User login


You are here

Journal Club Theme of February 2016: Deformation Mechanics of Granular Materials: Local Deformation of Polymer-bonded Sugar at High Strain Rate Loading

addis's picture

Deformation Mechanics of Granular Materials:

Local deformation of Polymer-bonded sugar at high strain rate loading

 Addis Kidane, Suraj Ravindran

Department of Mechanical Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208



Understanding the damage mechanisms in granular materials, such as concrete, polymer bonded explosive (PBX), sands, armor protection materials, etc., under dynamic loading has been a great interest for a long time. The mechanics of granular materials, in general, have been studied in the last four decades for example, [1-9] and many models are proposed.  In the case of soft polymer bonded hard materials such as PBX, due to significant properties mismatch and presence of voids and cracks, the failure mechanism is complex. The computational models are developed over the years to predict the deformation behavior of these materials.

On the other hand, a lack of high temporal and high spatial resolution methods hinder experimental community in understanding the local deformation mechanism of heterogeneous materials at high rate loading. Recently, using X-ray DIC system, Lu et al [10] measured the in-plane deformation of borosilicate glass beads (granular material) subjected to impact loading. Though the  method, is a bit complex, potentially play a great role in understanding the damage mechanisms in heterogeneous materials.  An alternative and a complementary method, an optical based high-speed digital image correlation, has been recently used to measure the local deformation of a copper  at subgrain scale [11]. Recently using high-speed camera along with high-magnification optical system, we are able to measure the local deformation in PBS at a framing rate of up to 1 million/ sec and a spatial resolution of 10 µm/pixel [12].

The question we would like to ask is

What are the major local deformation mechanisms?

In this month’s iMechanica Journal Club, we would like to highlight recent efforts to quantify the local damage mechanisms in PBS. This brief overview, focus only on results from DIC based surface measurement at meso-scale, but we hope it will initiate further discussions in the field including from different approaches and simulations.

PBS is a polymer bonded sugar, a known simulant of PBX. It is made of relatively hard sugar crystal bonded by the soft binder. The grain size of the sugar varies from 300- 500 µm. The specimen preparation and detailed experimental procedure can be obtained elsewhere [12]. The specimens are loaded in Split Hopkinson pressure bar under compression and images are processed using Vic 2D digital image correlation software.

 The experimental result shows that the deformation is highly localized as shown in Fig 1.   Most of the deformation are confined to the polymer binder rich area and where crystals are far apart. More importantly, the deformation formed a clear local band like structure, at a very small axial strain. The observed local damage initiation mechanisms are;

  Fig 1

Crystal Rotation

Crystal rotation and sliding have been observed in granular materials under quasi-static and dynamic loading conditions [13, 14]. Figure 2 shows the rotation of each crystal as a function of applied global strain. The magnitude and direction of rotation vary from grain to grain. It is also observed that, in some cases, two or more grains form a group and rotate together up to a certain loading time. For example C2, C4 and C5 form a pair and rotate together up to a strain of 0.8% in an anticlockwise direction. There is no relative rotation between C2, C4 and C5 until this time. On the other hand, some crystals in contact with another rotating crystal are shown to be stationary or rotates in a different direction, which could create sliding and friction between the adjacent crystals. For example C1, which is in contact with C2, rotates in opposite direction but not significantly, which could cause potential sliding friction with C2. In addition, relative rotation between the adjacent crystals can cause delamination at the interface and could be a potential failure mode in PBX.


Shear band formation

 Shear bands formed in this material have been captured as shown in Fig 3. In PBX, at intermediate strain rate, the shear bands can be formed due to two main mechanisms 1) softening due to damage accumulation (micro-cracking), and 2) thermal softening due plastic strain dissipation as heat.  In metals, shear band formation due to thermal softening requires global strain between 10-50%. But in PBX the strain required to form shear-band is one order less than the strain required due to thermal softening. It is clearly observed even at small global strain the localized strain is one order higher, which could cause thermal softening, and the micro cracks could cause the mechanical softening. Therefore, shear band formation can be due to the combined effect; thermal softening due to high strains formed locally in the polymer binder and softening due to damage accumulation in the material. 


