Note: Dynamic meso-scale full field surface deformation measurement ofheterogeneous materialsS. Ravindran, A. Tessema, and A. Kidane Citation: Review of Scientific Instruments 87, 036108 (2016); doi: 10.1063/1.4944488 View online: http://dx.doi.org/10.1063/1.4944488 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/87/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Note: Dynamic strain field mapping with synchrotron X-ray digital image correlation Rev. Sci. Instrum. 85, 076101 (2014); 10.1063/1.4887343 Experimental studies of precursors to failure in granular material AIP Conf. Proc. 1542, 475 (2013); 10.1063/1.4811971 Strain‐Structure Relationship at Meso‐scale for 2D Granular Materials AIP Conf. Proc. 1145, 377 (2009); 10.1063/1.3179938 Deformation Field in Indentation of Granular Materials AIP Conf. Proc. 1145, 263 (2009); 10.1063/1.3179909 The Study of Internal Deformation Fields in Granular Materials Using 3D Digital Speckle X‐Ray FlashPhotography AIP Conf. Proc. 620, 1105 (2002); 10.1063/1.1483731

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REVIEW OF SCIENTIFIC INSTRUMENTS 87, 036108 (2016)

Note: Dynamic meso-scale full field surface deformation measurementof heterogeneous materials

S. Ravindran, A. Tessema, and A. Kidanea)

Department of Mechanical Engineering, the University of South Carolina, Columbia,South Carolina 28209, USA

(Received 29 October 2015; accepted 6 March 2016; published online 18 March 2016)

A dynamic experiment at mesoscale is developed to measure local deformation and strain in gran-ular materials at high temporal and spatial resolutions. The experimental setup is comprised of ahigh-speed camera along with a high magnification extension tube. The method is demonstrated bymeasuring the full field strain across and in the boundary of the crystals at a high temporal resolutionin polymer bonded sugar crystals and glass beads filled epoxy particulate composite specimens underdynamic loading. In both cases, the local strain heterogeneity is captured successfully. The measuredstrain and deformation field can be further used to obtain the relative motion of each crystal, crystalrotation, and the relative displacement between the polymer interface and the crystal, which arevery critical to understand the local failure mechanisms in heterogeneous materials. C 2016 AIPPublishing LLC. [http://dx.doi.org/10.1063/1.4944488]

Since it was proposed in 1949 by Kolsky, the Kolsky barhas been widely used to characterize materials under dynamicloading conditions.1 The recent development of optical sys-tems and digital based experiments extended the techniqueto accommodate non-homogeneous and anisotropic materials.Dynamic properties of heterogeneous materials have beeninvestigated in Kolsky bars along with photoelasticity anddigital image correlation (DIC).2–5 Though these opticallybased measurements with a high temporal resolution at macroscale have been valuable techniques to understand the failuremechanism at continuum scale, they could not provide insightsinto the local deformation mechanisms.6–10 Due to the materialinherent heterogeneity, measuring deformation at sub-grainscale level is paramount to fully understand the fundamentalfailure mechanisms of granular materials.

DIC has been effectively implemented to measure defor-mations at submicron scale under quasi-static loading.11,12

However, high temporal digital image based measurementsat a high spatial resolution are still not well established.Recently, high speed X-ray has been used for full field strainmeasurement and damage assessment at high temporal andspatial resolutions.13,14 For strain measurement, ultrafastX-rays and X-ray speckles (inherent features) are used toobtain the images before and after deformation.14 The appli-cation of X-ray DIC has been demonstrated successfully.14

However, due to its complex experimental setup, difficulty inobtaining appropriate X-ray speckles and high cost associatedwith commissioning and running the setup, the X-ray DIC islimited to few users.

The demand for understanding the dynamic local defor-mation and failure mechanisms of heterogeneous materialsnecessitates alternative and relatively simple optical full-fielddeformation measurements at sub-grain scale. Bodelot et al.,15

a)Author to whom correspondence should be addressed. Electronic mail:kidanea@cec.sc.edu.

recently using a high speed camera, HPV-2, equipped withan Infinity K2 long-distance microscope, measured the defor-mation of copper at a framing rate of 500 000 frames/secand achieved a spatial resolution of 15.2 µm/pixel. In thisnote, an optical based experimental setup that can be used toobtain surface strain fields and deformation in heterogeneousmaterials at a speed up to one million frames per second andspatial resolution of 10 µm/pixel is presented. To demon-strate the technique, two material systems: (1) polymer bondedsugar crystals, 85% sugar crystals of size varying 200-800 µmwith 15% of plasticized hydroxyl terminated polybutadiene(HTPB) and (2) glass filled epoxy particulate composite, 80%spherical glass beads of diameter between 200 and 400 µmwith 20% epoxy are used and their local deformation underdynamic loading is measured.

A conventional specimen size, dimensions 18 × 12× 12 mm, is used to make sure that the representative volumeelement is enough to give the continuum scale response ofthe material when loaded with Kolsky bar. For the DIC,a high contrast, random, and isotopic pattern is needed. Itis important to choose the right size speckles according tothe image resolution of the optical system and experimentalsetup. As a “thumb of rule” for good displacement resolutionand accuracy, every speckle has to be sampled by at least3-5 pixels.16,17 To generate the needed speckles on the spec-imen surface, the specimen is grounded and dry polished withsilicon carbide paper of grit size varying from 240 to 1200 andthen fine polished with diamond particles of 3 µm.

