Introduction

Composite modified double base propellant (CMDB) has the advantages of high specific impulse, low characteristic signal and gas cleaning, and is currently used as one of the main power sources of various medium and small-caliber solid rocket motors1. For solid rocket motor, its service life largely depends on the storage performance of solid propellant. During the storage process, due to the influence of external loads, CMDB propellant has physical damage2 and chemical aging3, and its mechanical properties are constantly degraded. After a certain storage life is reached, the mechanical properties of solid propellant will no longer meet the service index, resulting in the structural integrity of propellant charge column at the moment of ignition, leading to various safety hazards4. Therefore, in order to avoid the economic loss caused by early retirement of solid rocket motor and the harm caused by overdue service, it is necessary to reveal the aging mechanism of CMDB propellants and study the mechanical response of CMDB propellants with different aging times under complex loads.

Stephens et al.5 used Fourier transform infrared spectroscopy (FTIR) technology to conduct an in-depth study on the composite propellant stored in the natural state for 8.5 years, and the results showed that FTIR was highly sensitive to the microstructure of the composite propellant binder matrix. By identifying the infrared peak corresponding to the macro properties, the dynamic relationship between the infrared spectrum and the maximum elongation of propellants was established, which provides a possibility for estimating the aging life of propellants. Du et al.6 studied the variation law of the maximum elongation and crosslinking density of HTPB propellant during the pre-strain and high-temperature accelerated aging process, established the corresponding relationship between the crosslinking density and the maximum elongation, and revealed the macro and micro aging mechanism of HTPB propellant during the aging process. Lei et al.7 studied the initiation and propagation of microscopic cracks in uniaxial tensile process of solid propellant based on DIC method, established a damaged constitutive model by introducing the concept of normalized crack length, and developed the model for the second time and applied it to finite element software to simulate the uniaxial tensile test process of propellant. Gu et al.8 used differential scanning calorimetry, bromate titration, impact resistance test and field emission scanning electron microscopy to characterize the chemical stability, mechanical properties and microstructure of the propellant samples during aging. The results showed that the decomposition of nitrate worsened the chemical stability of the propellant. The decline in impact resistance is the result of binder network breakdown, binder and plasticizer phase separation, and interface dehumidification during aging. Zhang et al.9 studied the relationship between macroscopic mechanical properties and meso-structure of GAP based solid propellant during aging. The results showed that the maximum tensile strength, maximum elongation and dewetting strain decreased with the decrease of meso-interface strength during aging. Li et al.10 studied the aging reaction process of double-base propellants based on SEM and X-ray spectroscopy, and established a kinetic model of medium fixed agent consumption, which can provide reference for predicting the aging process of other propellants with nitrate compounds as their main energetic components. Hou et al.11 systematically investigated the debonding, damage nucleation, and crack propagation behaviors of HMX-MDB propellant under complex loading conditions through microstructural-scale numerical simulation methods. The research focused on the mechanical response of the propellant’s internal microstructure, revealing the microscopic mechanisms of energetic material failure, which provides important theoretical value for the structural integrity assessment and lifetime prediction of propellants.

CMDB propellant is a typical composite solid propellant. By incorporating particulate fillers such as oxidizers into a double-base propellant to enhance its energy characteristics, CMDB propellant shares certain structural similarities with other composite solid propellants. Its mechanical properties are influenced by numerous factors including aging time, temperature, and strain rate12,13. Relevant scholars14,15 obtained the mechanism of the material’s tension and compression asymmetry through tensile and compression tests under different test conditions, and based on microscopic and microscopic observation and analysis. Wang et al.16 studied the tensile and compressive asymmetrical mechanical properties of CMDB propellant, and the research results are similar to HTPB propellant, and CMDB propellant is more likely to reach the mechanical limit characteristics in the tensile state. Therefore, the maximum elongation can conveniently reflect the tensile capacity of the propellant, because when the strain is greater than the maximum elongation, there is obvious “dewetting” inside the propellant, that is, there are obvious holes and wire drawing phenomena between the interface of the solid particles and the adhesive, so that the effective carrying area of the propellant decreases sharply and the tensile curve presents an unstable state.

