Salim Chelouche,Djalal Trache,Ilyas Maamache,Ahmed Fouzi Tarchoun,Kamel Khimeche,Abderrahmane Mezroua

UER Proc′ed′es Energ′etiques,Ecole Militaire Polytechnique,EMP,BP 17 Bordj-El-Bahri,16046,Algiers,Algeria

Keywords:Chemometrics van’t hoff rule Natural aging Artificial aging Stability Storage

ABSTRACT The assessment of the real in-service-time(RIST)and the equivalent in-service-time(EIST)of double base rocket propellants(DBRPs)is of utmost importance for the safe storage and use of weapon systems as well as the efficiency of the accelerated aging plans.In this work,four DBRPs with similar chemical composition and different natural aging have been artificially aged at T=338.65 K for 4 months with sampling every 30 days.The unaged and artificially aged samples have been investigated by vacuum stability test(VST)at five isothermal temperatures(T=333.15 K,343.15 K,353.15 K,363.15 K,and 373.15 K).The volume of the evolved gases in VST was found to decrease with natural/artificial aging.Furthermore,the VST data were treated and subjected to principal component analysis(PCA).The results showed excellent discrimination of the DBRP samples according to their stability thermal properties.Most of the variance was described by the first principal component(PC1)whose scores were linearly correlated with the natural aging durations when PCA is applied on VST data obtained at T=363.15 K.In light of the obtained results,a new experimental way for the estimation of the real/equivalent IST was proposed,which takes into account the impact of the natural aging of the sample.The approach predicts successfully the RIST of two similar DBRPs with a relative deviation of less than 2%.At the specific heating temperature T=338.65 K,the developed model provides more conceivable EIST values,with asymptotic behavior against artificial aging duration evolution,thus overcoming some shortcomings of the common generalized van’t Hoff formula(GvH).

1.Introduction

Solid propellants are classified into two principal categories,i.e.,homogeneous and heterogeneous.In the former,the ingredients are linked chemically,leading to a homogeneous physical structure[1,2].Depending on the number of energetic ingredients(nitrate esters),homogeneous solid propellants can be single-base(nitrocellulose(NC)and additives)propellants,double-base(NC,nitroglycerine(NG),and additives)propellants,and triple-base(NC,NG,nitroguanidine,and additives)propellants.Being smokeless and having abundant raw material sources are among the main reasons for the wide application of double base propellant to solid rocket motors[3].

Because of the low bonding energy of the nitrate ester groups(155 kJ/mol)[4,5],these energetic materials undergo,even at normal storage conditions of temperature and humidity,a selfexothermic decomposition ultimately resulting in autocatalytic run-way reactions[4,6].The mechanisms governing the chemical degradation of the nitrate esters have been deeply discussed in the literature and several milestones have been achieved in this field[7,8].This hazardous situation can be prevented by adding chemical substances,commonly called stabilizers,which can inhibit this instability reaction and slow down its rate.However,under certain conditions,preferably avoided,this degradation leads to selfignition or even unexpected explosions.

Furthermore,the safe service time for double base rocket propellant(DBRP)could usually be assumed to be greater than 40 years[9].However,when the ammunitions are stored in severe conditions(very hot/humid regions)the actual service life could be far below that.Therefore,making an idea on the effective lifetime based on the year of manufacture of the energetic material could be erroneous,which increases the risks of an accident during storage in warehouses or during operation.Moreover,the prediction of the effective DBRP lifetime requires the achievements of kinetic modeling on data obtained by analytic techniques,which require fastidious operations,many steps,and high labor costs.Besides,these operations have to be conducted every time the lifetime is asked for.Hence,efforts should be directed to set new procedures for the prediction of the real in-service-time(RIST)of DBRP during its whole lifetime.

On the other hand,the determination of the accurate equivalent in-service-time(EIST)is of paramount importance when artificial aging plans are carried out.This treatment is often followed by the scientific community when energetic materials are investigated[10-13].The accelerated aging procedure aims to reduce significantly the time scale by heating the samples at temperatures higher than the ambient.At the end of the heating cycle,samples with closer properties to those aged naturally for a long duration are obtained.

