3.1. Mesoscale Characteristics
In order to study the mesoscale characteristics of PTFE/Al/Bi
2O
3 composite material, scanning electron microscope (SEM, HITACHI S-4800, CamScan, Tokyo, Japan) was used. The mesoscale characteristics are shown in
Figure 3.
Figure 3a indicates that in the PTFE/Al/Bi
2O
3 composite, the PTFE matrix closely wrapped the Al and Bi
2O
3 particles.
Figure 3b–d show the distribution of elements in the sample. F, Al, and Bi elements represent the distribution of PTFE matrix, Al, and Bi
2O
3 in the sample, respectively. The distribution of elements also shows that the Al and Bi
2O
3 particles are uniformly distributed in the PTFE matrix and the particle and matrix are tightly bound.
Figure 4 presents the XRD pattern of PTFE/Al/Bi
2O
3 samples (Type D-1). As shown in
Figure 4, it indicates that PTFE, Al, and Bi
2O
3 existed in the samples, and no new substances had formed. It means that no chemical reaction occurred in the sample during mixing and sintering, and only physical mixing occurred among the components. The components within the PTFE/Al/Bi
2O
3 composite still retained their original physical and chemical properties. Therefore, the physical and chemical properties of composite materials can be estimated from the properties of three components. Take the burning rate as an example, according to the superposition principle of burning rate of multi-component materials, the burning rate of Type F is about 253.6 m/s, about 127 times of that of Type A [
13].
3.2. Impact Sensitivity
The impact sensitivity of PTFE/Al/Bi
2O
3 materials with different content was studied by the drop-weight test and compared by
H50. The drop-weight experiments were recorded as shown in
Figure 5 and
Figure 6. As shown in
Figure 5 and
Figure 6, samples may react when impacted by drop mass falling from a range of height. Among them, the range of falling height appeared in the experiment was as wide as 30 cm for Type A, while the falling height range of other types was all about 20 cm, which reflects that the critical reaction height of Type A under impact loading were relatively fuzzy.
According to the above drop-weight test results,
H50 of each type can be calculated as the following Equation:
where
A is the lowest height in the test;
B is the increment of height,
B = 5 cm in this test;
D is the number of reactions that occur in the test;
i is the ordinal number that falls from low to high, starting from 0; and
Ci is the number of times that the samples react at the certain height. By Equation (3), the
H50 of each type is listed in
Table 3. The variation trend of
H50 of PTFE/Al/Bi
2O
3 with the content of Bi
2O
3 is shown in
Figure 7.
The results show that the content of Bi2O3 has a significant influence on the impact sensitivity of PTFE/Al/Bi2O3 composites. Type A composite has the highest H50 reaching 100 cm, compared with composite adding the content of Bi2O3 from 4.452% to 35.616%. In detail, the H50 of PTFE/Al/Bi2O3 composite adding 75 μm-Bi2O3 decreases with the increase of the content of Bi2O3 ranging from 0% to 17.808%, while the H50 of the composite increases with the increase of the content of Bi2O3 ranging from 17.808% to 35.616%. The Type C-1 composite has the highest impact sensitivity, and the H50 of Type C-1 only 0.77 times of that of Type A. When the particle size of Bi2O3 is 150 μm, the H50 varies with the Bi2O3 content, which is similar to that of Bi2O3 particle size 75 μm.
The polynomial fitting result of
H50 with the change of content in
Figure 7 shows that the particle size of Bi
2O
3 has no fundamental influence on the general trend of
H50 with the change of content, but it has significant influence on the change rate of
H50 with the change of content, especially when the content of Bi
2O
3 is higher than about 20%. It is worth noting that the minimum
H50 of PTFE/Al/ Bi
2O
3 with large particle size Bi
2O
3 is lower than that with small particle size Bi
2O
3. The reasons may be that Bi
2O
3 particle size affects the failure behavior of PTFE/Al/Bi
2O
3 composites under the compression, thus affecting the reaction performance of the composites.
The material is subjected to strong compression and failure, and the particles rub against each other, forming ‘hot spots’. The addition of Bi2O3 in the PTFE/Al system affects the impact sensitivity mainly from the following two aspects. As the content of Bi2O3 increases, on the one hand, the number of hot spots in the material increases, making the reaction easier to be triggered, leading to the material impact sensitivity increase. On the other hand, in the PTFE/Al/Bi2O3, the contact area of active PTFE/Al may be reduced due to the separation caused by Bi2O3 particles, and a portion of the impact energy is transferred to the Bi2O3 particles, leading to the material impact sensitivity reduction.