In the study of tensile failure properties of propellants, environmental temperature’s impact on material performance is a primary focus, alongside the critical relationship between strain rate and tensile characteristics. The variation range of strain rate under the loading condition of solid rocket motor propellant column is very large, which can reach hundreds of millions of times. For example, the strain rate during curing and cooling is generally 10−7~10−8 s−117, and it can reach 0.1 ~ 1 s−1 during ignition and pressure construction18. The strain rate of the flight acceleration load is between the two19, and the storage and transportation process is basically a small fluctuation state at a certain strain level, and the strain rate is very small. Therefore, the effect of strain rate on tensile failure performance of propellant should be paid attention to in practical application.

In engineering practice, it is difficult to carry out tests under all conditions of the material and obtain its performance parameters. More often, the master curve is constructed through part of the tests combined with the equivalence principle, and then backdeduced, which can shorten the test cycle and test cost. At present, the master curve model of solid propellant has been studied more, and the master curve model of elongation considering aging effect is rarely reported. Liu et al.20,21 analyzed the aging mechanism of CMDB propellant by carrying out uniaxial tensile tests under different test conditions, combined with scanning electron microscopy and gas chromatography tests, and established a strength master curve model considering aging effect. Liu et al.22 carried out a quasi-biaxial tensile test of HTPB propellant under low temperature dynamic loading with different thermal aging times. Based on the test results, a master curve model of quasi-biaxial elongation and strength at low temperature and high strain rate was constructed. Wang et al.23 carried out uniaxial tensile tests of aging HTPB propellant under dynamic loading at low temperature, established a master curve model of elongation and strength combined with the aging dynamic model, and found that aging time, test temperature and strain rate have important effects on the mechanical properties of the propellant.

In summary, there were few researches on aging mechanical properties test and elongation master curve of CMDB propellant. In this paper, uniaxial tensile tests and SEM tests were carried out for thermal aging CMDB propellant to analyze the maximum elongation and section morphology changes during aging of CMDB propellant. Based on existing theories, the master curve of CMDB propellant elongation considering aging effect was studied, and the elongation master curve model considering aging effect was established. The maximum elongation of CMDB propellants under different aging time, temperature and strain rate was predicted, which provided guidance for the life prediction of CMDB propellants and the structural integrity analysis of solid propellant.

Materials and methods

Materials

The composite modified double base (CMDB) propellant in this paper was obtained from Shanxi Xing ‘an Chemical Industry Co. Ltd. Taiyuan, China. The propellant specimen was cut from a plate with dimensions of 120 mm × 25 mm × 10 mm according to P. R.C. GJB 770B-2005 test method of propellant, featuring a gauge length of 70 mm, as shown in Fig. 1. The main components and mass fraction of CMDB propellant: 18% of nitrocellulose (NC), 20% of nitroglycerine (NG), 56% of 1,3,5,7-tetranitro-1,3,5,7-tetrazocane (HMX) and 3,4-dinitrofurazanyl oxyfurazan (DNTF), 1% of N-methyl-4-nitroaniline (MNA), and 5% of other ingredients.

Fig. 1
figure 1

Dumbbell sample of the CMDB propellant.

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Thermal accelerated aging test

The thermal accelerated aging test temperature is usually selected according to the type of propellant and the test purpose. In order to ensure the effectiveness of the thermal accelerated aging test results, it is particularly important to select the accelerated aging test temperature and sampling time reasonably. Although the accelerated aging test period can be significantly shortened by increasing the test temperature, excessive increase of the accelerated aging test temperature may cause the chemical aging reaction of the propellant to be inconsistent with the reaction under natural aging condition, and may cause safety accidents. On the contrary, if the test temperature is too low, the aging test cycle will be too long, the test cost will be increased, and the purpose of accelerated test will not be met24,25. At the same time, the thermal accelerated aging test should be continued until the solid propellant performance parameters drop below the specified limit value.

Therefore, in order to ensure the effectiveness of the thermal accelerated aging test, the modified double base propellant was subjected to thermal accelerated aging test at 343.15 K and removed after different aging times (20, 35, 50, 65, 80 and 100 days). According to the previous research findings of our study team, thermal accelerated aging of CMDB propellants at 343.15 K for 20, 50, 80, and 100 days was approximately equivalent to ambient storage for 7.68 years, 10.15 years, 14.26 years, and 16.18 years, respectively26. This equivalence has been previously discussed and will not be reiterated here.

In order to eliminate the influence of external air and ambient humidity change on thermal accelerated aging test, CMDB propellant was sealed with aluminum foil sealed bag and placed in aging oven for high temperature accelerated aging test. Figure 2 shows the physical diagram of the sealing package of aging oven and CMDB propellant specimen.

