Shelf-life prediction and correlation between maximum elongation and stabilizer depletion of CMDB propellant

Shelf-life prediction and correlation between maximum elongation and stabilizer depletion of CMDB propellant | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Shelf-life prediction and correlation between maximum elongation and stabilizer depletion of CMDB propellant Jia-ming Liu, Zong-tao Guo, Jian Zheng, Xiong Chen, Jin-sheng Xu This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-3126969/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 06 Sep, 2023 Read the published version in Mechanics of Time-Dependent Materials → Version 1 posted 7 You are reading this latest preprint version Abstract In order to predict the storage life of composite modified double base propellant (CMDB propellant) at 298.15K, the correlation between the maximum elongation and the stabilizer depletion of CMDB propellant was studied. The thermal accelerated aging tests were carried out at 323.15K, 333.15K, 343.15K and 353.15K. The changes of MNA content and maximum elongation at different thermal aging temperatures were analyzed and a modified exponential aging model for CMDB propellant was proposed. With MNA content and maximum elongation as aging characteristics, the storage life of CMDB propellants at 298.15K was predicted using the modified Arrhenius equation. The aging mechanism of CMDB propellant was analyzed and the correlation function model of maximum elongation and stabilizer depletion was established. The results show that the maximum elongation and MNA content decrease with aging time and aging temperature increasing. The fitting correlation coefficients of modified exponential aging model are all greater than 0.97, which can better describe the changes of MNA content and maximum elongation of CMDB propellant. The storage life of CMDB at 298.15K is estimated to be 19.19 years and 18.09 years, respectively. The validity of the correlation function between the maximum elongation and the stabilizer depletion is verified. The overall error is less than 15%, which provides a reference for predicting the maximum elongation of CMDB propellant by the consumption of MNA. CMDB propellant Maximum elongation MNA content Correlation Aging model Shelf-life prediction Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 1. Introduction Composite modified double base (CMDB) propellants have been widely used in modern military and aerospace fields because of their high energy, high strength and low characteristic signal (Zhang et al., 2022 , Zhang et al., 2022 ). Due to aging of CMDB propellant during storage, its properties deteriorate with the increase of storage time, which affects the storage life of CMDB propellant (Liu et al., 2022 ). After reaching the critical life span, there will be great safety risks to continue service (Yildinm and Oezupek, 2011 , Bin et al., 2015 ). However, premature disposal will cause unnecessary economic losses and waste of resources. Therefore, it is of great significance to accurately predict the storage life of CMDB propellant for the storage and use safety of solid rocket motor. Due to the advantages of thermal accelerated aging method such as short test cycle, low test cost, high test efficiency and life evaluation in advance (Wang and Qiang, 2021 ), the thermal accelerated aging method is often used in the research of solid propellant aging to obtain propellant properties under different aging times and establish aging models (Du et al. , 2020, Wang et al., 2020 ). The Arrhenius equation or Berthelot equation was used to predict the storage life of propellant at the actual storage temperature (Pan et al. , 2021). The Berthelot equation describes the relationship between storage life and storage temperature. The storage life of propellant can be predicted in actual storage condition only by measuring the critical life at each thermal aging temperature (Sammour, 1994 , Liu et al., 2016 ). However, Berthelot equation cannot be used to describe the tendency of propellant properties with aging time (Himanshu, 2011 ). The Arrhenius equation needs to obtain the aging rate constant through aging model, establish the relationship between aging rate and aging temperature, and then predict the aging rate of propellant under actual storage condition, which can be used to describe the tendency of propellant performance with aging time (Sadasivan and Bhaumik, 1984 ). Since the Arrhenius equation assumes that the preexponential factor and activation energy are constant, the influence of temperature on the pre-exponential factor and activation energy is ignored, leading to large errors in the life prediction results (Laidler et al. , 1996). Therefore, to ensure the accuracy of life prediction, the Arrhenius equation needs to be modified. CMDB propellant combines the advantages of double base propellant (DBP) and composite propellant (CSP), adding oxidizer, high energy explosive and metal powder into nitrocotton/nitroglycerin (NC/NG) matrix to obtain higher energy and excellent mechanical properties (Han et al., 2017 ). However, the nitrate bond of nitrate compounds is prone to oxidative fracture, causing decomposition reaction, releasing nitrogen oxides and heat, and the released nitrogen oxides will accelerate the decomposition of nitrate compounds, forming an autocatalytic reaction (Liqiong et al., 2019 ). Therefore, 1 ~ 5% stabilizer is added to CMDB propellant to absorb nitrogen oxides and inhibit or delay the autocatalytic reaction of nitrate ester (Elbasuney et al., 2019 ). Manfred et al. (Bohn and Volk, 1992 , Bohn, 2010 , Manfred, 2009 ) conducted thermal aging at 50 ℃~90 ℃ for four DB propellants, determined the stabilizer depletion in the aging process by HPLC, established the stabilizer depletion equation, greatly improved the life prediction of propellant, and revealed the aging mechanism of DB propellant. The experimental results show that the stabilizer reacts with nitrogen oxides and is consumed during storage of DB propellant. Zhao et al. ( 2006 ) conducted thermal aging of various DB propellants at 65 ℃~95 ℃, and measured the stabilizer content of the propellants at different aging times. The experimental results showed that NG content and stabilizer content in the propellant were the main factors affecting the storage life of the propellant, and the more stabilizer content remained, the longer the safe storage life of the propellant. Li et al. ( 2021 ) tested the storage properties of DB propellants under different aging times by means of scanning electron microscopy and infrared spectrum analysis. Based on the aging theoretical model and the Arrhenius equation, a kinetic model of stabilizer depletion was established, which provided a theoretical basis for predicting the storage life of propellants by stabilizer content. Therefore, based on the above research results, the stabilizer content in propellant can be used as the aging characteristic to predict the storage life of propellant. In addition, due to the effects of chemical aging and physical damage, the maximum elongation of propellant decreases with the aging time. Zhou et al. (2016) conducted thermal aging experiments on HTPB propellants under different constant strains, and established aging models with maximum elongation as aging characteristics to predict the life of HTPB propellants. The study proved the feasibility of using maximum elongation as aging characteristics to predict the storage life of propellants. The macro mechanical properties of propellants are closely related to the micro structure, and the change of micro structure will directly affect the macro mechanical properties of propellants (such as strength, elongation and modulus) (Liu et al., 2022 , Du et al., 2021 ). Sekkar et al. (2015) studied the cross-linking density of HTPB propellants composed of different binders and found that there was a strong linear relationship between the cross-linking density and macroscopic mechanical properties (maximum elongation and Young's modulus). The storage properties of propellants could be predicted by testing the cross-linking density of propellants. Li et al. ( 2019 ) tested the crosslinking density and maximum elongation of HTPB coating through the thermal aging test, and established the corresponding relationship between the maximum elongation and the crosslinking density. The predicted results obtained by using the corresponding relationship were in good agreement with the predicted results of the maximum elongation. Du et al. ( 2021 ) carried out prestrain thermal aging test on HTPB coating, analyzed the variation of crosslinking density, established the relationship model between maximum elongation and crosslinking density, and realized the transformation of failure criterion between maximum elongation and crosslinking density, which can be used to evaluate the storage properties of propellant. Choi et al. (2000; 2001) found through research that a large number of samples are needed to obtain the change trend of macroscopic mechanical properties of materials in the aging process, and the test error is relatively large. However, the sample size for testing crosslinking density is less than 1cm×1cm, and the test error is relatively small. The relative error of aging test can be greatly reduced by testing the change of crosslinking density. Due to different bond systems, CMDB propellant and HTPB propellant have essential differences in aging characteristics, but they are similar in aging mechanism, because the change of microstructure is one of the main factors affecting the change of macro mechanical properties (Yang et al., 2016 , Yang et al., 2016 ). At present, most of the research on the storage life prediction of CMDB propellant focuses on the change of component content of CMDB propellant, and there are few studies on the change of macro mechanical properties, and the correlation between stabilizer depletion and macro mechanical properties is rarely reported. Therefore, it is necessary to study the correlation between stabilizer depletion and macro mechanical properties, establish the relationship between macro mechanical properties and stabilizer depletion, and directly predict the macro mechanical properties of propellants by stabilizer depletion, which can overcome the problems such as tedious testing process and large sample consumption, and provide theoretical support for the life prediction of CMDB propellants. Thermal accelerated aging tests of CMDB propellant were carried out at 323.15 K, 333.15 K, 343.15 K and 353.15 K, and the changes of maximum elongation and MNA content of CMDB propellant were analyzed. A modified exponential aging model was established. Based on the modified Arrhenius equation, the aging life of CMDB propellants was predicted by taking the maximum elongation and MNA content as aging characteristics, respectively. The aging mechanism of CMDB propellant was analyzed, and the correlation between maximum elongation and MNA depletion was established, and the validity of the correlation was verified. 2. Materials and methods 2.1. Materials The composite modified double base (CMDB) propellant in this paper was obtained from Shanxi Xing 'an Chemical Industry Co. Ltd. Taiyuan, China. In order to facilitate the experimental test, the standard dumbbell type propellant sample is selected, with the dimension of 120 mm × 25 mm ×10 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. 2.2. Accelerated aging test The thermal accelerated aging test of CMDB propellant was conducted in an electric oil bath incubator. The experimental temperature of thermal accelerated aging was set as 323.15 K, 333.15 K, 343.15 K and 353.15 K. At the same time, in order to ensure that the humidity change range was less than 10% during the aging process, the test samples were placed in an aluminum foil sealed bags for sealing. The relevant research shows that the sampling interval should be short when the thermal aging temperature is high, and long when the thermal aging temperature is low (Pan and Liu, 2021 , Du et al., 2021 ). Therefore, the thermal aging temperature and sampling time are shown in Table 1 . After aging, the aged samples were placed in a dryer and cooled down naturally to room temperature for 24 hours before corresponding tests were conducted. Table 1 Sampling time of thermal accelerated aging test Temperature / K Sampling time / d 323.15 50 100 150 200 250 300 360 333.15 20 45 70 95 120 145 180 343.15 10 20 35 50 65 80 100 353.15 3 6 12 19 27 35 - 2.3. Uniaxial tensile test Uniaxial tensile test was carried out on CMDB propellant dumbbell-shaped samples by uniaxial tensile testing machine to test the maximum elongation. The experimental temperature was controlled at 298.15 ± 1 K, and the tensile rate was chosen to be 100 mm/min until the specimen was completely fractured. Uniaxial tensile tests were carried out on 5 to 8 repeated samples for each aging condition (temperature, time), and the average value of maximum elongation was obtained. 