Transverse relaxation characteristic and stress relaxation model considering molecular chains of HTPB coating based on pre-strained thermal aging

Yong-qing Du ,Jin Zheng ,**,Gui-bo Yu ,Jin-zhung Zhi

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

b Intelligent Manufacturing Institute,Hebei College of Industry and Technology,Shijiazhuang,050003,China

Keywords:HTPB Pre-strain aging Transverse relaxation characteristic Molecular chain Stress relaxation model

ABSTRACT In order to accurately describe the transverse relaxation characteristic and stress relaxation modulus of HTPB coating during pre-strain thermal aging process,a one month thermal aging test was carried out at 70 °C with pre-strain of 0%,3%,6% and 9%,respectively.The low-field 1H NMR and stress relaxation modulus tests were carried out for HTPB coating at different aging stages.The stress relaxation model considering the molecular chains was proposed according to the changes of crosslinking chain and dangling chain of HTPB coating during pre-strain aging.The results showed that with the increase of aging time,the decay rate of transverse relaxation curve became faster,the transverse relaxation time decreased,the value of combined parameter qMrl increased,the proportion of crosslinking chain decreased,while the proportion of dangling chain increased.Moreover,the stress relaxation modulus increased,the crosslinking network structure of HTPB coating became denser and the degree of crosslinking increased.At the initial aging stage,the pre-strain will destroy the crosslinking network structure of HTPB coating to a certain extent.With the increase of aging time,the effect of pre-strain will gradually weaken and the influence of aging on materials will gradually increase.The correlations between the stress relaxation model considering the molecular chains and the test results were more than 0.9950,which can accurately describe the stress relaxation modulus of HTPB coating during the pre-strain thermal aging process.

1.Introduction

HTPB coating is an important part of solid rocket motor,which excellent mechanical performance is the key to ensure the combat effectiveness of solid rocket motor[1,2].The thermal oxidative aging is the most common factor affecting the properties of materials[3,4],during which process the microstructure of the material will generally undergo the interruption of macromolecular chains and crosslinking reaction[5].On the one hand,the proportion of dangling chain increases due to the chain scission of the polymer network in the presence of high temperature and oxygen;on the other hand,the extra crosslinking reaction caused by macromolecular free radicals or double bonds will take place in the internal material,finally forming a denser crosslinking network in the long aging time[6].The increase of crosslinking density in the aging process greatly weakens the deformation ability of the material and makes it more inclined to rigid body.At the same time,the chain scission reaction and random crosslinking reaction of polymer chains make the regularity of the crosslinking network worse,and the stress transfer ability gradually weakened,which further affecting the mechanical properties of the material[7].

NMR technology has been widely used in the measurement of polymer microstructure and aging.This method has the advantages of non-destructive and fast,and can determine the different relaxation mechanisms and rates related to molecular motion in polymers.It is very sensitive to the changes of molecular chain structure and relaxation time of different types of polymer chain caused by crosslinking or chain scission during aging[8,9].Allen et al.[10]tested the aging properties of SBR under the conditions of heat and ultraviolet light,and revealed the molecular structure change and aging mechanism of SBR by means of NMR and IR.Daniel et al.[11]conducted the thermal oxygen aging test of HTPB at 80°C and found that the transverse relaxation time of HTPB can reflect the thermal oxygen aging change of materials sensitively.Jabez et al.[12]found that the change of molecular weight distribution of HTPB in the process of manufacturing and storage can be effectively characterized by transverse relaxation time.

HTPB coating has typical viscoelastic mechanical characteristic.Under static or dynamic load,HTPB coating will appear creep,stress relaxation and other phenomena,which is related to the molecular chain structure of HTPB coating[13].Chi et al.[14]found that aging has a significant impact on the elastic part of the relaxation modulus of HTPB coating,but has a small impact on the viscous part,so they ignored the impact of the viscous part on the stress relaxation modulus of HTPB coating,and established a stress relaxation model with aging effect.Mojtaba et al.[15]studied the effect of hydrothermal aging on stress relaxation of materials,and predicted the long-term stress relaxation behavior using Kohlrausch-Williams-Watts(KWW)expression.Rui et al.[16]considered the effect of physical aging and obtained a scheme to simplify stress relaxation data.Liang et al.[17]proposed a new stress relaxation empirical model based on the relaxation function of the dual variable parameter Maxwell model.Zheng et al.[18]proposed a modified standard linear solid state(SLS)model to describe the compressive stress relaxation behavior of materials.This model not only made up for the deficiency of the empirical model,but also considered the change of the intrinsic viscosity of the material in the process of thermal oxygen aging.The above researches are mainly based on macro mechanics,without considering the change of molecular chain structure in the aging process.Marina et al.[19]verified the correctness of the proposed micro molecular chain motion mechanism through experiments,which showed that the viscoelastic behavior can be accurately described by considering the influence of different time scales of molecular chain motion on the relaxation process.Therefore,it is feasible and valuable to establish the stress relaxation model by considering the change of molecular chain.

