Yong-qiang Du,Jian Zheng,Gui-bo Yu

Shijiazhuang Campus,Army Engineering University,Shijiazhuang,050003,China

Keywords: HTPB coating Crosslinking density Aging model Storage life prediction Berthelot

ABSTRACT In order to predict the storage life of a certain type of HTPB(hydroyl-terminated polybutadiene)coating at 25°C and analyze the in fluence of pre-strain on the storage life,the accelerated aging tests of HTPB coating at 40°C,50°C,60°C,70°C with the pre-strain of 0%,3%,6%,9%,respectively were carried out.The variation regularity of the change of crosslinking density was analyzed and the aging model of HTPB coating under pre-strained thermally-accelerated aging was proposed.The storage life of HTPB coating at 25°C was estimated by using the Berthelot equation as the end point of the aging life with a 30%decrease in maximum elongation.The results showed that the change of crosslinking density of HTPB coating increased with the increase of aging temperature and aging time,and decreased with the increase of pre-strain.Under 0%pre-strain,the relationship between the change of crosslinking density of HTPB coating and the aging time can be described by the logarithmic model with the con fidence probability greater than 99%.The stress relaxation phenomenon existed under 3%,6%and 9%pre-strained aging.The aging model considering chemical aging and pre-strain was established with the con fidence probability greater than 90%.The storage life of HTPB coating was 15.2935 years at 25°C under 0%prestrain,which was reduced by 13.9007%,75.6949%and 89.7859%under 3%,6%and 9%pre-strain,respectively.The existence of pre-strain has a serious impact on the storage life of HTPB coating,therefore,the pre-strain should be avoided as much as possible during the actual storage.

1.Introduction

HTPB coating is widely used in solid rocket motor because of its convenient processing performance and good mechanical properties[1].The aging phenomenon of HTPB coating exists during the storage process and the degradation of its performance will seriously affect the storage life of HTPB coating,which will result in huge potential safety hazard and economic loss.The accurate prediction of the storage life of HTPB coating has always been the focus of domestic and foreign scholars[1,2].

Generally,the method of high temperature accelerated aging is usually used to establish the aging model of material properties[3],and then the Arrhenius equation[4]or Berthelot equation[5]are applied to predict the service life of materials at the actual storage temperature.The Arrhenius equation assumes that the apparent activation energy is the constant,which neglects the effect of temperature on the apparent activation energy and the life prediction result is larger[6].The Berthelot equation describes the relationship between aging life and temperature.It is not necessary to obtain the reaction rate constant or the change rate of the performance.As long as the critical life at each aging temperature is measured,the storage life at given temperature can be extrapolated.Therefore,compared with the Arrhenius equation,the Berthelot equation can simplify the processing of test data,and the life prediction result is smaller than that extrapolated by the Arrhenius equation,which is closer to the actual storage life[5,7].

As the molecular structure parameter of HTPB coating,the change of crosslinking density will directly affect the macro mechanical properties(such as strength,elongation,modulus,etc.)[8].Valanis and Peng[9,10]used the crosslinking density as the characterization parameter of aging properties to establish the deformation dynamic equation of the material,and explained the in fluence of aging on the macro mechanical properties from the perspective of molecular motion for the first time.Choi et al.[11,12]studied the effect of thermal aging on the change of crosslinking density of NR vulcanizates at 40°C,60°C and 80°C with the aging time up to 20 days.The results showed that the crosslinking density increased with thermal aging time.Woo et al.[13]studied the thermal aging properties of NBR and EPDM.In order to eliminate the error caused by the difference of crosslinking density of the initial sample,the change of crosslinking density after and before thermal aging was selected to characterize aging properties.It was also concluded that the crosslinking density increased with the increase of aging time and temperature.Choi et al.[14]found that measuring the macro mechanical properties of materials often required relatively large sample size,while the sample size used to measure the crosslinking density was less than 1 cm×1 cm.Sample size should be small to minimize the test errors.By measuring the change of crosslinking density rather than the change of macro mechanical properties,the relative error of the test can be greatly reduced.At the same time,the storage life of the material at 25°C was predicted by using 50%and 100%increase of crosslinking density as failure criteria.Li et al.[15]estimated the storage life of HTPB coating by establishing the conversion relationship between the maximum elongation and the crosslinking density,and the predicted result was in good agreement with that of the maximum elongation.