Fig. 2
figure 2

Aging oven and CMDB propellant specimen sealing package diagram.

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Uniaxial tensile test

In order to obtain the maximum elongation of CMDB propellant specimens under different aging times, uniaxial tensile test was carried out by QJ211B-20KN universal tensile machine (Test speed: 0.001 mm/min ~ 500 mm/min). Before the test, the specimen was kept at the test temperature for 2 h. The test temperatures are 233.15 K, 253.15 K, 273.15 K, 293.15 K and 323.15 K. Based on the test speed range of the testing machine, referring to the previous research results in the selection of strain rate27, considering that this study mainly studies the quasi-static tensile mechanical properties of the propellant, and at the same time to save test time, Therefore, 3.3 × 10−4 s−1, 3.3 × 10−3 s−1 and 3.3 × 10−2s−1 were selected as the uniaxial tensile strain rates. The test was repeated five times in each group. The test data are analyzed using Grubbs’ test to identify and remove outliers, and the mean value was subsequently calculated for the remaining valid data.

SEM analysis

To examine the meso-morphology of the tensile fracture surface of CMDB propellant after aging, a scanning electron microscope (SEM) SU3500 was employed to conduct SEM analyses. The SEM images of the tensile fracture surface of CMDB propellant at various aging times are acquired. The operating conditions of the SEM are as follows: high vacuum mode, tungsten filament emission, acceleration voltage of 15 kV, working distance of 10 mm, and magnification of 500 times.

Results and discussion

Variation of maximum elongation of CMDB propellant

To determine the variation of maximum elongation of CMDB propellant during aging, uniaxial tensile tests are conducted on CMDB samples with varying aging times using a QJ211B-20KN universal tensile machine. The resulting stress-strain curves, illustrated in Fig. 3, reveal that the peak stress indicates the material’s maximum tensile strength under specific conditions, while the corresponding strain value represents the maximum elongation of the propellant under those conditions.

Fig. 3
figure 3

Uniaxial tensile stress-strain curve and maximum elongation.

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After thermal accelerated aging of CMDB propellant at 343.15 K, the maximum elongation εm varies with aging time ta under different test conditions, as shown in Fig. 4(a)-(c). It can be seen from Fig. 4(a)-(c) that aging time has a significant impact on the maximum elongation of the propellant, and there is a monotonically decreasing relationship between the maximum elongation and aging time, so the maximum elongation is suitable for describing the aging degree of CMDB propellant.

Fig. 4
figure 4

Curves of maximum elongation of aging CMDB propellants under different test conditions.

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The maximum elongation of CMDB propellant under thermal accelerated aging at different temperatures varies with the strain rate, as shown in Fig. 5. According to Fig. 5, under the same aging time, when the temperature is low (233.15 K, 253.15 K and 273.15 K), the maximum elongation decreases with the increase of the strain rate. When the temperature is higher (293.15 K and 323.15 K), the maximum elongation increases with the increase of strain rate.

CMDB propellant is a polymer material based on NG and NC, with a large amount of HMX particles added, and its mechanical properties are greatly affected by temperature. With the change of temperature, CMDB propellant exhibits three physical states: glassy state, viscoelastic state and rubber state. CMDB propellants exhibit hard and brittle mechanical properties at low temperature, which is called glassy state. With the increase of temperature, the propellant material enters the glass transition zone. In this temperature range, the modulus changes obviously with temperature, and the material shows a certain deformation ability. This stage is called viscoelastic state. As the temperature continues to rise, the material enters the rubber state, the temperature rises, and the modulus reaches a certain value28. The glass transition temperature of CMDB propellant is relatively high. The CMDB propellant used in this paper is a viscoelastic material at 293.15 K and 323.15 K, and is approximately a brittle material below 273.15 K. This phenomenon is basically consistent with the research results of related scholars23. The British Marine Naval Technical Agency also pointed out that in the range of 0–50 °C, CMDB propellants have visco-brittleness transition29, which is also an important cause of low-temperature launch accidents of solid motor.

Fig. 5
figure 5

Curves of maximum elongation versus strain rate of aged CMDB propellants under different test temperature.

