Effect of neutral polymeric bonding agent on tensile mechanical properties and damage evolution of NEPE propellant

M.Wubuliisn , Ynqing Wu ,*, Xio Hou , Kun Yng , Hongzheng Dun ,Xinmei Yin

a State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing,100081, PR China

b The Fourth Institute of China Aerospace Science and Technology Corporation, Xi'an, 710025, PR China

c School of Aerospace Engineering, Beijing Institute of Technology, Beijing,100081, PR China

d Science and Technology on Aerospace Chemical Power Laboratory, Hubei Institute of Aerospace Chemotechnology, Hubei, 441003, PR China

Keywords:Solid propellant Bonding agent Mechanical properties Damage evolution Cohesive-zone model Interface debonding

ABSTRACT Introducing Neutral Polymeric bonding agents(NPBA)into the Nitrate Ester Plasticized Polyether(NEPE)propellant could improve the adhesion between filler/matrix interface, thereby contributing to the development of new generations of the NEPE propellant with better mechanical properties.Therefore,understanding the effects of NPBA on the deformation and damage evolution of the NEPE propellant is fundamental to material design and applications.This paper studies the uniaxial tensile and stress relaxation responses of the NEPE propellant with different amounts of NPBA.The damage evolution in terms of interface debonding is further investigated using a cohesive-zone model (CZM).Experimental results show that the initial modulus and strength of the NEPE propellant increase with the increasing amount of NPBA while the elongation decreases.Meanwhile,the relaxation rate slows down and a higher long-term equilibrium modulus is reached.Experimental and numerical analyses indicate that interface debonding and crack propagation along filler-matrix interface are the dominant damage mechanism for the samples with a low amount of NPBA,while damage localization and crack advancement through the matrix are predominant for the ones with a high amount of NPBA.Finally,crosslinking density tests and simulation results also show that the effect of the bonding agent is interfacial rather than due to the overall crosslinking density change of the binder.

1.Introduction

Composite solid propellants are composed of highly-filled energetic fillers (e.g., aluminum (Al), ammonium perchlorate (AP))and lightly cross-linked polymer matrix.They have been widely used in the current generation of solid rocket motors(SRMs)due to their high specific impulse,predictable combustion behaviors,and reliable mechanical properties.To meet the increasing requirements for the power performance of propellants, new highly energetic fillers (e.g., Hexanitro-hexaazaisowurzitane (CL-20)) are preferably introduced into the Nitrate Ester Plasticized Polyether(NEPE) propellant.However,the poor bonding performance at the filler/matrix interface possibly causes interface debonding [1,2],further influencing the structural integrity or even the combustion stability of SRMs.

Accordingly, to provide propellants with higher energy and similar or better mechanical properties, efficient bonding agents are usually introduced into the propellant formulation [3-5].Our experimental findings regarding the NEPE propellant showed that the introduction of Neutral Polymeric bonding agents (NPBA)significantly influenced the mechanical response of the propellant,even at low concentrations (e.g., 0.1 wt% of the propellant), as shown in Fig.1.The desired mechanical properties can be attained by modifying the amount of bonding agents.Therefore, a better understanding of the effects of bonding agents on the deformation and damage of the propellant is crucial to material design and applications.

Fig.1.Effect of NPBA on the deformation of the NEPE samples: (a) Before testing; (b) With NPBA 0.1 wt% of the propellant; (c) Without NPBA (terminated before fracture).

Solid propellants usually exhibit nonlinear viscoelastic behavior featured by relaxation and creep.Their mechanical properties are affected by extrinsic (e.g., strain rate, temperature) and intrinsic factors (e.g., formulation).Concerning the former, considerable effort has been contributed to represent the mechanical response of propellants at different strain rates, temperatures, and confining pressures [6-10].Besides, investigating microstructural changes during loadings through in-situ observations has been the main focus of other contributions [11-13].The results showed the interface debonding to be one of the main damage mechanisms resulting in void formation and crack growth [14].Therefore,several viscoelastic constitutive models based on homogenized continuum methods accounting for interface debonding are proposed, illustrating stress softening and dilatation by interval variables [15,16] or the stiffness reduction method [17-19].Other contributions attempt to examine the effect of damage evolution from the view of porosity[1,20]or normalized crack length[21,22],yet still with the assumption of interface debonding as the primary damage mechanism.Although the studies reviewed above have produced valuable results and worked well in predicting stressstrain responses of the propellant, the effects of bonding agents are not taken into account, which is the key contributor affecting the interface behavior and could have remarkable influences on the mechanical responses of propellants, as shown in Fig.1.