Commonly,the generalized van’t Hoff rule(GvH)is often used to design time-temperature profiles[14-16].Nevertheless,the use of the GvH formula to predict the equivalence between natural/artificial aging for DBRP presents some shortcomings,more particularly when long aging plans are expected.EIST depends on the value of the reaction rate change factor(F)often taken constant or computed based on kinetic modeling on the degradation reaction data[14,17].Moreover,the EISTs are found to be unrealistic and inconceivable when the time loads became more important.Indeed,taken F constant leads to a constant evolution of the EISTs with time load progress,and eliminates the impact of natural aging.Consequently,new experimental methodologies should be set to determine exactly the equivalence between natural/artificial aging.

This study was devoted to the establishment of a new experimental way for the estimation of the real/equivalent in-servicetime by the application of a chemometric tool,viz,principal component analysis(PCA)to vacuum stability test(VST)data.To the best of our knowledge,it is the first time that PCA is applied to VST data.It should be noted that VST is a reliable and wellinforming quantitative stability test,which was mainly developed for judging the actual stability status of propellants[18,19].Furthermore,VST was successfully used to determine the kinetic parameters for the decomposition reaction of solid propellants[20,21]as well as the compatibility between the components of energetic mixtures[22,23].

Chemometric tools have proven their capabilities of differentiation and discrimination in the field of energetic materials[24-26].Chemometric employs multivariate statistics,applied mathematics,and computer science via methods frequently employed in core data-analytic to address problems in chemistry,biochemistry,medicine,biology,and chemical engineering[27].Moreover,PCA,which aims to reduce the dimension of the data,is the most used multivariate analysis technique as it is a starting point in the data mining process[28].Therefore,the PCA algorithm applied to VST data should lead to an efficient procedure for the prediction of the real/equivalent in-service-time of DBRPs.

In this work,four DBRPs presenting similar chemical composition and different natural aging periods have been artificially aged for 4 months at T=338.65 K according to the NATO standardization agreement requirements(STANAG 4117).Sampling was carried out every 30 days.The unaged and artificially aged samples were analyzed by VST at five isothermal temperatures(T=333.15 K,343.15 K,353.15 K,363.15 K,and 373.15 K).The obtained data were treated and subjected to PCA.Based on the scatter plot as well as the PC scores obtained for the unaged samples,a new methodology is established for the prediction of the real and equivalent inservice-time.Two similar DBRPs with different natural aging were used to validate the procedure of the RIST assessment.Moreover,the obtained EIST values were compared to those provided by the GvH formula according to three cases.

2.Experimental and methods

2.1.Materials

All experiments were carried out on four DBRPs stored in the same warehouse and presented different natural aging periods,i.e.,DBRP1(naturally aged for 31.9 years),DBRP2(naturally aged for 29.9 years),DBRP3(naturally aged for 18.7 years),and DBRP4(naturally aged for 10.9 years).The propellants present the same chemical composition with 52 wt.% of nitrocellulose(NC),30 wt.%of nitroglycerine(NG),2.5 wt.% of methyl centralite(MC),5 wt.%dibutyl phthalate(DBP),and 10.5 wt.% of other additives,encompassing ballistic additives(to reduce the sensitivity of the burning to pressure fluctuation),operational additives(refractory products and flash suppressant additives),and graphite(to facilitate some manufacture operations).Because of their hardness,the propellants extracted in one piece were grated into very small pieces using a special rasp.The layer corresponding to the inhibitor(～2 mm)was initially removed.

2.2.Artificial aging

This approach often used when energetic materials are investigated,offers in short interval time samples with characteristics and properties comparable to samples naturally aged for long periods,thus allows saving a lot of time in investigations.The procedure requirements were inspired by the NATO standardization agreement STANAG 4117[29],which consists of a heating cycle of each DBRP for 4 months in an oven at 338.65±0.1 K.For each propellant,sampling was carried out every 30 days of heating.

In what follows A0 refers to the samples,which have not been aged artificially but already present different natural aging periods.However,A1,A2,A3,and A4 stand to the samples artificially aged for 1,2,3,and 4 months,respectively.