3.3. Prediction Model for PTFE-Based Reactive Material Impact Sensitivity
In order to analyze the influence of Bi2O3 content on impact sensitivity of PTFE-based reactive material, the model based on the ‘hot spots’ theory, is presented to predict the H50 of materials. Two reactions, PTFE/Al and Al/Bi2O3, occurred in the PTFE/Al/Bi2O3composite material. In order to simplify the analysis, the following assumptions are made: (1) all particles in the material are distributed randomly and uniformly and tightly packed by the PTFE matrix without pores; (2) particles are spherical with average size.
As analyzed in
Section 3.2, the content of Bi
2O
3 affects the impact sensitivity of materials from two aspects: (1) as the number of Bi
2O
3 particle increases, the number of hot spots formed by slide friction increases, which benefits to induce reaction; (2) as proportion of Al/Bi
2O
3 reactants increases, the reaction threshold of PTFE/Al/Bi
2O
3 composite increases, which impedes the reaction.
When the hot spots formed by interparticle slip is the dominant mechanism of induced reaction, the following three conditions are necessary: (1) the influence range of the friction hot spots includes the reactants; (2) the reaction temperature threshold is lower than the melting point of the friction particles; (3) the temperature of hot spot is higher than reaction threshold temperature. If all conditions are met, the material will be ignited. It is worth noting that due to the small size of the hot spot, the influence range of hot spot temperature is the particles involved in the friction and PTFE matrix. Therefore, the concept of effective hot spot is proposed, which refers to the hot spot that can induce the reaction. In PTFE/Al/Bi2O3 composite material, effective friction hot spot refers to the hot spot formed by friction between Al and Al and Bi2O3, respectively. This is because the melting point of Al is only 933 K below the reaction threshold of Al and Bi2O3. Hot spots only could induce the reaction between Al and PTFE.
The temperature rise due to slide friction between particles is expressed as [
16]
where
is temperature rise caused by friction between particles,
and
are thermal conductivity of two particles,
a is the radius of actual contact area,
μ is the coefficient of friction,
L is normal pressure, and
u is relative velocity, respectively.
It assumes that the average relative velocity between particles is equal to half of the drop mass velocity in the drop-weight test. Then,
u when the drop height is
H50 can be expressed:
where g is the gravitational acceleration which is 9.8 m·s
–2. The friction between two particles during mechanical impact belongs to a random independent event, and the friction probability of Al/Al and Al/Bi
2O
3 fraction can be expressed as
and
by the volume fraction, respectively. Considering the uneven temperature and proportion of two-type hot spots, the weighted average temperature rises because of hot spots, and can be approximately expressed as
where
and
are volume fraction of Al and Bi
2O
3, respectively.
is temperature rise. Assume the temperature rise caused by adiabatic shear and heating at creak tips mechanism is
Tother, ignoring variation because of Bi
2O
3 content, the hot spot temperature of the material under the action of a drop mass can be expressed as
where
T,
T0 are ultimate and initial temperature of hot spot, respectively.
and
are thermal conductivity of Al and Bi
2O
3, respectively.
Hot spot induced material reaction is not only related to hot spot temperature but also affected by hot spot size. The size of hot spots strongly depends on the chemical reaction rate. When the reaction rate
k is higher than the critical reaction rate
kc, the hot spot size satisfies the starting condition. According to Arrhenius formula, the rate of the chemical reaction can be expressed as
where
A is the pre-exponential factor;
Ea is the active energy; R is the gas content; and
T is the temperature, respectively. When
, that is to say, the hot spot size reaches the reaction condition, which is reflected as the chemical reaction temperature threshold at the macro level. The reaction temperature threshold can be expressed as
Since constants (
A,
Ea, and
kc) are affected by multiple factors, such as particle size and shape, it is difficult to get detailed data, so this paper directly introduces the reaction temperature threshold to consider the judgment of reaction parameters (
A,
Ea, and
kc) on whether the reaction occurs or not. When PTFE-based granule composites are impacted, the particles within the materials are randomly rubbed against each other. Therefore, the reaction threshold temperature of PTFE/Al/Bi
2O
3 composite with different Bi
2O
3 content can be estimated as
where
Tc is the reaction threshold temperature of composite material and
and
are the mass fraction of the reactant Al/Bi
2O
3, and PTFE/Al, respectively.
and
are the reaction threshold temperature of PTFE/Al and Al/ Bi
2O
3, respectively. When
T ≥
Tc, the material reaction is triggered. Combined with Equations (5), (7), and (10), the
H50 of PTFE/Al/Bi
2O
3 composite material with the content of Bi
2O
3 particles can be expressed as
The parameters used in the model are listed in
Table 4 [
17].
Figure 8 depicts the calculated results of Equation (11).
