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Polymer Testing 28 (2009) 627–635

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Polymer Testing

journal homepage: www.elsevier .com/locate/polytest

Material Behaviour

Fracture behavior of PBX simulation subject to combined thermaland mechanical loads

Z.W. Liu a,*, H.M. Xie b, K.X. Li a, P.W. Chen c, F.L. Huang c

a Dept. of Mechanics, School of Astronautics, Beijing Institute of Technology, Beijing 100081, Chinab FML, Dept. of Eng. Mechanics, Tsinghua University, Beijing 100084, Chinac National Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology, Beijing 100081, China

a r t i c l e i n f o

Article history:Received 25 March 2009Accepted 12 May 2009

Keywords:PBXsParticulate compositeFracture behaviorCreep strain

* Corresponding author. Tel.: þ86 10 68912736.E-mail address: liuzw@bit.edu.cn (Z.W. Liu).

0142-9418/$ – see front matter � 2009 Elsevier Ltddoi:10.1016/j.polymertesting.2009.05.011

a b s t r a c t

The fracture behavior and mechanical properties of a Polymer Bonded Explosives (PBX)simulation material were studied using the Digital Image Correlation (DIC) method. Thefracture mechanism was analyzed as the material was subjected to combined thermal andmechanical loads. The macroscopic fracture mode changed from mainly shear action toa combination of extension and shear action, whereas the microscopic fracture changedfrom cleavage fracture and transcrystalline rupture to interfacial debonding, breaking offiller particles and a combination of transcrystalline and intercrystalline rupture. Micro-analysis of the creep properties showed the random nature of initial damage and theinteraction between creep, damage and nearby damage, were the main reasons for thelocal creep strain repetition increase. During the process of high temperature creep,extensive cracks are first formed followed by the initiation and extension of shear cracks,eventually joining and causing a macroscopic fracture within the material. The mainmicroscopic fracture mode has been found to be intercrystalline cracking and bindertearing failure.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

PBX is a particle filled composite materials comprised of90–95% weight of powerful secondary explosive crystalsheld together by a polymeric binder of 5–10% weight, and isused in a wide variety of applications ranging from rocketpropellants to the explosive charge in conventional muni-tions. The possibility of accidental initiation during manu-facture, transport or handling is of great concern, and themechanical properties of such materials, subjected toa range of conditions, is an important criteria in deter-mining a safe working life. The mechanical properties canalso affect the explosive performance to some degree andexcessive temperature and mechanical loads often weakenthese properties during the long-term storage and

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transport. Security and reliability for the application andstorage of PBX require good creep and relaxation properties[1]. The ingredient material of the polymeric matrix hasa typical viscoelastic character, and damage and creepdeformation at high temperatures is inevitable duringstorage and transport. Some previous research results haveshown that damage and creep deformation can result in thechange of physical and mechanical properties, conse-quently influencing the explosive performance [2]. Hence,it is very important to study the micro-fracture mechanismand creep behavior under high temperatures in order tounderstand the micro-damage and failure mechanisms,which will significantly contribute to the design andhandling of new PBX materials.

A number of investigations on the mechanical proper-ties and fracture behavior have already been performed atroom temperature, although research into micro-fracturemechanisms under high temperatures has been limited.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635628

The development of creep deformation mainly depends onstress, time, loading speed and temperature, and severalimprovements have been made: Reference [3] has studiedthe viscoelastic properties of PBX using a diameter disk test,and proved that the test is an efficient and economical wayto characterize the mechanical properties of explosivematerials. Reference [4] proposed that there is a nonlinear

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Pnj ¼ 1

hf�xi; yj

�� f

ihg�

x0i; y0j�� g

iffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPm

i ¼ 1

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�f ðxi; yjÞ � f

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constructive relation to describe the mechanical behaviorof PBX, based on experimental data obtained under simpletension and at different temperatures and strain rates.Reference [5] proposed that there is a nonlinear viscoelasticconstructive relationship with damage. The Norton–Baileycreep law, based on time hardening theory, says that thecreep strain rate only relies on time when both stress andtemperature are given [6,7]. Reference [8] showed that thecreep property of the polymer is the main factor in influ-encing the creep damage properties of PBX, despite thepolymer content being very low, and also discusses theinfluence of granularity both on the initial creep damageand on the probability of creep damage occurring.

