The dependence of the non-linear creep properties for TATB-based polymer bonded explosives on the molecular structure of polymer binder

Abstract

The influences of molecular structure of polymer binders on the mechanical properties and non-linear time dependent creep of the 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)-based polymer bonded explosives (PBXs) at different temperatures and stresses were investigated. A copolymer of chlorotrifluoroethylene and vinylidene fluoride (PF1) and a copolymer of chlorotrifluoroethylene, vinylidene fluoride, tetrafluoroethylene, and hexafluoropropylene (PF2) were used as polymer binders. An increase of the storage modulus and glass transition temperature was observed for PF2, compared to that of PF1. The compressive and tensile properties of TATB-based PBX with PF2 were higher than the one with PF1 at both ambient temperature and elevated temperature. The creep resistance also showed clear dependence on the molecular structure of polymer binders. It was found that the incorporation of tetrafluoroethylene and hexafluoropropylene comonomers in PF2 resulted in a decrease of the constant creep strain rate and the maximal creep strain values and an increase of creep rupture time for TATB-based PBX. Non-linearity in the creep response was modeled using the six-element mechanical model. The predicted theoretical results coincided quite well with the experimental data. Compared with the formulation containing PF1 as binder, an increase in the elastic modulus E₂, E₃ and bulk viscosity η₄ was observed for TATB-based PBX with PF2 under the same conditions. Three-point bending master curves of creep strain were constructed using a time–temperature superposition (TTS) concept. The formulation with PF2 showed consistently lower creep strain than the formulation with PF1 in the entire time scale.

---

1. Introduction

During the past decades, as a kind of particle highly filled composite material, polymer bonded explosive (PBX) is extensively applied in military fields ranging from rocket propellants to explosive charges.^1,2 During long-term storage and transport, PBX may be subjected to combined thermal and mechanical loads, and then creep relaxation behavior can take place. In recent years, the creep behavior of polymer-based composites has been of great interest in academic and industrial fields because of its significant influence on dimensional stability, long-term durability, and reliability. The addition of various inorganic fillers into a polymer matrix is a common and convenient method to improve creep resistant properties.^3–5 However, the filler content in these composites is very low, which is totally different from PBX with high content explosive particles. A number of investigations on the creep behavior of PBXs have also been performed.^6,7 It is believed that the creep behavior of PBX is dependent on the type of explosive, the percentage and type of binder, the stress level and test temperature. A custom designed apparatus, which uses a combination of extensometers and linear variable differential transformers coupled with a data acquisition system, thermal controls, and gravitational loading, was used to measure the time-dependent creep strain in plastic-bonded explosives with high fidelity.⁸ Micro-analysis of the creep properties of PBX simulation was performed using SEM combined with a digital image correlation (DIC) method.⁹ During the process of high temperature creep, extensive cracks were first formed followed by the initiation and extension of shear cracks, eventually joining and causing a macroscopic fracture within the material. The main microscopic fracture mode was found to be inter-crystalline cracking and binder tearing failure.

It is now well accepted that as one kind of the most commonly used binders with the advantages of good physical and chemical stability, excellent aging resistance, heat resistance, and great compatibility with other components in composite explosives, a fluoropolymer is of great interest in academic and industrial fields.^10–14 Compared to general hydrocarbons, the high density of a fluoropolymer brings on enhancements of density and performance for PBX. Furthermore, the oxygen balance is enhanced when hydrogen atoms (fuel) on a polymer main chain are replaced by fluorine atoms (oxidizer), resulting in better properties of composite explosives. Consequently, several PBX materials, such as LX-17 (92.5% 1,3,5-triamino-2,4,6-trinitrobenzene TATB and 7.5% a copolymer of chlorotrifluoroethylene and vinylidene fluoride kel-F800 by weight) and PBX-9502 (95% TATB and 5% kel-F800 by weight), have been formulated with fluoropolymer as a binder in the last decades.^15–17

Generally, PBX is comprised of 90–95% by weight of explosive crystals and 5–10% by weight of a polymeric binder.¹⁸ The polymeric matrix in PBX is typically a viscoelastic material, and creep deformation is inevitable at a certain temperature and loading stress.^19–23 It is recognized that despite the polymer content being very low, the creep property of a polymer is the main factor in influencing the creep damage properties of PBX.²⁴

However, researches on the influences of molecular structure of a polymer binder on the creep performance of PBX are relatively limited. In our previous work, studies on the effects of the addition of a reinforcing agent (styrene copolymer) to the original fluoropolymer binder system on three-point bending creep behaviors were conducted.²⁵ Experimental results showed that due to addition of styrene copolymer with high glass transition temperature and high mechanical strength, the creep resistance performance of the modified formulation was improved with reduced creep strain, constant creep rate, and prolonged creep failure time.