Crystal Fracture

Along large interface deformation, crystal fracture is captured in this work. Surprisingly, only a few crystals are fractured, and their location seems arbitrary.  It is difficult to know what makes some crystal fail but others don’t, but a close looking  in the crystals and their neighbor could give insights. For example, a large crystal if it surrounded by another large crystal, is a favorable condition for crystal fracture. In such cases, the number of crystal to crystal contact points will be less and increases the probability of stress concentration. It is distinctly visible from the Fig. 4a that C14 and C13 are crystals have a single point contact, where a sharp corner of C14 hitting C13. Consequently, these conditions cause stress concentration and finally fracturing of C13. An initial crack formed from during materials preparation is also a favorable condition for crystal fracture. Initial crack is apparent in crystals, C4, C6 and C19. From the deformation image, it is clear that the initial crack starts to grow as loading progress and leads to fracture C6 and C19 but not C4.  The large polymer-rich region ahead of crystal C4, might cause a possible force chain mechanism or rigid body rotation. In any way, having a think region of polymer binder between adjacent crystals  will effectively reduce the probability of crystal fracture.


Challenges and opportunities.

·         Capturing hot spot formation in PBX under dynamic loading is  still a great challenge

·         Measuring temperature at high temporal and high spatial resolution could help to confirm what mechanism leads to hot spot formation.

·         With the current method, 10 µm/pixel was achieved and this length scale is great for crystals with the order of 100 µm. To study materials with fine grains, a higher magnification system is required. Due to its low depth of field at high magnification, an optical system may not be adequate to capture nanoscale length deformation at high strain rate loading… any alternative method, or solution could help the society…

Note: additional related studies in the field can be obtained from 19-34. 


1.    Baer, M. R., and J. W. Nunziato. "A two-phase mixture theory for the deflagration-to-detonation transition (DDT) in reactive granular materials." International journal of multiphase flow 12.6 (1986): 861-889.

2.    Jaeger, Heinrich M., Sidney R. Nagel, and Robert P. Behringer. "The physics of granular materials." Physics Today 49.4 (2008): 32-38.

3.    Mühlhaus, H. B., and I. Vardoulakis. "The thickness of shear bands in granular materials." Geotechnique 37.3 (1987): 271-283.

4.    Johnson, Paul C., and Roy Jackson. "Frictional–collisional constitutive relations for granular materials, with application to plane shearing." Journal of Fluid Mechanics 176 (1987): 67-93.

5.    Goodman, M. A., and S. C. Cowin. "A continuum theory for granular materials." Archive for Rational Mechanics and Analysis 44.4 (1972): 249-266.

6.    Nedderman, Ronald Midgley. Statics and kinematics of granular materials. Cambridge University Press, 2005.

7.    Oda, Masanobu, Junichi Konishi, and Siavouche Nemat-Nasser. "Experimental micromechanical evaluation of the strength of granular materials: effects of particle rolling." Mechanics of materials 1.4 (1982): 269-283.

8.    Sadd, Martin H., QiMing Tai, and Arun Shukla. "Contact law effects on wave propagation in particulate materials using distinct element modeling." International Journal of Non-Linear Mechanics 28.2 (1993): 251-265.

9.    Daraio, Chiara, et al. "Energy trapping and shock disintegration in a composite granular medium." Physical Review Letters 96.5 (2006): 058002

10. Zhu, and S.N. Luo, Phys. Rev. B 92, 144101 (2015).

11.  L. Bodelot, J. P. Escobedo-Diaz, C.P. Trujillo, D.T. Martinez, E.K. Cerreta, G.T. Gray, G. Ravichandran,  Int. J. Plas. , 74, 58 (2015)

12.  S. Ravindran, A. Tessema, A. Kidane, Local deformation and failure mechanisms of polymer bonded energetic materials subjected to high strain rate loading" Journal Dynamic Behavior of Materials.