The model analysis shows that when the content of Bi2O3 is low, the number and temperature of hot spots dominate H50 of the PTFE/Al/Bi2O3 composite materials, leading to the decline of the H50 with the increase of Bi2O3 content. When the content of Bi2O3 is high, the ignition threshold dominates H50, leading to the improvement of H50 with the increase of Bi2O3 content.
On the whole, the above model can predict the change law of H50 with Bi2O3 content, but compared with the experimental value, the model predicts the slow change rate of H50 with Bi2O3 content, which is because the model only considers the influence of friction hot spots and ignores the change of temperature rise under the influence of content induced by other mechanisms. When the Bi2O3 content was less than 5%, the model predict lower than the experimental results. The main reason is that friction is not the dominant mechanism of hot spot formation in the low particle content composite material. As PTFE matrix content increases, the material shows good toughness, and the temperature rise caused by adiabatic shear and heating at the crack tip is underestimated, so the prediction results of the model are lower than the experimental results. When the Bi2O3 content is in the range of 5%–30%, the model prediction is higher than the experimental results. According to the mechanical characteristic analysis of other PTFE/Al materials, the failure strain of the composite material in the range of particle content increases to the maximum and then declines, and the failure strain affects the exothermic change of the crack tip, leading to the prediction model error. When the Bi2O3 content is higher than about 30%, the model prediction is slightly better than the experimental composite, because friction contributes more to the formation of hot spots in the composite with high particle content.
3.4. Energy Release Performance under a Certain Impact
Figure 9 and
Figure 10 displays the reaction phenomena of composite materials with different Bi
2O
3 content under a certain impact. As shown in the
Figure 9 and
Figure 10, when the samples are compressed by a drop-weight with a fall height of 140 cm, the samples all react violently, and the reaction intensity strongly depends on the content of Bi
2O
3.
The moment of contact between the drop-weight and the sample is 0. The samples are intensely compressed first, after about 1.3 to 1.65 ms reaction starting. These results imply that the content and particle size of Bi2O3 have no significant effect on the delay time of composite materials. Type A composite has the lowest reaction intensity, compared with PTFE/Al composite material adding 4.452% to 35.616% Bi2O3. With the increase of Bi2O3 content, the reaction degree increases first, and then reduces. The most violent reaction of PTFE/Al/Bi2O3 occurs at the Bi2O3 content of 4.452% to 8.904%. The experiments indicate that PTFE/Al/Bi2O3 with proper Bi2O3 content, which is called optimum content of Bi2O3, could maximize the reaction degree of the PTFE/Al/Bi2O3 composite.
The content of Bi2O3 has a significant influence on the reaction duration. The reaction duration of the sample without Bi2O3 (Type A) is about 4.2 ms. In general, as the content of Bi2O3 increases, the reaction duration is prolonged; while, when the content of Bi2O3 exceeds a certain value, the reaction duration is shortened. When the particle size of Bi2O3 is 75 μm, there is no significant difference in reaction duration (about 5.2 ms) in range from 4.452% to 17.808%. When the content exceeds 17.808%, the reaction duration shortens. For the samples with 150 μm-Bi2O3, when the content of Bi2O3 is 8.904%, the reaction duration reaches about 6.3 ms at most. As the content of Bi2O3 continues to increase, the reaction duration of samples shortens. It can be illustrated from reactions, which occur in the PTFE/Al/Bi2O3 composite materials, PTFE/Al reacts at a lower temperature, but the burning rate of PTFE/Al is slow and the reaction has significant non-self-sustainability. Al/Bi2O3 reacts at a higher critical temperature, comparing with the PTFE/Al, and the burning rate of Al/Bi2O3 is faster. In the PTFE/Al/Bi2O3 composite, the PTFE/Al reaction occurs first, and releases a large amount of heat. A large amount of heat will induce the reaction between Al and Bi2O3. A large amount of heat released by the reaction Al/Bi2O3 and the high burning rate is conducive to the reaction, improving the self-sustainability of reaction. Thus, the reaction duration of the material is prolonged. However, the increase of Bi2O3 content means that the content of PTFE/Al decreases, and the heat released by the reaction of PTFE/Al decreases, which is not conducive to induce the secondary reaction of Al/Bi2O3, leading to more incomplete reaction and shorter reaction duration.