In the following,recent studies aiming to represent the effects of bonding agents on the mechanical properties of the propellant are reviewed.Abd elall and Lin[3]reported that bonding agent content has a great influence on the strain corresponding to maximum stress and that desired mechanical properties can be obtained by adjusting the percentages.Deng et al.[4] believed that adding bonding agents relieved interface debonding by improving the adhesions between oxidizers and the matrix, thereby increasing the tensile strength and modulus.Landsem et al.[5]concluded that bonding agents of 0.02 wt% roughly doubled both the tensile strength and elastic modulus of the propellant relative to the agentfree ones.The analyses of molecular dynamics also supported that bonding agents significantly improve the interface bonding energy and strong hydrogen bonds [23,24].In this regard, one may speak about the vital role of the bonding agent in mechanical properties enhancement [25] from the view of improved interface behavior,which was experimentally measured and verified at the interface level by the in-situ Raman spectroscopy [26].However, most of them focused on the preparation and selection of the bonding agent with less care on the characterization of the mechanical properties,and the effect of bonding agents on relaxation behavior was not provided.

Numerical studies based on the cohesive zone model(CZM)are considered to be an effective way to better understand the impact of bonding agents on the interface behavior,allowing a closer look at the damage evolution and the mechanical response of propellants [27,28].Gilormini et al.[29] investigated the volume change and stress-strain responses of a filled rubbery polymer using CZM.de Francqueville et al.[30,31]presented experimentally and numerically the impact of interface debonding on the mechanical behavior of a composite with different fillers,thanks to the CZM capturing the key features of local damage evolution.Results suggested that the interface behavior has a first-order impact compared to other elements (e.g., fillers shape).Similar attempts were made by others and provided helpful results regarding the link between microstructural damage and the mechanical behavior of such polymers [32-35].Nonetheless, there is still a lack of quantitative comparison of damage associated with bonding agents, and the effect of bonding agents on damage evolution has not been sufficiently explored.

In summary, although efforts have been made to represent the effect of bonding agents on the mechanical properties of propellants, the scope of the analysis is mostly limited to analytical comparison,and the local damage evolution is not well understood.The main objective of this paper is to experimentally study the effect of NPBA on the mechanical behavior of the NEPE propellant.Uniaxial tensile tests under various strain rates and stress relaxation tests are conducted, and quantitative damage in terms of volume ratio is obtained by the digital image correlation (DIC)method.The next objective is to represent the damage evolution via Scanning electron microscopy (SEM) and micromechanical simulations of propellants containing different amounts of NPBA.The correlation between the microstructural damage evolution and the macro-mechanical response of the propellant is analyzed.As part of this goal, variations in the tensile strength and elastic modulus are addressed in terms of the bonding agent.

The remainder of this paper is organized as follows: Section 2 describes the characterization of the NEPE propellant, including experimental procedures and the computational model.Then, the experimental results at different strain rates and microstructural damage evolution are detailed in Section 3.Section 4 further discusses the underlying mechanism of the bonding agent with the interface.Conclusion and future work close the paper.

2.Material characterization

2.1.Materials

The bonding agent:Neutral Polymeric bonding agents(NPBA)are generally used in nitramine propellants with energetic binder systems.They contain a great number of polar functional groups in side groups, which shows strong affinity interaction to the polar particles.In addition, the NPBA molecular chain contains active hydroxyl groups, which can be connected with the binder matrix network through a curing reaction.