2.4. Determination of MNA In this study, Agilent technologies 7890A gas chromatograph was used to determine the mass fraction of MNA in CMDB propellant samples at different aging time. The sample was extracted with diethyl ether, and the nitrate, stabilizer and plasticizer in the extract were separated in the chromatograph. High purity MNA was used as internal standard, and the content of MNA was calculated by internal standard method. Three parallel measurements were made for each sample, and the average of the experimental results was taken to ensure the accuracy of the test results. The mass fraction of MNA in samples with internal standard method was calculated by the following equation: $$w=\frac{{{m_s}H{f_s}}}{{m{H_s}}} \times 100\%$$ 1 Where w is the mass fraction of MNA in CMDB propellant sample, %; m is the mass of CMDB propellant sample, g; m s is the mass of internal standard, g; H is the peak height of MNA in CMDB propellant sample, mm; H s is the peak height of internal standard, mm; f s is the correction factor corresponding to MNA in CMDB propellant sample and internal standard, and its calculation equation is as follows: $${f_s}=\frac{{{m_{MNA}}{H_s}}}{{{m_s}H}}$$ 2 Where m MNA is the mass of MNA in CMDB propellant sample, g. 2.5. SEM analysis In order to observe the meso-morphology of the tensile fracture surface of CMDB propellant after aging, scanning electron microscope (SEM) SU3500 was used to carry out SEM experiments, and the SEM images of the tensile fracture surface of CMDB propellant under different aging time were obtained. Working conditions of scanning electron microscope are as follows: high vacuum mode, tungsten thermistor emission, acceleration voltage of 15kV, working distance of 10 mm, magnification of 500 times. 3. Results and discussion 3.1. Establishment of aging model Generally, the aging properties of materials are described by the Layton equations, including linear, exponential and logarithmic models (Layton, 1975 ): $$P={P_0}+K{t_a}$$ 3 $$P={P_0}\exp ( - K{t_a})$$ 4 $$P={P_0}+K\log {t_a}$$ 5 where P is the property of materials at aging time t a ; P 0 is constant; K is the rate constant of the aging reaction, which is related to the thermal aging temperature; t a is the aging time, d. However, the fitting results of the three aging models of the Layton equation are not accurate for the aging properties, which leads to large deviations in the prediction results. Therefore, this paper optimizes and improves based on the exponential model, and proposes a modified exponential aging model as follows: $$\begin{gathered} P={P_{01}}\exp ( - K{t_a})+{P_{02}} \hfill \\ {P_0}={P_{01}}+{P_{02}} \hfill \\ \end{gathered}$$ 6 Where P is the property of materials at aging time t a ; P 0 is unaged material parameters; P 01 and P 02 are constants independent of thermal aging temperature; K is the rate constant of the aging reaction, which is related to the thermal aging temperature; t a is the aging time, d. 3.2. Modification of Arrhenius equation The study of chemical reaction kinetics began in the late 19th century, and the Arrhenius equation was widely used to predict the storage life of materials (Pan and Liu, 2021 ). Previous studies (Li et al., 2021 ) have shown that the aging reaction rate K follows the Arrhenius equation: $$\ln K=\ln A - \frac{{{E_a}}}{{RT}}$$ 7 Where K is the reaction rate constant, d − 1 ; A is the pre-exponential factor, d − 1 ; E a is the activation energy of reaction, J/mol; T is the absolute temperature, K; R is the universal gas constant, 8.314 J/(mol⋅K). In general, the preexponential factor and activation energy are assumed to be constants independent of the storage temperature, but this assumption is only applicable to a small temperature range, and the prediction accuracy is poor when the extrapolation temperature range is large (Yang et al., 2021 ). Therefore, in order to ensure the accuracy of storage life prediction, it is necessary to modify the Arrhenius equation. Laidler ( 1996 ) established the modified Arrhenius equation on the basis of the Arrhenius equation, and proposed that the preexponential factor was a temperature-dependent function, expressed as: $$\ln K=\ln \left( {A{T^m}} \right) - \frac{{{E_a}}}{{RT}}$$ 8 where ( A T m ) is the temperature dependent pre-exponential factor, A and m are constants. Based on the modified Arrhenius equation, Li et al. ( 2019 ) obtained the modified expression of activation energy through derivation and proved that there is a linear relationship between activation energy E a and temperature T as follows: $${E_a}=E+nRT$$ 9 Where E a is the activation energy of reaction, J/mol; E and n are constants. The modified Arrhenius equation is established by substituting Eq. ( 9 ) into Eq. ( 8 ) as shown in Eq. ( 10 ), in which the pre-exponential factor and activation energy are considered to be related to temperature. $$\ln K=\ln A{\text{+}}m\ln T - \frac{{E+nRT}}{{RT}}$$ 10 Where K is the reaction rate constant, d − 1 ; A , m , n and E are constants; T is the absolute temperature, K; R is the universal gas constant, 8.314 J/(mol⋅K). 3.3. Shelf-life prediction 3.3.1. Shelf-life prediction based on MNA content The change curve of MNA content of CMDB propellant at different thermal aging temperatures (323.15 K, 333.15 K, 343.15 K and 353.15 K) is shown in Fig. 2 . It can be seen from Fig. 2 that the content of MNA as a stabilizer in CMDB propellant decreases with the increase of aging time, which is due to the reaction of MNA with the aging decomposition products of CMDB propellant (Elbasuney et al., 2018 ). At different thermal aging temperatures, the decreasing rate of MNA content in CMDB propellant increases with the increase of thermal aging temperature, but the change rule of MNA content is basically the same, indicating that high temperature accelerates the aging process of CMDB propellant and promotes the reaction between MNA and aging decomposition products (Bohn, 2010 ). Linear, exponential, logarithmic and modified exponential aging models were used to non-linearly fit the changes of MNA content in the aging process of CMDB propellants at different thermal aging temperatures. The fitting results are shown in Tables 2 and 3 . Through the fitting results of Tables 2 and 3 , it can be seen that the correlation coefficients of the modified exponential aging models established in this paper are all above 0.97. Compared with the linear, exponential and logarithmic aging models, the fitting results have a higher correlation with the existing exponential models. The modified exponential aging model can better fit the change of MNA content in the aging process, and then more accurately calculate the aging reaction rate K of CMDB propellant at different thermal aging temperatures characterized by MNA content. Figure 3 shows the fitting curve of the modified exponential aging model. Through Fig. 3 , it can be seen that the modified exponential aging model can well fit the change of MNA content in the aging process of CMDB propellant at different thermal aging temperatures. Table 2 fitting results of existing aging models models Temperature/K w 0 K R 2 Linear models 323.15 1.0132 − 9.5702×10 − 4 0.9132 333.15 1.0201 − 0.00254 0.9391 343.15 1.0344 − 0.00671 0.9084 353.15 1.0106 − 0.0147 0.9164 Logarithmic models 323.15 1.5909 − 0.3447 0.8825 333.15 1.5675 − 0.4162 0.8459 343.15 1.6457 − 0.5916 0.8501 353.15 1.22358 − 0.4199 0.8391 Exponential models 323.15 1.0206 0.00112 0.9202 333.15 1.0315 0.00311 0.9161 343.15 1.0577 0.00907 0.9357 353.15 1.02417 0.01893 0.9418 Table 3 fitting results of modified aging model models Temperature/K w 01 w 02 K R 2 Modified exponential models 323.15 0.7162 0.2838 0.00148 0.9748 333.15 0.7162 0.2838 0.00395 0.9899 343.15 0.8791 0.1209 0.00886 0.9919 353.15 0.7162 0.2838 0.02064 0.9946 Where w 0 is constant, w 01 and w 02 are constants independent of thermal aging temperature. The aging rate K of CMDB propellant characterized by MNA content at different thermal aging temperatures obtained by Eq. ( 6 ) is shown in Table 3 . The Eq. ( 10 ) was used to fit the aging rate K of CMDB propellant characterized by MNA content at different thermal aging temperatures. The fitting parameters of the modified Arrhenius equation were shown in Table 4 , and the fitting curve of the modified Arrhenius equation was shown in Fig. 4 . As can be seen from Fig. 4 , the aging rate curve with MNA content as aging characteristic can be well fitted by modified Arrhenius equation. Table 4 Parametric fitting results of modified Arrhenius equation. A n E m R 2 2.1891×10 − 7 0.7889 80486.3 − 2 0.9993 The modified Arrhenius equation fitting parameters shown in Table 4 were substituted into Eq. ( 10 ), and the aging rate of CMDB propellant with MNA content as aging characteristic at room temperature 298.15 K was calculated as K = 1.1044×10 − 4 mol/(cm 3 ⋅d). In predicting the storage life of solid propellant, a 50% reduction in stabilizer content is usually taken as the failure criterion of the material (Li et al., 2019 ). Therefore, in this paper, the MNA content decreased by 50% as the aging failure criterion of CMDB propellant. By substituting aging reaction rate K = 1.1044×10 − 4 mol/(cm 3 ⋅d) and MNA content w = 0.5% into Eq. ( 6 ), the storage life of CMDB propellant at room temperature 298.15 K is 7607 days, i.e. 20.84 years. 3.3.2. Shelf-life prediction based on maximum elongation The change curves of maximum elongation of CMDB propellant during storage at different thermal aging temperatures (323.15K, 333.15K, 343.15K and 353.15K) are shown in Fig. 5 . It can be seen from Fig. 5 that the maximum elongation of CMDB propellant decreases with the aging time, which is due to the chemical aging and physical damage of CMDB propellant during storage (Liu et al., 2022 ). At different thermal aging temperatures, the decrease rate of maximum elongation of CMDB propellant increases with the increase of aging temperature, but the change rule is basically the same, indicating that high temperature accelerates the aging process of CMDB propellant. By comparing the variation curve of MNA content, it can be seen that the maximum elongation of CMDB propellant is similar to the variation trend of MNA content in the aging process. Linear, exponential, logarithmic and modified exponential aging models were used to non-linearly fit the changes of maximum elongation in the aging process of CMDB propellants at different thermal aging temperatures. The fitting results are shown in Tables 5 and 6 . Through the fitting results of Tables 5 and 6 , it can be seen that the correlation coefficients of the modified exponential aging models established in this paper are above 0.98. Compared with the linear, exponential and logarithmic aging models, the fitting results have a higher correlation with the existing exponential models. The modified exponential aging model can better fit the change of maximum elongation in the aging process, and then more accurately calculate the aging reaction rate K of CMDB propellant at different thermal aging temperatures characterized by maximum elongation. Figure 6 shows the fitting curve of the modified exponential aging model. Through Fig. 6 , it can be seen that the modified exponential aging model can well fit the change of maximum elongation in the aging process of CMDB propellant at different thermal aging temperatures. Table 5 Fitting results of existing aging models models Temperature/K ε m0 K R 2 Linear models 323.15 0.2289 − 1.3314×10 − 4 0.9074 333.15 0.2256 − 2.3287×10 − 4 0.8591 343.15 0.2049 − 9.3202×10 − 4 0.8059 353.15 0.2148 − 0.00276 0.8997 Logarithmic models 323.15 0.2948 − 0.0419 0.9279 333.15 0.2625 − 0.0321 0.9175 343.15 0.2561 − 0.0644 0.9309 353.15 0.2413 − 0.0701 0.9444 Exponential models 323.15 0.2301 0.00125 0.9308 333.15 0.22663 0.00316 0.8769 343.15 0.2112 0.00624 0.8551 353.15 0.21975 0.01728 0.8861 Table 6 Fitting results of modified aging model models Temperature/K ε m01 ε m02 K R 2 Modified exponential models 323.15 0.15598 0.08 0.00211 0.9874 333.15 0.15598 0.08 0.00456 0.9867 343.15 0.15598 0.08 0.02296 0.9801 353.15 0.15598 0.08 0.04518 0.9821 Where ε m0 is constant, ε m01 and ε m02 are constants independent of thermal aging temperature. The aging rate K of CMDB propellant characterized by maximum elongation at different thermal aging temperatures obtained by Eq. ( 6 ) is shown in Table 6 . The Eq. ( 10 ) was used to fit the aging rate K of CMDB propellant characterized by maximum elongation at different thermal aging temperatures. The fitting parameters of the modified Arrhenius equation were shown in Table 7 , and the fitting curve of the modified Arrhenius equation was shown in Fig. 7 . As can be seen from Fig. 7 , the aging rate curve with maximum elongation as aging characteristic can be well fitted by modified Arrhenius equation. Table 7 Parametric fitting results of modified Arrhenius equation. A n E m R 2 15.3631 3.9832 91359.2 − 2 0.9974 The modified Arrhenius equation fitting parameters shown in Table 7 were substituted into Eq. ( 10 ), and the aging rate of CMDB propellant with maximum elongation as aging characteristic at room temperature 298.15 K was calculated as K = 2.1162×10 − 4 mol/(cm 3 ⋅d). In predicting the storage life of solid propellant, a 50% decrease in mechanical properties is usually taken as the failure criterion of the material (Li et al., 2019 ). Therefore, in this paper, the maximum elongation decreased by 50% as the aging failure criterion of CMDB propellant. By substituting aging reaction rate K = 2.1162×10 − 4 mol/(cm 3 ⋅d) and maximum elongation ε m = 0.1177 into Eq. ( 6 ), the storage life of CMDB propellant at room temperature 298.15 K is 7007 days, i.e. 19.19 years. It can be seen from Sections 3.3.1 and 3.3.2 that compared with existing aging models, the modified exponential aging model proposed in this paper can better fit the maximum elongation and MNA content change curves of CMDB propellant during storage at different thermal aging temperatures, and more accurately obtain aging reaction rate K at different thermal aging temperatures. Meanwhile, the modified Arrhenius equation was used to improve the life prediction accuracy of CMDB propellant at room temperature. The relative error of 20.84 years predicted by MNA content is 8.59% compared with 19.19 years predicted by maximum elongation, indicating that the prediction results based on MNA content are in good consistency with those based on maximum elongation. 