The state of two samples, Type A (without Bi
2O
3) and Type D-1 (with 75 μm-Bi
2O
3), after impact, are shown in
Figure 11. There is a large amount of carbon black remaining on the anvil after the reaction of Type A sample, while less carbon black after reaction of Type D-1 sample. The amorphous carbon generated by the reaction is mainly distributed on the edge of the residue sample. Besides, carbon also exists on the surface of the Type A sample. The phenomenon indicates that Type D-1 reacts more thoroughly than Type A under the drop mass height of 140 cm. That is probably because Bi
2O
3 could react with amorphous carbon of PTFE/Al reaction product at high temperature [
18], so the reaction degree is improved and the carbon black reduces. Compared with Type D-1 residue, Type A residue is more complete, which also indicates that the reaction rate of Type A is lower than that of Type D-1, and opportune Bi
2O
3 content is conducive to the reaction.
3.5. Reaction Mechanism
In order to understand the chemical reaction mechanism of the PTFE/Al/Bi
2O
3 composites, the reacted residue of Type D-1 sample is analyzed by X-ray diffraction (XRD), and the result is shown in
Figure 12. The results show that AlF
3, Bi
24Al
2O
39, and Bi
48Al
2O
75 are produced during the reaction. Among them, AlF
3 is the product of the reaction between Al and gaseous C
2F
4 generated by PTFE cracking. In addition, the reaction also generates amorphous carbon, which could not be detected by XRD. Bi
24Al
2O
39 and Bi
48Al
2O
75 are two kinds of mixed crystals formed by Bi
2O
3 and Al
2O
3 at high temperature. Bi
2O
3 reacts with Al to form Al
2O
3 and Bi, and unreacted melted Bi
2O
3 (melting point: 1098 K) wraps Al
2O
3 to form
xBi
2O
3·Al
2O
3. Bi, the other product of the reaction between Al and Bi
2O
3, is also not detected in the product. It is because that, Bi, whose boiling point is only 1833 K, forms Bi vapor due to the high temperature during the reaction process. The formation of
xBi
2O
3·Al
2O
3 crystal also indicates a small Al and Bi
2O
3 participation reaction. It implies that the materials react incompletely under the low impact load. The analysis in
Section 3.4 also indicates that C and Bi
2O
3 may have subsequent reactions. Combining the analysis above, the possible chemical reaction process of the PTFE/Al/Bi
2O
3 composite can be described as:
The above analysis shows that when PTFE/Al/Bi2O3 composite material is impacted, not only does it react with PTFE and Bi2O3, respectively, with Al as the oxidant, but also PTFE in the composite reacts with Bi as the oxidant; in addition, Bi2O3 may further oxidize reaction product C. Therefore, Bi2O3 can effectively improve the energy release characteristics of PTFE/Al-based energetic materials.
In general, the PTFE/Al/Bi
2O
3, a kind of granular composite reactive materials, would be initiated due to the ‘hot spots’, which are probably formed by the sliding friction, adiabatic shear, and heating at crack tips, during mechanical impact.
Figure 13 presents the residue of Type D, including reacted and unreacted samples. There is a remarkable difference between reacted and unreacted sample residue. There are several open cracks in the edge of the reacted residue, some of which have black marks and obvious melted marks (
Figure 13a,c). While there are only open cracks at the unreacted residue edge (
Figure 13b,d). These phenomena imply that the reaction is most likely to begin at the open crack in the material and that the formation of the crack is related to the material reaction. The black marks show that the sample reacts incompletely. The edge open cracks of Type D-2 residue are more obvious than that of Type D-1, indicating that the ductility of the material adding large particle size Bi
2O
3 is weaker than that of adding small particle size Bi
2O
3 material (
Figure 13b,d).
Figure 14 shows the microscopic characteristics of the cracks in the reacted and unreacted samples. There are no reaction products, such as carbon and bismuth, in shear cracks of unreacted residues. There are fibers, whose direction is perpendicular to that of crack that can be observed clearly, from unreacted residue SEM images. The morphology of crack is similar to that of brittle fracture. Morphology features of unreacted residue are significantly different from those of reacted residue. The crack edge of the sample in which the reaction occurred was irregular and appeared coral-like, which is formed by melted and recrystallization of PTFE in the reaction zone during the reaction. It can be seen from
Figure 14b that when the material reacts partially, the reaction zone is generally located at the crack, which also indicates that exothermic heat at the crack tip is an important factor for ignition.
Combined with the results in
Section 3.2, it indicates that the mechanism of PTFE/Al/Bi
2O
3 composite impact-induced reaction could be described as: (1) under mechanical impact, violent plastic deformation of the material results in the rise of the overall temperature of the material; (2) during the intense compression of granular composite material, violent friction occurs, resulting in hot spots and local temperature rise, which are randomly distributed with in the composite; (3) under the action of strong shear, cracks are formed at the edge of the material, and heat is released from the crack tip, making the crack tip to form hot spots. Considering the above three aspects, the hot spot at the crack tip of the material has the highest temperature and is the easiest to trigger the reaction.