The fundamental understanding of effects of molecular structure of polymer binder on the creep relaxation of PBX is still unclear. In this work, we focus on two kinds of fluoropolymers with different molecular structures serving as binders. The main objective of this study was to investigate the creep processes of TATB-based PBX by three-point bending creep measurements. Studies on effects of molecular structure on the dynamic mechanical behaviors and static mechanical properties of PBXs were also conducted.

2. Experimental section

2.1 Materials

TATB (purity 99%, particle size about 17 μm) was obtained from Institute of Chemical Materials, CAEP, China. Two fluoropolymers with different molecular structure were used as polymer binder, i.e. a copolymer of chlorotrifluoroethylene and vinylidene fluoride, labeled as PF1, and a copolymer of chlorotrifluoroethylene, vinylidene fluoride, tetrafluoroethylene, and hexafluoropropylene, labeled as PF2. The molecular structures of PF1 and PF2 were –[–(–CF₂–CH₂–)_a–(–CF₂–CFCl–)_b–]_n– and –[(–CF₂–CH₂–)_a–(–CF₂–CFCl–)_b–(–CF₂–CF₂–)_c–(–CF₂–CFCF₃–)_d]_n–. The weight average molecular weight of PF1 is 1.13 × 10⁵ g mol⁻¹ with a polydispersity index of 2.13. The weight average molecular weight of PF2 is 5.47 × 10⁴ g mol⁻¹ with a polydispersity index of 1.93. Both PF1 and PF2 were provided by Zhonghao Chenguang Chemical Industry Co., Ltd. China. The other chemicals and reagents used in the presented study were commercially purchased and used as received.

2.2 Sample preparation

A formulation, which contained 95% TATB and 5% PF1 by weight, was labeled as PBX-1. Another formulation, with TATB and PF2 with the same molar ratio, was prepared and labeled as PBX-2. First, TATB (180 g) was added to H₂O (180 mL) and dispersed while stirring at 70 °C in a vacuum. Then the polymer binder solution with ethyl acetate and butyl acetate as the mixed solvent was added dropwise. After removing the organic solvent, the precipitate was filtered, and then washed to give the molding powders of TATB-based formulations. Before mould pressing, the molding powders were carefully dried in a vacuum oven at 60 °C for 12 h to eliminate the influences of moisture content on experimental results. Afterwards, the molding powder product was pressed in a mould and transformed into explosive pellet. The pellet density was about 97% of the theoretical density after compression.

2.3 Mechanical characterization of the composites

All static mechanical tests were performed with a universal testing machine (5582, INSTRON, USA). According to GB/T1040-2006, the dumbbell-shaped specimens of fluoropolymers were punch-cut from the compression-molded sheets and tested in a uniaxial tensile configuration under a constant crosshead speed of 50 mm min⁻¹. Specimens of explosive pellets with dimensions of ϕ 20 mm × 20 mm and ϕ 20 mm × 6 mm (diameter × height) for compressive (according to GJB-772A-97 standard method 418.1)²⁶ and Brazilian test were molded at 120 °C. Details of the Brazilian test process were reported by Wen et al.²⁷ At least three specimens of each composite were tested, and the average values were reported.

Dynamic mechanical analysis (DMA) of fluoropolymer and TATB-based formulations with dimensions of 30 mm × 10 mm × 1–2 mm (length × width × thickness) was conducted with a DMA 242C apparatus (Netzsch, Germany) in three-point bending creep mode at a frequency of 1 Hz. The heating rate was set for 1 °C min⁻¹.

2.4 Three-point bending creep tests

The creep tests were recorded with a Netzsch DMA 242C instrument using a three-point bending sample holder with a span of 20 mm. Three-point bending creep tests were carried out on specimens 30 mm long × 10 mm wide and approximately 1.5 mm thickness. The specimens were loaded for 5400 s at four temperatures and three stress levels.