In order to further study the microscopic fracturebehavior and creep properties, it is necessary to observewhole field deformations in real time. The traditionalmeasuring techniques are only capable of provided a singlepoint strain by means of a strain gauge or an average strainin a specific direction using a displacement sensor. DICmethod is an efficient optical method for measuringinhomogeneous deformation by providing whole fieldcontour maps of displacements with high sensitivity. Here,the DIC method combined with Scanning ElectronMicroscopy (SEM) observation was used to investigate themicroscopic fracture behavior and creep properties of PBXunder high temperatures.

2. Experimental method and procedure

2.1. Materials prepared

The PBX simulation material is a particulate compositein which the crystalline explosive has been replaced by KCLparticles at 90% weight, with a binder of fluoro-rubber; thesame material as real HMX-based PBX. The PBX simulationmaterial was pressed into block specimens of different sizein steel dies for 1.5 h under a temperature of 100 �C andpressure of 200 MPa.

2.2. Deformation measurement by DIC methods

As an image correlation technique, the DIC method usessurface images where speckle points of light may changetheir positions during any movement or deformation, andspeckle image correlation processing searches for displaced

speckle points in a pair of images. To obtain the in-planedisplacement components, u and v, in the x and y directionsfor a pair of such images, a pixel subset with m� n pixels isused as a searching sub-region. To eliminate the influenceof image background, a normalized cross-correlationcoefficient, C

� ðu; vÞ, of the grey intensity is commonly usedto define the correlation degree as [9]:

where f ðxi; yiÞ is the grey level at point Fðxi; yiÞ in one of theimages serving as the reference frame; gðx0i; y0iÞ is that atpoint Gðx0i; y0iÞ in another image as the deformed frame; fand g are the mean grey scale values of the pixels involvedin the subsets, respectively; and the searching parameters,u� and v�, are the components of the vector linking thesubset centers. The correlation coefficient, C

� ðu; vÞ, iscomputed against the parameters u�, v� and the matchingspots are obtained when the correlation coefficient,C�ðu; vÞ, reaches a maximum, then u� ¼ uhx0i � xi, andv� ¼ vhy0i � yi respectively. The displacement resolution ofthe DIC method can be extended to 0.05 pixels by inter-polating the correlation map to fractional locations of thepixels. Here, the linear interpolation, the polynomial splineapproximation, and other interpolations may be utilized. Adetailed analysis of the systematic errors due to differentinterpolations was made by Schrier et al. [9].

2.3. Experimental device and procedure

2.3.1. Compressive tests under different temperatureA loading test machine (type WDW3050) was used with

an additional high temperature control box, a window forobservation and a CCD camera to capture images. Thethermal load was imposed at 30 �C, 60 �C and 90 �C for10 min each to ensure the whole material had uniformtemperature. The mechanical loads were applied at a highvelocity until the material broke. The captured images fromthe CCD camera were used for DIC analysis.

2.3.2. Creep tests under different temperatureThe mechanical loading device consisted of a lever and

weight system frequently used in photoelastic testing, andis the same as described in [10]. The high temperaturecontrol box was used with the observation window andCCD camera for DIC analysis. A micro-creep test at room-temperature was performed under SEM.

