thermal conductive network formed during the rearrangement of GNPs mainly induced by the different volume expansion between conductive fillers and the matrix during heating. Finally, with further increasing temperature from 70 C to 90 C, the thermal conductivity decreased again. Besides the thermal conductivities of TATB and GNPs further decreased, the intersheet average distance between the GNPs increased as the result of the difference in the thermal expansion of polymer binder and conductive fillers, which would harm the thermal conductive network in PBX, causing the thermal conductivity decreased at high temperature. 3.3. Theoretical study of the thermal conductivity Although the thermal conductivity behavior of PBX with GNPs has been adequately discussed above, the theoretical analysis of the thermal transport behavior of these composites was rather limited. Recently, a theoretical model, which was proposed by Chu [34] and had well described the effective thermal conductivity of graphenebased composites, would be firstly adopted to describe the thermal conductivity of PBX filled by GNPs with different loadings. By taking into account all the effects of the thermal conductivity anisotropy, aspect ratio, concentration, interfacial thermal resistance, and interaction among GNPs, the theoretical description for the thermal conductivity GNP-based composites was ultimately given as:
Ke 2=3½f 1=pa þ1 ¼ Km HðpÞ þ 1=ðKx =Km 1Þ
(1)
where Km is the thermal conductivity of the matrix, Ke is the thermal conductivity of the GNP-based composites, f denotes the volume fraction of the GNPs, a is a critical conductivity exponent involving structural information and depending on the intrinsic conductivity of the filler and/or of the contacts between them, and thus is taken as a fitting parameter. L and c are the length and thickness of the GNP, respectively. H(p) is well-known geometrical factors dependent on the aspect ratio, p ¼ L/c, and given by Ref. [35]:
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi ln p þ p2 1 p 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 HðpÞ ¼ 3ffi p 1 p2 1
(2)
The comparison between theoretical calculations and experimental data for PBX with GNPs at 20 C is shown in Fig. 5, while the data and theoretical calculations at 30 C 90 C was shown in Fig. 5 inset. As seen, Equation (1) could provide the best fit for the measured experimental data and well described the nonlinear thermal conductivity behavior with GNPs content. The fitted parameter a was in the range of 1/2-2, which brought into correspondence with the reported results for the GNP based composites [34]. More importantly, it was interesting to note that, the nonlinear thermal conductivity behavior of GNP based PBX had already occurred at such low GNP volume fractions (0%e8%), with the conductivity-volume fraction curve exhibiting upward-convex dependence. By comparison, only at relatively high volume fractions, obvious upward-convex dependence could be observed for GNP based polymer composites. The nonlinear dependence was related to the different GNP interaction patterns at various GNP
26
G. He et al. / Composites Science and Technology 131 (2016) 22e31
Fig. 4. Schematic diagrams of the percolation network: (a) PBX-0.05, (b) PBX-0.15, (c) PBX-0.5, (d) PBX-1, (e) microstructural representation of PBX.
14
30 50 70 90
(Ke-Km)/Km
10
=1.83 =1.77 =1.74 =1.77
40 C, =1.78 60 C, =1.73 80 C, =1.73
(K -K )/K
12
C, C, C, C,
8 6
f (vol.%)
4 o
20 C, =1.81
2 0 0
2
4
6
8
10
12
14
f (vol.%) Fig. 5. Model predictions of the effective thermal conductivity of PBXs based on TATB as a function of GNP loading (fg) compared with the experimental data.
concentrations. The upward-convex trend might imply that the GNP began to contact each other, contributing to the formation of the corresponding thermally conductive paths. That was to say, for PBX, the percolation effect, which was related to the thermally conductive network, was more easily to happen at a low volume fraction of GNP. And this was to a great extent decided by the special structure of GNP based PBX, shown in Fig. 4e. Therefore, the theoretical study could help in further designs of GNP composites with optimal or desired thermal conductivity. On the other hand, as a particle highly filled polymer composite, PBX is comprised of explosive crystals as the fillers suspended in a polymeric binder. For the PBX modified by GNPs, there were two kinds of fillers including explosive crystals and GNPs distributed in the polymer binder matrix. In our previous study [7], the prediction the thermal conductivity of this three-phase polymer composites had been successfully described by using Agari model [36], which was very helpful for understanding the effects of contact of fillers with each other or the formation of thermal conductivity pathway on the thermal behavior of GNP based PBX. In this work, the thermal conductivity of PBX modified by GNPs was firstly described by Agari model. According to this model, the thermal conductivity
G. He et al. / Composites Science and Technology 131 (2016) 22e31
27
of polymer composites would be estimated in parallel and series conductions, shown in Fig. 6. In the parallel conduction, thermal conductivity of the composite would be the highest in the event that all fillers were gathered to form a conductive block and another block of polymer was arranged in parallel in the direction of thermal flux. And for the series conduction, thermal conductivity was the lowest in the case where these blocks were arranged in a series in the direction of thermal flux. Thermal conductivities of polymer composites in the parallel and series conductions could be estimated, respectively, by the following equations: Parallel conduction:
Twophase lc ¼ Vf 1 lf1 þ
1 Vf 1 lp
Threephase lc ¼ Vf1 lf 1 þ Vf 2 lf2 þ
1 Vf1 Vf2 lp
(3)
(4)
Series conduction:
. i Twophase lc ¼ 1=½Vf 1 lf1 þ 1 Vf 1 =lp
Fig. 6. Thermal conductivity model for polymer based composites: (a) parallel model of two-phase system, (b) series model of two-phase system, (c) parallel model of three-phase system, (d) series model of three-phase system.