Due to the in fluence of cooling process after curing,dead weight,storage temperature cycle and other factors,HTPB coating will inevitably be affected by strain during storage,which will greatly reduce the mechanical properties[16,17].The results showed that the maximum strain of HTPB coating was about 10%under the combined action of gravity load and thermal load[18].Wang et al.[19]found that the predicted storage life at 5%constant strain was reduced by half,which was the result of the combined effect of thermo-oxidative aging and strain.At the aging temperature of 70°C,the effect of thermo-oxidative aging was signi ficant,while at natural temperature,the effect of strain was prominent.Zhang et al.[20]showed that the effect of strain during the storage process was equivalent to reduce the apparent activation energy.Under long-term effect of stress and strain caused by various loads,the molecular chain scission and microcracks were formed gradually,which will lead to cumulative damage and eventually lead to the structural failure and the decrease of the storage life.Zou et al.[21]obtained the dualistic regression aging model of the maximum elongation of HTPB propellant under the thermal-mechanical coupled effect by synthesizing the linear model and the exponential model.The probability of meeting the requirement of elongation after natural storage for 10 years was 0.9 based on the proposed model.Zhou et al.[22]carried out high temperature accelerated aging tests with constant strain of 3%,6%and 9%,respectively and established the aging model by taking the maximum elongation as the aging evaluation parameter.It was found that the crosslinking density had a strong linear correlation with elongation,tensile strength and Young’s modulus[23],which can be used in the evaluation of aging properties of materials[24].It can be seen from above researches that current aging models mostly take the macro mechanical properties(elongation,strength,etc.)as the aging evaluation parameters,and the research on the life prediction with the crosslinking density as the characterization parameters is relatively few.

In this paper,the accelerated aging tests of HTPB coating were carried out at 40°C,50°C,60°C and 70°C with the pre-strain of 0%,3%,6%and 9%,respectively.The variation regularity of the change of crosslinking density of HTPB coating was analyzed,and the aging model of HTPB coating under the pre-strained thermally-accelerated aging was established.The storage life of HTPB coating at 25°C was estimated by the Berthelot equation.

2.Materials and methods

2.1.Materials

The HTPB coating used in this paper was provided by Stateowned No.845 factory in Xi’an,China,which was a polyurethane material composed of adhesive HTPB and curing agent TDI(toluene diisocyanate).At the same time,the DOS(diisooctyl sebacate)was added as plasticizer,zinc oxide was added as intensi fier,activator and sulfurizer,silica was used to improve ablation and corrosion resistance,and molecular sieve was used as catalyst and adsorbent.According to the design proportion,the final test sample was obtained by curing at 70°C for 5 days.

2.2.Pre-strained thermally-accelerated aging test

The pre-strained thermally-accelerated aging test of HTPB coating was carried out in an electric oil bath incubator.The test temperature was set to 40°C,50°C,60°Cand 70°C,respectively with the temperature fluctuation range was±1°C and the relative humidity of the test environment was less than 50%RH(relative humidity).The samples of HTPB coating were cut into dumbbell shape(as shown in Fig.1)according to QJ 915-85 I standard,and were stretched to the pre-strain of 0%,3%,6%and 9%,respectively for aging test.The device that applies pre-strain to the dumbbellshaped sample is shown in Fig.2.The sampling time interval at high aging temperature should be short,while the interval should be long at low aging temperature.The aging temperature and sampling time are shown in Table 1.After the sample was taken out,it should be placed in a vacuum drying box for natural cooling for 24 h.

Table 1 Sampling time of the thermally-accelerated aging test.

2.3.Crosslinking density test

The crosslinking density of the aged HTPB coating was measured in VTMR20-010V-T type low-field1H NMR tester.The test temperature was set to 90°C(which was 120°C higher than the glass transition temperature of HTPB coating and the glass transition temperatureTgof HTPB coating used in the paper is about-55°C based on the method of dynamic mechanical analysis)[25].The aged dumbbell-shaped HTPB coating sample was cut into the rectangular strip of 10 mm×6 mm×2 mm,and then preheated in the crosslinking density tester for 30min before the test.The change of crosslinking density was calculated according to Eq.(1):

Fig.1.Dumbbell-shaped sample of the HTPB coating.

Fig.2.Device for pre-strain application.

whereν0andνtare the crosslinking density before and after aging,respectively,10-4mol/cm3.

2.4.Maximum elongation test

The dumbbell-shaped HTPB coating samples aged at 70°C were put on the Instron 5982 material testing machine to test the maximum elongation.The test temperature was controlled within 25±2°C,and the tensile rate was set to 100 mm/min until the sample was broken.According to the 413.1 method in GJB 770B-2005[26],the maximum elongation of the aged HTPB coating was calculated.