The propellant: NEPE propellant used in the experiments comprises GAP (glycidyl azide polymer), AP, CL-20, Al, and other additives (e.g., stabilizer, NPBA).The basic formulation and size distribution are displayed in Table 1.Three types of samples were prepared with different amounts of NPBA relative to the overall propellant while keeping the other contents unchanged.They are denoted in the following as BA-0% (0 wt%), BA-0.1% (0.1 wt%), and BA-0.5%(0.5 wt%).

The microstructures of the samples from SEM before testing are shown in Fig.2.There are quite a few bare fillers and the interface between the fillers and the matrix of BA-0% is clear, as shown in Fig.2(a),indicating a rather poorly bonded interface.The interfaceof BA-0.1% is blurred and the fillers merge well into the matrix.Although a small number of microvoids and interface debonding still exist(Fig.2(b)),the bonding performance appears to be much better compared with BA-0%.Fig.2(c) displays a more delicate filler/matrix interface, where the fillers seem to be fully coated by the matrix in BA-0.5% compared to BA-0% and BA-0.1%.It can be inferred that NPBA adsorbs onto the fillers and attaches them to the matrix, thus improving the bonding performance.

Table 1 Formulation of the NEPE propellant.

2.2.Experiments

A universal material testing machine was employed to perform the uniaxial tensile tests and relaxation tests at room temperature.The samples were designed according to the GJB 770B-2005 as dumbbell-shaped with a gauge length of 70 mm and a cross-section of 10 × 10 mm, as shown in Fig.3(a).Before testing, each sample has been kept for 48 h at 25°C in a controlled dryer below 10% of relative humidity.They were then loaded along the 2-direction at a speed of 50 mm/min, 100 mm/min and 200 mm/min.Before testing, white and black speckles were randomly painted on the sample's surface, and then the deformation field and volume ratio were measured by the DIC method [36] during the tensile tests(Fig.3).The optical images were recorded by a HIKvision MVCH120 camera and the frames taken by the camera were postprocessed using commercial software (VIC-2D, Correlated Solution, Inc., West Columbia, SC, USA).An example of reference and deformed configuration captured for the tested propellant is seen in Fig.3(b).The damaged surface of the NEPE propellant was scanned by SEM after testing.At least five replicas were tested for each condition and their average was taken as the result.

Fig.2.The SEM microstructure of NEPE samples before testing: (a) BA-0%; (b) BA-0.1%; (c) BA-0.5%.

Fig.3.Experimental setup(a)dimensions and schematic diagram of the test specimen,and the sample was stretched along the 2-direction(b)region of interest during the test(c)the contour plots of stretch ratio λ2 and λ3 measured by DIC method.

The mean stretch ratio λi(along the i-th direction) over the region of interest during tensile loading is

where L0iand Lidenote the original and current length along the ith direction,n is the number of DIC mesh elements and j represents the j-th element in the region of interest as shown in Fig.3(b).

Assuming that the stretch ratios of two transverse directions are the same (or, equivalently), i.e.,λ1=λ3, the volume ratio Θ reads,

where V and V0are the current and original volume.Eq.(2) indicates that the volume ratio is readily determined quantitatively from DIC data (Fig.3(c)).

The NEPE propellant exhibits a typical viscoelastic behavior.Thereby, the relaxation response of the propellant is examined using tensile relaxation tests, and the relaxation modulus is then expressed in terms of Prony series.

where E(t) denotes the relaxation modulus, E∞the equilibrium modulus, and Ei,τithe Prony coefficients.

Rewriting the relaxation modulus in the form of dimensionless parameters gives

2.3.Computational model

As mentioned in the introductory part, interface debonding is usually considered the main damage in tension and could significantly influence the mechanical response of the propellant.Since CZM is quite effective in evaluating the interfacial performance of filled polymers, this section presents a numerical CZM approach incorporating the effect of the bonding agent to model the interface between the fillers and the matrix.