3. Results and discussion

3.1 The properties of polymer binders

Fig. 1 shows the influence of molecular structure on the DMA curves of polymer binders. It can be seen that the incorporation of tetrafluoroethylene and hexafluoropropylene comonomers in PF-2 results in an increase of the storage modulus (E′) in the whole temperature range, compared to that of PF-1. The storage modulus gradually decreases with the experimental temperature, then begins to abruptly decline, and finally keeps constant. The onset temperature of the storage modulus in the DMA curve, i.e. the temperature at which the storage modulus begins to abruptly decline for PF-2 is 50.1 °C, which is 12.8 °C higher than that of a PF-1 sample (37.3 °C). At 60 °C, the storage modulus retention of the PF-2 is 32.3% (determined by the ratio of the modulus value at 60 °C to the modulus value at room temperature), while PF-1 is less than 2.7%.

Fig. 1 Effects of molecular structure on the DMA curves of polymer binders: (a) storage modulus (E′), (b) loss factor (tan δ).

The loss tangent data (tan δ) presented in Fig. 1b confirms the temperature dependence of the storage modulus but provides a more exact indication of the glass transition temperatures. The PF-1 shows the glass transition in the range 35–90 °C with a glass transition temperature (T_g) of 49.5 °C which is the peak value of the loss factor curve. PF-2 showed the glass transition in the range 50–100 °C with a T_g of 68.5 °C, which is 19 °C higher than that of PF-1. It is well accepted that the glass transition temperature is affected by the chain structure of a polymer. The increase of glass transition temperature is believed to be attributed to the introduction of the tetrafluoroethylene and hexafluoropropylene comonomers into the copolymer PF2. Due to the symmetrical substitution on the quaternary carbon for polyvinylidene fluoride (PVDF), the barrier to internal rotation of polymer main chain is low with good chain flexibility. Consequently, the glass transition of PVDF is visible at about −30 °C.²⁸ Compared with PVDF, the substituent groups are manifolded and the glass transition temperature of polychlorotrifluoroethylene (PCTFE) investigated by Khanna²⁹ is reported to be 75 °C. The replacement of all hydrogen atoms along the carbon backbone by fluorine atoms with higher polarity for polytetrafluoroethylene (PTFE), has a marked influence on the internal rotation of polymer main chain and intermolecular reaction. It is clearly revealed the glass transition temperature for PTFE is 130 °C.³⁰ The replacement of one out of every four fluorine atoms along the carbon backbone of PTFE with a larger CF₃ unit prevents the glass transition, resulting in a higher glass transition temperature of 150 °C for completely amorphous poly(hexafluoropropylene) (PHFP).³¹ Therefore, copolymerization with tetrafluoroethylene and hexafluoropropylene shifts the glass transition process to a higher temperature, which is clearly visible on the DMA result.

The tensile mechanical tests of the two fluoropolymers have also been conducted. The characteristics of the polymer binders, including glass transition temperature T_g, tensile strength and elongation at break are listed in Table 1. Compared with the PF-1, the tensile strength of PF-2 is increased by 5.9%.

Table 1 Property parameters of polymer binders

Sample	Glass transition temperature/°C	Tensile strength/MPa	Elongation at break/%
PF1	49.5	20.90	211.0
PF2	68.5	22.13	244.8

---

3.2 Characterization of the TATB-based PBXs

Fig. 2 indicates the dependence of the storage modulus (E′) and loss factor (tan δ) on the temperature for pure TATB and TATB-based PBXs. Due to the small storage modulus for polymer binder (Fig. 1), the storage modulus of TATB-based PBX, which contains 5% polymer binder, is smaller than pure TATB. The excellent mechanical behavior and high glass transition temperature of the polymer binder PF-2 is reflected with the PBX-2, both on the magnitude and temperature dependence of storage modulus. PBX-2 shows higher storage modulus in the whole temperature range, compared to that of PBX-1. In addition, the storage modulus of PBX-1 strongly decreases with increasing temperature. While for PBX-2, the viscoelastic behavior is quite stable up to at least 120 °C, with storage modulus decreasing slightly from 7.63 GPa at 0 °C to 5.93 GPa at 120 °C. The storage modulus of PBX-2 at 60 °C (7.00 GPa) is at least 27.0% higher than that of PBX-1. There is no obvious transition process for pure TATB in the test temperature range, while the TATB-based PBX exists a glass transition temperature which is an inflexion of the loss factor curves, corresponding to the T_g of corresponding polymer binder, as shown in Fig. 2b.

Fig. 2 Plot of storage modulus (E′) and loss factor (tan δ) versus temperature for pure TATB and TATB-based PBXs: (a) storage modulus (E′), (b) loss factor (tan δ).