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Aging mechanism analysis

Under uniaxial tensile loading, CMDB propellant exhibits progressive intensification of stress concentration at particle-matrix interfaces with increasing tensile stress. This mechanical response leads to the development of interfacial voids (dewetting phenomenon) as the interfacial bonding deteriorates under sustained deformation30. With the increase of the load, some particles/matrix interface reaches the critical load, and micro-cracks form between particles and matrix, which further affects the stress distribution. Under tensile load, the crack tip will form a stress concentration zone, which will accelerate the failure of the matrix and the dehumidification rate of the particles. In addition, with the increase of strain, the particle dehumidification phenomenon increases, and the microcracks further expand, and eventually lead to the fracture failure of CMDB propellant31. Therefore, the damage state of CMDB propellant at the mesoscopic level, including particle/matrix interface properties, particle dehumidification, pores and micro-cracks, will directly affect the macroscopic mechanical properties of CMDB propellant.

In this paper, SU3500 cold field emission scanning electron microscope was used to study the tensile section morphology of CMDB propellant at different aging time and accelerated aging temperature of 343.15 K. Figure 6 shows the SEM results of the tensile section of CMDB propellants with different aging times at the test temperature of 298.15 K and strain rate of 3.3 × 10−2 s−1. It can be seen from Fig. 6 (a) ~ (d) that with the extension of aging time, the microscopic damage in the propellant cross-section gradually intensifies. It can be seen from Fig. 6 (a) that the particle distribution in the section of the unaged propellant is clear, a large number of bare solid fillers appear, and no obvious micro-cracks and micro-pores are found at the fracture. It can be seen from Fig. 6 (b) that, compared with the SEM results of the cross-section of non-aged propellants, the interface between particles and matrix in the cross-section of the propellants at the age of 20 days is more blurred, with obvious particle dehumidification phenomenon accompanied by micro-cracks. As can be seen from Fig. 6 (c), when the propellant is aged for 50 days, the particle dehumidification phenomenon in the propellant cross section is more serious, and there are many micro-cracks. As can be seen from Fig. 6 (d), when aging for 100 days, the microscopic damage in the propellant cross section is further aggravated, and the particles are dehumidified and micro-pores are formed. From the above SEM results and existing research conclusions, it can be seen that with the aging process, the CMDB propellant matrix (NC and NG) undergoes slow decomposition, resulting in the formation of pores between the particles and the matrix21. This gradually reduces the bonding performance at the interface between the matrix and the particles, intensifies the dehumidification of the particles, and at the same time, the decomposition and consumption of the matrix components will lead to the formation of pores inside the matrix, which gradually expand into microcracks with the extension of aging time. And eventually expand to form micro-pores. Considering that under the action of external tensile loads, stress concentration will occur at the internal damage points of the propellant, resulting in a decrease in the carrying capacity of the propellant, the changes in the mesoscopic structure of the propellant during the aging process will lead to the deterioration of its macroscopic mechanical properties. The mesoscopic damage mechanism of aging is applicable to explain the variation law of the maximum elongation of the propellant with aging time as shown in Fig. 4.

Fig. 6
figure 6

SEM images of tensile fracture of CMDB propellant under different aging time.

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Figures 7 and 8 show the SEM results of CMDB propellant tensile section at strain rate of 3.3 × 10−2 s−1 and test temperature of 323.15 K and 233.15 K without aging and 100 days after aging, respectively. By comparing the SEM results of CMDB propellant tensile section at the test temperature of 323.15 K, 298.15 K and 233.15 K, it can be seen that when the test temperature is 323.15 K, there is no significant difference between the SEM results of the tensile section of the unaged propellant and that of the test temperature of 298.15 K, As shown in Fig. 7(a). During the aging period of 100 days, there are many pits in the cross section of CMDB propellant formed by dewetting, and the dewetting phenomenon between matrix and particles is more serious, as shown in Fig. 7(b). When the test temperature is 233.15 K, the SEM results of the tensile section of the unaged propellant are compared with those of 298.15 K. Microscopic damage of CMDB propellant during 100 days of aging includes not only dewetting, micro-cracks and micro-viods, but also particle breakage, and matrix micro-cracks extend along the particle breakage region, as shown in Fig. 8(b).

Fig. 7
figure 7

SEM image of tensile section at test temperature 323.15 K.

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Fig. 8
figure 8

SEM image of tensile section at test temperature 233.15 K.