3.Results and discussion

3.1.The change of crosslinking density

The aging curves of the change of crosslinking density of HTPB coating under 0%,3%,6%and 9%pre-strain,respectively are shown in Fig.3.It can be seen from Fig.3 that under the pre-strained thermally-accelerated aging,the change of crosslinking density of HTPB coating increased with the aging time,which was mainly due to the effect of oxidative crosslinking,the material’s crosslinking structure was more compact and resulted in the increase of the crosslinking density[14,27].Under the same aging time,the change of crosslinking density of HTPB coating increased with the increase of aging temperature,but it did not change the variation regularity of the change of crosslinking density,which indicated that high temperature accelerated the aging reaction rate and promoted the aging process of HTPB coating[28,29].At the same aging temperature,the change of crosslinking density of HTPB coating decreased with the increase of pre-strain.This was mainly because that the molecular chain of HTPB coating was reoriented and the crosslinking degree of the molecular chain was reduced under the effect of pre-strain.With the increase of pre-strain,the molecular chain was disentangled,crystallized and even destroyed,which resulted in the destruction of the crosslinking network structure and the decrease of the crosslinking density of the material[30-32].With the increase of aging time,the effect of pre-strain on HTPB coating decreased gradually due to the phenomenon of stress relaxation,and the effect of aging increased gradually[33].

3.2.Establishment of the aging model under 0%pre-strain

Generally,the logarithmic model,linear model and exponential model are used to describe the aging properties of materials[34]:

whereνcis the change of crosslinking density at aging timet,%;νc0is constant;kis the rate constant of the aging reaction,which is related to the aging temperature;tis the aging time,d.

The logarithm model,linear model and exponential model were respectively used to fit the test results of the change of crosslinking density of HTPB coating under 0%pre-strain by Levenberg-Marquardt method[35],and the fitting results are shown in Table 2.

Table 2 Fitting results of aging models under 0%pre-strain.

R0.01=0.874,which is the correlation coef ficient when the con fidence probability is 99%.It can be concluded from the fitting results that the logarithmic model has the highest fitting correlation,and the correlation coef ficients are all greater thanR0.01,which indicate that the con fidence probability of using the logarithmic model to describe the test results is greater than 99%.Therefore,the logarithm model can be used to accurately describe the variation regularity of the change of crosslinking density of HTPB coating under 0%pre-strain.

3.3.Establishment of the aging model under pre-strain

The change of crosslinking density of HTPB coating was the result of the combined effect of chemical crosslinking and prestrain.Therefore,the aging model of the change of crosslinking density can be expressed as follows:

whereνcis the change of crosslinking density caused by chemical crosslinking.According to the analysis results in Section 3.2,νcis described by the logarithm model,%;νpis the change of crosslinking density caused by the pre-strain,%.

There was stress relaxation in the process of pre-strained thermally-accelerated aging,that is:

Whereσ0andσ1are constants;τpis the relaxation time,d.

Fig.3.The aging curves of the change of crosslinking density under 0%,3%,6%and 9%pre-strain,respectively.

According to the stress-strain relationship of the crosslinking elastomer[36],the crosslinking density is directly proportional to the stress under the condition of constant strain,that is:

Wherekσis the proportional coef ficient.

Combined Eq.(6)with Eq.(7),νpcan be expressed as follows:

whereνp0andνp1are constants;νp0=kσσ0;νp1=kσσ1.

In combination with Eqs.(2),(5)and(8),the test results of the change of crosslinking density under 3%,6%and 9%pre-strains were fitted.The model fitting curves are shown in Fig.4 and the correlation coef ficients which indicate the degree of correlation between model fitting results and test results are shown in Table 3.

As shown in Fig.4,the fitting curves of aging model can accurately describe the variation regularity of the change of crosslinking density under pre-strained thermally-accelerated aging.R0.10=0.669,which is the correlation coef ficient when the con fidence probability is 90%.It can be seen from Table 3 that the correlation coef ficient between model fitting results and test results under 3%pre-strain at 70°C is less thanR0.01(but the correlation coef ficient is greater thanR0.10,i.e.the con fidence probability is greater than 90%),the other fitting correlation coef ficients are all greater thanR0.01,i.e.the con fidence probability is greater than 99%.The results show that the aging model can accurately and effectively describe the change of crosslinking density of HTPB coating under the condition of pre-strained thermally-accelerated aging.

Table 3 Correlation coef ficients between model fitting results and test results.

Table 4 Fitting results of the maximum elongation using the logarithmic model.

Fig.4.The fitting curves of the aging model under 0%,3%,6%and 9%pre-strain,respectively.

3.4.The change of maximum elongation

There is a strong correlation between the crosslinking density and the maximum elongation.In order to use the change of crosslinking density to predict the storage life of HTPB coating,the failure criterion corresponding to the maximum elongation needs to be equivalently converted to be characterized in terms of the change of crosslinking density[15].

The aging curves of the maximum elongation of HTPB coating at 70°C is shown in Fig.5.

Fig.5.The aging curves of the maximum elongation at 70°C.