In this paper,a one month pre-strain thermally-accelerated aging test was carried out on HTPB coating.The transverse relaxation characteristic of HTPB coating during aging was tested and analyzed by low-field1H NMR.The stress relaxation modulus of HTPB coating at different aging stages was measured,and a stress relaxation model was proposed considering the change of molecular chains.

2.Materials and methods

2.1.Materials

The HTPB coating used in the test is provided by the stateoperated No.845 factory in Xi’an,China,and the size and specific composition are referred to Ref.[20],which are shown as follows.

According to the manufacturing process of the No.845 factory,the HTPB is used as adhesive,the TDI is used as the curing agent,the diisooctyl sebacate is used as the plasticizer,the zinc oxide is used as the reinforcing,active and vulcanizing agent,the silicon dioxide is used to improve the performance of ablation and corrosion resistance,and the molecular sieve is used as the catalytic agent and adsorbent(Fig.1).

2.2.Aging test

Fig.1.Sample of HTPB coating.

The thermally-accelerated aging test of HTPB coating was conducted in the type DU288 oil bath thermostat.The test temperature was 70°C±1°C and the humidity in the thermostat was kept less than 50% by using silica desiccant.The samples of HTPB coating were stretched to the pre-strain of 0%,3%,6% and 9%,respectively for aging test.After aging for 3 d,6 d,12 d,20 d,and 30 d,the samples of HTPB coating were taken out and natural cooled to room temperature in a vacuum drying oven for 24 h.

2.3.Transverse relaxation characteristic test

The transverse relaxation characteristic of HTPB coating was measured by low-field1H NMR.The test temperature was 90°C.The HTPB coating samples were cut into rectangular strips of 10 mm×6 mm×2 mm and preheated at 90°C for 30 min before the transverse relaxation characteristic test.The transverse relaxation of the hydrogen protons of the HTPB coating tested by lowfield1H NMR is caused by the intramolecular and intermolecular hydrogen proton dipole interactions.At the NMR test temperature,the dipole interactions are considered to be the effect of the average of the thermal molecular motions.Since the hydrogen protons are used as probes for the NMR measurements,the transverse relaxation of the HTPB coating can be explained by the single chain model(XLD model)[21-23].

2.4.Stress relaxation modulus test

The stress relaxation modulus of HTPB coating was tested in Instron 5982.The test was conducted at room temperature of 25°C±2°C and using silica desiccant to keep the humidity of the test environment less than 50%.The stress relaxation modulus of HTPB coating samples aged at different stages were tested according to method 413.4 in GJB 770B-2005[24](see Fig.1).

3.Results and discussion

3.1.Effect of pre-strain aging on transverse relaxation characteristic

3.1.1.Analysis of transverse relaxation curve

The internal molecular chain scission and crosslinking reaction will occur at the same time during the whole aging process[25].In order to explore the changes of different types of molecular structure in HTPB coating during aging,the low-field1H NMR test was carried out[26,27],and the decay curves of transverse relaxation with relaxation time of HTPB coating were obtained as shown in Fig.2.

Fig.2.The decay curves of transverse relaxation of HTPB coating.

The decay of transverse relaxation is related to the low frequency motion of the polymer chain,which is very sensitive to the change of the crosslinking network structure during aging.The higher the crosslinking density,the shorter the transverse relaxation time,and the faster the decay of the transverse relaxation curve with the relaxation time[28,29].It can be seen from Fig.2 that with the increase of aging time and decrease of pre-strain,the decay rate of transverse relaxation curve of HTPB coating became faster,which demonstrated that the crosslinking density of HTPB coating increased gradually during pre-strain aging,and the crosslinking network of material was denser.

The transverse relaxation decay curve of HTPB coating was fitted with the modified single chain model(XLD model)[21-23]:

whereM(t)/M(0)is the change of transverse relaxation with time after normalization;M(0)is the initial and reference point;M(t)is the transverse relaxation value at relaxation timet;Ais the proportion of crosslinking chain signal in the total signal,%;(1-A)is the proportion of dangling chain signal in the total signal,%;T2is the transverse relaxation time,ms;qis the dipolar interaction,which is the ratio factor between the second moment higher than the glass transition temperature and the rigid second moment;Mrlis the dipole moment in the rigid lattice molecule,m/s2;qMrlis the average residual part of the second moment of the two pole interaction,m/s2;A0has no practical physical significance.The analysis of the fitting parameters was shown in the following section.