3. Experimental results and discussion

3.1. Compressive tests under different temperature

The specimens of PBX simulation material had a size of10�10�16 mm3, and the compressive experiments wereperformed at room temperature (22 �C), 30 �C, 60 �C and

Fig. 1. A relationship curves of stress and strain under combined thermaland mechanical loading.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635 629

90 �C at a strain rate of V¼ 4.17e�4 s�1. The resultingrelationship curve for stress and strain was fitted by theleast square method and is shown in Fig. 1. A test curveunder a strain rate of 2.08e�3 s�1 was also conducted atroom temperature for comparison purposes. Fig. 1 showsthat the higher the loading strain rate, the larger thecompressive strength, which agrees with the previouswork [11]. It can also be seen that as the temperatureincreases from 30 �C to 60 �C, then to 90 �C, the compres-sive strength decreases from 42.5 MPa to 29.1 MPa, then to14.9 MPa, declining by 31.5% and 64.9%, respectively,whereas the fracture strain increases by 79% and 187%,respectively. This indicates that temperature has a signifi-cant effect on the mechanical properties and fracturebehavior of this material.

Fig. 2. Specimen fractured.

In order to investigate the fracture mechanism underthermal and mechanical loading, speckle images werecaptured for the purpose of DIC analysis. As an example,Fig. 2 shows an image taken at 90 �C, where the blackdashed line shows the fracture path. Fig. 3 shows thedisplacement vector pattern under a compressive stress of10 MPa calculated by using DIC. Here, it can be seen that theupper right part staggers and flows to the lower rightapproximately along the diagonal line, while the lower leftpart flows to the left with respect to the right part. In somelocal areas, parts are split in opposite directions, and thereis a large variation in displacement distribution near thediagonal line area compared with other parts. All of thisindicates that the material is suffering from large extensionand shear stress under the combined thermal andcompressive loading. Fig. 4(a) and (b) shows the extensionand shear strain distribution, showing that both areconcentrated in an area near the diagonal line, with theextension strain being larger than the shear. This is proofthat the macroscopic rupture of the PBX simulation mate-rial is caused by extension and shear when subjected tocombined thermal and compressive loads, which differsgreatly from the brittle rupture caused by shear under onlycompressive loading [2]. As temperature increases, exten-sion plays a more important role in PBX fracture undercompressive loading and causes the overall strength todecline (as extension strength is much lower thancompressive strength); the contribution of shear conse-quently becomes smaller as temperature increases.

Fig. 5(a) and (b) shows the SEM images of the fracturesurface at both room temperature and 90 �C, respectively.

Fig. 3. Displacement vector.

Fig. 4. Strain component distribution. (a) Extensive strain. (b) Shear strain.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635630

In Fig. 5(a), it can be seen that most of the filler particlesexperience cleavage fracture, which indicates that therupture mode is mainly brittle and transcrystalline understatic compression loading. However, Fig. 5(b) showssmooth concave areas resulting from the binder after someparticles have been pulled out, other than several fracturedparticles. This indicates that during loading and the processof fracture some interfaces between the filler particles andbinder disbond because of extension, while some fillerparticles are broken because of extrusion and shear fromeach other. The interfacial debonding and filler particlesbreaking reflect that the rupture mode is both trans-crystalline and intercrystalline under combined tempera-ture and force loading.

3.2. Creep tests

Previous work [10,12] on creep investigation at roomtemperature has shown a special case where there is

Fig. 5. SEM images of the fracture surface. (

repetition of increase stages in the local creep strain–timecurve. In order to understand the micro-mechanism for thefluctuation trend of the creep curve, a micro-creep defor-mation test was performed under a SEM combined with theDIC method. For most loading devices used in SEM, theloading mode is not usually mechanically controlled, butrather displacement controlled, hence a creep test cannotbe performed directly in a SEM. However, an alternativeway to approximately characterize the micro-creep prop-erties is creep and fatigue experiments using a very lowfrequency fatigue test [13].

In this investigation, a very low frequency fatigue testwas used to approximately simulate the micro-creep testsusing three-point-bending in the SEM. Three-point-bending specimens of size 20� 3�6 mm3 were used, anda schematic diagram of these is shown in Fig. 6(a). A notchwith a depth of around 0.6 mm and a width of around0.3 mm was cut in the middle of the specimen. The SEMimage of the area near the notch is shown in Fig. 6(b).

a) At room-temperature. (b) At 90 �C.

