Study on Fracture Behaviour of a Polymer-BondedExplosive Simulant Subjected to Uniaxial CompressionUsing Digital Image Correlation Method

Z. Zhou, P. Chen, Z. Duan and F. Huang

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

ABSTRACT: Quasi-static uniaxial compression experiments were conducted on a polymer-bonded explosive (PBX) simulant. At macro-

scale, the deformation and fracture process of samples were recorded using a charge-coupled-device camera. Microscopic examination was

conducted to in situ observe the deformation and fracture processes of samples using SEM equipped with a loading stage. Microscopic damage

modes, including interfacial debonding and particle fracture, were observed. The digital image correlation (DIC) technique was used to

calculate the recorded images, and the macro- and micro-scale displacement and strain fields were determined. Crack initiation, crack

propagation, fracture behaviour and failure mechanism of samples were studied. The effects of aspect ratios on fracture behaviour and failure

mechanism of PBX simulant were analysed.

KEY WORDS: deformation and fracture, digital image correlation, polymer-bonded explosive, uniaxial compression

IntroductionIn particulate-reinforced composite materials, inhomoge-

neity plays an important role in composite fracture. When

the deformation of the material reaches a threshold value,

the conditions of the main defect growth change. This is

caused by the rise of the stress strain distribution hetero-

geneity and appearance of energy dissipation. Therefore,

particle fracture and nucleation of micro-voids take place

because of the interfacial debonding that occurs between

the particles and matrix. Failure also depends on the parti-

cle-to-matrix volume ratio. Polymer-bonded explosives

(PBXs) are highly particle-filled composites, in which high-

percent explosive granules (90–95% by weight) are distrib-

uted in soft polymer. With a much higher concentration of

particles than conventional polymeric composite, PBX may

exhibit different deformation and failure mechanisms.

Because of the explosion risks involved in its manufac-

ture, storage and transport, it is important to determine the

mechanical properties of PBXs in various loading condi-

tions. In the past two decades, much attention has been

paid to experimental characterisation of PBXs and their

constituents. Palmer and Field [1] studied the mechanical

deformation of b-HMX. Palmer et al. [2] analysed the fail-

ure strengths and deformation and fracture behaviour of

PBXs. Several other studies have focused on the charac-

terisation of heterogeneous microstructures [3, 4], fracture

and deformation [5–8], influence of temperatures and

strain rates on mechanical properties [9–12], and correla-

tion between microstructure and fracture behaviour [13] of

PBXs. Some attention has been paid to in situ observation

of microscopic deformation and failure of PBXs under

tensile stress in Brazilian tests [2, 13, 14]. Mechanical

properties of PBXs under compression have been reported

by some researchers [15–17]. Williamson et al. [15] inves-

tigated the effects of size on compressional failure strength

of a PBX simulant. However, the deformation and failure

mechanisms of PBXs under compression were not fully

investigated. Particularly, study on microscopic deforma-

tion and failure of PBXs under compression is rare.

Many techniques exist to quantify the deformation

present at the surface of a material. Strain gauges give a

measure of the average strain present at the area. However,

this method provides the deformation information at a

single point, and bonding the gauge on the material surface

may give local reinforcement. Optical techniques, on the

other hand, display many advantages, such as full-field

deformation measurement and many are non-contacting.

Peters and Sutton et al. [18–22] have previously applied the

idea of digital images correlation (DIC) to experimental

mechanics. Their work is based on correlating the images in

the spatial domain. This method works by comparing the

same zone within digital images captured before and after

deformation, then the deformation fields can be calculated,

helping indicate the process of damage evolution and

failure of samples. Recently, Rae et al. [14, 23, 24] have

applied the DIC technique to determine microscopic dis-

placement and strain field of PBX under Brazilian disc test.