(5)
. . i Threephase lc ¼ 1=½ Vf1 lf 1 þ Vf 2 lf 2 þ 1 Vf1 Vf 2 =lp
Fig. 7. Comparison of the experimental data and fitting results by Agari model for the PBXs based on TATB.
(6)
28
G. He et al. / Composites Science and Technology 131 (2016) 22e31 Table 1 Mechanical test results for the PBXs based on TATB.
Fig. 8. Variation trends of experimental thermal conductivity data and fitting results for the PBXs based on TATB.
Where lc is the thermal conductivity of composite, Vf1 and Vf2 are the weight fractions of filler phases 1 and 2 in the composite, lf1 and lf2 are the thermal conductivity of two corresponding filler phases 1 and 2, respectively. lp is the thermal conductivity of the polymer. The calculated thermal conductivity values by parallel (upper value) and series (lower value) conduction based on the volume fraction and thermal conductivity of individual component, as well as the experimental data, are shown in Fig. 7. As could be seen from Fig. 7a, the thermal conductivities of TATB and polymer binder were both very low, especially for polymer binder with a thermal conductivity of only 0.2 W/mK. With regard to the fitting results, the thermal conductivity of PBX-0 was intervenient between TATB and polymer binder and close to the fitting results by series model. After the introduction of GNPs, which had an intrinsic thermal conductivity up to 3000 W/mK, the thermal conductivity of PBX was significantly enhanced. According to the fitting results listed from Fig. 7c to f, all the thermal conductivities of GNPs based PBX were between the values calculated by series model and parallel model. Moreover, with the GNPs loading increasing, the thermal conductivity was gradually approaching parallel value, indicating that the thermal conduction mechanism gradually
Fig. 9. Brazilian stressestrain curves of PBXs based on TATB.
Sample
Fracture strength (MPa)
PBX-0 PBX-0.05 PBX-0.15 PBX-0.5 PBX-1
5.63 6.57 6.47 6.46 6.53
± ± ± ± ±
0.03 0.05 0.06 0.06 0.13
Fracture strain (102) 0.16 0.24 0.23 0.23 0.22
± ± ± ± ±
0.01 0.01 0.01 0.01 0.01
Modulus (GPa) 7.11 8.36 8.67 8.51 8.80
± ± ± ± ±
0.15 0.20 0.42 0.40 0.85
changed from series model to partial parallel model. This phenomenon was related to the formation of some thermal conductive paths due to the contact of GNPs with each other at a relatively high loading. To better observe the change trend of experimental data and fitting results with the content of GNPs, the obtained results of 20 C are displayed in Fig. 8. It could be found that the thermal conductivity fitted by parallel model was obviously higher than that fitted by series model, and had a linear increase until 2700 W/ mK with the concentration of GNPs. However, the thermal conductivity fitted by series model just had a nonlinear increase at the range of 0.5e3.0 W/mK with the content of GNPs increasing. Furthermore, the experimental thermal conductivity data and calculated values by Equation (1) had a nonlinear upward-convex dependence on the GNP loading, and gradually deviated away from the series model values more and more. Therefore, the thermal conduction mechanism of GNPs based composite could change from series thermal structure to parallel thermal structure with the GNP loading increasing.
3.4. Thermal shock resistance of PBX As an important property of PBX to resist severe thermal stress generated due to rapid temperature changes, the thermal shock resistance (TSR) was evaluated based on the experimental mechanical and thermal conductivity data measured for neat PBX and modified PBX. On the basis of the thermoelastic theories, by incorporating the effect of mechanical strength, thermal expansion and thermal conductivity, the theory of thermal shock resistance focusing attention on the initiation of fracture resulted from thermal stresses was presented by Kingery [37], who defined a parameter R0 for describing the thermal shock resistance of brittle materials, this parameter was represented as:
Fig. 10. Thermal shock resistance (TSR) of PBX formulations based on TATB.