2.3.Vacuum stability test

The Czech vacuum stability test known under the name of STABIL is usually used for the evaluation of the thermal stability of high explosives,propellants,rocket fuels,and pyrotechnics.To remove moisture,all the samples(2 g)have been dried in advance for 4 h in an oven at 333.15±0.1 K.These conditions(sample mass and drying time)were found optimal for the investigation of different types of propellants by VST including double base rocket propellants[30].Subsequently,the samples were introduced in special glass tubes evacuated to 0.2 kPa using a vacuum pump and put softly for 30 min to detect a possible loss of pressure induced by a gas leak.The tubes were then placed for 48 h into the heating block previously maintained at the following test temperatures:333.15 K,334.15 K,353.15 K,363.15 K,and 373.15 K,respectively.

Before carrying out the VST measurements,the heating block was calibrated using silicon oil provided by the manufacturer.Pressure transducers estimate every minute the pressure increase inside the test tubes.The results provided by the STABIL software are in the form of time dependence of the gas pressure evolved by the sample and corrected to standard conditions,according to Eq.(1).

where V(cm3),Vc(cm3),and Vt(cm3)refer,respectively,to the volume of all gases released by the sample,the volume of the pressure transducer,and that of the glass test tube,m(g)and d(g/cm3)are,respectively,the sample masse and the density,P1and P2(bar)are the initial and the final pressure,and T1(°C)and T2(°C)stand for the temperatures at the beginning and the end of the test.

2.4.Principal component analysis of VST data

VST,among other modern analytic instruments,provides a large amount of data.More explicitly,a VST curve may include several thousands of data points(in our case 2880 points for each temperature and each system)and its treatment without the use of powerful tools can lead to significant loss of information.PCA can avoid all of these issues by transforming the original variables into a smaller set of uncorrelated latent variables intended to be used by other methods.The latent variables with the highest concentration of information form lower-dimensional data,which can be visualized graphically[31].

The application of PCA method converts the VST data matrix X,which contains N lines(samples)and M columns(pressure)into:(1)a score matrix T corresponding to the sample coordinates in the new system of axes and(2)a loading matrix P presenting the relation between the variables,plus a residual matrix E.The mathematical presentation can be expressed as follow:

The dimensions of X,t,and P are(N×J),(N×A),and(A×J),respectively,with A is the number of principal components needed to describe the useful information in the data;N and J are the number of samples and variables,respectively,and E is the residual matrix,with same dimensions as X.This decomposition is particularly useful for converting X to a few information plots(scores and loadings plot)and for modeling the systematic structure in X.

Geometrically,this change of variables results in a change of axes,called principal components,chosen to be orthogonal[32].Each newly created axis defines a direction that describes a part of the global information[28].

3.Results and discussion

3.1.Vacuum stability test

VST provides a measure of all the gases evolved(N2,NOx,COx,…,etc.)by the propellant under certain vacuum and temperature.The obtained volumes per sample mass for the investigated DBRPs at the five isothermal VST temperatures are summarized in Table 1.The uncertainty associated with the released gases volume was evaluated based on repeated measurement of the samples and found to be less than 0.09 mL/g(<6%).Furthermore,the effect of the VST isothermal temperature on the evolved gas pressure for the unaged and artificially aged DBRP2 sample is presented in Fig.1,whereas the effect of the artificial aging on the released gas pressure at different test temperatures for DBRP3 samples is shown in Fig.2.It is worth noting that the remaining DBRPs in the previous cases present similar trends.

At the beginning of the test,the pressure of the released gases for all DBRP samples is found to roughly increase with the increase of the temperature,which can be related to the residual humidity content[18],even though a drying process was performed ahead.Then,the pressure increased gradually with time progress whose intensity is found to be proportional to the VST isothermal temperature.It should be noted that such type of investigation is scarce in the literature.However,Kucera and Havrankova found closer value(8.32 mL/g)for DBP,with closer NG content(28.3%),tested by VST(STABIL)at T=388.15 K for 20 h[33].

It is obvious from Table 1,that the volume of the evolved gases at each isothermal temperature decreases with artificial aging progress compared to the unaged samples,which is contrary to what was previously obtained for NC-based propellants[34].This can be related to NG(acts as a plasticizer in the DBRP sample)evaporation during heating.