Zhou et al. [25] used DIC to calculate strain fields and

analysed micro-scale deformation and fracture behaviour

of a PBX simulant under tensile stress. In addition, the

dynamic deformation and fracture behaviour of PBX was

experimentally studied by using split hopkinsion pressure

bar and DIC method under Brazilian test, and the tensile

stress and strain curves of discs were obtained [26]. Many

researchers paid much more attention to study the defor-

mation and mechanical properties of explosives using the

DIC technique, showing the DIC method has proved to be

a useful tool and can be widely used in the studies of

mechanical responses of materials.

In this article, the DIC technique was applied to study

the quasi-static compressional deformation and fracture

behaviour of PBX. Uniaxial compression tests were con-

ducted on block samples with aspect ratios of 1.8, 2.0 and

2.3, respectively. In addition, the microscopic damage

evolution in PBX was observed in situ using a SEM imaging

system incorporated with a loading stage. In addition, a

combination of the DIC method with SEM imaging system

was used to determine the strain distribution at micro-scale

326 � 2011 Blackwell Publishing Ltd j Strain (2012) 48, 326–332doi: 10.1111/j.1475-1305.2011.00826.x

An International Journal for Experimental Mechanics

level to study the microscopic failure mechanism of the

sample.

ExperimentsA PBX simulant material was used in this study, which is a

highly particle-filled composite comprised of Ba (NO3)2

particles (95% by weight) held together by the fluoro-

rubber (5% by weight). Moulding powder was produced by

a conventional slurry process, in which the Ba (NO3)2

particles agglomerated, as they were coated with the binder

dissolved in an organic solvent. The test samples were

made by hot pressing the moulding powder in a steel

mould. To obtain short and cylinder-shaped samples, the

following parameters were used: pressing pressure at

200 MPa, temperature at 100 �C and pressing for 1 h. The

test specimens were all machined from those cylindrical

samples.

Prior to the experiment, the speckles were prepared on

the sample’s surface by spraying white and black paints

alternatively. Figure 1 shows the schematic of the testing

setup, the specimen was loaded on the material test system

(MTS). A charge-coupled-device camera was used to in situ

observe the movement of speckles before and after defor-

mation. The frame rate was 5 frames per second, and the

resolution of images was 1624 · 1236 pixels2. The DIC

technique was used to process these images. The subset size

of 29 · 29 pixels2 and the step size of 5 pixels were chosen

for DIC analysis to determine the displacement and strain

fields, respectively.

To investigate the microstructure of the sample, polish-

ing is required. First, specimens were ground using fine

emery papers (#1000), after which polishing was carried

out using a fine polishing paste. Finally, gold was sprayed

on the specimen surface to form a conductive layer. The

SEM used in this work was S-570 from the Hitachi Corpo-

ration. A loading stage was installed inside the SEM

chamber, which enabled the SEM to acquire images during

each loading step. Therefore, the microscopic damages can

be observed in situ. In our work, a specially modified uni-

axial compression test was carried out in SEM for hetero-

geneous strain field measurement at micro-scale level. The

length, width and thickness of the sample were 9, 5 and

5 mm, respectively (as shown in Figure 2). A pre-notch

with a 0.2 mm width and 2 mm length was cut along the

diagonal line of the specimen. To facilitate crack propaga-

tion along the diagonal of the specimen, grooves were

machined on the back and along the diagonal of the

specimen. In the SEM imaging system, the accelerator

voltage of 25 KV, a probe current of 100 lA and the image

size of 412 · 478 pixels2 were used to record the SEM

images. The area of interest (labelled as ‘Area I’ in Figure 2)

was in situ observed. With increasing external force, a series

of SEM images were obtained [25]. Afterwards, the DIC

method was applied to process these SEM images to cal-

culate the displacement and strain full fields.