G. He et al. / Composites Science and Technology 131 (2016) 22e31
R0 ¼
sð1 nÞk Ea
(7)
Where s is the mechanical strength; E is the Young’s modulus; a is the linear expansion coefficient; n is the Poisson’s ratio; and k is the thermal conductivity. The mechanical properties obtained by quasi-static Brazilian test are listed in Fig. 9 and Table 1. It was found that the strength, fracture strain and modulus were all obviously increased with the addition of GNPs, indicating that the PBX could be both reinforced and toughened by the incorporation of GNPs. Then, the calculated TSR values according to Equation (7) were displayed in Fig. 10. As could be seen, similar to the change trend of thermal conductivity, the TSR of PBX was enhanced after the addition of GNPs. And the enhanced effect was more pronounced with the GNPs loading increasing. The results showed a
29
pronounced maximum of TSR ¼ 24.41 W/m at a GNP loading of 1 wt%, about 343% higher than that of neat PBX. Thus the GNP filler demonstrated a severely enhanced effect on the thermal shock resistance through the high efficient thermal conductivity and mechanical property enhancement. 3.5. Numerical simulation on thermal impact of PBX Based on a two dimensional axis symmetric model, the temperature field and thermal stress field of TATB based PBX formulations during thermal impact process were simulated by the finite element software ANSYS. The details of calculation model and process for the thermal conductivity and thermal stress could be found in our previous literature [5]. And the obtained temperature and stress distribution results of low temperature impact test from 60 C to 20 C were shown in Fig. 11. The temperature distributions were all calculated at the case that the temperature difference was maximum for each formula. From Fig. 11, in the PBX cylinder, the maximum temperature appeared at the center while the minimum temperature appeared at the edge of end face. And the maximum temperature gradient appeared at the middle of side face. With the thermal conductivity of PBX increasing, the maximum temperature difference decreased in the low temperature impact process, due to the fact that the heat could be quickly transferred with the thermal conductivity increasing. Moreover, the maximum stress distribution occurred when the temperature difference became largest. In the impact process, the surface of PBX cylinder was subjected to tensile stress, and the center was subjected to compressive stress. By comparison, the tensile stress could more easily cause the damage of PBX, as the tensile strength of PBX was very low. From the right section of Fig. 11, the maximum tensile stress appeared at the middle of side face significantly decreased with the thermal conductivity of PBX increasing. Therefore, the enhanced thermal conductivity was contributed to reduce thermal stress in the PBX when faced rapid temperature changes. 3.6. Thermal stability of PBX The effect of GNPs on the thermal stability of TATB based PBX was evaluated by a TGA/DSC instrument. The obtained curves are displayed in Fig. 12 (the inset shows DSC curves). It could be found that the GNPs had nearly no effect on the thermal behavior of PBX. The decomposition temperature of TATB had very little change with the addition of GNPs. This phenomenon was due to the fact that
Fig. 11. Contour of temperature distribution (left) and major principal stress distribution (right) of PBX cylinder based on TATB in low temperature impact test: (a) PBX-0, (b) PBX-0.5, (c) PBX-1.
Fig. 12. TGA/DSC curves of PBX formulations based on TATB.
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G. He et al. / Composites Science and Technology 131 (2016) 22e31
Fig. 13. The relationship between sensitivity and thermal conductivity for CL-20 formula: (a) impact sensitivity, (b) friction sensitivity.