To begin with,a representative volume element(RVE)of 1500×1500 μ m[37]randomly filled with nearly circular AP and elliptical CL-20 particles is chosen as shown in Fig.4a.A symmetric boundary condition(SBC) was applied for uniaxial tension[32,33].All nodes on the bottom and left edges of RVEs were symmetric with respect to the Y-and X-axes.The top and right edges of RVEs remained plain during tension.Loading rates of 17.85 μ m/s, 35.7 μ m/s and 71.4 μ m/s were assigned to all nodes on the top edge of RVEs, corresponding to the loading speed of 50 mm/min, 100 mm/min,200 mm/min in the tests, respectively.Note that since interface debonding is primarily driven by the larger particles, while the smaller ones serve as stiffeners for the binder [38], only the large particles(70-200 μm)are taken into account and the remainder is supposed to form the composite matrix.As a result, the volume fraction of fillers in the RVE is 41%, which is lower than the filling ratio of 60% in the real material (see Table 1).

The bilinear CZM in the case of purely normal(or,equivalently,purely tangent) loading is modified by introducing the amount of bonding agent ω into the interface parameters, as illustrated in Fig.4(b).For simplicity reasons, the normal and tangential behaviors have taken to be similar,thus the traction-separation equation is expressed as

where T and δ are the normal (or tangential) traction and separation,K(ω)=Tc(ω)/δ0the interface stiffness.The damage parameter is defined as,

Fig.4.(a) Numerical model RVE with fillers/matrix interface and boundary conditions for (b) uniaxial loadings traction-separation relationship of bilinear CZM.

3.Results

This section represents the effect of NPBA and strain rate on the mechanical response of the propellant.Numerical simulations are run with ABAQUS software to quantify the damage evolution, and the results are compared with SEM observations and volume growth.

where Tn(ω) and Tt(ω) denote the normal and tangential traction,δ0, δfare the elastic limit and corresponding critical value of separation.The Macaulay brackets〈•〉allow distinguishing the effect of separation from compression on the interface.

There are only three independent parameters to define the cohesive law,i.e.,Tc(ω),K(ω)and δf.According to the experimental results by Prakash et al.[26], the bonding agent mainly affects the interface strength Tc(ω) while the critical separation δfremains approximately constant.Moreover,de Francqueville et al.[30]also pointed out that complete interface debonding was possible before the macroscopic material failure,thus limiting the value of δfto the order of the fillers.Therefore,the other two parameters required for the CZM are investigated while keeping δf= 0.11 mm [26,30].

For simplicity reasons, the nearly incompressible matrix is modeled by the Neo-Hookean hyperelastic strain energy,

where I1is the first invariant of right Cauchy-Green deformation tensor.The hyperelastic coefficient C10is obtained by fitting the stress-strain curve before the initiation of damage [39].C10= 0.12 MPa and Poisson's ratio of 0.4995.A strain energy criterion is applied for matrix failure[28,37]and the value of 2.7 MPa could be chosen by recording the maximum strain energy during the simulation of a tensile test performed on a random microstructure.When the failure criterion of the matrix is met, the corresponding elements are removed from the RVEs and thus some connected regions between the fillers may appear during the simulation(see subsection 3.3).The particles are regarded as linear elastic with Young's modulus of 19.5 GPa for AP and 17.24 GPa for CL-20, and Poisson's ratio of 0.25 [2,34].

3.1.Uniaxial tensile tests

Representative stress-strain curves and volume ratio (e.g.,100 mm/min case) of tested samples are displayed in Fig.5.As expected, a significant increase in tensile strength was observed with the increasing amount of the NPBA while the elongation was found to decrease.This can be well explained by the volume growth due to the appearance of interface debonding and void formation as shown in Fig.5(b), where damage initiation seems to be delayed and the volume ratio Θ is smaller for the sample with a higher amount of NPBA(e.g.,sample BA-0.5%)due to the better interfacial behavior (Fig.2(c)), further indicating that NPBA can remarkably improve the adhesion of the interface.

It's worth mentioning that NPBA also affects the failure mode of the propellant as shown in the inserted picture in Fig.5(b), while the cross-section of sample BA-0.1% was observed to maintain its square shape (even after fracture) and sudden failure happened,sample BA-0%was extremely strained and developed a tear/visible macro-crack before complete failure.Such differences may be explained through damage evolution at the microscale,which will be discussed later.