This means that the NG migration,diffusion,and evaporation processes are the dominant processes rather than the decomposition reaction of the nitrate esters(NC and NG).Actually,in a DBRP,NG,which is a volatile compound[35],forms weak bonds with NC,making it more mobile and consequently moving more easily to the propellant block surface[36].More explicitly,during the first month of heating,most of the NG molecules migrate to the surface of the propellant pieces and then evaporate when subjected to VST(for 48 h with higher heating temperature).With the progress of aging,the quantity of the NG migrating to the surface became less and less important,which influences the volume of the released gases,and found decreasing with aging progress.Indeed,the NG depletion time was determined by an isothermal thermogravimetry(TG)carried out at T=373.15 K and was found equal to 82 days for similar DBRP(NC～54%,NG～35%,～3.0% of diethyl phthalate,and～8% of other additives)artificially aged at T=363.15 K[37].

On the other hand,the volume of the released gases for all DBRPs samples(A0-A4)was found to increase with the increase of the VST isothermal temperature due to the catalytic effect of the temperature on the degradation reaction[34].This effect was found to be more significant at higher test temperatures(363.15 K and 373.15 K).

3.2.PCA of VST data

As shown in Fig.1(T=333.15 K),VST raw data were smoothed using nonlinear curve fits to eliminate noises in the VST signal when subjected to PCA.The data are mean-centered but not autoscaled,although auto-scaling is the most used preprocessing in chemometrics.This can be connected to the blow-up of variables with small values in VST data at the beginning of the test.

The eigenvalues,as well as the percentage of variance expressed by each principal component,are given in Tables S1(PCA applied to all samples)and S2(PCA applied separately to each DBRP)in the supplementary materials(SM),and shown in Fig.3(PCA applied to all samples).Typically,the scores for PC1 and PC2 gain the first interest,and one should first verify how much of the total variance is preserved by the respective projection axes.However,the following criteria can be used to select the number of the relevant principal components[38]:

-Principal components describing 90% of the total variation are retained.

-Determine the eigenvalues average and exclude those which are lower to it.

Referring to the two previous criteria,only PC1 should be retained as it represents about 99.74% of the relevant variance in the VST data.For a presentation of the studied samples in their new multidimensional variables space,at least two PCs should be retained.It is obvious from Tables S1 and S2 that PC2 describes the second higher variance in the VST data.The total variance for the first two factors is found 99.93% when PCA is applied to all DBRPs samples,99.98%,99.99%,99.99%,and 99.96% when PCA is applied separately to each DBRP samples(DBRP1-DBRP4).These sums are high enough for an excellent representation of the dimensional variables space in two-dimensional projection and could be informative to cluster samples within.Likewise,it was reported that if more than 90% of the total variance is preserved,the twodimensional representation is excellent[39].

Fig.1.Gases-evolved pressure evolution by DBRP2 samples against VST time progress/effect of artificial aging.

Furthermore,plot(a)in Fig.4 shows the scatter plot from PCA of VST data obtained for all the studied DBRPs samples at the five VST isothermal temperatures,comprising the first two PCs(PC1 and PC2).Commonly,each resulting cluster contains samples that have similar characteristics and present closer properties;hence the further away the groups are,the more the differences are[24,40].It should be noted that the scatter plots when PCA is applied separately to each DBRP,show similar discrimination.The variation in the scores of the investigated samples for all the studied propellants(unaged and artificially aged)shows that five groups presenting distinct stability properties can be easily distinguished.The clustering has been indicated by drawing ellipses in plot(a)in Fig.4.One can easily verify that each cluster corresponds to a specific VST isothermal temperature,i.e.,the five clusters contain the samples analyzed in VST at 333.15 K,343.15 K,353.15 K,363.15 K,and 373.15 K,respectively.

Fig.2.Gases-evolved pressure evolution by DBRP3 samples against VST time progress/effect of VST temperature.

Fig.3.Eigenvalues for the 99 Principal Components/PCA applied to all the studied samples(100).

Fig.4.Scatter plot from PCA of VST data:(a)at all isothermal temperatures;(b)at T=K.

Cluster 1,Cluster 2,and DBRP1-DBRP2 samples in cluster 3 are characterized by negative values of PC1,while DBRP3-DBRP4 samples in Cluster 3,Cluster 4,and Cluster 5 are given by positive values.Moreover,it should be pointed out that the PC1 score for all samples increases,from negative to positive values,with VST isothermal temperature increase;hence the temperature effect on the samples’thermal properties is best expressed by the first principal component.Additionally,the increase in VST temperature results in an increase in the distances between clusters.