A Brazilian test was initially used to estimate the properties of brittle materials such as rocks.^32,33 Then the Brazilian test was introduced to the field of explosives by Johnson.^34,35 It is well accepted that the Brazilian disc test is the most convenient substitute of a direct tensile test with specimens made from brittle materials. Specimens of pure TATB and TATB-based PBXs have a shape of cylindrical pellets (20 mm ϕ by 6–20 mm height), and the compressive and Brazilian experiments were performed at room temperature and elevated temperature (60 °C). The resulting relationship curve for stress and strain or displacement is shown in Fig. 3. Pure TATB and TATB-based PBXs fail in a brittle mode, as demonstrated by the sudden discontinuity in the stress–strain curve at the maximal stress. Compared with pure TATB, TATB-based PBXs show a significant increase in the mechanical strength and elongation with breaks under the same condition, indicating that the interfacial bonding role of polymer binder enhances the mechanical properties of PBX. It was observed that the higher the temperature, the smaller the compressive and tensile strength. As the temperature increased from 20 °C to 60 °C, the compressive strength of PBX-1 decreased from 25.81 MPa to 15.46 MPa, declining by 40.1%, and the tensile strength of PBX-1 decreased from 4.76 MPa to 2.33 MPa, declining by 51.1%. This indicates that temperature has a significant effect on the mechanical properties of TATB-based PBXs. PBX-1 displays a larger variation in mechanical properties than PBX-2 with increasing temperature. It can also be seen that PBX-2 has up to 7.2% and 4.2% higher compressive and tensile strengths at 20 °C than PBX-1, and up to 33.9% and 17.2% higher compressive and tensile strengths at 60 °C than PBX-1, which agrees with the above DMA results. These differences in mechanical properties are related to the differences in the glass transition temperature and mechanical response of the polymer binders within TATB-based PBXs.

Fig. 3 The typical mechanical response for pure TATB and TATB-based PBXs at room temperature and elevated temperature: (a) compressive test at room temperature, (b) compressive test at 60 °C, (c) Brazilian test at room temperature, (d) Brazilian test at 60 °C.

3.3 Three-point bending creep tests

Creep tests are utilized to provide time-dependent deformation under constant loads. Fig. 4 demonstrates the creep response for pure TATB and TATB-based PBXs samples as a function of time under different stresses at 60 °C. Compared with pure TATB, TATB-based PBXs show a significant increase in the creep strain under the same conditions. The results could be attributed to the viscoelastic properties of polymer binders. The instantaneous elastic deformation, high elastic deformation, and viscous flow are simultaneous during the creep process. Therefore, the creep strain of a polymer binder is much larger than pure TATB, leading to the increase of creep strain in TATB-based PBXs with the addition of polymer binders.

Fig. 4 Three-point bending creep strain curves of pure TATB and TATB-based PBXs under different stresses at 60 °C: (a) pure TATB; (b) PBX-1; (c) PBX-2.

A constant creep strain rate is known to be a good indicator of creep resistance of polymer composites. As an example, Fig. 5 presents a typical variation of creep strain with creep time for PBX-1 at 60 °C/4 MPa. Usually, creep strain varies linearly with creep time during the steady state creep stage, as plotted in Fig. 5. The constant creep strain rate is the coefficient of creep strain to creep time which is acquired from the slope of the fitting line during the steady state creep stage.

Fig. 5 The linear fit of the creep strain curves during steady creep stage of PBX-1 at 60 °C/4 MPa.

Table 2 summarizes creep performance parameters of TATB-based PBXs under different stresses at 60 °C, including the constant creep strain rate, maximal creep strain, and creep rupture time. The experimental results demonstrate that usage of PF2 with a high glass transition temperature and high mechanical strength is an effective way to improve creep properties of formulations with reduced creep strain, constant creep strain rate, and prolonged creep failure time. For example, it is found that the constant creep strain rate and maximal creep strain of PBX-1 at 60 °C/4 MPa are 1.397 × 10⁻⁸ s⁻¹ and 6.356 × 10⁻⁴. With respect to the composite PBX-2 that contains 5% PF2, the constant creep strain rate and maximal creep strain are reduced by 66.7% and 57.4%. Under higher loading stress (7 MPa and 9 MPa), the creep failure of the sample PBX-1 occurred at 4155 s and 660 s, respectively. Under the same conditions, the modified formulation displays a long-term creep process and no creep rupture time could be obtained, suggesting that creep resistance is improved by the introduction of PF2. The constant creep strain rate, maximal creep strain values, and creep failure time of the composites reflect the difference of the polymer binders: the replacement PF1 with PF2 binder is accompanied with a significant reduction in constant creep strain rate, maximal creep strain, and an increase of creep failure time.