GNPs were distributed only in polymer binder (as shown in Fig. 4e), and thus could not have an interaction with the explosive. However, as one of the most thermally stable insensitive explosive, TATB and TATB based PBX have no urgent demand to improve thermal stability. 3.7. Mechanical sensitivity of PBX In this work a CL-20 based PBX formula has been selected to study the effect of enhanced thermal conductivity by GNPs on the mechanical (impact and friction) sensitivity, as TATB-based PBX is so insensitive that the mechanical sensitivity is usually zero. The impact sensitivity and friction sensitivity of CL-20 based formulas were tested, and the relationships between mechanical sensitivity and thermal conductivity were displayed in Fig. 13. Both the impact and friction sensitivity decreased significantly with the relative thermal conductivity of CL-20 based PBX increasing. The high thermal conductivity is contributed to heat transfer in the PBX during stimuli. Therefore, the probability of hot-spot generation (heat localization) was decreased. And this is consistent with most research results and sensitivity decreased mechanism in the review literature [27]. 4. Conclusion In summary, the low thermal conductivity of PBX was enhanced by incorporation of the 2D GNPs. The experimental results revealed that the thermal conductivity of PBX was nonlinearly increased with the GNP loading increasing, due to the formation of highly effective thermal network. And by incorporating all the effects of GNP parameters, the nonlinear dependence of the thermal conductivity on GNPs content was well fitted by an analytical model. The following conclusions could be drawn: (1) With the low GNPs loadings of 0.05 wt% and 0.15 wt%, the thermal conductivity of PBX was only slightly enhanced. However, the enhanced effect was more pronounced with the GNPs loading increased to 0.5 wt% and 1 wt%, ascribed to the fact that interactions between GNPs could lead to the formation of a more efficient thermal conductivity percolating network. (2) The nonlinear dependence of thermal conductivity of PBX on GNPs content has been successfully described by a theoretical model. And the effective thermal network could change the thermal conduction mechanism from series thermal structure to parallel thermal structure. Through the evaluation of the thermal shock resistance (TSR), the GNP filler demonstrated a strong enhanced effect on the thermal shock resistance and largely surpassed the performance of neat
PBX at a loading of 1 wt%. Moreover, the numerical simulation on thermal impact of PBX demonstrated that the enhanced thermal conductivity could reduce thermal stress in the PBX when faced rapid temperature changes. (3) The mechanical (impact and friction) sensitivity of sensitive CL-20 based formula significantly decreased with the relative thermal conductivity enhanced by GNP filler. Acknowledgments The authors are grateful to the National Natural Science Foundation of China (11502245, 11502248, 11402238) and the Science and Technology Fund of CAEP (2014B0302037) for financial support of this work. References [1] P.J. Rae, S.J.P. Palmer, H.T. Goldrein, J.E. Field, A.L. Lewis, Quasi-static studies of the deformation and failure of PBX 9501, Proc. R. Soc. Lond. Ser. A 458 (2025) (2002) 2227e2242. [2] P. Chen, H. Xie, F. Huang, T. Huang, Y. Ding, Deformation and failure of polymer bonded explosives under diametric compression test, Polym. Test. 25 (3) (2006) 333e341. [3] Z. Qiao, J. Shen, J. Wang, B. Huang, Z. Yang, G. Yang, K. Zhang, Fast deflagration to detonation transition of energetic material based on a quasi-core/shell structured nanothermite composite, Compos Sci. Technol. 107 (1) (2015) 113e119. [4] Z. Liu, H. Xie, K. Li, P. Chen, F. Huang, Fracture behavior of PBX simulation subject to combined thermal and mechanical loads, Polym. Test. 28 (6) (2009) 627e635. [5] X. Wei, S. Wu, X. Tang, Numerical simulation and experimental study on thermal damage of HMX based polymer bonded explosive, Chin. J. Explos. Propellants 37 (4) (2014) 9e13. [6] C.R. Siviour, M.J. Gifford, S.M. Walley, W.G. Proud, J.E. Field, Particle size effects on the mechanical properties of a polymer bonded explosive, J. Mater. Sci. 39 (4) (2004) 1255e1258. [7] C. Lin, G. He, J. Liu, L. Pan, S. Liu, Construction and thermal properties of nanostructured polymer bonded explosives with graphene, RSC Adv. 5 (119) (2015) 98514e98521. [8] Z. Han, A. Fina, Thermal conductivity of carbon nanotubes and their polymer nanocomposites: a review, Prog. Polym. Sci. 36 (7) (2011) 914e944. [9] E.T. Thostenson, C. Li, T.W. Chou, Nanocomposites in context, Compos. Sci. Technol. 65 (3e4) (2005) 491e516. [10] C. Yu, L. Shi, Z. Yao, D. Li, A. Majumdar, Thermal conductance and thermopower of an individual single-wall carbon nanotube, Nano Lett. 5 (9) (2005) 1842e1846. [11] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Two-dimensional gas of massless dirac fermions in graphene, Nature 438 (7065) (2005) 197e200. [12] A.A. Balandin, S. Ghosh, W.Z. Bao, I. Calizo, D. Teweldebrhan, F. Miao, C.N. Lau, Superior thermal conductivity of single-layer graphene, Nano Lett. 8 (3) (2008) 902e907. [13] C. Lee, X. Wei, J.W. Kysar, J. Hone, Measurement of the elastic properties and intrinsic strength of monolayer graphene, Science 321 (5887) (2008) 385e388. [14] S.K. Ja cimovski, M. Bukurov, J.P. Setraj ci c, D.I. Rakovi c, Phonon thermal conductivity of graphene, Superlattice Microst. 88 (1) (2015) 330e337. [15] D.L. Nika, E.P. Pokatilov, A.A. Balandin, Theoretical description of thermal transport in graphene: the issues of phonon cut-off frequencies and
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