3.4. Correlation model between maximum elongation and MNA depletion of CMDB propellant 3.4.1. Analysis of aging mechanism When CMDB propellant is in uniaxial tensile state, with the increase of tensile stress, the stress concentration between particles and matrix is gradually intensified, and particles and matrix begin to debond each other, which is called de-wetting (Francqueville et al., 2021 ), and cavities are formed around particles. As the load increases, some particles bond to the interface to a critical load, resulting in dewetting and the formation of microcracks between the particles and the matrix. Microcrack will affect the stress distribution. Under the tensile load, the crack tip will become the stress concentration area, thus accelerating the failure of the matrix and the dehumidification rate of the particles. In addition, with the increase of strain, de-wetting particles gradually occupy the majority, and microcracks will expand and form large cracks, leading to fracture failure of CMDB propellant (Sun et al., 2015 ). Therefore, the damage states of CMDB propellant at meso-level, including particle de-wetting, pores and microcracks, directly affect the macroscopic mechanical properties of CMDB propellant. In this paper, scanning electron microscope SU3500 was used to carry out scanning electron microscope experiments, and scanning electron microscope images of CMDB propellant tensile fracture surface under different aging times were obtained, as shown in Fig. 8 . As can be seen from Fig. 8 (a), the particle profile of the unaged specimen is clear, and no obvious micro-cracks or micro-pores are found in the matrix in the fracture surface. In Fig. 8 (b)-(d), due to the influence of aging, the particle contour is no longer clear, and there are de-wetting and micro-cracks in the fracture surface. As shown in Fig. 8 (d), when thermal aging lasted for 100 days, severe de-wetting and obvious micropores existed in the fracture surface. Therefore, with the increase of storage time, the damage state of CMDB propellant at the meso-level is continuously intensified, which leads to the continuous reduction of the maximum elongation of CMDB propellant, thus proving the rationality of the change curve of maximum elongation with aging time shown in Fig. 5 . For the composite solid propellants, the chemical aging is the main reason which leads to the aggravation of the damage of the matrix and the decrease of the macro-mechanics in the mesoscopic level (Liu et al., 2022 , Du et al., 2021 , Du et al., 2019 ). CMDB propellant is a composite solid propellant consisting of nitrocotton (NC) and nitroglycerin (NG) as the binder matrix, adding energetic additives and solid fillers such as metal fuel. Nitrocellulose (NC) as an important component of CMDB propellant matrix, the activation energy is 120–190 kJ/mol, stored at room temperature can also occur slow decomposition (Mušanić et al., 2013 ), the decomposition is caused by the chemical bond homolytic reaction of O-NO 2 , as shown in Eq. ( 11 ), the decomposition products such as ṄO 2 , NO and HNO 2 are generated. In the presence of decomposition products, nitrofoam (NC) and nitroglycerin (NG) undergo autocatalytic reactions to accelerate their own decomposition (Elbasuney et al., 2018 , Elbasuney et al., 2019 ), as shown in Eqs. ( 12 ) and ( 13 ), and release a large amount of heat, affecting the structural integrity of the propellant matrix, thus causing major safety hazards. $$\mathop {\text{N}}\limits^{\cdot } {\text{O+}}{{\text{O}}_2} \to 2\mathop {\text{N}}\limits^{\cdot } {{\text{O}}_2} \leftrightarrow {{\text{N}}_2}{{\text{O}}_4}$$ 11 $$\mathop {\text{N}}\limits^{\cdot } {\text{O}}+\mathop {\text{N}}\limits^{\cdot } {{\text{O}}_2}+{{\text{H}}_{\text{2}}}{\text{O}} \to 2{\text{HN}}{{\text{O}}_2}$$ 12 $$3\mathop {\text{N}}\limits^{\cdot } {{\text{O}}_2}+{{\text{H}}_{\text{2}}}{\text{O}} \to 2{\text{HN}}{{\text{O}}_3}+\mathop {\text{N}}\limits^{\cdot } {\text{O}}$$ 13 The main process of oxidation and decomposition of CMDB propellant matrix cannot be stopped, but the addition of MNA can react with decomposition products to prevent the occurrence of autocatalytic reaction, and thus prolong the storage life of propellant (Qiufan et al., 2017 ). The reaction equations of MNA and decomposition products are shown in Eqs. ( 14 ) and ( 15 ). With the increase of storage time, MNA reacts continuously with nitrogen oxides, resulting in the continuous reduction of MNA content in CMDB propellant (Liqiong et al., 2019 ), which proves the rationality of the change curve of MNA content with aging time shown in Fig. 2 . $${\text{MNA+}}\mathop {\text{N}}\limits^{\cdot } {{\text{O}}_{\text{2}}} \to {\text{MNA}} \cdot {\text{+HN}}{{\text{O}}_{\text{2}}}$$ 14 $${\text{MNA}} \cdot {\text{+}}\mathop {\text{N}}\limits^{\cdot } {\text{O}} \to {\text{N-NO-MNA}}$$ 15 At the same time, due to the continuous oxidation decomposition reaction of nitrocotton (NC) in the storage process, the decomposition products are produced constantly. Therefore, there is a certain relationship between the depletion of MNA and the depletion of nitrocotton (NC), and the change of MNA content can be used to indirectly characterize the change of nitrocotton (NC) content in CMDB propellant matrix (Zhang et al., 2022 , Asthana et al. , 1989). Nitrocellulose (NC) is an important part of the binder matrix of CMDB propellant. The depletion and decomposition of nitrocellulose (NC) lead to the formation of pores and microcracks in the matrix, poor bonding between solid particles and matrix, resulting in particle debonding, which affects the macroscopic mechanical properties and leads to the decrease of maximum elongation. Therefore, there is a certain relationship between MNA content and maximum elongation. 3.4.2. Establishment of correlation model between maximum elongation and MNA depletion At present, most of the reports on the storage properties of composite propellants only pay attention to the changes of macroscopic mechanical properties or microscopic chemical components. There are few reports that combine the macroscopic mechanical properties and microscopic chemical components of composite propellants and apply them to the aging life prediction of composite propellants. According to the aging mechanism analysis in the previous section, there is a certain relationship between the MNA content w and the maximum elongation ε m . It can be seen from Fig. 2 and Fig. 5 that under different thermal aging temperatures, MNA content w and maximum elongation ε m can be regarded as functions of aging time respectively, and both functions change monotonically with aging time. The reduction of MNA content w under a certain aging time is defined as the MNA depletion w d under the current aging time, that is, \({w}_{d}=1\text{\%}-w\) . Therefore, with the same aging time, the MNA depletion w d is the independent variable and the maximum elongation ε m is the dependent variable, and the corresponding relationship between the MNA depletion w d and the maximum elongation ε m is established as shown in Fig. 9 . It can be seen from Fig. 9 that MNA depletion w d of CMDB propellant has a strong correlation with the maximum elongation ε m . With the increase of MNA depletion w d , the maximum elongation ε m decreases monotonically. Eq. ( 16 ) was used to fit the experimental results in Fig. 9 , and the results are shown in Table 8 . $${\varepsilon _m}={B_1}\exp ( - {w_d}/{B_2})+{B_3}$$ 16 Where ε m is the maximum elongation; w d is the MNA depletion, %, \({w}_{d}=1\text{\%}-w\) ; B 1 , B 2 and B 3 are constants. Table 8 Fitting results of macro and micro corresponding relation functions B 1 B 2 B 3 R 2 0.1346 0.3491 0.1014 0.9674 To verify the validity of the corresponding relationship between MNA depletion w d and maximum elongation ε m , the maximum elongation ε m ( ε m = 0.2024, 0.1773, 0.1584, 0.1442 and 0.13354) corresponding to different MNA depletion w d ( w d = 0.1%, 0.2%, 0.3%, 0.4% and 0.5%) were calculated respectively. According to section 3.3.1 of a MNA content as aging characteristics calculated CMDB propellant aging rate K ( K = 1.1044×10 − 4 mol/(cm 3 ⋅d)) under 298.15 K, Eq. ( 6 ) was used to calculate the corresponding aging time t ( t = 1901.9 d, 3303.3 d, 4704.6 d, 5905.7 d and 7007 d) under different MNA depletion w d ( w d = 0.1%, 0.2%, 0.3%, 0.4% and 0.5%). According to section 3.3.1 of a maximum elongation as aging characteristics calculated CMDB propellant aging rate K ( K = 2.1162×10 − 4 mol/(cm 3 ⋅d))under 298.15 K, Eq. ( 6 ) was used to calculate the corresponding maximum elongation ε m ( ε m = 0.1843, 0.1575, 0.1389, 0.1266 and 0.1177) under different aging time t ( t = 1901.9 d, 3303.3 d, 4704.6 d, 5905.7 d and 7007 d). The maximum elongation ε m calculated by the two methods is compared, and the calculated error values between the two methods are shown in Fig. 10 . As can be seen from Fig. 9 , Eq. ( 16 ) can well describe the change between MNA depletion and maximum elongation. As can be seen from Fig. 10 , the error between the maximum elongation calculated by Eq. ( 16 ) and the maximum elongation calculated by the aging model is small, and the overall error is less than 15%. The results show that the relationship between the MNA depletion and the maximum elongation proposed in this paper is feasible. Based on this function, the relationship between macroscopic and microscopic storage properties of CMDB propellant was established, that is, the maximum elongation of CMDB propellant under this content could be predicted by measuring the MNA content in CMDB propellant after aging at room temperature. 4. Conclusions In this paper, the thermal accelerated aging test of CMDB propellant was carried out, the changes of MNA content and maximum elongation of CMDB propellant were analyzed, and the modified exponential aging model of CMDB propellant was established. With MNA content and maximum elongation as aging characteristics, the storage life of CMDB propellants at 298.15 K was predicted using the modified Arrhenius equation. The aging mechanism of CMDB propellant was analyzed and the correlation function model of MNA depletion and maximum elongation was established. The main conclusions are as follows: (1) Based on the existing aging model, a modified exponential aging model was established to fit the variation curves of MNA content and maximum elongation respectively. The fitting correlation coefficients were both greater than 0.97. The model could accurately describe the variation of MNA content and maximum elongation of CMDB propellant. (2) With MNA content and maximum elongation decreasing by 50% as aging failure criterion and MNA content and maximum elongation as aging characteristics, the modified Arrhenius equation was used to predict the storage life of CMDB at 298.15 K to 19.19 years and 18.09 years, respectively, and the relative error of the two prediction results was 6.08%. The result showed that the prediction result based on MNA content was in good agreement with this based on maximum elongation. (3) There is a good correlation between the MNA depletion and the maximum elongation of CMDB propellant. According to the test data of the MNA content and the maximum elongation under different aging time, the correlation function model of the MNA depletion and the maximum elongation was established. The relative error between the maximum elongation calculated by this model and the maximum elongation calculated by the aging model was less than 15%. The results show that the correlation function model of MNA depletion and maximum elongation established in this paper is effective. By measuring the MNA content after aging of CMDB propellant at room temperature, the maximum elongation of CMDB propellant can be predicted. References ASTHANA, S. N., DIVEKAR, C. N. & SINGH, H. (1989), "Studies on thermal stability, autoignition and stabilizer depletion for shelf life of CMDB propellants", Journal of Hazardous Materials, Vol. 21 No. 1, pp. 35–46. 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(2006), "A study of kinetic behaviours of the effective centralite/stabilizer consumption reaction of propellants using a multi-temperature artificial accelerated ageing test", Journal of Hazardous Materials, Vol. 145 No. 1, pp. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 06 Sep, 2023 Read the published version in Mechanics of Time-Dependent Materials → Version 1 posted Editorial decision: Major revision 27 Jul, 2023 Reviews received at journal 27 Jul, 2023 Reviewers agreed at journal 05 Jul, 2023 Reviewers invited by journal 04 Jul, 2023 Editor assigned by journal 04 Jul, 2023 Submission checks completed at journal 03 Jul, 2023 First submitted to journal 30 Jun, 2023 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. 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06:14:32","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-3126969/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-3126969/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11043-023-09634-8","type":"published","date":"2023-09-06T15:02:36+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":39812455,"identity":"f06af545-d171-4416-b538-977a1fdda2c6","added_by":"auto","created_at":"2023-07-10 17:16:53","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":4740,"visible":true,"origin":"","legend":"\u003cp\u003eDumbbell sample of the CMDB propellant.\u003c/p\u003e","description":"","filename":"Onlinefloatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/7e5cf43c9460d6f1183e3866.png"},{"id":39812459,"identity":"80ac64a7-66b0-4b05-a598-f207685d9378","added_by":"auto","created_at":"2023-07-10 17:16:53","extension":"jpeg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":73439,"visible":true,"origin":"","legend":"\u003cp\u003eThe change curves of MNA content at different thermal aging temperatures.\u003c/p\u003e","description":"","filename":"floatimage2.