3.1.2.The value of T2

Daniel et al.[11]tested the1H NMR relaxation properties of HTPB polyurethane elastomers aged at 80°C,and found that the oxidative aging of HTPB polyurethane elastomers at high temperature resulted in additional crosslinking and densification of materials,resulting in loss of elasticity and deterioration of material properties.The transverse relaxation timeT2has a high sensitivity to thermal aging,and with the increase of thermal aging time,the transverse relaxation timeT2decreased approximately linearly.The aging properties of HTPB polyurethane elastomers can be effectively analyzed by using the transverse relaxation time as a parameter.Daniel’s study considered the thermal oxygen aging,but did not add the factor of pre-strain.Jabez et al.[12]found that the transverse relaxation timeT2obtained by1H NMR can sensitively capture the small changes in molecular weight and molecular weight distribution of HTPB prepolymer,and can be effectively applied to the manufacturing and storage process of HTPB prepolymer.Jabez’s study confirmed the sensitivity of the transverse relaxation time in capturing the microstructure changes of HTPB prepolymer,which provided a theoretical basis for this study.

Fig.3.The variation of transverse relaxation time with pre-strain aging time.

The transverse relaxation timeT2of HTPB coating with different pre-strain aging time is shown in Fig.3.It can be seen from Fig.3 that under different pre-strain conditions,the transverse relaxation time of HTPB coating decreased with the aging time.This was mainly because that the crosslinking network of the material became closer and the degree of crosslinking increased with the increase of aging time[30].At the same aging time,the pre-strain had a great influence on the material before aging for 12d.The transverse relaxation time of HTPB coating increased with the increase of pre-strain,which indicated that the pre-strain would destroy the crosslinking network of the material and reduce the crosslinking degree of the material[31].When the aging time was more than 12d,the influence of pre-strain on the material decreased gradually due to the stress relaxation phenomenon[13].The variation trend of the transverse relaxation time of HTPB coating with the increase of pre-strain was less monotonous than that when the aging time was less than 12d,which was mainly related to the joint action of oxidative crosslinking and degradative chain scission of HTPB coating aging[32,33].

3.1.3.The value of qMrl

The combined parameterqMrlis used to calculate the crosslinking density of HTPB coating.The higher theqMrlvalue,the higher the crosslinking density of the corresponding material[6].The variation ofqMrlwith pre-strain aging time is shown in Fig.4.

Fig.4.The variation of qMrl with pre-strain aging time.

The value ofqMrlof HTPB coating increased with aging time,which indicated that the crosslinking density of the material increased with aging time.At the same aging time,the value ofqMrlof HTPB coating decreased with the increase of pre-strain,which demonstrated that the existence of pre-strain will reduce the crosslinking density of the material.When the pre-strain was 3%,theqMrlof HTPB coating decreased slightly;while the pre-strains were 6% and 9%,theqMrlof HTPB coating decreased significantly,which indicated that the large strain had a serious destructive effect on the crosslinking structure,and then affected the mechanical properties of the material[34-36].

3.1.4.Crosslinking chain and dangling chain

The change curves of the proportion of crosslinking chain in HTPB coating with the pre-strain aging is shown in Fig.5.

Under the aging condition of 0% pre-strain,the proportion of crosslinking chain of HTPB coating decreased with the increase of aging time,and the proportion of dangling chain increased gradually.The crosslinking density of HTPB coating was the result of the interaction between the crosslinking chain and the dangling chain[37].It can be seen from the test results that the role of the crosslinking chain was gradually weakened in the aging process,while the role of the dangling chain was gradually enhanced.By the time of aging for 30d,the proportion of the dangling chain has exceeded 50%.The change of the proportion of crosslinking chain and dangling chain was mainly due to the effect of degradative chain scission during the aging process[32,33].

Under the condition of pre-strain aging,the changes of crosslinking chain and dangling chain of HTPB coating were different from that under the condition of 0% pre-strain aging.Under the condition of 3% pre-strain aging,the decrease of the proportion of crosslinking chain and the increase of the proportion of dangling chain were not obvious when the aging time was less than 12d.Compared with the aging condition of 0% pre-strain at the same aging time,the proportion of crosslinking chain of the HTPB coating under 3%pre-strain aging was slightly higher,and the proportion of dangling chain was slightly lower.This was mainly due to the rearrangement orientation of the molecular chain of HTPB coating under the condition of low strain stretching.At the same time,the crystallization in the material due to stretching played the role of physical crosslinking point and prevented the molecular chain from disentangling and inhibited the reduction of crosslinking chain[38-41].With the increase of aging time,the effect of pre-strain gradually weakened,and the interaction between oxidative crosslinking and degradative chain scission resulted in the decrease of the proportion of crosslinking chain and the increase of the proportion of dangling chain.