The area of interest (AOI) is marked and the microstruc-tural image of the AOI is taken before loading using an opticalmicroscope. During speckling, a thin layer of white paint wasapplied, using an airbrush, on the specimen surface coveringthe AOI and left to dry partially. A black toner powder sizevary from 12 to 20 µm is deposited on top of the partially driedwhite paint by blowing the powder onto the surface using an airgun and was kept to dry completely. With this process, randomhigh contrast and isotropic speckle patterns are obtained.

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036108-2 Ravindran, Tessema, and Kidane Rev. Sci. Instrum. 87, 036108 (2016)

FIG. 1. Schematic representation of the dynamic meso-scale deformationmeasurement experimental setup.

Schematic representation of the proposed experimentalsetup is shown in Fig. 1. The setup comprises of a Kolsky barwith input and output bars made of polycarbonate, data acqui-sition, oscilloscope, strain gages, amplifier, and high magni-fication optical system. The high magnification optical sys-tem incorporates a high speed camera and high magnificationextension tube focused at the AOI of the specimen. The high-speed cameras used in this experiment are SA-X2 by Photronat 100 000 frames/s and HPVX-2 by Highland Imaging at1 000 000 frames/s and the high magnification extension tubeis from Navitar. Lighting is provided using two cold lightlight-emitting diode (LED) lamps and one single point halogenflexible light pipe (not shown in schematic) that is kept as closeas possible to the specimen without obstructing the cameraview. Post processing is done with the help of commerciallyavailable software Vic2D, by Correlated Solution, Inc., anddetails of the correlation parameters used in our study are givenin Table I. The theory and further description of DIC techniquecan be found elsewhere.16–18

The measurement noise level was estimated by correlating15 still images taken just before the start of the dynamic test.The strain was computed using the parameters given in Table I.The noise level in strain was in the order of 1000 micro-strainfor both cameras, with an uncertainty of 0.2% for SA-X2 and0.33% for HPVX-2, which is accurate enough to capture thelarge local deformation expected in heterogeneous materials.

Fig. 2 shows the local strain field with the correspondingmicrostructure of a polymer bonded sugar (PBS) subjected

TABLE I. Experimental post-processing parameters.

Camera/parameters Photron HPVX-2

Field of view 3840 × 2640 µm2 4200 × 2600 µm2

Framing rate 1 × 105 frames/s 1 × 106 frames/sSubset size 11 × 11 pixel2 9 × 9 pixel2

110 × 110 µm2 96 × 96 µm2

Step size 1 pixel/10 µm 1 pixel/10.66 µmFilter size 9 pixel/90 µm 9 pixel/96 µmResolution 10 µm/pixel 10.66 µm/pixelInterpolation type Optimized 8-tapMatching criterion Zero-normalized squared differencesStrain tensor type Lagrangian

FIG. 2. (a) Microstructure of PBS specimen with crystals numbered and thecorresponding (b) axial, (c) transverse, and (d) shear strain fields, at 160 µs.

to dynamic loading at instant 160 from the time the loadingstarts. As shown in the figure, highly heterogeneous strainlocalization is captured using the proposed experimental setup.It is important to note that the local axial strain is as highas 8% for only 3.5% of global axial strain. In addition, thelateral strain is localized predominantly at 45◦ from the load-ing axis indicating a local shear band formation. The shearformation observation is also supported by the local shearstrain field shown in Fig. 2(c). The local tensile transversestrain (Fig. 2(b)) is as high as 8%, indicating the possibilityof interface failure and delamination of crystals.

It can be seen that the strain localization is confined atthe polymer rich interfaces between particles while most ofthe particle stays within the elastic range. It is also noticedthat the high strain localization occurred in the region wheresmall crushed crystal powders are bonded together with thebinder and surrounded by large crystals. For example, the areasurrounded by the crystals 10, 15, and 19 is rich in polymerand shows high strain localization indicating a hot spot area inthe material for failure initiation. On the other hand, there aresome cases where the lateral strain in the crystals is higher thanthe failure strain of the sugar crystal, for example, crystals 13,6, and 20. This indicates that there are locations where crystalsfracture. Though it is hard to identify the reason for the largestrain observed in some crystals, the existence of initial flawwas the cause at least for crystal 6. The initial crack on crystal6 seen in Fig. 3(a) expands and opens up as loading progressand causes high strain localization as shown in the local lateralstrain plot in Fig. 3(c).The sharp point contact between crystals13 and 14 could form stress concentration on crystal 13 and ledto crystal 13 to fracture and could be the reason for the largestrain observed in that region.