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According to the above SEM results and existing research conclusions, when the tensile test temperature is higher (323.15 K), the propellant is softer, the modulus is lower, the particle/matrix interface bonding property is lower, and the internal mesoscopic damage mode of the propellant is mainly dewetting. With the decrease of tensile test temperature, the propellant is harder, the modulus is higher, the particle/matrix interface bonding performance is higher, and the particle breakage is caused by the increase of tensile stress. Therefore, as the tensile test temperature decreases, the maximum propellant elongation gradually decreases, as shown in Fig. 5.

Figure 9 shows the SEM results of CMDB propellant tensile section at strain rate 3.3 × 10−4 s−1 and temperature 323.15 K and 233.15 K after aging for 100 days. By comparing Fig. 7 (b) and Fig. 9 (a), it can be found that the dehumidification phenomenon of CMDB propellant at a strain rate of 3.3 × 10−4 s−1 at a temperature of 323.15 K is more serious than that at a strain rate of 3.3 × 10−2 s−1, and a large number of dehumidification pits exist in the section. When the temperature is high, due to the soft propellant and low modulus, at the strain rate of 3.3 × 10−4 s−1, the micro-cracks generated during tensile loading have enough time to expand to the interface between particles and matrix, and the propellant dehumidification is more serious. Therefore, at the temperature of 323.15 K, the maximum elongation of CMDB propellant increases with the increase of strain rate, as shown in Fig. 5. By comparing Fig. 8 (b) and Fig. 9 (b), it can be found that at 233.15 K, when the strain rate is 3.3 × 10−4 s−1, the particle breakage phenomenon in the CMDB propellant tensile section is slightly reduced than that at the strain rate 3.3 × 10−2 s−1, and the damage phenomenon in the section is less. When the temperature is low, the stress wave of tensile load increases with the increase of strain rate, and the incidence of particle breakage increases32,33. Therefore, the maximum elongation of CMDB propellant at 233.15 K decreases with the increase of strain rate, as shown in Fig. 5.

Fig. 9
figure 9

SEM image of tensile section at strain rate 3.3 × 10−4 s−1.

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Maximum elongation master curve model considering aging effect

Research demonstrates that temperature and time exhibit equivalent effects on the mechanical behavior of most viscoelastic materials. The property evolution curves of these materials under different constant temperatures display remarkable similarity. By applying horizontal shifts along the logarithmic time scale, these temperature-dependent curves can be superimposed to form a master curve. Materials exhibiting this characteristic are classified as thermorheologically simple materials.

This phenomenon arises from temperature-dependent variations in molecular thermal motion energy. Elevated temperatures enhance molecular mobility, accelerating relaxation processes and effectively compressing the timescale of material response. Conversely, reduced temperatures suppress molecular motion, prolonging the characteristic response time. Consequently, altering the temperature scale produces equivalent effects to modifying the time scale in viscoelastic material analysis – a fundamental concept known as the time-temperature equivalence principle34.

As mentioned above, under different aging times, the maximum elongation εm changes significantly with the changes of temperature and strain rate, which basically conforms to the hypothesis of simple heat flow variable materials and satisfies the time-temperature equivalent principle. Thus, the maximum elongation at different temperatures and strain rates can be plotted as a master curve. Before this, the equivalence of time-temperature equivalence principle and strain rate-temperature equivalence principle are explained. Taking the WLF model as an example, the temperature shift factor \(\:\text{l}\text{g}\left({a}_{T}\right)\) can be expressed as:

$$\lg \left( {{a_T}} \right) = \lg (\frac{t}{{{t_{ref}}}}) = - \frac{{{C_1}(T - {T_{ref}})}}{{{C_2} + (T - {T_{ref}})}}$$
(1)

where C1 and C2 are material parameters; t and tref are the time required to obtain the same propellant mechanical property parameters at test temperature T and reference test temperature Tref, respectively. When propellant is loaded at a certain test temperature and strain rate, the relationship between the strain rate \(\:\dot{\epsilon\:}\) at the test temperature and the strain rate \(\:{\dot{\epsilon\:}}_{ref}\) at the reference test temperature can be obtained as:

$$\dot \varepsilon = {\rm{d}}\varepsilon /{\rm{d}}t = {\rm{d}}\varepsilon /{\rm{d}}\left( {{t_{ref}} \cdot {a_T}} \right) = \left( {1/{a_T}} \right){\rm{d}}\varepsilon /{\rm{d}}{t_{ref}} = \left( {1/{a_T}} \right){\dot \varepsilon _{ref}}$$
(2)

