Aluminum powder can greatly increase the potential energy of composite energetic material, such as explosives and propellants.^[1–4] However, much of the potential cannot be released due to incomplete combustion. The study of aluminum powder combustion theory in detonation environment is of great significance to solve the above problem and enrich the theoretical model of metal powder combustion.

Natural aluminum particles have the core–shell structure.^[5] The structure response is the mechanical behavior of the aluminum particle structure caused by external influences. An aluminum ignition and combustion occurs after oxide shell separation, so the response mechanism of the core–shell structure of aluminum particle before ignition is the focus of aluminum powder combustion theory. The study of core–shell structural response of aluminum particle under slow heating conditions is conducted in detail.

Eisenreich^[6] researched the slow thermal response of aluminum powder for certain size ranges with different stages of aluminum oxidation being observed. His conclusions were supported and referenced by other scholars, such as Hasani and Korshunov.^[7–9] Further, Eisenreich^[10] noted that the alumina layer has a phase change in oxidation, but there was no quantitative correlation between the dynamic changes of phase transformation and oxidation.

Dreizin^[11] studied Al particle combustion in air using a pulsed micro-arc discharge. He found that the Al particle combustion corresponds to different temperatures, internal particle compositions, and flame shapes. Trunov^[12,13] also noted that the growth of the crystal phase change caused by the micron aluminum oxide layer is directly related to the aluminum oxidation behavior.

Trunov^[14,15] proposed a reaction model for the aluminum slow weighting process as affected by the shell phase transformation for micro-aluminum. The phase change of the alumina was divided into four stages. For stage 1, the reaction temperature is less than 800 K, the natural amorphous state of the alumina shell grows, the crystal shape changes to γ-Al₂O₃, and the oxide layer thickens. During stage 2, between 800 K and 910 K, the transfer rate of the active material through the oxide layer increases, further promoting the phase change. At stage 3, between 910 K to 1320 K, the γ-Al₂O₃ oxide layer thickens and changes to θ-Al₂O₃ and then α-Al₂O₃. For stage 4, the layer continues to change to α-Al₂O₃ and the thickness grows further.

Bradstant^[16] studied the slow oxidation behavior of micro/nano aluminum powder in a CO₂ atmosphere. The maximum reaction temperature was 1250 °C and the results showed that the aluminum of less than was oxidized completely. Using scanning electron microscopy (SEM), the oxidation products were characterized and an alumina hollow shell was observed. Combining energy dispersive spectrometer (EDS) analysis and phase characterization, the results showed that when the temperature of the thermal analysis increased from 600 °C to 1000 °C, the carbon content of the solid phase also began to increase and then decrease. It is thought that this was the result of Al and CO₂ generating Al₂OC and Al₄O₄ C. Liu^[17] did similar research and established the “eruption model”.

Researchers also studied the combustion of aluminum particles. Glassman^[18,19] first suggested that the metal particle burning was similar to droplet combustion, with the ignition depending on the melting and boiling point of the metal and oxide. He speculated that the stable aluminum combustion condition was melted alumina when the reaction temperature reached the boiling point of aluminum.

Further research confirmed the model proposed by Glassman.^[20,21] Olsen^[22] found that during the combustion, the generated liquid alumina would gather on the surface of particles, forming an alumina cap. Allen^[23] studied nano-aluminum powder under high temperature combustion heat, verifying the Altman hypothesis. But previous research has also shown that the burning of aluminum began before the temperate reached the boiling point when the shell burst.^[24] The reason for this may be different temperature and pressure environments^[25] or mechanical stresses.^[26]

In summary, the previous research focused on the structure response of aluminum particle in the thermal analysis (below 1500 K), and the combustion model of aluminum particles in the high temperature combustion environment (above 3000 K and below 10 MPa). However, the investigation on aluminum particle combustion in detonation environment (above 3000 K and more than 5 GPa) is deficient, which is significantly important to increase the efficiency of aluminum particle combustion. The purpose of this paper is to understand the mechanism of the structural response of aluminum core–shell particles in detonation environment.

Combined with the literature and experimental results, the potential mechanism for the separation of aluminum core–shell particles in detonation environment is as follows.

(I) Thermal stress. The density of solid aluminum is 2.7 g/cm³, and the density of liquid aluminum is 2.4 g/cm³. Therefore, when the aluminum core is melted, its volume expands by 12%. The aluminum shell swells and ruptures due to internal tensile stress.

(II) Detonation wave. The detonation wave pressure is greater than 10 GPa in the aluminized explosive reaction zone. Such high pressure causes a large deformation of the aluminum powder, which makes alumina shell fail to crack, forming cracks on the surface of the aluminum.

In the detonation environment, high temperature and strong impact are present simultaneously, and the two factors should be considered comprehensively. By calculating the separation time required for the two methods, the main cause of the core–shell deconstruction in the detonation environment can be determined.

(III) Crystal transformation and phase transformation of alumina. Thermal analysis results^[27,28] show that as the temperature increases, the alumina changes from an amorphous state to γ and θ states, eventually forming a stable α state. When the crystal form of alumina changes, its density increases all the time, causing the volume of alumina to decrease, which causes the alumina to not completely cover the aluminum core, resulting in shell–core separation.

In summary, the crystal transformation and phase transformation of alumina are the main reasons for shelling in thermal analysis environment (300 °C–1100 °C); in the combustion reaction, thermal stress is the main reason; in the detonation environment, high temperature and strong impact are present simultaneously, and the two factors should be considered comprehensively. By calculating the separation time required for the two methods, the main cause of the core–shell deconstruction in the detonation environment can be determined.