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/22db347b35ceacd2dc215e00.jpeg"},{"id":39812456,"identity":"2f880b97-e35c-4b3f-b154-1b3b93196df6","added_by":"auto","created_at":"2023-07-10 17:16:53","extension":"jpeg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":72227,"visible":true,"origin":"","legend":"\u003cp\u003eThe fitting curves of MNA content at different thermal aging temperatures.\u003c/p\u003e","description":"","filename":"floatimage3.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/03fcae7f2c0608783b104c80.jpeg"},{"id":39812824,"identity":"6cce209e-7bb6-451a-a293-73f1fae0f618","added_by":"auto","created_at":"2023-07-10 17:24:53","extension":"jpeg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":92150,"visible":true,"origin":"","legend":"\u003cp\u003eFitting curve of aging rate with MNA content as aging characterization\u003c/p\u003e","description":"","filename":"floatimage4.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/8e1e9365a59909ee1f505e54.jpeg"},{"id":39812461,"identity":"dfbef8fb-41ea-4ab7-9765-f73e82593c48","added_by":"auto","created_at":"2023-07-10 17:16:53","extension":"jpeg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":159538,"visible":true,"origin":"","legend":"\u003cp\u003eThe change curves of the maximum elongation at different thermal aging temperatures.\u003c/p\u003e","description":"","filename":"floatimage5.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/6da2633cf99b59dd5fceb63f.jpeg"},{"id":39813379,"identity":"2db7f719-be28-482b-979b-d433ae02e9d8","added_by":"auto","created_at":"2023-07-10 17:32:53","extension":"jpeg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":147291,"visible":true,"origin":"","legend":"\u003cp\u003eThe fitting curves of the maximum elongation at different thermal aging temperatures.\u003c/p\u003e","description":"","filename":"floatimage6.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/04de3d03a8cccf3803c7b81d.jpeg"},{"id":39812826,"identity":"9cb48ec5-8ccb-4a9d-980c-413335556775","added_by":"auto","created_at":"2023-07-10 17:24:53","extension":"jpeg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":94644,"visible":true,"origin":"","legend":"\u003cp\u003eFitting curve of aging rate with maximum elongation as aging characterization\u003c/p\u003e","description":"","filename":"floatimage7.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/4920156da5e3ca510535ee3a.jpeg"},{"id":39812464,"identity":"06951464-4741-4170-b5ed-4183c294f2de","added_by":"auto","created_at":"2023-07-10 17:16:54","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":386770,"visible":true,"origin":"","legend":"\u003cp\u003eSEM images of tensile fracture of CMDB propellant under different aging time\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/b42986ac4380d4447ab93e20.png"},{"id":39812463,"identity":"724bf311-18d3-4e01-b292-49ac974ba7da","added_by":"auto","created_at":"2023-07-10 17:16:54","extension":"jpeg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":130686,"visible":true,"origin":"","legend":"\u003cp\u003eRelation between MNA depletion and maximum elongation of CMDB propellant\u003c/p\u003e","description":"","filename":"floatimage9.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/22c14f30d477d8a742870099.jpeg"},{"id":39812462,"identity":"bd9110e7-8f18-4f68-bc8c-2f4dbcd1f93d","added_by":"auto","created_at":"2023-07-10 17:16:53","extension":"jpeg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":46958,"visible":true,"origin":"","legend":"\u003cp\u003eError between the calculation results of macro and micro correspondence relationship and the calculation results of aging model\u003c/p\u003e","description":"","filename":"floatimage10.jpeg","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/df0a3d7d4a39bb0f6577d794.jpeg"},{"id":42947360,"identity":"558e0425-c003-455a-a39a-beceda5ca60b","added_by":"auto","created_at":"2023-09-11 15:08:43","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1060230,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-3126969/v1/1a5b12fd-202a-4fb9-96fc-fa475ddd829a.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Shelf-life prediction and correlation between maximum elongation and stabilizer depletion of CMDB propellant","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eComposite modified double base (CMDB) propellants have been widely used in modern military and aerospace fields because of their high energy, high strength and low characteristic signal (Zhang et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e, Zhang et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Due to aging of CMDB propellant during storage, its properties deteriorate with the increase of storage time, which affects the storage life of CMDB propellant (Liu et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). After reaching the critical life span, there will be great safety risks to continue service (Yildinm and Oezupek, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e2011\u003c/span\u003e, Bin et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). However, premature disposal will cause unnecessary economic losses and waste of resources. Therefore, it is of great significance to accurately predict the storage life of CMDB propellant for the storage and use safety of solid rocket motor.\u003c/p\u003e \u003cp\u003eDue to the advantages of thermal accelerated aging method such as short test cycle, low test cost, high test efficiency and life evaluation in advance (Wang and Qiang, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), the thermal accelerated aging method is often used in the research of solid propellant aging to obtain propellant properties under different aging times and establish aging models (Du \u003cem\u003eet al.\u003c/em\u003e, 2020, Wang et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). The Arrhenius equation or Berthelot equation was used to predict the storage life of propellant at the actual storage temperature (Pan \u003cem\u003eet al.\u003c/em\u003e, 2021). The Berthelot equation describes the relationship between storage life and storage temperature. The storage life of propellant can be predicted in actual storage condition only by measuring the critical life at each thermal aging temperature (Sammour, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1994\u003c/span\u003e, Liu et al., \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). However, Berthelot equation cannot be used to describe the tendency of propellant properties with aging time (Himanshu, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). The Arrhenius equation needs to obtain the aging rate constant through aging model, establish the relationship between aging rate and aging temperature, and then predict the aging rate of propellant under actual storage condition, which can be used to describe the tendency of propellant performance with aging time (Sadasivan and Bhaumik, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e1984\u003c/span\u003e). Since the Arrhenius equation assumes that the preexponential factor and activation energy are constant, the influence of temperature on the pre-exponential factor and activation energy is ignored, leading to large errors in the life prediction results (Laidler \u003cem\u003eet al.\u003c/em\u003e, 1996). Therefore, to ensure the accuracy of life prediction, the Arrhenius equation needs to be modified.\u003c/p\u003e \u003cp\u003eCMDB propellant combines the advantages of double base propellant (DBP) and composite propellant (CSP), adding oxidizer, high energy explosive and metal powder into nitrocotton/nitroglycerin (NC/NG) matrix to obtain higher energy and excellent mechanical properties (Han et al., \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). However, the nitrate bond of nitrate compounds is prone to oxidative fracture, causing decomposition reaction, releasing nitrogen oxides and heat, and the released nitrogen oxides will accelerate the decomposition of nitrate compounds, forming an autocatalytic reaction (Liqiong et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Therefore, 1\u0026thinsp;~\u0026thinsp;5% stabilizer is added to CMDB propellant to absorb nitrogen oxides and inhibit or delay the autocatalytic reaction of nitrate ester (Elbasuney et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Manfred et al. (Bohn and Volk, \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1992\u003c/span\u003e, Bohn, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2010\u003c/span\u003e, Manfred, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2009\u003c/span\u003e) conducted thermal aging at 50 ℃~90 ℃ for four DB propellants, determined the stabilizer depletion in the aging process by HPLC, established the stabilizer depletion equation, greatly improved the life prediction of propellant, and revealed the aging mechanism of DB propellant. The experimental results show that the stabilizer reacts with nitrogen oxides and is consumed during storage of DB propellant. Zhao et al. (\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e2006\u003c/span\u003e) conducted thermal aging of various DB propellants at 65 ℃~95 ℃, and measured the stabilizer content of the propellants at different aging times. The experimental results showed that NG content and stabilizer content in the propellant were the main factors affecting the storage life of the propellant, and the more stabilizer content remained, the longer the safe storage life of the propellant. Li et al. (\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) tested the storage properties of DB propellants under different aging times by means of scanning electron microscopy and infrared spectrum analysis. Based on the aging theoretical model and the Arrhenius equation, a kinetic model of stabilizer depletion was established, which provided a theoretical basis for predicting the storage life of propellants by stabilizer content. Therefore, based on the above research results, the stabilizer content in propellant can be used as the aging characteristic to predict the storage life of propellant. In addition, due to the effects of chemical aging and physical damage, the maximum elongation of propellant decreases with the aging time. Zhou et al. (2016) conducted thermal aging experiments on HTPB propellants under different constant strains, and established aging models with maximum elongation as aging characteristics to predict the life of HTPB propellants. The study proved the feasibility of using maximum elongation as aging characteristics to predict the storage life of propellants.\u003c/p\u003e \u003cp\u003eThe macro mechanical properties of propellants are closely related to the micro structure, and the change of micro structure will directly affect the macro mechanical properties of propellants (such as strength, elongation and modulus) (Liu et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e, Du et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Sekkar et al. (2015) studied the cross-linking density of HTPB propellants composed of different binders and found that there was a strong linear relationship between the cross-linking density and macroscopic mechanical properties (maximum elongation and Young's modulus). The storage properties of propellants could be predicted by testing the cross-linking density of propellants. Li et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) tested the crosslinking density and maximum elongation of HTPB coating through the thermal aging test, and established the corresponding relationship between the maximum elongation and the crosslinking density. The predicted results obtained by using the corresponding relationship were in good agreement with the predicted results of the maximum elongation. Du et al. (\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) carried out prestrain thermal aging test on HTPB coating, analyzed the variation of crosslinking density, established the relationship model between maximum elongation and crosslinking density, and realized the transformation of failure criterion between maximum elongation and crosslinking density, which can be used to evaluate the storage properties of propellant. Choi et al. (2000; 2001) found through research that a large number of samples are needed to obtain the change trend of macroscopic mechanical properties of materials in the aging process, and the test error is relatively large. However, the sample size for testing crosslinking density is less than 1cm\u0026times;1cm, and the test error is relatively small. The relative error of aging test can be greatly reduced by testing the change of crosslinking density. Due to different bond systems, CMDB propellant and HTPB propellant have essential differences in aging characteristics, but they are similar in aging mechanism, because the change of microstructure is one of the main factors affecting the change of macro mechanical properties (Yang et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2016\u003c/span\u003e, Yang et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). At present, most of the research on the storage life prediction of CMDB propellant focuses on the change of component content of CMDB propellant, and there are few studies on the change of macro mechanical properties, and the correlation between stabilizer depletion and macro mechanical properties is rarely reported. Therefore, it is necessary to study the correlation between stabilizer depletion and macro mechanical properties, establish the relationship between macro mechanical properties and stabilizer depletion, and directly predict the macro mechanical properties of propellants by stabilizer depletion, which can overcome the problems such as tedious testing process and large sample consumption, and provide theoretical support for the life prediction of CMDB propellants.