By arranging Eq. (2), we can get Eq. (3) as:

$$\lg \left( {{a_T}} \right) = \lg (\frac{{\dot \varepsilon }}{{{{\dot \varepsilon }_{ref}}}}) = - \frac{{{C_1}(T - {T_{ref}})}}{{{C_2} + (T - {T_{ref}})}}$$
(3)

It can be seen that the time-temperature equivalence principle and the strain rate-temperature equivalence principle are essentially the same. According to Eq. (3), the maximum elongation master curve at the reference test temperature can be constructed by shifting the maximum elongation curves obtained at different test temperatures along the logarithmic strain rate axis until overlapping with the reference curve, where the translation distance is the temperature shift factor \(\:\text{l}\text{g}\left({a}_{T}\right)\) of the propellant at the current test temperature.

Temperature shift factors \(\:\text{l}\text{g}\left({a}_{T}\right)\) of the elongation master curve under different aging time are recorded respectively, as shown in Fig. 10. It can be seen that the temperature shift factors \(\:\text{l}\text{g}\left({a}_{T}\right)\) of propellants under different aging times show a nonlinear decreasing relationship with temperature, basically meeting the change form of WLF model, and aging time has little influence on the temperature shift factors of propellants. Therefore, the WLF model (Eq. (3)) is used in this paper to fit the temperature shift factor, thereby determining the parameters C1 and C2 of the WLF model. It can be seen that the fitting effect of the WLF model is good, and it can accurately describe the nonlinear relationship between the temperature shift factor and the temperature of the propellant under different aging time, and the same fitting curve of the WLF model can describe the relationship between the temperature shift factor and the temperature of the propellant under different aging time.

Fig. 10
figure 10

Temperature Shift Factor Fitting Results for Maximum Elongation Master Curves Across Aging Times.

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According to the strain rate-temperature equivalent principle, the maximum elongation curve of CMDB propellant under different aging time after translation and superposition is obtained with 298.15 K as the reference temperature Tref. Where the relationship between the maximum elongation εm and the reduced strain rate \(\:\text{l}\text{g}(\dot{\epsilon\:}\cdot{a}_{T})\) can be expressed as23:

$${\varepsilon _m} = {A_1} + {A_2}\exp \left\{ { - 2 \times {{\left[ {{A_3}\lg ({a_T} \cdot \dot \varepsilon ) + {A_4}} \right]}^2}} \right\}$$
(4)

where A1, A2, A3 and A4 are the optimal fitting parameters. Using Eq. (4), the master curves of maximum elongation for the propellant under different aging times are fitted, as shown in Fig. 11. The results indicate that Eq. (4) effectively describes the low-temperature region (T ≤ 273.15 K) of the master curves, with fitting errors less than 5% compared to experimental data. For the ambient temperature region, the fitting performance is moderate, with some fitted values exceeding experimental results and errors ranging from 5 to 16% across aging times. In the high-temperature region, the fitting quality deteriorates significantly, with certain fitted curves underestimating experimental data and errors between 10% and 22% under varying aging conditions.

Additionally, since Eq. (4) does not account for the influence of aging on the maximum elongation, parameters need to be individually fitted for each specific aging time’s master curve. This limitation hinders the characterization of the propellant’s maximum elongation during the aging process and imposes an additional workload on researchers due to the necessity of repeated model fitting.

Fig. 11
figure 11

Elongation master curve of propellant with different aging time.

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It can be seen from Fig. 11 that under different aging times, the elongation master curve of propellant has the same trend, showing a trend of first rising and then decreasing, and the aging time only affects the value of the master curve. Therefore, considering the characteristic that aging time only affects the value of the master curve, based on Eq. (4), the aging influence factor \(\:q\left({t}_{a}\right)\) is introduced to establish the elongation master curve model considering the aging effect. The specific form is as follows:

$${\varepsilon _m} = q\left( {{t_a}} \right) \cdot ({A_5} + {A_6}\exp ( - 2 \times {({A_7}\log ({a_T} \cdot \dot \varepsilon ) + {A_8})^2}))$$
(5)

Considering that aging time only affects the value of the master curve, it is assumed that the aging influence factor \(\:\text{q}\left({t}_{a}\right)\) for the unaged propellant is q(0) = 1. Equation (5) is applied to fit the elongation master curve of the unaged propellant in Fig. 11(a), and the parameters A5, A6, A7 and A8 are obtained as listed in Table 1.