Fig.6 shows the effect of strain rate on the mechanical response at room temperature and the propellant exhibits strain rate dependence in the studied strain rate range.Fig.7 displays the quantification of the initial modulus Ee(at a strain of 8%) [10],tensile strength σmand elongation εbunder different cases.As the strain rate is increased,a clear increase of Eeand σmcan be seen to take place for all types of samples, whereas εbdecreases.Meanwhile, the same trend (e.g., increasing σmand decreasing εb) is observed with an increasing amount of NPBA for a given strain rate.However,in terms of the variation in Ee,σmand εb,the effect of the amount of NPBA seems to be more significant than that of strain rates in the studied scope, suggesting that more attention may be needed for intrinsic factors before looking at the influence of the extrinsic ones.

Fig.5.Uniaxial tensile test: (a) Stress-strain response; (b) Damage-induced volume change and failure modes.

Fig.6.Stress-strain response of the propellant under various strain rates: (a) BA-0%; (b) BA-0.1%; (c) BA-0.5%.

Fig.7.Variation of mechanical properties of the propellant with the amount of NPBA: (a) Initial modulus; (b) Tensile strength; (c) Elongation.

Notably, the elongation of the samples with and without NPBA changed much more than the tensile strength or initial elastic modulus, indicating that NPBA not only improves the interfacial performance but may also affect the polymer network of the matrix, which further influences the mechanical response of the propellant [40,41].

3.2.Stress relaxation tests

The tested samples were first loaded to the appointed strain of 5% at a strain rate of 100 mm/min and then held the deformation for 10 min,during which the force variation with time was recorded to obtain the relaxation modulus.

Fig.8(a)shows the results of tensile relaxation experiments.As one could expect,samples with higher amount of NPBA correspond to higher stress levels due to the higher initial modulus (Fig.7(a)).Moreover, the overall trend of the curves appears to be different,which can be better illustrated in terms of the dimensionless Prony series based on Eq.(4), as shown in Fig.8(b).It's observed that NPBA has a noticeable influence even on the relaxation performance of the propellant,which was rarely reported in the available literature.

To be more specific,the force-time relationship was rewritten in the form of normalized stress as shown in Fig.8(c).As can be seen that with a lower amount of NPBA comes a more rapid reduction in the relaxation rate, as well as a lower long term equilibrium modulus.A possible explanation is that since the fillers constitute the bulk of the propellant(e.g.,up to 90 wt%),enhanced interfacial performance allows part of the fillers to act as a'bond'of the matrix network, inhibiting the slippage and sliding of the chains to some extent [42].So far, one may speak about the effect of NPBA on the relaxation behavior improvement of the propellant.However, it should be stressed that the changes in mechanical properties may be the coupled effect of the interface and the matrix,which will be discussed further in the next Section.

3.3.Damage evolution

Using DIC method, volume changes during the loading were calculated from Eq.(2).Fig.9(a) shows the evolution of volume ratio in samples BA-0% and BA-0.5% at various strain rates.The results demonstrate that the volume change exhibits an increasing trend with the increasing strain rates,which is similar to the results reported for solid propellants[7,15,17,18,21].Indeed,the strain rate has a remarkable influence on the volume change, but not so remarkable compared to the amount of NPBA.Furthermore, the damage evolution in the view of the macroscale differs.For sample BA-0%, Fig.9(b) presents clearly detectable voids at several locations over the sample surface, indicating possible sites for the matrix tearing and macro-crack formation.For sample BA-0.5%,however, no such voids are observed and the ultimate failure is triggered just after the presence of strain concentrations at the annotated position, as shown in Fig.9(c).

Fig.8.Stress relaxation response: (a) Force-time curve; (b) Dimensionless Prony series; (c) Normalized stress relaxation.

Fig.9.Damage evolution measured by DIC: (a) Volume ratio; (b) Strain contour plots of BA-0% along 2-direction; (c) Strain contour plots of BA-0.5% along 2-direction.