Fig. 6. Specimen images. (a) Schematic diagram of specimens. (b) SEM image around a notch tip.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635 631

The frequency of the fatigue test was 0.1 Hz, and themechanical load applied to specimens was from 60.00 N to60.10 N in increments of 0.10 N to simulate the micro-creeptests with a load of around 60.05 N.

A two-dimensional micro-creep deformation field wasmeasured on the SEM images using the DIC method.Fig. 7(a) and (b) shows the two-dimensional extensivestrain fields in the ABCD region near the notch when creeptime equals 5000 s and 9000 s, respectively, and it can beseen that the extension strain field is not uniform. InFig. 7(a), the local areas E and F show a significant strainconcentration that may be caused by original damage nearthe notch. Even with an increase in creep time, the creepstrain has not increased significantly in the areas near theoriginal damage. However, a new local strain concentrationarea will appear, such as in local areas G and H shown inFig. 7(b). Comparing this to Fig. 7(a), the creep strain rate inareas E and F has slightly decreased, in particular, the strain

Fig. 7. 2D extension strain distribution during creep near a notch with a different

magnitude in local area F has declined to an average level ascreep time increases. It can be speculated that the localcreep repetition increase or decrease stage is a result of theinteraction between creep and damage, which can beexplained from understanding the microstructure andinternal damage. The pressed PBX is a composite witha high concentration of particles with a random distribu-tion of initial damage in the form of cavities, interfacialdebonding and crystal fractures, amongst others [8]. Someof this initial damage can be activated, and some newdamage generated, at a relatively low stress and strain level[14], which can be further supported by the existence ofsubcritical fractures [15]. In addition, a micro-crack maypropagate at different rates with respect to the differentfailure forms. This is because it is easier for a micro-crack topropagate along the boundary of particles throughdebonding, especially for particles with an initial debond-ing and uncoating, than through binder rupture. The

creep time. (a) Creep time equal to 5000 s. (b) Creep time equal to 9000 s.

Fig. 8. Shear strain distribution during creep near a notch. (a) Creep time equal to 4000 s. (b) Creep time equal to 6000 s. (c) Creep time equal to 9000 s.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635632

development of the damage accelerates the increase ofcreep strain rate, and creep deformation may also promotefurther evolution of damage and new damage initiation.A micro-crack may sometimes be impeded by an explosivegrain due to its orientation if the size of the micro-crack iscomparable with, or smaller than, the size of the grain. Inaddition, the interaction of neighboring particles may alsocontribute to the occurrence of the repeating increase ofcreep strain rate. This process will recur over and overagain, as long as the creep period is long enough, and moreand more damage will initiate and develop until thespecimen is completely destroyed.

In this test, initial damage can be seen in the specimensby observing the SEM images and a micro-crack in thebinder near local area E is shown in Fig. 6(b). During creep,the initial damage is activated and tends to evolve, thuscausing a significant strain concentration in the area.However, as the creep develops, further evolution ofdamage can be impeded by an explosive particle nearby, asshown in Fig. 6(b). Other initial damage can be activated, ornew damage will be initiated, such as in local areas G and H,where the strain rate of the material near area G rapidlyincreases, while the strain rate in local area E slightly

Fig. 9. Creep strain time curve.

decreases, as shown in Fig. 7(b). However, in the followingcreep time, the strain rate in area E can be increased again,caused by re-motivating the damage caused by creepdeformation, or nearby damage evolution. Therefore, it canbe concluded that the distribution of random initialdamage and the interaction between creep and damage, aswell as other nearby damage, are the main causes of localcreep repetition increase or decrease.

Shear strain can also be generated in local areas duringsuch creep deformation in the PBX material. Fig. 8(a) showsan area of localized shear strain concentration, which ispresented in pairs in local region I near the notch, whereasFig. 8(b) shows the evolution of the shear strain concen-tration in the binder accumulation region. From thesefigures, it can be seen that the maximum size of the shearstrain varied from around 0.01 to 0.015 for creep periodswithin the 4000 s to 6000 s range. The relative shift amongadjacent explosive particles can occur during creep defor-mation due to the difference of creep deformation velocityand magnitude between the explosive particles and the

Fig. 10. Fracturing specimen.