Table 1 Fitting parameters of the elongation master curve of unaged propellant.
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Based on the aforementioned fitting results, the parameter values listed in Table 1 are substituted into Eq. (5) to fit the maximum elongation master curves of the propellant under different aging durations. This process revealed the variation of the aging influence factor with aging time, as illustrated in Fig. 12. To accurately describe the relationship between the aging influence factor and aging time, Eq. (6) is employed for fitting, obtaining the fitting parameters q1, q2and ta1. The fitting results are shown in Fig. 12.

$$q({t_a}) = {q_1} + {q_2}\exp ( - \frac{{{t_a}}}{{{t_{a1}}}})$$
(6)

where q1, q2 and ta1 are constants. The fitting flowchart for the master curve model of maximum elongation considering aging effects is shown in Fig. 13.

Fig. 12
figure 12

The fitting results of aging influence factor \(\:\text{q}\left({t}_{a}\right)\).

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Fig. 13
figure 13

Master Curve Fitting Flowchart​.

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In order to verify the accuracy of the elongation master curve model considering aging effect, the master curve model shown in Eq. (5) is used to predict the elongation master curve of propellant under different aging time respectively, and the predicted results are compared with the elongation master curve that fitted one by one by Eq. (4), as shown in Fig. 14. It can be seen that the prediction results calculated by Eq. (5) have a high coincidence degree with the fitting results obtained by using Eq. (4). Therefore, the elongation master curve model considering aging effect shown in Eq. (5) can better describe the elongation master curve of the CMDB propellant under thermal acceleration aging at 343.15 K for 0 days to 100 days (which is equivalent to storage at room temperature for 0 years to 16.18 years), and can reasonably predict the maximum elongation of the propellant within the temperature range of 233.15 K to 323.15 K and the strain rate range of 10−4 s−1 to 104 s−1.

Fig. 14
figure 14

Comparison of elongation master curve prediction results under different aging time.

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Conclusions

In this paper, the thermal accelerated aging test of CMDB propellant was carried out to obtain the change law of the maximum elongation of CMDB propellant during the thermal accelerated aging process. The change of the microscopic damage of the propellant during the accelerated aging process is analyzed through SEM test, and the aging characteristics and aging mechanism of CMDB propellant are explored and analyzed. The elongation master curve model considering aging effect is established. The main conclusions are as follows:

(1) The effects of aging time, test temperature and strain rate on the maximum elongation of CMDB propellant during thermal accelerated aging are analyzed. Aging time, strain rate and temperature have significant effects on the maximum elongation. Under different test temperatures and strain rates, the maximum elongation decreases with the aging time. Under the same aging time, the maximum elongation increases with the increase of strain rate when the test temperature is 323.15 K and 298.15 K, and decreases with the increase of strain rate when the test temperature is 273.15 K, 253.15 K and 233.15 K.

(2) In the aging process, the microscopic damage phenomenon inside the propellant is increasing, which leads to the deterioration of the macroscopic mechanical properties. With the extension of aging time, the bonding property between the propellant matrix and the particles gradually decreases, the particle dehumidification phenomenon is intensified, and micro-cracks appear in the matrix, and micro-holes are formed in the particle dehumidification area in the late aging period, which results in the maximum elongation and initial damage strain decreasing with the extension of aging time. At the same aging time, temperature and strain rate mainly affect the failure mode of propellant. When the tensile temperature is 323.15 K, the main failure mode of propellant is particle dehumidification. With the increase of strain rate, particle dehumidification becomes more and more serious. When the tensile temperature is 233.15 K, the failure mode of the propellant changes to dehumidification as the leading factor, accompanied by particle breakage. The particle breakage phenomenon increases with the increase of strain rate.

(3) Based on the maximum elongation test results of propellants under different conditions and the strain rate-temperature equivalence principle, the elongation master curves of propellants under different aging durations are established. By introducing an aging influence factor into the existing elongation master curve model, a modified elongation master curve model incorporating aging effects is proposed. The validity of this model is verified through comparison with individually fitted elongation master curves. Results demonstrate that the model can reasonably predict the maximum elongation of propellants under different aging durations, temperatures, and strain rate conditions.