Table 2 The creep performance parameters of TATB-based PBXs under different conditions

Sample	Experimental conditions	Constant creep strain rate/s^−1	Maximal creep strain	Creep rupture time/s
PBX-1	30 °C/4 MPa	4.982 × 10^−9	2.300 × 10^−4	>5400
	45 °C/4 MPa	1.076 × 10^−8	3.899 × 10^−4	>5400
	60 °C/4 MPa	1.397 × 10^−8	6.356 × 10^−4	>5400
	80 °C/4 MPa	1.834 × 10^−8	8.246 × 10^−4	>5400
	60 °C/7 MPa	5.152 × 10^−8	1.020 × 10^−3	4155
	60 °C/9 MPa	—	7.423 × 10^−4	660
PBX-2	30 °C/4 MPa	3.294 × 10^−9	1.326 × 10^−4	>5400
	45 °C/4 MPa	3.341 × 10^−9	1.391 × 10^−4	>5400
	60 °C/4 MPa	4.654 × 10^−9	2.710 × 10^−4	>5400
	80 °C/4 MPa	5.973 × 10^−9	4.346 × 10^−4	>5400
	60 °C/7 MPa	9.631 × 10^−9	5.214 × 10^−4	>5400
	60 °C/9 MPa	1.111 × 10^−8	6.353 × 10^−4	>5400

---

A creep mechanism of PBX has been studied from the theory of deformation and sliding of molecular chain of the polymer by Ding et al.²⁴ It was shown that the creep property of the polymer was the main factor influencing creep-damage properties of the composite even though polymer content was very small. The motion of a chain segment accounts for the enhanced three-point bending creep resistance of PBX-2. As mentioned above by DMA results, the glass transition temperatures of PF-1 and PF-2 are 49.5 °C and 68.5 °C, respectively. The glass transition is dependent on the relative degree of freedom for molecular motion within a given polymeric material. Molecular features which either increase or reduce this mobility will cause differences in the value of T_g. The main molecular chain of PF1 is composed of saturated single bonds, therefore, a molecular chain could internally rotate surrounding a single bond, leading to a low T_g. However, due to the fact that the main molecular chain of PF2 contains comonomers of tetrafluoroethylene with high content of polar fluorine atoms, and hexafluoropropylene with high steric hindrance –CF₃ groups, the proportion of single bonds which could internally rotate is small and chain stiffness is high, resulting in hindrance of chain segment motion. During the creep test at 60 °C, PF-1 is in a rubbery elastic state with freely chain segment movement. However, PF-2 is in a glassy state with frozen chain segments. Consequently, relaxation time of the motion of chain segment and intermolecular inner frictional resistance is higher for PF-2, which is beneficial for creep resistance. Besides, the higher mechanical strength of PF-2 is another reason for improved creep resistance of PBX-2.

Loading stress dependence of creep response for the TATB-based PBXs in the range from 4 MPa to 9 MPa is also displayed in Fig. 4. As illustrated in Fig. 4, a prominent decrease of creep rupture time of TATB-based PBXs is achieved by an increase of loading stress. For example, the 60 °C/7 MPa test resulted in failure of PBX-1 at approximately 4155 s, while the sample did not show any signs of impending failure under lower stress (4 MPa) at the same temperature. When loading stress is further increased to 9 MPa, creep strain increases rapidly with creep time and final creep rupture occurs at 660 s. Decrease of viscosity which is caused by increasing loading stress is believed to be the major contribution to this behavior. As a consequence, easier motion within a molecular chain is achieved as loading stress increases.

Fig. 6 describes creep strain in relation to temperature for pure TATB and TATB-based PBXs as a function of time under 4 MPa. As expected, compared with pure TATB, a prominent increase of the creep strain of TATB-based PBXs is achieved by incorporation of polymer binder at all temperatures. Creep performance parameters of TATB-based PBXs at different temperatures are also listed in Table 2. As can be seen in Fig. 6 and Table 2, all of the specimens display a long-term creep process and no creep rupture time could be obtained within the observation time scale. Experiments show a significant increase in creep strain and constant creep strain rate of TATB-based PBXs with increased temperature. Maximal creep strain at 5400 s and constant creep strain rate of PBX-1 at 80 °C are measured to be 8.246 × 10⁻⁴ and 1.834 × 10⁻⁸ s⁻¹, respectively, which are 2.6-fold and 2.7-fold improvement in comparison to that at 30 °C. A possible explanation is that this behavior could be related to the enhancement of thermodynamic mobility of the chains. The energy of thermodynamic motion and the intermolecular free space increase with increased temperature.