Similarly, the local strain distribution is captured at ahigher rate for the glass-epoxy particulate composite spec-imen. Though the strain heterogeneity looks similar to the oneshown in PBS, in the case of glass-epoxy composites, the strainlocalization initiated and reached the local failure strain early.Since the epoxy is way harder than the HTPB binder, thisis expected. At 0.43% global strain, the axial strain reachesas high as 3% and the local transverse strain reaches as high

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036108-3 Ravindran, Tessema, and Kidane Rev. Sci. Instrum. 87, 036108 (2016)

FIG. 3. (a) Microstructure of glass beads-epoxy specimen with crystalsnumbered and the corresponding (b) axial, (c) transverse, and (d) shear strainfields, at 14 µs (0.42% global axial strain).

as 8%. The high local transverse strain shown in Fig. 3(c)indicates that a fracture might have already initiated at thislocation. It is also interesting to note that the crack seemsto initiate as the epoxy binder and the fracture path deviateas it approaches the glass boundary. More importantly, thelocal transverse strain trend indicates that there might be aforce chain mechanism with a favorable path for the force asobserved in granular materials at macro-scale.19,20

In summary, an optical based experimental setup is devel-oped and the deformation of the dynamically loaded granularsamples is measured at sub-grain-scale and up to a framing rateof 1 × 106/s. It is demonstrated that the existing optical systemcan be used for the mesoscale dynamic experiment to measurelocal strain in granular materials at high temporal and spatialresolutions. The experimental system provided quantitativedata on local strain information in heterogeneous materials.In general, it is observed that the local strain field is highlyheterogeneous, mostly confined in the polymer-rich region,and propagates as load progress and leads to shear bandingin the material. The obtained full field local information canbe further used to measure the relative motion of each crystal,

crystal rotation, and the relative displacement between theinterface and the crystals, which are very critical to understandthe local failure mechanisms in heterogeneous materials. Theexperimental method can be extended and used to obtain strainfield in other granular materials of even a smaller crystal sizeby using higher magnification lenses.

The financial support of the Air Force Office of ScientificResearch (AFOSR) under Grant No. FA9550-14-1-0209 isgratefully acknowledged.

1H. Kolsky, Proc. Phys. Soc. Sect. B 62, 676 (1949).2A. Shukla, C. Y. Zhu, and Y. Xu, J. Eng. Mech. 118, 190 (1992).3R. Hurley, E. Marteau, G. Ravichandran, and J. E. Andrad, J. Mech. Phy.Sol. 63, 154 (2014).

4L. Roy Xu and A. J. Rosakis, Int. J. Dam Mech. 14.3, 215 (2005).5A. Kidane, ISRN Mater. Sci. 2013, 1.6J. E. Balzer, C. R. Siviour, S. M. Walley, W. G. Proud, and J. E. Field, Proc.R. Soc. A 460, 781 (2004).

7D. L. Grote, S. W. Park, and M. Zhou, Int. J. Impact Eng. 25, 869 (2001).8D. M. Williamson, C. R. Siviour, W. G. Proud, S. J. P. Palmer, R. Govier,K. Ellis, P. Blackwell, and C. Leppard, J. Phys. D: Appl. Phys. 41, 085404(2008).

9Q. B. Zhang and J. Zhao, Eng. Fract. Mech. 102, 288 (2013).10Z. Zhou, P. Chen, Z. Duan, and F. Huang, Strain 48, 326 (2012).11M. A. Sutton, N. Li, D. C. Joy, A. P. Reynolds, and X. Li, Exp. Mech. 47,

775 (2007).12A. D. Kammers and S. Daly, Exp. Mech. 53, 1743 (2013).13L. Lu, D. Fan, B. X. Bie, X. X. Ran, M. L. Qi, N. Parab, J. Z. Sun, H. J. Liao,

M. C. Hudspeth, B. Claus, K. Fezzaa, T. Sun, W. Chen, X. L. Gong, and S.N. Luo, Rev. Sci. Instrum. 85, 076101 (2014).

14J. Y. Huang, Y. Li, Q. C. Liu, X. M. Zhou, L. W. Liu, C. L. Liu, M. H. Zhu,and S. N. Luo, Phys. Rev. B 92, 144101 (2015).

15L. Bodelot, J. P. Escobedo-Diaz, C. P. Trujillo, D. T. Martinez, E. K. Cerreta,G. T. Gray, and G. Ravichandran, Int. J. Plas. 74, 58 (2015).

16T. C. Chu, W. F. Ranson, and M. A. Sutton, Exp. Mech. 25, 232 (1985).17M. A. Sutton, J. J. Orteu, and H. Schreier, Image Correlation for Shape,

Motion and Deformation Measurements: Basic Concepts, Theory and Ap-plications (Springer Science and Business Media, 2009).

18M. Bornert, F. Brémand, P. Doumalin, J. C. Dupré, M. Fazzini, M. Grédiac,F. Hild, S. Mistou, J. Molimard, J. J. Orteu, L. Robert, Y. Surrel, P. Vacher,and B. Wattrisse, Exp. Mech. 49, 353 (2009).

19R. C. Hurley, K. W. Lim, G. Ravichandran, and J. E. Andrade, Exp. Mech.56, 217 (2015).

20M. H. Sadd, Q. Tai, and A. Shukla, Int. J. Non-Linear Mech. 28(2), 251(1993).

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