Damage and Fracture Analysis of PBX

Uniaxial compression of specimensThe specimens with dimensions of 10 · 10 · 18 mm3,

10 · 10 · 20 mm3 and 10 · 10 · 23 mm3, respectively,

were compressed uniaxially in MTS. The loading was

increased in a displacement control mode with the speed of

0.1 mm min)1. In this study, the applied compressive load

was normalised by the cross-section area of the specimen,

and the displacement along loading axis was normalised by

the initial length of the specimen. Figure 3 shows the

resulting relationship of the compressive stress versus

strain. The specimens had a linear behaviour at the

beginning of the test, and the compression load followed a

x

P

Sample

Computer

CCD

Light

MTS

y

Figure 1: Experimental setup

Sample

Area I

Pre-notch

x

y

Figure 2: Uniaxial compression test in SEM

Figure 3: Stress–strain curves of specimens with different aspectratios

� 2011 Blackwell Publishing Ltd j Strain (2012) 48, 326–332 327doi: 10.1111/j.1475-1305.2011.00826.x

Z. Zhou et al. : Study on Fracture Behaviour of a PBX Simulant

period of linear ascension. As the load reached maximum

value, it corresponded with the fracture of the specimen,

after which the load decreased. The magnitude of failure

strength values was approximately 58.5, 49.5 and

47.1 MPa, corresponding to specimens with aspect ratios of

1.8, 2.0 and 2.3, respectively. The results show that the

failure strength decreases with increase in the aspect ratio.

Similar results were also reported by Williamson et al. [15].

Experimental works have shown that damage initiation

and localisation play an important role in the mechanical

behaviour of the sample made of brittle materials [27]. The

stress–strain relationship of the specimens is not the direct

response of the material, but the average response of the

structure (Figure 3). However, as the external force is

applied, some damages, e.g. micro-cracks, may exist in the

specimen; therefore, it is important to detect the damage

initiation and predict possible propagation of cracks for

safety evaluations of the sample. In the following, we used

the DIC technique to calculate the deformation field dis-

tribution; doing so helped us study the damage evaluation

and failure mechanisms of the samples.

Fracture path prediction from strain distributionFigure 4 shows the strain distributions on the specimen

surface, just prior to fracturing of the specimen. A con-

centrated tensile strain band was localised in the central

area of the specimen along the loading axis (see Figure 4A);

meanwhile, a localised shear strain band was concentrated

in the area near the diagonal corner (see Figure 4C). The

experimental results indicate that deformation and fracture

of this specimen is dominantly caused by extension and

shear stress action.

Figure 5 shows the strain distributions of the specimen

with a size of 10 · 10 · 23 mm3. A concentrated tensile

(A) (B) (C)

Figure 4: Strain component distributions of the sample with aspect ratio of 2.0. (A) Extensive strain (exx), (B) Compressive strain (eyy) and(C) Shear strain (exy)

(A) (B) (C)

Figure 5: Strain component distributions of the sample with aspect ratio of 2.3. (A) Extensive strain (exx), (B) Compression strain (eyy) and(C) Shear strain (exy)

328 � 2011 Blackwell Publishing Ltd j Strain (2012) 48, 326–332doi: 10.1111/j.1475-1305.2011.00826.x

Study on Fracture Behaviour of a PBX Simulant : Z. Zhou et al.

strain band was localised along the loading axis and spread

from the top of the specimen to the bottom (see Figure 5A).

The maximum tensile strain value was approximately 0.06,

while the compressive and shear strain magnitudes were

comparatively small (see Figure 5B, C). The fracture of this

specimen is significant and caused by extension action.

Comparing this to Figure 4, the results indicate that the

fracture mechanism of block samples is relative to the size

of the specimen.

The displacement vector field can give a quantitative

measurement. Figure 6A shows the vector field of dis-

placement of the sample with an aspect ratio of 2.0. It is

seen that the two wedges of materials were driven down-

ward and upward into the material with clearly visible

shear regions, and the central materials moved to the left

and right sides approximately perpendicular to the loading

axis. The vector arrows are scaled and present a displace-

ment from the beginning of the test, giving a clear

indication of the failure mechanism. Figure 6B shows the

displacement vector pattern of the sample with an aspect

ratio of 2.3. The materials simultaneously flowed to the

right and the left side perpendicular to the loading axis;

meanwhile, a tensile crack was observed on the sample

surface.