Basically,most distances between object points will reflect well the distances in the high-dimensional variable space,when the two-dimensional presentation is excellent[39].Therefore,the higher the pressure variation is,the higher the distance between object points is.It is obvious from Fig.2 that the evolution of the evolved gases pressure at the same instant“t”from the degradation reaction increases with the increase of the VST temperature.Moreover,the intensity of this evolution was found to be more and more important while passing from a temperature to a higher temperature.This can explain the increase of distance between the five clusters(according to the PC1 axis)in Fig.4 with the increase of the VST isothermal temperature.

To highlight the effect of natural/artificial aging on the thermal stability properties of the studied DBRPs,PCA was applied on VST data obtained for all the DBRPs samples at T=373.15 K.The choice of the highest VST temperature was to increase the variations between samples according to their stability properties and consequently the distance between clusters.Plot(b)in Fig.4 shows the obtained scatter plot.It should be noted that similar discriminations were found for the other VST temperatures.From plot(b),it is obvious that the natural/artificial aging affects the distribution of the samples in a different way than that of the VST isothermal temperature.Indeed,with natural/artificial aging progress,the PC1 scores moved from positive to negative values.Moreover,the loss of the thermal stability under both types of aging is mainly expressed by the first component PC1,which presents about 86.46% of the total variance.

3.3.Procedure for the estimation of the real in-service-time(RIST)

Before the establishment of the procedure,an attempt was made to determine the VST temperature,which better describes the variation in the thermal properties with natural aging progress according to a particular regression.Fig.5 shows the PC1 scores evolution for the unaged DBRP(1-4)with respect to their respective natural aging durations at different VST temperatures.Based on the fitting parameters,the particular isothermal temperature of 363.15 K was found to be the most suitable to present this variation following a linear regression(Eq.(3)).

Fig.5.The evolution of PC1 scores by PCA applied to VST data of DBRP1-4 against their natural aging at all VST temperatures.

where a and b are the regression constants and nA(years)is the natural aging period.

This finding is of paramount importance as it allows determining the RIST of a DBRP by incorporating its PC1 score acquired after performing PCA on VST treated data(Eq.(4)).

The samples whose VST data will be subjected to PCA are:

1.The DBRPs stored under normal storage conditions and whose actual shelf life(based on their manufacture date)are known;

2.The propellant we want to determine its real in-service-time(RIST).

This procedure allows judging on the exact remaining shelf life for the propellant if stored in severe conditions(very hot/humid regions).

Two DBRPs(5 and 6)presenting natural aging durations of 20.5 years and 14.7 years,respectively,and stored in the same conditions than the DBRPs used for the establishment of the procedure(DBRP1-DBRP4)were used to validate the approach.The two propellants have been analyzed by VST at T=363.15 K and the obtained results are shown in Fig.6.Then,the treated data for DBRPs(1-5)and DBRPs(1-4+6)are subjected to PCA separately.The scores obtained for the DBRPs(1-4),in each case,are plotted against their respective natural aging.The eigenvalues,as well as the scores for each principal component,are given in Table S5-Table S8 in the SM.As shown in Fig.S1 and Fig.S2 in the SM,the evolution of the PC1scores of the samples against their natural aging is well correlated by a linear fit.Using the correlation parameters and the PC1 scores obtained for DBRP5 and DBRP6,the RISTs have been assessed.Table 2 summarizes the obtained results.The uncertainty associated with the estimated RIST was found to be less than 0.2 years.

It is obvious from Table 2 that the developed procedure evaluated the RIST for DBRP5 and DBRP6 with relative deviations of 2.0%and 0.8%,respectively,thus highlighting the accuracy of the methodology.

Fig.6.Gases-evolved pressure evolution against VST time progress for DBRP5 and DBRP6 at T=363.15 K.

Table 2The Real In-Service-Time estimated for DBRP5 and DBRP6 by the developed procedure.