To better understand the experimental results, a closer look is taken at the damage evolution in the microstructure upon loading and provide a rationale for experimental observations, 2D finite element simulations were performed taking into account the possible filler/matrix interface damage.The interface parameters are obtained using trial-and-error method [32] against the test curves of 200 mm/min, and the corresponding values are Tc(0%) = 0.35 MPa, K(0%) =10 MPa/mm and Tc(0.5%) = 2.6 MPa,K(0.5%) = 40 MPa/mm for samples BA-0% and BA-0.5%, respectively.Fig.9(a) compares the volume ratio obtained from the simulations and tests for both samples at a strain rate of 100 mm/min.The predicted results well match the measured ones, providing a good validation of the simulation in the studied scope.Figs.10 and 11 show the microstructural changes in samples BA-0%and BA-0.5%during tension, where both are characterized by sets of interface debonding, microvoid formation and growth, and catastrophic cracks induced by binder failure.

However, as one can read in Fig.10, most of the fillers are detached from the matrix in BA-0%, which is consistent with the visible,completely clean surface of the particle(zoomed-in view of the SEM image).Moreover, the interface debonding is distributed uniformly without localization and the crack growth is likely to occur through the filler/matrix interface randomly, which is also observed in the SEM image.Hence it can be interpreted that the mechanical behavior is mainly decided by the matrix at large strains due to the poor interface performance, thus presenting a good elongation but lower tensile strength (Figs.6 and 7).

In contrast, much fewer fillers are undergoing interfacial damage in BA-0.5%, and there are matrix fibrils around the fillers (also seen on the zoomed-in view of the SEM image),proving that even the matrix/filler interface is damaged, it is far from being completely broken, as shown in Fig.11.What's more,the interface debonding is highly localized and the crack advancement tends to proceed through the matrix along specific paths,which is the case in the SEM image.This indicates a strong bonding performance between the matrix and filler,resulting in a higher tensile strength but breaking early (see Fig.5).

4.Discussion

4.1.Effect of bonding agent on the matrix

Fig.10.Damage evolution of BA-0% at the microscale, numerous debonded interfaces occurred and cracks advanced through the filler/matrix interface.

The matrix of the propellant is amorphous polymers made up of long flexible macromolecular chains and the chains can slip over one another under loading [42].The bonding agents bridge the fillers to the matrix network by reaction with the curing agent forming a well-bonded interface surrounding the fillers [3,25],during which chains may be linked through the bonding agent and curing agent,as shown in Fig.12(a).This may more or less affect the crosslinking density, thus influencing the slipping and sliding behaviors of chains as deformation increases.In this regard, further differences in the shear modulus of the binder can then be evaluated based on an “ideal” network assumption [40].

where μm,ρ and ϖ are the shear modulus,density,and crosslinking density of the matrix, and R denotes the gas constant.

Therefore, the crosslinking density of the same batch of propellant as in the mechanical tests was measured at 298 K using the Low-field Nuclear Magnetic Resonance technology (LF-NMR).The results normalized by the average crosslinking density of sample BA-0%(i.e.,2.081×10-4mol/mL)are presented in Fig.12(b).As can be seen, the crosslinking density increases slightly with the increasing amount of NPBA,but remains rather small compared to the variation of the initial modulus of the propellent(Fig.7(a)).This indicates that the effect of NPBA is interfacial and not due to an overall increase in crosslinking density of the matrix, which was also verified experimentally in existing Ref.[43].

Nonetheless,due to the lack of definitive mechanical properties of the matrix with different amounts of NPBA, this paper herein avoids claiming decisive remarks with regard to the effect of NPBA on the matrix.The effect of NPBA on the structural network and mechanical properties of the matrix is yet to be unveiled, which will be the objective of future work.

4.2.Effect of bonding agent on the interface

Experimentally evaluating the effect of the bonding agent on the mechanical properties of the interface is not yet available to the authors.One reason is that there is no obvious way to precisely determine the interface parameters at the microscale despite several experimental attempts being reported [26,38].This paper consequently prefers the finite element method with the modified CZM introduced in the previous section.