Figure 7 shows the respective fracture morphologies of

specimens of varying aspect ratios for comparison. Typical

fracture morphology was observed for the sample having

an aspect ratio of 1.8; as shown in Figure 7A, the fracture

path was nearly along the diagonal line, showing that the

sample fractured significantly by shear stress. With

increasing of the aspect ratio, the fracture mode of the

sample changed. Fracture surface can be seen obviously at

the top left corner in Figure 7B. The main crack ran from

the upper left corner to the lower left corner; it ran along

the loading axis in the centre of the sample. The result

shows the fracture is caused mainly by the extension and

shear stress action. When aspect ratio increased to a critical

value, shear action did not work (as shown in Figure 7C). In

the figure, a single crack can be seen, which was caused by

the extension stress action; In addition, the failure plane

can be seen parallel to the loading axis. Figure 7 shows that

fracture morphologies of block samples are strongly relative

to the specimen’s size, and the observed fracture morpho-

logies are in agreement with the results predicted from the

displacement and strain fields.

In addition, comparative analysis of the Figure 7A–C, the

results show that the valid fracture test can be carried out

by performing the sample having an aspect ratio of 1.8, and

the typical mechanical parameters can be determined.

Figure 7A shows the photograph of the separated speci-

men. The value h is approximately 63�, allowing the angle

of internal friction to be calculated; the resulting value

corresponds to 36�. Based on the Mohr–Coulomb criteria

[28], the shear stress s can be given by s = lrn + c, where rn

is the normal stress acting on the failure plane, c is the

cohesion and l is the friction coefficient. The angle of

internal friction of the material / is relative to the friction

coefficient through the relationship l = tan/ and can be

calculated by h = p/4 + //2. In the equation, h is the angle

made between the failure plane normal and the loading

axis. In our work, the ultimate compressive engineering

stress of the specimen of aspect ratio 1.8 was 58.5 MPa.

(A) Aspect ratio of 2.0 (B) Aspect ratio of 2.3

Figure 6: Displacement vector fields of the samples with differentaspect ratios. (A) Aspect ratio of 2.0, (B) Aspect ratio of 2.3.

(A) (B) (C)

Figure 7: Fracture morphologies of specimens with varying aspect ratios. (A) 1.8, (B) 2.0 and (C), 2.3

� 2011 Blackwell Publishing Ltd j Strain (2012) 48, 326–332 329doi: 10.1111/j.1475-1305.2011.00826.x

Z. Zhou et al. : Study on Fracture Behaviour of a PBX Simulant

Therefore, the value for the coefficient of cohesion was

calculated to be 14.8 MPa.

Microscopic damage examination and analysis from strain

distributionSEM was used to in situ examine the micro-structure of the

block sample with an aspect ratio of 1.8, because typical

shear fracture was observed in this sample. The results

showed that different forms of failure, including interfacial

debonding and particle fracture, were observed (see

Figure 8). Intergranular failure because of interfacial

debonding can be clearly seen in the figures. Moreover,

considerable particle fractures are also present (indicated as

arrows in Figure 8). Particularly, obvious microscopic

cracks occurred in large particles (labelled as A and B in

Figure 8B). In hot-pressed PBX, pressing not only consoli-

dates the moulding powder but also induces micro-cracks

to explosive crystals [13]. Therefore, under external

compressive loads, particle fractures may occur when the

particles are pre-damaged during pressing, and their ori-

entation impedes crack growing path. These phenomena

can be more clearly seen in the fracture route of the sample

(see Figure 10). The above results are obviously different

from the microscopic failure modes because of tensile stress

observed in Brazilian test [29] (see Figure 9), in which the

crack path mainly follows the boundaries of large particles,

and the particle fracture is rare. The predominant failure

mode of debonding under tensile stress was also observed

by Palmer et al. [2] and Rae et al. [14].