Fig. 11. Displacement vector.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635 633

binder. This shift could cause mutual friction of fillerparticles surfaces, and may result in the interior slip of thefiller particles and a cleavage fracture. Thus, shear straincaused by explosive particle slip can also be produced inthe explosive particles during creep, as shown in area J ofFig. 8(b). The relative shift has occurred between twoexplosive particles along the arrow direction near area J, asshown in Fig. 6(b). Mutual friction caused by the relativeshift generated a larger frictional force, thus resulting ina large shear stress near the adjacent surface of the twoparticles. However, in the next creep period, the largershear strain concentration in area J disappeared, as shownin Fig. 8(c). The relative shift of another two adjacent

Fig. 12. Strain component distribution. (a

explosive particles has caused another shear strainconcentration in pairs near area K, which can be seen inFig. 8(c). From these reproducible tests, a conclusion can bedrawn that shear stress concentration will occur in pairs ina local area during creep, while after a period of creep itmay disappear in this area and reappear elsewhere in a pairat random. It has been reported that material temperaturemay be increased by work done with shear stress [16,17].From this test, it can be seen that the shear stressconcentration may not generate higher temperature due tothe quantity of heat accumulation caused by the work donewith shear deformation during creep. The main reason forthis is that the quantity of heat may not accumulate enoughin a fixed area, due to the initiation and disappearance ofshear stress at random local areas. Moreover, it cannotpropagate for long periods in a fixed area.

A creep test under 60 �C and 90 �C with compressivestresses of 20 MPa and 10 MPa were conducted using thesame test system as described in [10], with the resultingstrain–time curve shown in Fig. 9. It was reported that thetypical creep curve of the pure high polymer material canbe divided into three stages; transient creep, steady stateand accelerating creep [18]. Compared with the creepfeature of a high polymer, the PBX simulation material alsohas three specific creep stages under high temperature.However, there is no steady state creep stage in this study,which is substituted by a fast creep stage. The first stage isuniform deformation under compressive stress andthermal loading, and the second stage is particle movingand binder flow with the decrease of creep rate, becausemost of the particles are load supporting. The third stage ismicro-void, micro-crack initiation and evolution, as well asa particle fracture stage. The three stage division is notabsolute, in the third stage, termed accelerating creepstage, the damage inside the specimen develops rapidlyand keeps both the creep strain and the creep rateincreasing rapidly until the specimen is broken. Accordingto the damage mechanics, this process of the third stage

) Extensive strain. (b) Shear strain.

Fig. 13. A formed void and cavity.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635634

synthesizes the fast creep and the damage creep, and it ismainly the damage creep that contributes to the ultimatedestruction.

Fig. 10 shows a fracture specimen surface during creepat 90 �C in the third stage. The bold dashed and real lineshows the approximate crack path. Fig. 11 shows itsdisplacement vector pattern.

The displacement vector in Fig. 11 shows the materialflow direction and magnitude in detail. It can be seen thatthe material flows in the opposite direction symmetricallyin some local areas near the diagonal line. This indicatesthat many extensive cracks will initiate and evolve firstlyalong the direction of compressive loading near the diag-onal line during loading, such as the extensive cracksindicated by the bold real line. With the development andevolution of these extensive cracks, at the same time, someshear cracks initiate from the ends, such as the shear cracksindicated by the bold dashed line. With the evolution ofthese existing shear cracks, the extensive cracks are joinedto each other end-to-end by the shear cracks, and thenlarger penetrating cracks are formed. The material is finallyfractured along the complicated zigzag crack, which differs

Fig. 14. Crack route. (a) Cracking along particle

greatly from the creep fracture at room temperature andcompressive fracture under combined thermal andmechanical loading.