It can be seen from Fig.5 that under the pre-strained thermallyaccelerated aging,the maximum elongation of HTPB coating decreased with the aging time.At the same aging time,the maximum elongation of HTPB coating decreased with the increase of pre-strain.The change of the maximum elongation of HTPB coating showed an opposite tendency to that of the crosslinking density.This was mainly due to the increase of crosslinking density during the process of pre-strained thermally-accelerated aging,which resulted in the molecular structure of HTPB coating becoming more compact,the mobility of molecular chains was increased[37],and the deformation ability and flexibility of molecular chains were reduced[38].

Fig.6.The fitting curves of the maximum elongation at 70°C.

The logarithmic model(as shown in Eq.(9))was used for nonlinear fitting of the test results of the maximum elongation.The fitting curves are shown in Fig.6 and fitting results are shown in Table 4.The correlation coef ficients between model fitting results and test results are all greater thanR0.01,which indicate that the con fidence probability is greater than 99%.

Table 5 Storage life of HTPB coating under pre-strained thermally-accelerated aging.

Table 6 Fitting results of each parameter of the Berthelot equation.

Table 7 Storage life prediction results of the HTPB coating at 25°C.

whereεmis the maximum elongation at aging timet,%;εm0is constant;kmis the rate constant of the aging reaction.

Combined Eq.(5)with Eq.(9)and expressed the aging timetusing the maximum elongation,the relational model of maximum elongation and the change of crosslinking density can be obtained:

The 30%reduction of the maximum elongation can be used as the failure criterion to predict the storage life[39].The equivalent conversion results of the failure criterion corresponding to the change of crosslinking density can be obtained by Eq.(10).That is,the failure criterion corresponding to the change of crosslinking density of 0%,3%,6% and 9% pre-strains is 32.3848%,18.6009%,-44.0488%and-55.4435%,respectively.

3.5.Storage life prediction

In this paper,the storage life of HTPB coating was predicted by the Berthelot equation:

whereτis the storage life at a given temperatureT,d;Tis absolute temperature,K;Bis the temperature coef ficient of decomposition speed related to mechanical properties;Ais the coef ficient related to mechanical properties,test conditions and time used.

By substituting the equivalent conversion results of the failure criterion corresponding to the change of crosslinking density into Eq.(5),the storage life of HTPB coating under the condition of prestrained thermally-accelerated aging can be obtained,and the results are shown in Table 5.

Substituting the calculation results in Table 5 into Eq.(11),the fitting results of each parameter of the Berthelot equation were obtained,as shown in Table 6.

TakingT=298.15 K,the storage life of HTPB coating at room temperature of 25°C can be extrapolated.The results are shown in Table 7.

According to the prediction results in Table 7,the storage life of the HTPB coating at 25°C under 0%pre-strain is 15.2935 years,and under 3%,6%and 9%pre-strains,the storage life of the HTPB coating has decreased by 13.9007%,75.6949%and 89.7859%,respectively.Especially under 6%and 9%pre-strains,the storage life are reduced by more than half,which are consistent with the research of Wang etc.[19].The results show that the existence of pre-strain will seriously damage the storage life of HTPB coating,and the occurrence of pre-strain should be avoided in actual storage as much as possible.

4.Conclusions

In this paper,the pre-strained thermally-accelerated aging test of HTPB coating was carried out,the variation regularity of the change of crosslinking density was analyzed,and the aging model of the change of crosslinking density of HTPB coating was established.The storage life of HTPB coating at 25°C was predicted by the Berthelot equation.The main conclusions are as follows:

(1)The change of crosslinking density of HTPB coating increased with the increase of aging temperature and aging time,and decreased with the increase of pre-strain.The change of crosslinking density of HTPB coating was the combined result of chemical crosslinking and pre-strain.

(2)Under 0%pre-strained aging,the relationship between the change of crosslinking density of HTPB coating and the aging time can be described by a logarithmic model with a con fidence probability greater than 99%.The stress relaxation phenomenon existed in the pre-strained aging process,and the aging model considering chemical aging and pre-strain was established.The model can accurately describe the variation regularity of the change of crosslinking density of HTPB coating and the con fidence probability is greater than 90%.

(3)The failure criterion characterized by the change of crosslinking density of HTPB coating was obtained by equivalent conversion.The storage life of HTPB coating at 25°C under 0%pre-strain was predicted to be 15.2935 years by the Berthelot equation.Under 3%,6%and 9%pre-strained aging,the storage life of HTPB coating decreased by 13.9007%,75.6949%and 89.7859%,respectively.The existence of pre-strain will signi ficantly shorten the storage life of HTPB coating.

Declaration of competing interest

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

Acknowledgements

This work was supported by the National Defense Pre-Research Projects[grant number ZS2015070132A12002].