Fig.13(a) displays the effect of interface stiffness K(ω) on the mechanical performance, which has a strong impact on the initial modulus Eeof the propellant, as observed in other filled polymers[44], further illustrating the dominant effect of the bonding agent on the interface performance.Note that the numbers in Fig.13(a)indicate the corresponding interface/propellant properties of the tested samples.It is possible in this regard to attribute interface stiffness as the main contributor to the variations of the initial modulus of the propellant.However, the improvement over the initial modulus of the propellant by an increase in interface stiffness is limited.

The effect of interface strength Tc(ω) on the stress-strain response of the propellant is gathered in Fig.13(b).As one could expect,the tensile strength of the propellant is enhanced with the increasing interface strength.More interestingly,the fitted curve of tensile strength σmshows an exponential relationship with the interface strength Tc(ω)(Fig.13(b)),as is the case for initial modulus Eeversus K(ω)(Fig.13(a)), which further proves that NPBA mainly affects the interface performance.What's more,high values of the interface strength induce high tensile strength σmin the propellant.Note that due to the lack of appropriate matrix failure criteria, the elongation unfortunately cannot be predicted well at present.

Fig.11.Damage evolution of BA-0.5%at the microscale, much less deboned interface happened and crack proceeded through the matrix.

Fig.12.The role of bonding agent in the propellant: (a) Schematic diagram of mechanism of action; (b) Change in crosslinking density due to NPBA.

This microstructural damage analysis leads to the general conclusion that the bonding agent brings about enhanced interface performance but with an upper limit (see the fitted curves in Fig.13), which is the main mechanism affecting the mechanical properties and damage evolution of the propellant.

5.Conclusions

The effects of NPBA on the mechanical behaviors and damage evolutions of the NEPE propellant were studied through experimental and numerical approaches.Quantitative volume changes due to damage were obtained by DIC.Simulations accounting for interface debonding were performed through modified CZM incorporating the effect of the bonding agent.The influence of the bonding agent on the matrix was also discussed by measuring crosslinking density.

Fig.13.Influence of interface performance on the mechanical response: (a) Initial modulus Ee of the propellant versus interface stiffness K (ω); (b) Tensile strength σm of the propellant versus interface strength Tc(ω).

Results indicated that the initial modulus and tensile strength of the propellant increase with the increasing amount of NPBA while elongation decreases.The strain rate has a similar effect, but it is not so significant compared to NPBA.Meanwhile, NPBA leads to different trends in the relaxation curves; specifically, a lower amount of NPBA results in a more rapid reduction in the relaxation rate and a lower long-term equilibrium modulus.From a macroscopic point of view,clearly detectable voids and matrix tearing are observed over the sample surface for a lower amount of NPBA,but not for the ones with a larger amount of NPBA which maintain their original square shape and undergo abrupt failure just after strain concentrations.Moreover, comparisons between SEM images and simulation results illustrate that the micromechanism of failure in both samples was interface debonding, microvoid nucleation, and catastrophic cracks capable of subcritical advancement.The differences are that the samples with a lower amount of NPBA are characterized by a large number of uniformly distributed interface debonding and randomly orientated microcracks, with nucleation and progression of damage proceeding along the filler-matrix interface.The ones with a higher amount of NPBA favor damage localization along with much less debonding interfaces,and several cracks along specific paths are observed in the microstructure followed by damage advancement through the matrix.Finally, comparisons between experimental and numerical results also show that the effect of the bonding agent is interfacial,e.g.,enhancing the initial modulus and tensile strength(with upper limits),rather than due to the overall crosslinking density change of the matrix.

Experimentally characterization of the interface properties and pure binder with varying amounts of NPBA is currently in progress.As future work, a precise relationship between the macromechanical properties of the propellant and the amount of NPBA might be considered to provide an application-oriented understanding of material formulation.In addition, a more appropriate and detailed matrix failure criteria would probably allow more insightful interpretations for the elongation variation.

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.

Acknowledgments

The authors would like to thank Joint key programs of National Natural Science Foundation of China (U22B20131) for supporting this project.