3.1. The rupture time of thermal stress

The melting point of aluminum is 933 K.^[29] TNT/Al (80/20) explosive detonation temperature is 3309 K by cast formula.^[30] Taking 10- aluminum particles as an example, the time for the alumina shell and aluminum core rising to the melting point (t_mel) is calculated. t_mel can be treated as the time when the shell is ruptured by thermal stress 1 where Q(x) is the amount of heat required to rise to the melting point of aluminum (in the unit of J), P(x) is the endothermic power (in the unit of W), and x is the distance from the aluminum surface to the center (in the unit of m). When considering the phase change of substance, 2 where is the specific heat capacity of different phases of the material (in the unit of ), m is the mass of the substance (in the unit of kg), and is the substance enthalpy of phase change (in the unit of J/kg), and 3 where q is the heat flux (in the unit of W/m²), and S(x) is the heated area (in the unit of .

According to Fourier’s law 4 where λ is the thermal conductivity of the substance, which is taken as for aluminum, and for alumina.

Bring the heat capacity, phase change enthalpy, and other parameters^[29] into the formula, and t_mel can be calculated.

When the diameter of aluminum particle is , the shell rises to 933 K for 0.013 ns and the core is 53.6 ns. The t_mel values for particles of other diameters are shown in Table 3.

Table 3.

Table 3.

Table 3. Heating time of different aluminum particle sizes reaching the aluminum melting point. . Diameter of aluminum particles/ 2 10 30 90 tmel/ns 5.9 53.6 248.2 1343.5

Table 3. Heating time of different aluminum particle sizes reaching the aluminum melting point. .

3.2. Breakage time of alumina shell by detonation wave

To investigate the mechanical response of aluminum particle in the detonation shock wave, the finite element software AUTODYN^[31] is employed. The aluminum with core diameter of and shell thickness of 20 nm is chosen for the study. The calculation model is shown in Fig. 5, where the core, shell, and TNT are labeled in blue, red, and green, respectively. Four gauge points are set, which are located at the axes of the explosive, aluminum edge, half radius, and core center.

Fig. 5.

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	Fig. 5. The diagram of simulation model.

The simulation model consists of TNT, aluminum, and alumina. The location of the detonation of the TNT is to the left of the surface. The relationship between pressure and the relative volume of the TNT product is as described by the Jones–Wilkins–Lee (JWL) state equation.^[32] The constitutive equations of aluminum are described by the Von Mises model^[33] and the constitutive equations of alumina are described by the Johnson–Holmquist (JH) model.^[34]

The detonation shock wave impacts the aluminum particle with a force of tens of GPa. The different mechanical properties of alumina and aluminum lead to different types of deformation: the alumina shell fails and fractures under the shock wave and the aluminum core experiences elastic-plastic deformation. Figure 6 shows the process of the detonation wave impacting on the particle.

Fig. 6.

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	Fig. 6. The pressure nephogram of aluminum particles in different times.

Figure 7 shows the particle deformation and failure process. By analyzing the breakage of the shell, the most serious shock wave attack angle is 45° with the top and back also being damaged.

Fig. 7.

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	Fig. 7. Deformation and failure process of aluminum and alumina shell.

Based on this simulation, the shell breakage times for different particle sizes are obtained, and the results are shown in Table 4.

Table 4.

Table 4.

Table 4. The breakage time of alumina shell for different particle sizes. . Particle size/ 2 10 30 90 Breakage time/ns 1.3 3.3 8.7 24.5

Table 4. The breakage time of alumina shell for different particle sizes. .

At the same particle size, the alumina shell breakage of the detonation wave impact is significantly less than t_mel caused by the thermal stress. Therefore, the rupture of the aluminum particle shell in the detonation environment is mainly caused by the impact of the detonation wave.

The velocity curves of four gauges are calculated, as shown in Fig. 8. The speed of the gauge points is extracted as 1488 m/s for gauge #1, 946 m/s for gauge #2, 975 m/s for gauge #3, and 927 m/s for gauge #4. Therefore, after the shell bursts, the detonation product moves faster than the aluminum and the edge speed is higher than the center; the outer aluminum will be peeled, which subsequently promotes core contact with the detonation product and burning.

Fig. 8.

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	Fig. 8. The velocity curves of gauges.

According to the detonation product and simulation results, the structure response of aluminum particle can be divided into three stages. In the first stage, the spherical particles are squeezed by the detonation wave, and the windward side shell cracks. During the second stage, the particle rebounds, the shell breaks and is peeled by the detonation product stripping with internal aluminum core stress, and the internal aluminum steam burns with the detonation products. For the third stage, the detonation product alumina cannot be attached to the surface of the core, so the aluminum keeps evaporating and burning with some product being attached to the container wall and some condensing into sub-micron particle clusters. The structural response of aluminum particle is shown in Fig. 9.

Fig. 9.

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	Fig. 9. The structural response diagram of aluminum particle in detonation environment.

The analysis of the aluminum particle product for detonation environments demonstrates that the aluminum particle burns in a gaseous state and condenses into a sub-micron particle cluster.

The rupture of the aluminum particle shell in the detonation environment is mainly caused by the impact of the detonation wave. The result shows that the detonation wave impacts on the aluminum particles, resulting in shell cracking and then, due to the shrinkage-expansion of the aluminum core and stripping of the detonation products, the cracked shell is fractured and peeled with the aluminum reacting with the detonation product.

The core–shell structure response of the aluminum particle in a detonation environment provides a foundation for studying the combustion behavior and revealing the burn mechanism of aluminum particles in such environments.