13.  Tordesillas A, Muthuswamy M, Walsh SD (2008) Mesoscale measures of nonaffine deformation in dense granular assemblies. J Eng Mech 134:1095–1113.

14.  Kuhn MR, Bagi K (2004) Contact rolling and deformation in granular media. Int J Solids Struct 41:5793–5820.

15.  D. a. LaBarbera and M. a. Zikry, Int. J. Solids Struct. 62, 91 (2015).

16.  A. Barua, S. Kim, Y. Horie, and M. Zhou, J. Appl. Phys. 113, (2013).

17.  A. Barua, Y. Horie, and M. Zhou, J. Appl. Phys. 111, (2012).

18.  Barua A, Horie Y, Zhou M (2012) Microstructural level response of HMX–Estane polymer-bonded explosive under effects of transient stress waves. In: Proc. R. Soc. London A Math. Phys. Eng. Sci. The Royal Society, pp 3725–3744

19.  Roessig KM (2002) Mesoscale mechanics of plastic bonded explosives. In: AIP Conf. Proc. IOP INSTITUTE OF PHYSICS PUBLISHING LTD, pp 973–978

20.  Peterson PD, Mortensen KS, Idar DJ, et al. (2001) Strain field formation in plastic bonded explosives under compressional punch loading. J Mater Sci 36:1395–1400.

21.  Zhou Z, Chen P, Duan Z, Huang F (2012) Study on Fracture Behaviour of a Polymer‐Bonded Explosive Simulant Subjected to Uniaxial Compression Using Digital Image Correlation Method. Strain 48:326–332.

22.  Prentice HJ, Proud WG, Walley SM, Field JE (2010) The use of digital speckle radiography to study the ballistic deformation of a polymer bonded sugar (an explosive simulant). Int J Impact Eng 37:1113–1120.

23.  Siviour CR, Grantham SG, Williamson DM, et al. (2009) Novel measurements of material properties at high rates of strain using speckle metrology. Imaging Sci J 57:326–332.

24.  Siviour CR, Grantham SG (2009) High resolution optical measurements of specimen deformation in the split Hopkinson pressure bar. Imaging Sci J 57:333–343.

25.  Field SGG and CRS and WGP and JE (2004) High-strain rate Brazilian testing of an explosive simulant using speckle metrology. Meas Sci Technol 15:1867.

26.  Siviour C., Laity P., Proud W., et al. (2008) High strain rate properties of a polymer-bonded sugar: their dependence on applied and internal constraints. Proc R Soc A Math Phys Eng Sci 464:1229–1255. doi: 10.1098/rspa.2007.0214

27.  Balzer JE, Siviour CR, Walley SM, et al. (2004) Behaviour of ammonium perchlorate-based propellants and a polymer-bonded explosive under impact loading. Proc R Soc A Math Phys Eng Sci 460:781–806. doi: 10.1098/rspa.2003.1188

28.  Drodge DR, Williamson DM (2016) Understanding damage in polymer-bonded explosive composites. J Mater Sci 51:668–679.

29.  Rae PJ, Palmer SJP, Goldrein HT, et al. (2002) Quasi-static studies of the deformation and failure of PBX 9501. Proc R Soc A Math Phys Eng Sci 458:2227–2242. doi: 10.1098/rspa.2002.0967

30.  Zhou Z, Chen P, Huang F, Liu S (2011) Experimental study on the micromechanical behavior of a PBX simulant using SEM and digital image correlation method. Opt Lasers Eng 49:366–370.