3.4.Procedure for the estimation of the equivalent in-service-time(EIST)

The generalized van’t Hoff’s rule(GvH)allows evaluating the inservice-time at given in-storage temperatures from the equivalent time-temperature loads during the artificial aging(Eq.(5))[13].This methodology was found to be suitable to establish the timetemperature profiles[14].

where tE(year)is the in-service-time at the temperature TE(°C),tT(d)stands to the heating test duration at the temperature TT(°C),F is the reaction rate change factor per 10°C of temperature change,andΔTFrefers to the temperature interval for the actual value of F.

The factor F,computed via Eq.(6)was deduced from the work of van’t Hoff,who compiled and compared reaction rates obtained at different temperatures.The change of temperature by 10°C increases the reaction rate constants by an average factor of 3,the range often is 2-4[17].

Ea(kJ/mol)denotes the activation energy and R(J/(mol·K))is the universal gas constant.

An attempt was made to highlight some shortcomings with the use of the GvH rule for the estimation of the EIST,particularly,when long artificial aging periods are expected.Hence,three situations appear and should be discussed separately.

1stcase:The EIST values are determined by taking the reaction rate change factor(F)constant.Indeed,it was found that a factor F=3.5 can be used efficiently to determine the equivalent loads for DBRP with a similar chemical composition[10].This statement was valid for Earanging from 90 kJ/mol to 150 kJ/mol and for heating temperatures ranging from 40 K to 110 K.

2ndcase:The EIST values are determined by taking the reaction rate factor(F)constant for each DBRP and computed based on the Eaof the unaged samples.

3rdcase:For each propellant,the Eaof the unaged samples is determined at the end of each heating cycle(1,2,and 3 months)and used for the assessment of the reaction rate factors.The corresponding EISTs were subsequently evaluated.

It should be noted that the activation energies for the degradation reaction of the unaged samples and those artificially aged after each heating cycle have been estimated by fitting model on VST data.That approach was not detailed here and can be found in the literature[21,23].

Table 3 recaps the Eavalues as well as the F factors obtained for each sample.Furthermore,the EISTs obtained for the three situations discussed above are summarized in Table 4 and plotted in Fig.7 against their respective accelerated aging periods.

From Table 4,it is obvious that taking F constant results in constant progress in the EIST values,which can lead to unrealistic and inconceivable values for an extended heating cycle.Indeed,a linear evolution is established between the EIST and the heating cycle duration.Broadly,different phenomena occur during the accelerated aging of DBRP including NG migration,diffusion,and evaporation as well as the chemical decomposition of the nitrate esters(NG+NC)among other processes,which should lead to variable progress in the EIST.Likewise,the effect of the natural aging of the unaged DBRPs is not taken into account when evaluating the EIST.

The use of F constant for each propellant and computed based on the Eavalues for the unaged samples leads to very high values of the EIST.Similarly to the first situation,the evolution of the EIST against artificial aging was found to be also linear.

The EISTs values obtained in the third situation present an asymptotic evolution with respect to the artificial aging duration increase.However,the obtained values are unrealistic and very high.

In light of these results,a new experimental way for the determination of the equivalent in-service-time is proposed.PCA is applied to VST data(obtained at T=363.15 K)of the unaged DBRPs(1-6)in addition to the aged sample(X)that we want to determine its EIST.The obtained eigenvalues and scores for each principal component are given in Tables S7-S38 in the SM,whereas the evolution of the PC1 scores(obtained for the unaged samples)with respect to the natural aging are displayed in Figs.S3-S18 in the SM.As demonstrated before,linear regression is established between the PC1 Scores of the unaged DBRP1-6 and their respective natural aging durations.Using the obtained correlation parameters and the PC1 score for the aged sample DBRP(X),the equivalent natural inservice-time is evaluated for each propellant at every time of accelerated aging(aged DBRP1-4).Furthermore,the equivalent inservice-times are deduced by subtracting the natural aging of unaged samples from the equivalent natural in-service-times assessed previously.The obtained EIST values are reported in Table 4.The uncertainty associated with the estimated E.ISTs is found to be less than 0.3 years.

Table 3Reaction rate change factor(F)and Arrhenius parameters obtained by fitting model on VST data.

Table 4The equivalent in-service-time estimated for aged DBRPs by the generalized van’t Hoff rule and the developed procedure in this work.