Fig. 6 Three-point bending creep strain curves of pure TATB and TATB-based PBXs at different temperatures under 4 MPa: (a) pure TATB; (b) PBX-1; (c) PBX-2.

3.4 Modeling of the creep behavior

The six-element mechanical model, which is regarded as a series connection structure of a Maxwell model and two Kelvin–Voigt models, can effectively describe the three-point bending creep behaviors of TATB-based PBXs with high precision.⁶ Consequently, the six-element mechanical model is employed to describe the creep process in this study, as shown in Fig. 7. During the creep process, the stress is kept constant and the total strain of polymer composite material PBX could be determined by:where ε(t) denotes a function of creep strain ε with creep time t, ε₁ is the instantaneous elastic deformation, ε₂ and ε₃ are the high elastic deformation, ε₄ is the viscous flow deformation, σ₀ is the initial stress, E₁ is the elastic modulus of instantaneous elastic deformation, E₂ and E₃ are the elastic modulus of high elastic deformation, τ₂ and τ₃ are the relaxation time, and η₄ is the bulk viscosity.

Fig. 7 Schematic drawing of six-element mechanical model.

Experimental curves of the creep process at various temperatures are fitted by means of the six-element mechanical model using OriginPro 8.0 software. As an example, Fig. 8 gives the nonlinear fitting result of PBX-1 at 30 °C/4 MPa. Experimental results have shown that the six-element mechanical model fits work remarkably well for the experimental data of TATB-based PBXs.

Fig. 8 Three-point bending creep strain curve and non-linear fitting curve of PBX-1 at 30 °C/4 MPa.

The values of six parameters obtained from the nonlinear fit for PBX-1 and PBX-2 are summarized in Table 3. As can be seen from the fitting results, the parameters including elastic modulus E₂, E₃ which are associated to the springs of Kelvin–Voigt units, and the bulk viscosity η₄ which is related to the Maxwell dashpot and reflects the irrecoverable creep strain of TATB-based PBXs, display a decreasing trend with the temperature. On the other hand, the parameters E₂, E₃, and η₄ seem to increase with the presence of PF2 as polymer binder which indicates an enhanced creep resistance performance. Incorporation of tetrafluoroethylene and hexafluoropropylene monomers in PF2 binder leads to hindrance of molecular thermodynamic movement. Macroscopically, the rigidity of material increases, leading to an increase of elastic modulus E₂ and E₃. The relative slide of a molecular chain of PF2 binder could be more difficult than that of PF1, resulting in the increase of η₄. The trend of parameters E₂, E₃, and η₄ with temperate and the molecular structure of polymer binder is consistent with the creep resistance of TATB-based PBXs, revealing that the parameters E₂, E₃, and η₄ may reflect the change of creep behavior of TATB-based PBXs.

Table 3 The fitting parameters of six-element model under different conditions

Sample	Test condition	E1/MPa	E2/MPa	τ2/s	E3/MPa	τ3/s	η4/MPa s	R^2
PBX-1	30 °C/4 MPa	5.760 × 10^5	9.999 × 10^4	974.50	2.419 × 10^4	25.08	1.150 × 10^9	0.99410
	45 °C/4 MPa	2.720 × 10^5	4.359 × 10^4	745.24	1.723 × 10^4	15.52	4.394 × 10^8	0.99889
	60 °C/4 MPa	4.431 × 10^5	2.128 × 10^4	734.98	1.043 × 10^4	24.82	3.779 × 10^8	0.99721
	80 °C/4 MPa	5.341 × 10^5	1.403 × 10^4	665.43	8.773 × 10^3	28.96	2.727 × 10^8	0.99812
PBX-2	30 °C/4 MPa	4.011 × 10^5	1.499 × 10^5	1317.55	4.731 × 10^4	11.17	2.688 × 10^9	0.99826
	45 °C/4 MPa	3.148 × 10^5	1.087 × 10^5	588.81	3.604 × 10^4	16.94	9.999 × 10^8	0.99637
	60 °C/4 MPa	1.655 × 10^5	3.458 × 10^4	448.79	3.507 × 10^4	12.34	8.376 × 10^8	0.99753
	80 °C/4 MPa	9.403 × 10^4	4.021 × 10^4	599.70	1.503 × 10^4	15.03	7.594 × 10^8	0.99816

---

3.5 Creep strain master curve

Fig. 9 depicts the double logarithmic plots of three-point bending creep strain as a function of creep time for pure TATB and TATB-based PBXs at different temperatures under 4 MPa. As clearly demonstrated in Fig. 9, the pattern of creep strain curves is similar. With increasing temperature, the creep strain gradually reinforces.