31.  Gray III GT, Blumenthal WR, Idar DJ, Cady CM (1998) Influence of temperature on the high-strain-rate mechanical behavior of PBX 9501. In: tenth Am. Phys. Soc. Top. Conf. Shock compression Condens. matter. AIP Publishing, pp 583–586

32.  Zhao H, Gary G, Klepaczko JR (1997) On the use of a viscoelastic split hopkinson pressure bar. Int J Impact Eng 19:319–330. doi: 10.1016/S0734-743X(96)00038-3

33.  Herbold EB, Nesterenko VF, Benson DJ, et al. (2008) Particle size effect on strength, failure, and shock behavior in polytetrafluoroethylene-Al-W granular composite materials. J Appl Phys 104:103903.

34.  Hu Z, Luo H, Bardenhagen S, et al. (2015) Internal Deformation Measurement of Polymer Bonded Sugar in Compression by Digital Volume Correlation of-Tomography. Exp Mech 1:289–300.

Image icon Fig1187.04 KB
Image icon Fig289.23 KB
Image icon Fig352.45 KB
Image icon Fig495.81 KB


en_brown's picture

More on this work is available free in the Journal of Dynamic Behavior of Materials upcoming Special Issue  JDBM is now accepting papers for consideration for the second issue of 2016.

Yong Zhu's picture

Hi Addis,

Thanks for leading the discussion on this interesting topic in experimental mechanics. As we know, digitial image correlation (DIC) has been widely used now in measuring full-field deformation and strain from 2D to 3D. Recently I have seen that DIC is receiving increasing interest for dynamic measurements. Could you give us an update on the recent advances in high-speed DIC such as capabilities (e.g., tempo/spatial resolutions), challenges and representative applications? Thanks.


addis's picture


You are right recently DIC is receiving high interest for dynamic deformations measurement, and in my opinion, there are two driving factors.

1)      The current improvement and capability of high speed imaging. Currently, there are cameras that can take images at a framing rate above 1 million per second and at a spatial resolution of 400×250 pixel2. . At this speed, a high-quality deformation can be measured. For example, in Hopkinson bar experiment, where the loading duration is in the order of 100 µs, we can get above 100 high-quality images for DIC analysis.

The main challenge as far as DIC as high rate loading is, measuring small deformation/strain. Small deformation is still challenging at quasi-static loading conditions, but by image averaging the data/noise ratio can be improved. Since there will be no time to take multiple images at the same loading, during high strain rate loading, noise reduction by averaging is difficult  and accurate deformation/strain measurement using DIC is challenging. In the case of large deformation, the limit was the imaging system but it is improving year by year.

A detail information regarding high-speed DIC can be obtained in the paper by F. Pierron · M.A. Sutton · V. Tiwari, Experimental Mechanics (2011) 51:537–563  

2)      Another reason for recent increase interest in high-speed DIC is the need for understanding failure mechanisms in materials at meso-scale (between Nano and macro) including at high strain rate condition. Heterogeneous materials, like granular materials, even polycrystalline metal at mesoscale, required a full field method to capture the local deformation.

As far as I know, the first high-speed DIC based on ultrafast/high-speed X-ray is by Lu, et al ( Using PCI/radiograph x-ray and DIC they quantitatively the 3D strain fields in materials with strain noise error in the order of 10-3. Based on an optical system, I think the first high magnification DIC work is by Bodelot et al ( Using a high-speed camera, HPV-2, and Infinity K2 long-distance microscope they could map the deformation field in a copper. They achieved a spatial resolution of 15.2 μm/pixel at 500, 000 frames/sec. Recently we used HPVX-2 with Navitar lens and achieved a spatial resolution of 10.2 μm/pixel at 1 million frames/sec (

 There are some challenges such as, getting the right speckle size, lighting issue and depth of field of the cameras as you go higher magnification, otherwise full field local deformation can be measured even at higher resolution. 

 I would like to hear from others working in the field. 

Subscribe to Comments for "Journal Club Theme of February 2016: Deformation Mechanics of Granular Materials:  Local Deformation of Polymer-bonded Sugar at High Strain Rate Loading "

Recent comments

More comments


Subscribe to Syndicate