It is obvious that this new experimental way leads to more fair results.By the way,the progress in the EISTs are found to decrease with artificial aging evolution,which is expected since the heating temperature(T=338.15 K)impact is more pronounced at the first stages of the thermal degradation.On the other hand,the effect of the natural aging on the EIST values is well appreciated since the samples presenting the highest natural aging durations show at the beginning of the artificial aging the highest EIST values.Moreover,the EIST presents an asymptotic evolution with artificial aging times as shown in Fig.7.

Efforts were then directed to correlate the evolution of the EIST with the artificial aging duration progress at the specific heating temperature T=338.65 K taking into account the effect of the natural aging of the propellant.The asymptotic behavior(see Fig.S19 in SM)was found to be best correlated via the following equation(Eq.(7)):

where a and b stand to the regression constant,whereas A(d)denotes the artificial aging duration.The Fitting parameters,the Reduced Chi-Sqr,and the adjusted R-square for the regression fit for each DBRP are given in Table S39 in the SM.

Thereafter,the regression constants(a and b)found for each DBRP are plotted against their respective natural aging durations and shown in Fig.S20 in the SM.The evolution was found to be best correlated according to an exponential fit(Eq.(8)).

where A1,A2,and k are the correlation fit constants and nA(year)refers to the natural aging duration of the sample.The Fitting parameters,the Reduced Chi-Sqr,and the adjusted R-square for the regression fits are given in Table S40 and shown in Fig.S20 in the SM.

The model governing the approach(Eq.(9))is obtained by Substituting Eq.(8)in Eq.(7).

Using the regression parameters values,Eq.(9)could be written as follow:

Fig.7.EIST evolution against artificial aging durations for all the studied DBRPs by the developed procedure as well as by GvH formula:F1 and F2 stand to the EISTs computed based on F factors corresponding to the second and third GvH studied cases,respectively.

The established model allows estimating the EIST(year)for the specific heating temperature(338.65 K)according to the desired artificial aging loads and by taking into consideration the effect of the natural aging.

For new synthesized DBRP with similar/closer chemical composition,the EIST can be evaluated according to Eq.(11).

where A(days)is the artificial aging load at T=338.65 K.

4.Conclusion

When severe storage conditions are expected,the accurate assessment of the real in-service-time(RIST)is of utmost importance to ensure safe storage and use.Likewise,the correctness of the results from artificial aging plans is strongly linked to the precision of the equivalent in-service-time(EIST)from the timetemperature profiles.In front with the scarcity of works devoted to the assessment of these two parameters,a new experimental way based on the application of the PCA chemometric tool to VST data was proposed.

Contrary to what was found for the common NC basedpropellants,the results of the VST carried out at five different isothermal temperatures on four DBRPs,aged for 4 months at T=338.65 K(sampling every 30 days),showed a diminution of the released gases volume with natural/artificial aging time progress.This behavior is connected to the predominance of the nitroglycerine migration,diffusion,and evaporation phenomena during the first stages of degradation.

As a first attempt,the principal component analysis was successfully applied to VST data allowing excellent discrimination of DBRPs samples according to their stability properties.The first principal component was found to describe most of the variance in the thermal properties of the DBRP samples with natural/artificial aging progress.Moreover,the data from the particular VST temperature of 363.15 K was found to best correlate the evolution of the PC1 scores of the unaged DBRPs with respect to their respective natural aging duration following a linear fit.

In light of the obtained results,a new experimental way,based on the application of the PCA to VST data obtained at T=363.15 K was proposed for estimating the real in-service-time.The approach was validated by two similar DBRPs,presenting different natural aging,with a relative deviation of less than 2%.

To overcome the limits of the GvH rule often used to set timetemperature profiles,especially when long artificial aging plans are carried out,the procedure was successfully employed for the assessment of the equivalent in-service-time for different time loads at the heating temperature cycle of 338.65 K.The developed model provides more conceivable and fair EIST results and takes into account the impact of the natural aging of the propellant.Furthermore,the predicted EISTs follow an asymptotic evolution with respect to the artificial aging time.For new synthesized DBRP with similar chemical composition,a simple model was proposed to predict the EIST.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A.Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.dt.2020.04.008.