\u003c/p\u003e \u003cp\u003eThermal accelerated aging tests of CMDB propellant were carried out at 323.15 K, 333.15 K, 343.15 K and 353.15 K, and the changes of maximum elongation and MNA content of CMDB propellant were analyzed. A modified exponential aging model was established. Based on the modified Arrhenius equation, the aging life of CMDB propellants was predicted by taking the maximum elongation and MNA content as aging characteristics, respectively. The aging mechanism of CMDB propellant was analyzed, and the correlation between maximum elongation and MNA depletion was established, and the validity of the correlation was verified.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Materials\u003c/h2\u003e \u003cp\u003eThe composite modified double base (CMDB) propellant in this paper was obtained from Shanxi Xing 'an Chemical Industry Co. Ltd. Taiyuan, China. In order to facilitate the experimental test, the standard dumbbell type propellant sample is selected, with the dimension of 120 mm \u0026times; 25 mm \u0026times;10 mm, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. 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.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Accelerated aging test\u003c/h2\u003e \u003cp\u003eThe thermal accelerated aging test of CMDB propellant was conducted in an electric oil bath incubator. The experimental temperature of thermal accelerated aging was set as 323.15 K, 333.15 K, 343.15 K and 353.15 K. At the same time, in order to ensure that the humidity change range was less than 10% during the aging process, the test samples were placed in an aluminum foil sealed bags for sealing. The relevant research shows that the sampling interval should be short when the thermal aging temperature is high, and long when the thermal aging temperature is low (Pan and Liu, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, Du et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Therefore, the thermal aging temperature and sampling time are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. After aging, the aged samples were placed in a dryer and cooled down naturally to room temperature for 24 hours before corresponding tests were conducted.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSampling time of thermal accelerated aging test\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"8\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTemperature / K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colspan=\"7\" nameend=\"c8\" namest=\"c2\"\u003e \u003cp\u003eSampling time / d\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e150\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e300\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e360\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e45\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e145\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e180\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e35\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e-\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Uniaxial tensile test\u003c/h2\u003e \u003cp\u003eUniaxial tensile test was carried out on CMDB propellant dumbbell-shaped samples by uniaxial tensile testing machine to test the maximum elongation. The experimental temperature was controlled at 298.15\u0026thinsp;\u0026plusmn;\u0026thinsp;1 K, and the tensile rate was chosen to be 100 mm/min until the specimen was completely fractured. Uniaxial tensile tests were carried out on 5 to 8 repeated samples for each aging condition (temperature, time), and the average value of maximum elongation was obtained.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4. Determination of MNA\u003c/h2\u003e \u003cp\u003eIn this study, Agilent technologies 7890A gas chromatograph was used to determine the mass fraction of MNA in CMDB propellant samples at different aging time. The sample was extracted with diethyl ether, and the nitrate, stabilizer and plasticizer in the extract were separated in the chromatograph. High purity MNA was used as internal standard, and the content of MNA was calculated by internal standard method. Three parallel measurements were made for each sample, and the average of the experimental results was taken to ensure the accuracy of the test results. The mass fraction of MNA in samples with internal standard method was calculated by the following equation:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$w=\\frac{{{m_s}H{f_s}}}{{m{H_s}}} \\times 100\\%$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003ew\u003c/em\u003e is the mass fraction of MNA in CMDB propellant sample, %; \u003cem\u003em\u003c/em\u003e is the mass of CMDB propellant sample, g; \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is the mass of internal standard, g; \u003cem\u003eH\u003c/em\u003e is the peak height of MNA in CMDB propellant sample, mm; \u003cem\u003eH\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is the peak height of internal standard, mm; \u003cem\u003ef\u003c/em\u003e\u003csub\u003e\u003cem\u003es\u003c/em\u003e\u003c/sub\u003e is the correction factor corresponding to MNA in CMDB propellant sample and internal standard, and its calculation equation is as follows:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${f_s}=\\frac{{{m_{MNA}}{H_s}}}{{{m_s}H}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003em\u003c/em\u003e\u003csub\u003e\u003cem\u003eMNA\u003c/em\u003e\u003c/sub\u003e is the mass of MNA in CMDB propellant sample, g.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e2.5. SEM analysis\u003c/h2\u003e \u003cp\u003eIn order to observe the meso-morphology of the tensile fracture surface of CMDB propellant after aging, scanning electron microscope (SEM) SU3500 was used to carry out SEM experiments, and the SEM images of the tensile fracture surface of CMDB propellant under different aging time were obtained. Working conditions of scanning electron microscope are as follows: high vacuum mode, tungsten thermistor emission, acceleration voltage of 15kV, working distance of 10 mm, magnification of 500 times.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.1. Establishment of aging model\u003c/h2\u003e \u003cp\u003eGenerally, the aging properties of materials are described by the Layton equations, including linear, exponential and logarithmic models (Layton, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1975\u003c/span\u003e):\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$P={P_0}+K{t_a}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$P={P_0}\\exp ( - K{t_a})$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$P={P_0}+K\\log {t_a}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere \u003cem\u003eP\u003c/em\u003e is the property of materials at aging time \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e; \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is constant; \u003cem\u003eK\u003c/em\u003e is the rate constant of the aging reaction, which is related to the thermal aging temperature; \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e is the aging time, d.\u003c/p\u003e \u003cp\u003eHowever, the fitting results of the three aging models of the Layton equation are not accurate for the aging properties, which leads to large deviations in the prediction results. Therefore, this paper optimizes and improves based on the exponential model, and proposes a modified exponential aging model as follows:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\begin{gathered} P={P_{01}}\\exp ( - K{t_a})+{P_{02}} \\hfill \\\\ {P_0}={P_{01}}+{P_{02}} \\hfill \\\\ \\end{gathered}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eP\u003c/em\u003e is the property of materials at aging time \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e; \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is unaged material parameters; \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e01\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eP\u003c/em\u003e\u003csub\u003e\u003cem\u003e02\u003c/em\u003e\u003c/sub\u003e are constants independent of thermal aging temperature; \u003cem\u003eK\u003c/em\u003e is the rate constant of the aging reaction, which is related to the thermal aging temperature; \u003cem\u003et\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e is the aging time, d.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Modification of Arrhenius equation\u003c/h2\u003e \u003cp\u003eThe study of chemical reaction kinetics began in the late 19th century, and the Arrhenius equation was widely used to predict the storage life of materials (Pan and Liu, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Previous studies (Li et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) have shown that the aging reaction rate \u003cem\u003eK\u003c/em\u003e follows the Arrhenius equation:\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\ln K=\\ln A - \\frac{{{E_a}}}{{RT}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eK\u003c/em\u003e is the reaction rate constant, d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; \u003cem\u003eA\u003c/em\u003e is the pre-exponential factor, d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e is the activation energy of reaction, J/mol; \u003cem\u003eT\u003c/em\u003e is the absolute temperature, K; \u003cem\u003eR\u003c/em\u003e is the universal gas constant, 8.314 J/(mol\u0026sdot;K).\u003c/p\u003e \u003cp\u003eIn general, the preexponential factor and activation energy are assumed to be constants independent of the storage temperature, but this assumption is only applicable to a small temperature range, and the prediction accuracy is poor when the extrapolation temperature range is large (Yang et al., \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Therefore, in order to ensure the accuracy of storage life prediction, it is necessary to modify the Arrhenius equation.\u003c/p\u003e \u003cp\u003eLaidler (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e1996\u003c/span\u003e) established the modified Arrhenius equation on the basis of the Arrhenius equation, and proposed that the preexponential factor was a temperature-dependent function, expressed as:\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\ln K=\\ln \\left( {A{T^m}} \\right) - \\frac{{{E_a}}}{{RT}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere (\u003cem\u003eA T\u003c/em\u003e\u003csup\u003e\u003cem\u003em\u003c/em\u003e\u003c/sup\u003e) is the temperature dependent pre-exponential factor, \u003cem\u003eA\u003c/em\u003e and \u003cem\u003em\u003c/em\u003e are constants.\u003c/p\u003e \u003cp\u003eBased on the modified Arrhenius equation, Li et al. (\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) obtained the modified expression of activation energy through derivation and proved that there is a linear relationship between activation energy \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e and temperature \u003cem\u003eT\u003c/em\u003e as follows:\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$${E_a}=E+nRT$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eE\u003c/em\u003e\u003csub\u003e\u003cem\u003ea\u003c/em\u003e\u003c/sub\u003e is the activation energy of reaction, J/mol;\u003cem\u003eE\u003c/em\u003e and \u003cem\u003en\u003c/em\u003e are constants.\u003c/p\u003e \u003cp\u003eThe modified Arrhenius equation is established by substituting Eq.\u0026nbsp;(\u003cspan refid=\"Equ9\" class=\"InternalRef\"\u003e9\u003c/span\u003e) into Eq.\u0026nbsp;(\u003cspan refid=\"Equ8\" class=\"InternalRef\"\u003e8\u003c/span\u003e) as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e), in which the pre-exponential factor and activation energy are considered to be related to temperature.\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\ln K=\\ln A{\\text{+}}m\\ln T - \\frac{{E+nRT}}{{RT}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eK\u003c/em\u003e is the reaction rate constant, d\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e; \u003cem\u003eA\u003c/em\u003e, \u003cem\u003em\u003c/em\u003e, \u003cem\u003en\u003c/em\u003e and \u003cem\u003eE\u003c/em\u003e are constants; \u003cem\u003eT\u003c/em\u003e is the absolute temperature, K; \u003cem\u003eR\u003c/em\u003e is the universal gas constant, 8.314 J/(mol\u0026sdot;K).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e3.3. Shelf-life prediction\u003c/h2\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1. Shelf-life prediction based on MNA content\u003c/h2\u003e \u003cp\u003eThe change curve of MNA content of CMDB propellant at different thermal aging temperatures (323.15 K, 333.15 K, 343.15 K and 353.15 K) is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e that the content of MNA as a stabilizer in CMDB propellant decreases with the increase of aging time, which is due to the reaction of MNA with the aging decomposition products of CMDB propellant (Elbasuney et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). At different thermal aging temperatures, the decreasing rate of MNA content in CMDB propellant increases with the increase of thermal aging temperature, but the change rule of MNA content is basically the same, indicating that high temperature accelerates the aging process of CMDB propellant and promotes the reaction between MNA and aging decomposition products (Bohn, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2010\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eLinear, exponential, logarithmic and modified exponential aging models were used to non-linearly fit the changes of MNA content in the aging process of CMDB propellants at different thermal aging temperatures. The fitting results are shown in Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Through the fitting results of Tables\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, it can be seen that the correlation coefficients of the modified exponential aging models established in this paper are all above 0.97. Compared with the linear, exponential and logarithmic aging models, the fitting results have a higher correlation with the existing exponential models. The modified exponential aging model can better fit the change of MNA content in the aging process, and then more accurately calculate the aging reaction rate \u003cem\u003eK\u003c/em\u003e of CMDB propellant at different thermal aging temperatures characterized by MNA content. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e shows the fitting curve of the modified exponential aging model. Through Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e, it can be seen that the modified exponential aging model can well fit the change of MNA content in the aging process of CMDB propellant at different thermal aging temperatures.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003efitting results of existing aging models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003emodels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTemperature/K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eK\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLinear\u003c/p\u003e \u003cp\u003emodels\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0132\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;9.5702\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9132\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0201\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.00254\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9391\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0344\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.00671\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9084\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0106\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.0147\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9164\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLogarithmic models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5909\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.3447\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8825\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.5675\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.4162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8459\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.6457\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.5916\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8501\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.22358\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.4199\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8391\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eExponential models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0206\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00112\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9202\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0315\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00311\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9161\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.0577\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00907\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9357\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.02417\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.01893\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9418\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003efitting results of modified aging model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003emodels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTemperature/K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e01\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e02\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eK\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eModified\u003c/p\u003e \u003cp\u003eexponential models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.2838\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.00148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9748\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.2838\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.00395\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9899\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.8791\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.1209\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.00886\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9919\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.7162\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.2838\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.02064\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9946\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWhere \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e0\u003c/em\u003e\u003c/sub\u003e is constant, \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e01\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003e02\u003c/em\u003e\u003c/sub\u003e are constants independent of thermal aging temperature.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe aging rate \u003cem\u003eK\u003c/em\u003e of CMDB propellant characterized by MNA content at different thermal aging temperatures obtained by Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) is shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The Eq.\u0026nbsp;(\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e) was used to fit the aging rate \u003cem\u003eK\u003c/em\u003e of CMDB propellant characterized by MNA content at different thermal aging temperatures. The fitting parameters of the modified Arrhenius equation were shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, and the fitting curve of the modified Arrhenius equation was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, the aging rate curve with MNA content as aging characteristic can be well fitted by modified Arrhenius equation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParametric fitting results of modified Arrhenius equation.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2.1891\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;7\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.7889\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e80486.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9993\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe modified Arrhenius equation fitting parameters shown in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e were substituted into Eq.\u0026nbsp;(\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e), and the aging rate of CMDB propellant with MNA content as aging characteristic at room temperature 298.15 K was calculated as \u003cem\u003eK\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.1044\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e mol/(cm\u003csup\u003e3\u003c/sup\u003e\u0026sdot;d).\u003c/p\u003e \u003cp\u003eIn predicting the storage life of solid propellant, a 50% reduction in stabilizer content is usually taken as the failure criterion of the material (Li et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Therefore, in this paper, the MNA content decreased by 50% as the aging failure criterion of CMDB propellant. By substituting aging reaction rate \u003cem\u003eK\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.1044\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e mol/(cm\u003csup\u003e3\u003c/sup\u003e\u0026sdot;d) and MNA content \u003cem\u003ew\u003c/em\u003e\u0026thinsp;=\u0026thinsp;0.5% into Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), the storage life of CMDB propellant at room temperature 298.15 K is 7607 days, i.e. 20.84 years.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2. Shelf-life prediction based on maximum elongation\u003c/h2\u003e \u003cp\u003eThe change curves of maximum elongation of CMDB propellant during storage at different thermal aging temperatures (323.15K, 333.15K, 343.15K and 353.15K) are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e that the maximum elongation of CMDB propellant decreases with the aging time, which is due to the chemical aging and physical damage of CMDB propellant during storage (Liu et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). At different thermal aging temperatures, the decrease rate of maximum elongation of CMDB propellant increases with the increase of aging temperature, but the change rule is basically the same, indicating that high temperature accelerates the aging process of CMDB propellant. By comparing the variation curve of MNA content, it can be seen that the maximum elongation of CMDB propellant is similar to the variation trend of MNA content in the aging process.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eLinear, exponential, logarithmic and modified exponential aging models were used to non-linearly fit the changes of maximum elongation in the aging process of CMDB propellants at different thermal aging temperatures. The fitting results are shown in Tables\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Through the fitting results of Tables\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and \u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, it can be seen that the correlation coefficients of the modified exponential aging models established in this paper are above 0.98. Compared with the linear, exponential and logarithmic aging models, the fitting results have a higher correlation with the existing exponential models. The modified exponential aging model can better fit the change of maximum elongation in the aging process, and then more accurately calculate the aging reaction rate \u003cem\u003eK\u003c/em\u003e of CMDB propellant at different thermal aging temperatures characterized by maximum elongation. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the fitting curve of the modified exponential aging model. Through Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e, it can be seen that the modified exponential aging model can well fit the change of maximum elongation in the aging process of CMDB propellant at different thermal aging temperatures.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFitting results of existing aging models\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003emodels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTemperature/K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em0\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eK\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLinear\u003c/p\u003e \u003cp\u003emodels\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2289\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;1.3314\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9074\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2256\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;2.3287\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8591\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2049\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;9.3202\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8059\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2148\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.00276\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8997\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eLogarithmic models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2948\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.0419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9279\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2625\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.0321\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9175\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2561\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.0644\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9309\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2413\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;0.0701\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9444\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eExponential models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00125\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.9308\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.22663\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00316\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8769\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.2112\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.00624\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8551\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.21975\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.01728\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.8861\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFitting results of modified aging model\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003emodels\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTemperature/K\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em01\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em02\u003c/em\u003e\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eK\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003eModified\u003c/p\u003e \u003cp\u003eexponential models\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e323.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.15598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.00211\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9874\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e333.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.15598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.00456\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9867\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e343.