Fig.5.Change curves of the proportion of crosslinking chain with pre-strain aging.

Compared with the aging of 0% and 3% pre-strains,the proportion of the crosslinking chain decreased rapidly and the proportion of the dangling chain increased significantly in aging for 3d when the pre-strains were 6% and 9%,which were mainly due to the larger strain effect leading to the molecular chain disentanglement,crystal distortion and even damage[38,42].With the increase of aging time,the proportion of crosslinking chain and dangling chain of HTPB coating changed into platform area,the proportion of crosslinking chain decreased slowly,and the proportion of dangling chain increased slowly,which were mainly due to the pre-strain effect and the combined effect of oxidative crosslinking and degradative chain scission in the aging process.

It can be seen from the above analysis that with the increase of aging time,the random occurrence of crosslinking reaction inside the material will obviously increase the heterogeneity of the material.The network crosslinking of HTPB coating resulted in the increase of crosslinking point and crosslinking density.Under the combined effects of pre-strain,oxidative crosslinking and degradative chain scission,the proportion of crosslinking chain of HTPB coating decreased gradually,while the proportion of dangling chain increased.

3.2.Stress relaxation model considering molecular chains

Chi et al.[14]tested the stress relaxation modulus of HTPB coating aged at 75°C for different time.It was found that the relaxation modulus of the coating increased after aging,but the effect of aging on the relaxation modulus of the coating was timedependent,and the change range of short-term relaxation modulus was very small.With the increase of stress relaxation loading time,the effect of aging on the relaxation modulus increased.At the same time,there was a good quantitative relationship between the elastic modulus and the gel fraction of the coating.Mojtaba et al.[15]studied the effect of thermal oxidative aging and hygrothermal aging on the relaxation behavior of polycarbonate blends.It was found that the thermal aging resulted in the increase of material modulus,while the moisture absorption had the opposite effect.With the increase of water content,the stiffness of the material decreased,and the modulus decreased with the relaxation of the material.Rui et al.[16]also concluded that thermal oxidative aging can increase the stress relaxation modulus of materials.Liang et al.[17]carried out a long-term stress relaxation test of glass fiber reinforced polymer composite and controlled the initial deflection of 10%,15% and 20%,respectively.It was found that the stress relaxation modulus of the material increased with the increase of the initial deflection.

Based on the previous studies,the stress relaxation tests were carried out on HTPB coating at different pre-strain aging stages,and the stress relaxation curves are shown in Fig.6.

With the increase of aging time and decrease of pre-strain,the stress relaxation modulus of HTPB coating increased gradually,which is same with the research of Layton[43].The results showed that with the increase of crosslinking degree,the crosslinking network became denser,and the stress relaxation modulus of HTPB coating increased gradually.At the same time,the increase of the viscous part of HTPB coating during the aging process,such as the dangling chain,will lead to the release of more stress during the relaxation process,which was also the reason for the increase of stress relaxation modulus of HTPB coating[6].

During the aging process,the stress relaxation modulus of HTPB coating can be divided into elastic part and viscous part,namely:

whereEis the stress relaxation modulus at different aging time,MPa;is the elastic part of the stress relaxation modulus,that is,elastic modulus,MPa;is the viscous part of the stress relaxation modulus,that is,viscous modulus,MPa.

According to the statistical theory of polymer[44],the elastic modulus of the material is directly proportional to the crosslinking density:

whereEε0is the elastic modulus without aging,MPa;kεis the aging reaction rate constant of elastic modulus;νais the crosslinking density at different aging time,10-4mol/cm3;ν0is the crosslinking density without aging,10-4mol/cm3.The test results of the crosslinking density of HTPB coating in this paper were shown in Ref.[20].

The viscous part of stress relaxation modulus of HTPB coating was mainly attributed to physical entanglement and dangling chain.Assuming that the changes of physical entanglement and dangling chain in HTPB coating during aging were from the extra crosslinking and the chain scission of polymer chain,and the chain scission or crosslinking reaction conforms to the first-order reaction kinetics[45],the evolution of viscous modulus can be expressed as follows:

Fig.6.Stress relaxation curves of HTPB coating under pre-strain aging.

whereEc0is the contribution of crosslinking chain to the viscous modulus without aging,MPa;Ed0is the contribution of dangling chain to the viscous modulus without aging,MPa;τc0andτd0are relaxation time without aging,s;fc0is the proportion of crosslinking chain of HTPB coating without aging,%;fd0is the proportion of dangling chain of HTPB coating without aging,%;fcais the proportion of crosslinking chain of HTPB coating at different aging time,which is obtained from Fig.5 in Section 3.1.4,%;fdais the proportion of dangling chain of HTPB coating at different aging time,andfda=1-fca,%;kc，kd，kτc，kτdare aging reaction rate constant.