The microscopic deformation and failure process of the

sample with an aspect ratio of 1.8 was further studied by

DIC analysis based on the recorded in situ SEM images.

Figure 10 shows the micrograph of the region in the front

of the pre-crack, where a microscopic crack initiated. This

area was magnified by SEM imaging system to in situ

observe the surface topography. For each loading step with

a force increment about 4P = 60 N, the image of this area

was recorded. Then, the DIC method was used to digitally

process these SEM images. The subset size of 29 · 29 pixels2

and the step size of 3 pixels were chosen for DIC analysis.

The area II of interest was analysed using DIC to determine

the microscopic strain fields.

Figure 11A and B show the extension and shear strain

distribution of the area II, respectively. The results indicate

that the specimen fractured under both extension and

shear stress action, especially the shear stress, plays a more

important role.

Figure 12 shows a typical fractograph of PBX simulant in

compression test. Extensive particle fractures can be

observed, causing the formation of a large number of

smaller particles. It is reasonable to conclude that particle

fractures under compression are mainly associated with

particle-to-particle contact because of high concentration

of particles in PBX simulant. The results of fracture surface

examination are in good agreement with the results

of in situ SEM observation, demonstrating that particle

(A) (B)

Figure 8: Typical micrograph of the sample with an aspect ratio of 1.8 in compression test with the presence of both interfacial debondingand crystal fractures

Figure 9: Typical micrograph of disc-shaped sample in Braziliantest indicating the predominant failure mode of debonding

330 � 2011 Blackwell Publishing Ltd j Strain (2012) 48, 326–332doi: 10.1111/j.1475-1305.2011.00826.x

Study on Fracture Behaviour of a PBX Simulant : Z. Zhou et al.

fracture is the dominant failure mode in compression

experiment.

ConclusionsAt the macro-scale level, the deformation and fracture

behaviour of a PBX simulant under quasi-static compres-

sion was studied using the DIC method. Based on vector

field plots of displacement, the deformation and fracture

behaviour of samples were studied, and the failure mech-

anism of samples was also analysed according to strain

distribution. The results show that the samples with dif-

ferent aspect ratios fractured in different ways. The

mechanical responses of PBX simulant were measured, and

the coefficient of cohesion was determined based on the

Mohr–Coulomb failure criteria. in situ SEM examination

was carried out to study the damage and fracture behaviour

of the sample with an aspect ratio of 1.8. The microscopic

strain fields were measured by DIC technique based on the

recorded in situ SEM images; the result indicates that the

sample with an aspect ratio of 1.8 fractured under shear

stress, showing good agreement with macroscopic fracture

observation. The method combining the DIC technique

with MTS and SEM loading system has proven to be suc-

cessful in the study of macroscopic and microscopic

deformation and failure of PBX simulant. Finally, SEM

examination showed that particle fracture was the domi-

nant failure mode in compression experiment.

ACKNOWLEDGEMENTS

This work was supported by the National Natural Science

Foundation of China (Grant No. 10832003), the NSAF

(Grant No. 11076032) and the National Basic Research Pro-

gram of China (Grant No. 613830202). The authors thank

Professor Nie Fude of the Institute of Chemical Materials of

the Chinese Physical Academy for providing the PBX simu-

lation materials.

Figure 10: SEM image of the region in the front of the pre-crackwith a typical fracture route observed

(A) (B)

Figure 11: Strain components. (A) Tensile strain (eyy) and (B) Shear strain (exy)

Figure 12: Typical fractograph of polymer-bonded explosive sim-ulant showing extensive particle fracture

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Z. Zhou et al. : Study on Fracture Behaviour of a PBX Simulant

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