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.15598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.02296\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9801\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e353.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.15598\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.04518\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.9821\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em0\u003c/em\u003e\u003c/sub\u003e is constant, \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em01\u003c/em\u003e\u003c/sub\u003e and \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em02\u003c/em\u003e\u003c/sub\u003e are constants independent of thermal aging temperature.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe aging rate \u003cem\u003eK\u003c/em\u003e of CMDB propellant characterized by maximum elongation at different thermal aging temperatures obtained by Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) is shown in Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. The Eq.\u0026nbsp;(\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e) was used to fit the aging rate \u003cem\u003eK\u003c/em\u003e of CMDB propellant characterized by maximum elongation at different thermal aging temperatures. The fitting parameters of the modified Arrhenius equation were shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, and the fitting curve of the modified Arrhenius equation was shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e, the aging rate curve with maximum elongation as aging characteristic can be well fitted by modified Arrhenius equation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab7\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 7\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eParametric fitting results of modified Arrhenius equation.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eA\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003en\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eE\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003em\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e15.3631\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.9832\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e91359.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u0026minus;\u0026thinsp;2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.9974\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe modified Arrhenius equation fitting parameters shown in Table\u0026nbsp;\u003cspan refid=\"Tab7\" class=\"InternalRef\"\u003e7\u003c/span\u003e were substituted into Eq.\u0026nbsp;(\u003cspan refid=\"Equ10\" class=\"InternalRef\"\u003e10\u003c/span\u003e), and the aging rate of CMDB propellant with maximum elongation as aging characteristic at room temperature 298.15 K was calculated as \u003cem\u003eK\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.1162\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e mol/(cm\u003csup\u003e3\u003c/sup\u003e\u0026sdot;d).\u003c/p\u003e \u003cp\u003eIn predicting the storage life of solid propellant, a 50% decrease in mechanical properties is usually taken as the failure criterion of the material (Li et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Therefore, in this paper, the maximum elongation decreased by 50% as the aging failure criterion of CMDB propellant. By substituting aging reaction rate \u003cem\u003eK\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.1162\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e mol/(cm\u003csup\u003e3\u003c/sup\u003e\u0026sdot;d) and maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1177 into Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e), the storage life of CMDB propellant at room temperature 298.15 K is 7007 days, i.e. 19.19 years.\u003c/p\u003e \u003cp\u003eIt can be seen from Sections \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003e3.3.1\u003c/span\u003e and \u003cspan refid=\"Sec13\" class=\"InternalRef\"\u003e3.3.2\u003c/span\u003e that compared with existing aging models, the modified exponential aging model proposed in this paper can better fit the maximum elongation and MNA content change curves of CMDB propellant during storage at different thermal aging temperatures, and more accurately obtain aging reaction rate K at different thermal aging temperatures. Meanwhile, the modified Arrhenius equation was used to improve the life prediction accuracy of CMDB propellant at room temperature. The relative error of 20.84 years predicted by MNA content is 8.59% compared with 19.19 years predicted by maximum elongation, indicating that the prediction results based on MNA content are in good consistency with those based on maximum elongation.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e3.4. Correlation model between maximum elongation and MNA depletion of CMDB propellant\u003c/h2\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e3.4.1. Analysis of aging mechanism\u003c/h2\u003e \u003cp\u003eWhen CMDB propellant is in uniaxial tensile state, with the increase of tensile stress, the stress concentration between particles and matrix is gradually intensified, and particles and matrix begin to debond each other, which is called de-wetting (Francqueville et al., \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2021\u003c/span\u003e), and cavities are formed around particles. As the load increases, some particles bond to the interface to a critical load, resulting in dewetting and the formation of microcracks between the particles and the matrix. Microcrack will affect the stress distribution. Under the tensile load, the crack tip will become the stress concentration area, thus accelerating the failure of the matrix and the dehumidification rate of the particles. In addition, with the increase of strain, de-wetting particles gradually occupy the majority, and microcracks will expand and form large cracks, leading to fracture failure of CMDB propellant (Sun et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). Therefore, the damage states of CMDB propellant at meso-level, including particle de-wetting, pores and microcracks, directly affect the macroscopic mechanical properties of CMDB propellant.\u003c/p\u003e \u003cp\u003eIn this paper, scanning electron microscope SU3500 was used to carry out scanning electron microscope experiments, and scanning electron microscope images of CMDB propellant tensile fracture surface under different aging times were obtained, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(a), the particle profile of the unaged specimen is clear, and no obvious micro-cracks or micro-pores are found in the matrix in the fracture surface. In Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e(b)-(d), due to the influence of aging, the particle contour is no longer clear, and there are de-wetting and micro-cracks in the fracture surface. As shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e (d), when thermal aging lasted for 100 days, severe de-wetting and obvious micropores existed in the fracture surface. Therefore, with the increase of storage time, the damage state of CMDB propellant at the meso-level is continuously intensified, which leads to the continuous reduction of the maximum elongation of CMDB propellant, thus proving the rationality of the change curve of maximum elongation with aging time shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFor the composite solid propellants, the chemical aging is the main reason which leads to the aggravation of the damage of the matrix and the decrease of the macro-mechanics in the mesoscopic level (Liu et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2022\u003c/span\u003e, Du et al., \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2021\u003c/span\u003e, Du et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). CMDB propellant is a composite solid propellant consisting of nitrocotton (NC) and nitroglycerin (NG) as the binder matrix, adding energetic additives and solid fillers such as metal fuel. Nitrocellulose (NC) as an important component of CMDB propellant matrix, the activation energy is 120\u0026ndash;190 kJ/mol, stored at room temperature can also occur slow decomposition (Mušanić et al., \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), the decomposition is caused by the chemical bond homolytic reaction of O-NO\u003csub\u003e2\u003c/sub\u003e, as shown in Eq.\u0026nbsp;(\u003cspan refid=\"Equ11\" class=\"InternalRef\"\u003e11\u003c/span\u003e), the decomposition products such as ṄO\u003csub\u003e2\u003c/sub\u003e, NO and HNO\u003csub\u003e2\u003c/sub\u003e are generated. In the presence of decomposition products, nitrofoam (NC) and nitroglycerin (NG) undergo autocatalytic reactions to accelerate their own decomposition (Elbasuney et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, Elbasuney et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), as shown in Eqs.\u0026nbsp;(\u003cspan refid=\"Equ12\" class=\"InternalRef\"\u003e12\u003c/span\u003e) and (\u003cspan refid=\"Equ13\" class=\"InternalRef\"\u003e13\u003c/span\u003e), and release a large amount of heat, affecting the structural integrity of the propellant matrix, thus causing major safety hazards.\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\mathop {\\text{N}}\\limits^{\\cdot } {\\text{O+}}{{\\text{O}}_2} \\to 2\\mathop {\\text{N}}\\limits^{\\cdot } {{\\text{O}}_2} \\leftrightarrow {{\\text{N}}_2}{{\\text{O}}_4}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ12\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ12\" name=\"EquationSource\"\u003e\n$$\\mathop {\\text{N}}\\limits^{\\cdot } {\\text{O}}+\\mathop {\\text{N}}\\limits^{\\cdot } {{\\text{O}}_2}+{{\\text{H}}_{\\text{2}}}{\\text{O}} \\to 2{\\text{HN}}{{\\text{O}}_2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e12\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ13\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ13\" name=\"EquationSource\"\u003e\n$$3\\mathop {\\text{N}}\\limits^{\\cdot } {{\\text{O}}_2}+{{\\text{H}}_{\\text{2}}}{\\text{O}} \\to 2{\\text{HN}}{{\\text{O}}_3}+\\mathop {\\text{N}}\\limits^{\\cdot } {\\text{O}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e13\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eThe main process of oxidation and decomposition of CMDB propellant matrix cannot be stopped, but the addition of MNA can react with decomposition products to prevent the occurrence of autocatalytic reaction, and thus prolong the storage life of propellant (Qiufan et al., \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2017\u003c/span\u003e). The reaction equations of MNA and decomposition products are shown in Eqs.\u0026nbsp;(\u003cspan refid=\"Equ14\" class=\"InternalRef\"\u003e14\u003c/span\u003e) and (\u003cspan refid=\"Equ15\" class=\"InternalRef\"\u003e15\u003c/span\u003e). With the increase of storage time, MNA reacts continuously with nitrogen oxides, resulting in the continuous reduction of MNA content in CMDB propellant (Liqiong et al., \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), which proves the rationality of the change curve of MNA content with aging time shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003cdiv id=\"Equ14\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ14\" name=\"EquationSource\"\u003e\n$${\\text{MNA+}}\\mathop {\\text{N}}\\limits^{\\cdot } {{\\text{O}}_{\\text{2}}} \\to {\\text{MNA}} \\cdot {\\text{+HN}}{{\\text{O}}_{\\text{2}}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e14\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equ15\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ15\" name=\"EquationSource\"\u003e\n$${\\text{MNA}} \\cdot {\\text{+}}\\mathop {\\text{N}}\\limits^{\\cdot } {\\text{O}} \\to {\\text{N-NO-MNA}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e15\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eAt the same time, due to the continuous oxidation decomposition reaction of nitrocotton (NC) in the storage process, the decomposition products are produced constantly. Therefore, there is a certain relationship between the depletion of MNA and the depletion of nitrocotton (NC), and the change of MNA content can be used to indirectly characterize the change of nitrocotton (NC) content in CMDB propellant matrix (Zhang et al., \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2022\u003c/span\u003e, Asthana \u003cem\u003eet al.\u003c/em\u003e, 1989). Nitrocellulose (NC) is an important part of the binder matrix of CMDB propellant. The depletion and decomposition of nitrocellulose (NC) lead to the formation of pores and microcracks in the matrix, poor bonding between solid particles and matrix, resulting in particle debonding, which affects the macroscopic mechanical properties and leads to the decrease of maximum elongation. Therefore, there is a certain relationship between MNA content and maximum elongation.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section3\"\u003e \u003ch2\u003e3.4.2. Establishment of correlation model between maximum elongation and MNA depletion\u003c/h2\u003e \u003cp\u003eAt present, most of the reports on the storage properties of composite propellants only pay attention to the changes of macroscopic mechanical properties or microscopic chemical components. There are few reports that combine the macroscopic mechanical properties and microscopic chemical components of composite propellants and apply them to the aging life prediction of composite propellants.