For the stress relaxation test results of HTPB coating without aging and with pre-strain aging,the Levenberg-Marquardt method[46]was used for nonlinear fitting.The fitting curves are shown in Fig.6 and the parameter fitting results are shown in Table 1～Table 5.

From Tables 2-5,it can be seen that under the condition of 0%pre-strain aging,the parameterkεincreased with the increase of aging time.In general,the parameterkcwas smaller than the parameterkdin the aging process,which indicated that the changing rate of elastic modulus increased gradually,and the increasing rate of the dangling chain was larger than that of the crosslinking chain.Under the condition of 3%,6%and 9%pre-strainaging,the parameterkεdecreased first and then increased with the increase of aging time.Generally,the parameterkcwas larger than the parameterkdfirst and then smaller than the parameterkd.This is mainly due to the influence of pre-strain at the initial aging stage.During the aging process,the influence of pre-strain was gradually weakened,and the role of oxidative crosslinking and degradation chain scission was gradually highlighted.

Table 1Fitting results of HTPB coating without aging.

Under 0%pre-strain aging,the parameterkτcdecreased with the increase of aging time,while the parameterkτdincreased gradually,indicating that the influence of the crosslinking chain on the relaxation property of the material decreased and that of the dangling chain increased gradually.Under the condition of 3%,6%and 9%pre-strain aging,the interaction among pre-strain,oxidative crosslinking and degradative chain scission competed with each other,which resulted in the change of parameterskτcandkτdwith aging time were not monotonous,but the parameterskτcwere larger than the parameterskτd,indicating that the influence of the dangling chain on the relaxation modulus during the pre-strain aging process occupied the leading role.

It can be seen from the fitting curves and fitting results that the correlation coefficients between model fitting curves and test results were all greater than 0.9950,the average relative errors were all less than 3.5523%,which verified that the stress relaxation model considering the molecular chains proposed in this paper can accurately describe the test results of stress relaxation modulus of HTPB coating.

Table 2Fitting results of stress relaxation model of 0% pre-strain aging.

Table 3Fitting results of stress relaxation model of 3% pre-strain aging.

Table 4Fitting results of stress relaxation model of 6% pre-strain aging.

Table 5Fitting results of stress relaxation model of 9% pre-strain aging.

4.Conclusions

In this paper,the pre-strain thermal aging test of HTPB coating was carried out,the transverse relaxation characteristic of HTPB coating during pre-strain aging were analyzed,and a stress relaxation model considering the molecular chains was proposed.The specific conclusions are as follows:

(1)With the increase of pre-strain aging time,the decay rate of transverse relaxation curves of HTPB coating became faster,the transverse relaxation timeT2was gradually reduced,the combined parameterqMrlrepresenting the crosslinking density increased with aging time while the proportion of crosslinking chain was gradually decreased.It is the contribution of the increment of physical crosslinking density;

(2)Before aging for 12 d,with the increase of pre-strain,the transverse relaxation timeT2was increased,the proportion of crosslinking chain increased first and then decreased,while the proportion of dangling chain decreased first and then increased.When the aging time was more than 12 d,the variation trends of the transverse relaxation time,the proportion of crosslinking chain and the proportion of dangling chain were less monotonous than those when the aging time was less than 12 d.Meanwhile,the combined parameterqMrldecreased with the increase of pre-strain.The existence of pre-strain at the early stage of aging will destroy the crosslinking network structure of HTPB coating to some extent,and reduce the crosslinking degree of materials.With the increase of aging time,the influence of pre-strain on the performance of HTPB coating was gradually weakened due to the phenomenon of stress relaxation,and the influence of oxidative crosslinking and degradative chain scission in the aging process was gradually strengthened;

(3)According to the change of crosslinking chain and dangling chain in the pre-strain aging process of HTPB coating,a stress relaxation model considering the molecular chains was proposed.The model can accurately describe the stress relaxation modulus of HTPB coating during pre-strain aging,and the correlation coefficients between model fitting curves and test results were all greater than 0.9950,the average relative errors were all less than 3.5523%.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.

Acknowledgements

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