Fig. 12(a) and (b) shows the extension and shear straindistribution. From these images, it can be seen that theextension strain has a larger magnitude than that of theshear strain distribution. The material fracture is macro-scopically caused by a combined extension and shearaction, especially the extension which plays a moreimportant role.

From the microscopic view, the accelerating creep stagemight predict a transition of the damage accumulationfrom crystals debonding to void coalescence, forminglarger voids or cracks in the material. This was proved bythe detailed SEM pictures at higher magnification, asshown in Fig. 13 for the specimen surface showing voidsformed by the debonding accumulation and binder frac-ture. With temperature increase, the fracture trenddevelops from brittle to ductile, increasing the number ofvoids, cavities and micro-cracks.

Fig. 14(a) shows that a crack is extending with somemicro-cracks originating along the boundaries of the largerparticles. Fig. 14(b) also shows some extended binder fila-ments bridging the crack surfaces, demonstrating that thebinder undergoes considerable deformation. The binderthreads in the cracking path also shows debonding andbinder tension fracture when the binder softens under hightemperature. Examination of the fracture path also showsthat the failure predominantly follows the boundaries ofthe fillers due to interfacial debonding. This indicates thatmost fracture cracks were initiated and propagated alongthe explosives simulation crystal surface during creep.

Fig. 15 is a typical fractograph of the PBX material inthermal creep tests, in which both filler particle surfacesand fractured binder are observed. Fig. 15 shows thata large number of the filler particles are completely pulledout and debond with a relatively rough surface covered byfractured binder, which differs from the creep at roomtemperature [19] in which most particles have smoothsurfaces. The examination of the fracture surfaces has also

boundaries. (b) Binder filament bridging.

Fig. 15. Fracture surface with intact particles.

Z.W. Liu et al. / Polymer Testing 28 (2009) 627–635 635

showed that the creep failure predominantly follows theboundaries of the explosive filler due to interfacialdebonding. The main fracture mode is intercrystallinecracking and binder tearing. It also can be seen that mostexplosive filler particles have not fractured during thecreep fracture, that is that the mechanical character of theexplosive filler has not be utilized well.

4. Conclusions

The fracture behavior of the PBX simulation materialwas investigated using the DIC method. From the fracturebehavior investigation, the micro-fracture mechanism wasanalyzed when the particulate composite was subjected tocombined thermal and mechanical loads. The resultsobtained show that, with the increase in temperature, thecompressive strength is greatly reduced. The macroscopicfracture mode changes from mainly shear action toa combined extension and shear action, while the micro-scopic fracture mode also changes from cleavage fractureand transcrystalline rupture to interfacial debonding, fillerparticle breaking and combined transcrystalline andintercrystalline rupture. Micro-analysis of the creep prop-erties was performed using SEM combined with the DICmethod. The results obtained show that the random natureof the initial damage, the interaction between creep anddamage, as well as between damage and nearby damage, isthe main causes for the increase in local creep repetition. Inaddition, localized shear stress concentration occurs inpairs. The creep strain curve presents three distinct stagesunder high temperature. During creep and fracture underhigh temperature, extensive cracks initiate and expand atfirst, and then shear cracks penetrate and join them

together causing the material to fracture on the macro-scopic level. The observed creep fracture surfaces show thatmost fracture cracks were initiated and propagated alongthe explosives simulation crystal surface during creep, andthat the main microscopic fracture mode is intercrystallinecracking and binder tearing failure.

Acknowledgements

This work is supported by the National Basic ResearchProgram of China through Grant No. 2004CB619304, theNational Natural Science Foundation of China (under grants10602010, 10625209, 10732080, 10472050, and ExcellentYoung Scholars Research Fund of Beijing Institute of Tech-nology. The Project supported by Beijing Natural SciencesFoundation (under grant 3072007) and the Program forNew Century Excellent Talents (NCET) in University,Chinese Ministry of Education (NCET-05-0059), ChineseMinistry of Education and the National Key Laboratory ofExplosion Science and Technology at BIT.

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