Fig. 9 Double logarithmic plots of three-point bending creep strain for pure TATB and TATB-based PBXs: (a) pure TATB; (b) PBX-1; (c) PBX-2.

Creep behavior that was observed at a high temperature within a short time also was observed at a low temperature within a long time. Based on the time–temperature superposition principle,³⁶ creep strain master curves were obtained at a reference temperature with a right shift of the curves at a temperature higher than the reference temperature and a left shift of the curves at a temperature lower than the reference temperature. The creep strain curve at reference temperature T_r and time t_r is received with a horizontal displacement of the creep strain curve at temperature T and time t:

D(T_r, t_r) = D(T_r, t/a_T) = D(T, t) (2)

where a_T is a shift factor. In this work, 30 °C was selected as the reference temperature for the master curve of creep strain function. Fig. 10 demonstrates the three-point bending creep strain master curves of pure TATB and TATB-based PBXs. With the addition of PF1 as a polymer binder, the predictable creep strain of PBX-1 at 30 °C/4 MPa is higher than that of pure TATB. Compared with PBX-1, the creep strain master curve of the PBX-2 shifts downward, suggesting that the creep resistance performance is enhanced. The time scale of experimental curves for TATB-based PBXs spans 3 magnitude orders, while the time scale of master curves of TATB-based PBXs spans 7 magnitude orders, indicating that the master curves could simulate the creep behavior of material in a broader time domain. It also can be seen that creep behavior up to 6.0 years and 15.4 years at 30 °C/4 MPa for PBX-1 and PBX-2 could be predicted by the short-term experimental data (5400 s) acquired at 30–80 °C under 4 MPa, respectively.

Fig. 10 Three-point bending creep strain master curves of pure TATB and TATB-based PBXs.

4. Conclusions

In this work, mechanical properties and creep behaviors of 1,3,5-triamino-2,4,6-trinitrobenzene (TATB)-based polymer bonded explosives (PBXs) containing two kinds of fluoropolymer with different molecular structures as polymer binders at different temperatures and stresses were investigated. Experimental results indicated that: (1) PBX with a copolymer of chlorotrifluoroethylene, vinylidene fluoride, tetrafluoroethylene, and hexafluoropropylene (PF2) showed higher compressive and tensile strength compared to the one with a copolymer of chlorotrifluoroethylene and vinylidene fluoride (PF1) as polymer binder. (2) Similar to static mechanical results, creep behavior of TATB-based PBXs greatly depended on the molecular structure of the fluoropolymer. PBX with PF2 was found to have better creep resistance than the one with PF1 as polymer binder. (3) The six-element mechanical model was successfully used to analyze non-linear behavior of TATB-based PBXs. The model analysis revealed an increase in the elastic modulus E₂, E₃ and bulk viscosity η₄ for the formulation containing PF2 compared to the one with PF1. (4) Based on the time–temperature superposition principle, creep strain master curves were obtained at a reference temperature of 30 °C. Creep behavior up to 15.4 years at 30 °C/4 MPa could be predicted by the short-term experimental data (5400 s) acquired at 30–80 °C under 4 MPa. Experimental results indicated that, compared with the formulation with PF1, creep resistance performance was enhanced by the presence of PF2 with a downward shift of the creep strain master curve. The results are helpful for a deeper understanding of the creep mechanism of TATB-based PBXs and the influence of molecular structure of a polymer binder.