\u003c/p\u003e \u003cp\u003eAccording to the aging mechanism analysis in the previous section, there is a certain relationship between the MNA content \u003cem\u003ew\u003c/em\u003e and the maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e that under different thermal aging temperatures, MNA content \u003cem\u003ew\u003c/em\u003e and maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e can be regarded as functions of aging time respectively, and both functions change monotonically with aging time. The reduction of MNA content \u003cem\u003ew\u003c/em\u003e under a certain aging time is defined as the MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e under the current aging time, that is, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{d}=1\\text{\\%}-w\\)\u003c/span\u003e\u003c/span\u003e. Therefore, with the same aging time, the MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e is the independent variable and the maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e is the dependent variable, and the corresponding relationship between the MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e and the maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e is established as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. It can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e that MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e of CMDB propellant has a strong correlation with the maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e. With the increase of MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e, the maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e decreases monotonically. Eq.\u0026nbsp;(\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e16\u003c/span\u003e) was used to fit the experimental results in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, and the results are shown in Table\u0026nbsp;\u003cspan refid=\"Tab8\" class=\"InternalRef\"\u003e8\u003c/span\u003e.\u003cdiv id=\"Equ16\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ16\" name=\"EquationSource\"\u003e\n$${\\varepsilon _m}={B_1}\\exp ( - {w_d}/{B_2})+{B_3}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e16\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e is the maximum elongation; \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e is the MNA depletion, %, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({w}_{d}=1\\text{\\%}-w\\)\u003c/span\u003e\u003c/span\u003e; \u003cem\u003eB\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e, \u003cem\u003eB\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e and \u003cem\u003eB\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e are constants.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab8\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 8\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eFitting results of macro and micro corresponding relation functions\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eB\u003c/em\u003e\u003csub\u003e1\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cem\u003eB\u003c/em\u003e\u003csub\u003e2\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cem\u003eB\u003c/em\u003e\u003csub\u003e3\u003c/sub\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003e\u003cem\u003eR\u003c/em\u003e\u003csup\u003e\u003cem\u003e2\u003c/em\u003e\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e0.1346\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.3491\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1014\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.9674\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo verify the validity of the corresponding relationship between MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e and maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e, the maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.2024, 0.1773, 0.1584, 0.1442 and 0.13354) corresponding to different MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e = 0.1%, 0.2%, 0.3%, 0.4% and 0.5%) were calculated respectively. According to section \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003e3.3.1\u003c/span\u003e of a MNA content as aging characteristics calculated CMDB propellant aging rate \u003cem\u003eK\u003c/em\u003e (\u003cem\u003eK\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1.1044\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e mol/(cm\u003csup\u003e3\u003c/sup\u003e\u0026sdot;d)) under 298.15 K, Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) was used to calculate the corresponding aging time \u003cem\u003et\u003c/em\u003e (\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1901.9 d, 3303.3 d, 4704.6 d, 5905.7 d and 7007 d) under different MNA depletion \u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003ew\u003c/em\u003e\u003csub\u003e\u003cem\u003ed\u003c/em\u003e\u003c/sub\u003e = 0.1%, 0.2%, 0.3%, 0.4% and 0.5%). According to section \u003cspan refid=\"Sec12\" class=\"InternalRef\"\u003e3.3.1\u003c/span\u003e of a maximum elongation as aging characteristics calculated CMDB propellant aging rate \u003cem\u003eK\u003c/em\u003e (\u003cem\u003eK\u003c/em\u003e\u0026thinsp;=\u0026thinsp;2.1162\u0026times;10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e mol/(cm\u003csup\u003e3\u003c/sup\u003e\u0026sdot;d))under 298.15 K, Eq.\u0026nbsp;(\u003cspan refid=\"Equ6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) was used to calculate the corresponding maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e (\u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.1843, 0.1575, 0.1389, 0.1266 and 0.1177) under different aging time \u003cem\u003et\u003c/em\u003e (\u003cem\u003et\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1901.9 d, 3303.3 d, 4704.6 d, 5905.7 d and 7007 d). The maximum elongation \u003cem\u003eε\u003c/em\u003e\u003csub\u003e\u003cem\u003em\u003c/em\u003e\u003c/sub\u003e calculated by the two methods is compared, and the calculated error values between the two methods are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, Eq.\u0026nbsp;(\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e16\u003c/span\u003e) can well describe the change between MNA depletion and maximum elongation. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, the error between the maximum elongation calculated by Eq.\u0026nbsp;(\u003cspan refid=\"Equ16\" class=\"InternalRef\"\u003e16\u003c/span\u003e) and the maximum elongation calculated by the aging model is small, and the overall error is less than 15%. The results show that the relationship between the MNA depletion and the maximum elongation proposed in this paper is feasible. Based on this function, the relationship between macroscopic and microscopic storage properties of CMDB propellant was established, that is, the maximum elongation of CMDB propellant under this content could be predicted by measuring the MNA content in CMDB propellant after aging at room temperature.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Conclusions","content":"\u003cp\u003eIn this paper, the thermal accelerated aging test of CMDB propellant was carried out, the changes of MNA content and maximum elongation of CMDB propellant were analyzed, and the modified exponential aging model of CMDB propellant was established. With MNA content and maximum elongation as aging characteristics, the storage life of CMDB propellants at 298.15 K was predicted using the modified Arrhenius equation. The aging mechanism of CMDB propellant was analyzed and the correlation function model of MNA depletion and maximum elongation was established. The main conclusions are as follows:\u003c/p\u003e \u003cp\u003e(1) Based on the existing aging model, a modified exponential aging model was established to fit the variation curves of MNA content and maximum elongation respectively. The fitting correlation coefficients were both greater than 0.97. The model could accurately describe the variation of MNA content and maximum elongation of CMDB propellant.\u003c/p\u003e \u003cp\u003e(2) With MNA content and maximum elongation decreasing by 50% as aging failure criterion and MNA content and maximum elongation as aging characteristics, the modified Arrhenius equation was used to predict the storage life of CMDB at 298.15 K to 19.19 years and 18.09 years, respectively, and the relative error of the two prediction results was 6.08%. The result showed that the prediction result based on MNA content was in good agreement with this based on maximum elongation.\u003c/p\u003e \u003cp\u003e(3) There is a good correlation between the MNA depletion and the maximum elongation of CMDB propellant. According to the test data of the MNA content and the maximum elongation under different aging time, the correlation function model of the MNA depletion and the maximum elongation was established. The relative error between the maximum elongation calculated by this model and the maximum elongation calculated by the aging model was less than 15%. The results show that the correlation function model of MNA depletion and maximum elongation established in this paper is effective. By measuring the MNA content after aging of CMDB propellant at room temperature, the maximum elongation of CMDB propellant can be predicted.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eASTHANA, S. N., DIVEKAR, C. N. \u0026amp; SINGH, H. 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(2006), \"A study of kinetic behaviours of the effective centralite/stabilizer consumption reaction of propellants using a multi-temperature artificial accelerated ageing test\", Journal of Hazardous Materials, Vol.\u0026nbsp;145 No. 1, pp.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"mechanics-of-time-dependent-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mtdm","sideBox":"Learn more about [Mechanics of Time-Dependent Materials](http://link.springer.com/journal/11043)","snPcode":"11043","submissionUrl":"https://submission.nature.com/new-submission/11043/3","title":"Mechanics of Time-Dependent Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"CMDB propellant, Maximum elongation, MNA content, Correlation, Aging model, Shelf-life prediction","lastPublishedDoi":"10.21203/rs.3.rs-3126969/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-3126969/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eIn order to predict the storage life of composite modified double base propellant (CMDB propellant) at 298.15K, the correlation between the maximum elongation and the stabilizer depletion of CMDB propellant was studied. The thermal accelerated aging tests were carried out at 323.15K, 333.15K, 343.15K and 353.15K. The changes of MNA content and maximum elongation at different thermal aging temperatures were analyzed and a modified exponential aging model for CMDB propellant was proposed. With MNA content and maximum elongation as aging characteristics, the storage life of CMDB propellants at 298.15K was predicted using the modified Arrhenius equation. The aging mechanism of CMDB propellant was analyzed and the correlation function model of maximum elongation and stabilizer depletion was established. The results show that the maximum elongation and MNA content decrease with aging time and aging temperature increasing. The fitting correlation coefficients of modified exponential aging model are all greater than 0.97, which can better describe the changes of MNA content and maximum elongation of CMDB propellant. The storage life of CMDB at 298.15K is estimated to be 19.19 years and 18.09 years, respectively. The validity of the correlation function between the maximum elongation and the stabilizer depletion is verified. The overall error is less than 15%, which provides a reference for predicting the maximum elongation of CMDB propellant by the consumption of MNA.\u003c/p\u003e","manuscriptTitle":"Shelf-life prediction and correlation between maximum elongation and stabilizer depletion of CMDB propellant","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2023-07-10 17:16:48","doi":"10.21203/rs.3.rs-3126969/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Major revision","date":"2023-07-27T19:58:13+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2023-07-27T09:34:10+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"c04faca9-55ae-4227-82a0-3881ca4da0f6","date":"2023-07-05T11:35:25+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2023-07-04T19:59:48+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2023-07-04T19:58:05+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2023-07-03T17:35:40+00:00","index":"","fulltext":""},{"type":"submitted","content":"Mechanics of Time-Dependent Materials","date":"2023-06-30T06:11:23+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"mechanics-of-time-dependent-materials","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"mtdm","sideBox":"Learn more about [Mechanics of Time-Dependent Materials](http://link.springer.com/journal/11043)","snPcode":"11043","submissionUrl":"https://submission.nature.com/new-submission/11043/3","title":"Mechanics of Time-Dependent Materials","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"4164ff0a-0b7d-4591-b716-4954f03c817d","owner":[],"postedDate":"July 10th, 2023","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"published-in-journal","subjectAreas":[],"tags":[],"updatedAt":"2023-09-11T15:05:45+00:00","versionOfRecord":{"articleIdentity":"rs-3126969","link":"https://doi.org/10.1007/s11043-023-09634-8","journal":{"identity":"mechanics-of-time-dependent-materials","isVorOnly":false,"title":"Mechanics of Time-Dependent Materials"},"publishedOn":"2023-09-06 15:02:36","publishedOnDateReadable":"September 6th, 2023"},"versionCreatedAt":"2023-07-10 17:16:48","video":"","vorDoi":"10.1007/s11043-023-09634-8","vorDoiUrl":"https://doi.org/10.1007/s11043-023-09634-8","workflowStages":[]},"version":"v1","identity":"rs-3126969","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-3126969","identity":"rs-3126969","version":["v1"]},"buildId":"WrCJVZZCHTDjtuVLN7oU0","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}