References

1. A. Wuillaume, A. Beaucamp, F. David-Quillot and C. Eradès, Propellants, Explos., Pyrotech., 2014, 39, 390–396.
2. Q. Yan, S. Zeman and A. Elbeih, Thermochim. Acta, 2012, 537, 1–12.
3. A. Zandiatashbar, C. R. Picu and N. Koratkar, Small, 2012, 8, 1676–1682.
4. Z. Yao, D. Wu, C. Chen and M. Zhang, Composites, Part A, 2013, 50, 65–72.
5. L. Tang, X. Wang, L. Gong, K. Peng, L. Zhao, Q. Chen, L. Wu, J. Jiang and G. Lai, Compos. Sci. Technol., 2014, 91, 63–70.
6. C. Lin, J. Liu, F. Gong, G. Zeng, Z. Huang, L. Pan, J. Zhang and S. Liu, RSC Adv., 2015, 5, 21376–21383.
7. X. Tu, B. Zhang, X. Wei and W. Wang, Chin. J. Energ. Mater., 2013, 21, 306–309.
8. F. J. Gagliardi and B. J. Cunningham, LLNL-CONF-402307, 2008.
9. Z. Liu, H. Xie, K. Li, P. Chen and F. Huang, Polym. Test., 2009, 28, 627–635.
10. D. M. Hoffman, Polym. Eng. Sci., 2003, 43, 139–156.
11. L. L. Stevens, D. M. Dattelbaum, M. Ahart and R. J. Hemley, J. Appl. Phys., 2012, 112, 023523.
12. Q. L. Yan, S. Zeman and A. Elbeih, Thermochim. Acta, 2013, 562, 56–64.
13. N. K. Bourne and G. T. Gray III, J. Appl. Phys., 2005, 98, 123503.
14. W. R. Blumenthal, G. T. Gray III, D. J. Idar, M. D. Holmes, P. D. Scott, C. M. Cady and D. D. Cannon, AIP Conf. Proc., 2000, 505, 671.
15. R. L. Gustavsen, R. J. Gehr, S. M. Bucholtz, R. R. Alcon and B. D. Bartram, J. Appl. Phys., 2012, 112, 074909.
16. C. Souers, P. Lewis, M. Hoffman and B. Cunningham, Propellants, Explos., Pyrotech., 2011, 36, 335–340.
17. W. Small IV, E. A. Glascoe and G. E. Overturf, Thermochim. Acta, 2012, 545, 90–95.
18. P. W. Cooper and S. R. Kurowski, Introduction to the Technology of Explosives, Wiley-VCH, New York, 1996, pp. 21–23.
19. A. Flores, F. J. Baltá Calleja and T. Asano, J. Appl. Phys., 2001, 90, 6006–6010.
20. G. Spathis and E. Kontou, J. Appl. Polym. Sci., 2004, 91, 3519–3527.
21. A. Ranade, K. Nayak, D. Fairbrother and N. A. D'Souza, Polymer, 2005, 46, 7323–7333.
22. M. Ganß, B. K. Satapathy, M. Thunga, R. Weidisch, P. Pötschke and A. Janke, Macromol. Rapid Commun., 2007, 28, 1624–1633.
23. Z. Dai, Y. Gao, L. Liu, P. Pötschke, J. Yang and Z. Zhang, Polymer, 2013, 54, 3723–3729.
24. Y. Ding, Y. Pan, R. Cai, X. Yu and Y. Yang, Chin. J. Energ. Mater., 2000, 8, 87–90.
25. C. Lin, S. Liu, X. Tu, Z. Huang, Y. Li, L. Pan and J. Zhang, Chin. J. Energ. Mater., 2013, 21, 506–511.
26. National Military Standard of China, Physical Experimental Methods, GJB/772A-97, 1997 (in Chinese).
27. M. Wen, W. Tang, X. Zhou, H. Pang and F. Zhu, Chin. J. Energ. Mater., 2013, 21, 490–494.
28. P. Frübing, F. Wang and M. Wegener, Appl. Phys. A: Mater. Sci. Process., 2012, 107, 603–611.
29. Y. P. Khanna and R. Kumar, Polymer, 1991, 32, 2010.
30. H. F. M. Mohamed, E. E. Abdel-Hady and S. S. Mohamed, Radiat. Phys. Chem., 2007, 76, 160–164.
31. N. A. Belov, A. A. Zharov, A. V. Shashkin, M. Q. Shaikh, K. Raetzke and Y. P. Yampolskii, J. Membr. Sci., 2011, 383, 70–77.
32. J. Claessona and B. Bohloli, Int. J. Rock. Mech. Min. Sci., 2002, 39, 991–1004.
33. Q. Z. Wanga, X. M. Jiaa, S. Q. Koub, Z. X. Zhang and P.-A. Lindqvist, Int. J. Rock. Mech. Min. Sci., 2004, 41, 245–253.
34. H. D. Johnson, MHSMP-78-08, 1978.
35. H. D. Johnson, MHSMP-81-22, 1981.
36. F. Achereiner, K. Engelsing, M. Bastian and P. Heidemeyer, Polym. Test., 2013, 32, 447–454.

---