Multi-scale Mechanical Characterization of PalmettoWood using Digital Image Correlation to Develop a Templatefor Biologically-Inspired Polymer Composites

S. Haldar & N. Gheewala & K.J. Grande-Allen &

M.A. Sutton & H.A. Bruck

Received: 11 June 2010 /Accepted: 10 October 2010 /Published online: 4 December 2010# Society for Experimental Mechanics 2010

Abstract Palmetto wood is garnering growing interest as atemplate for creating biologically-inspired polymer compo-sites due to its historical use as an energy absorbingmaterial in protective structures. In this study, quasi-staticthree-point bend tests have been performed to characterizethe mechanical behavior of Palmetto wood. Full-fielddeformation measurements are obtained using DigitalImage Correlation (DIC) to elucidate on the strain fieldsassociated with the mechanical response. By analyzingstrain fields at multiple length scales, it is possible to studythe more homogeneous mechanical behavior at the macro-scale associated with the global load-deformation response;while at the microscale the mechanical behavior is moreinhomogeneous due to microstructural failure mechanisms.Thus, it was possible to determine that, despite the presenceof discontinuous macro-fiber reinforcement, at the macro-scale the response is associated with classical bending andprogressive failure processes that are adequately describedby Weibull statistics proceeding from the tensile side of thespecimen. At the microscale, however, the failure mecha-nisms giving rise to the macroscopic response consist ofboth shear-dominated debonding between the fiber andmatrix, and inter-fiber matrix failure due to pore collapse.

These microscale mechanisms are present in both thecompressive and tensile regions of the specimen, mostlikely due to local macro-fiber bending, which is indepen-dent of the global bending state. The pore collapsemechanism observed during mechanical loading appears toimprove the energy absorption of the matrix material, thereby,transferring less energy and shear strain to the macro-fiber-matrix interface for initiation of debonding. However, thepore collapse mechanism can also accumulate substantialshear strain, which results in matrix shear cracking. Throughthese complex failure mechanisms, Palmetto wood exhibits ahigh resistance to catastrophic failure after damage initiation,an observation that can be used as inspiration for creating newpolymer composite materials.

Keywords Multiscale measurement . Palmetto wood .

Composite material . Digital image correlation .

Hierarchically-structured material . Multiple failuremechanism . Three-point bend experiment

Introduction

Palmetto wood is a natural heterogeneous material withhierarchical structure that has exhibited extraordinaryenergy absorbing capabilities when used as a protectivestructure during both the Revolutionary and Civil Wars.Hierarchically-structured materials like Palmetto woodhave recently drawn the attention of researchers interest-ed in understanding how their unique structure leads tooptimized properties (e.g., low density accompanied byhigh mechanical strength) that may serve as inspirationfor development of engineered materials. Efforts havealready been made to prepare biologically-inspired,synthetically-based, hierarchically-structured engineering

S. Haldar :H.A. Bruck (*, SEM member)Department of Mechanical Engineering, University of Maryland,College Park, MD, USAe-mail: bruck@eng.umd.edu

N. Gheewala :K.J. Grande-Allen (SEM member)Deparment of Bioengineering, Rice University,Houston, TX, USA

M.A. Sutton (SEM Fellow)Deparment of Mechanical Engineering,University of South Carolina,Columbia, SC, USA

Experimental Mechanics (2011) 51:575–589DOI 10.1007/s11340-010-9422-7

materials [1]. To do so, an in-depth understanding ofstructure-property relationships and failure mechanisms inthe inspirational material is necessary. For example,assessing the microscale mechanical behavior is helpfulin understanding the macro-scale fracture process in wood[2].

The unique hierarchical structure of the fibers inPalmetto wood to achieve mechanical strength and servethe biological purposes and its relationship to the mechan-ical behavior of the fibers has recently been characterized atmultiple length scales and related to the mechanicalbehavior of the fibers [3]. Through the use of opticalmicroscopy, the hierarchical structure of the Palmetto woodwas established previously, as shown in Fig. 1 over lengthscales ranging from the scale of Palmetto tree to thescale of the microfibers within the macrofibers embeddedin the porous cellulose matrix. The volume fraction ofmacrofibers of diameters of approximately 300–500 μmwas determined to be 12% and 20% in the optically darkand light regions respectively. Gas pycnometry had beenutilized to characterize the porosity in the cellulosematrix, as well as the bulk and true density of thePalmetto wood.

In this previous work, the understanding was limited tothe elastic behavior and strength of the Palmetto. However,

there is a need for a more advanced mechanical character-ization of the inelastic behavior of Palmetto wood atmultiple length scales to improve understanding of themechanisms that give rise to its extraordinary energyabsorbing capacity. Therefore, to understand the inelasticbehavior of Palmetto wood, and thereby provide thefoundation for developing heterogeneous materials withsimilar properties, appropriate mechanical characterizationtechniques are needed to elucidate on the deformationprocess at different length scales. Macro-scale measurementtechniques employing point-wise contact-based methods,such as strain gauges and extensometers, are suitable fordetermining global deformation and loading conditionsassociated with a homogenized strain response. However,micro-scale deformations are typically more inhomoge-neous and require more advanced techniques, such asphotoelasticity and interferometric techniques. These opti-cal measurement techniques have several key advantagesover point-wise contact-based techniques; most notablythey are non-contacting and allow full-field measurementsand digitization for computational analysis [4].

The most popular optical measurement techniques formeasuring inhomogeneous deformation fields at differentlength scales include interferometry-based techniques, suchas Moire, holography, and speckle, as well as non-

Fig. 1 Cross-section of hierarchical structure in Palmetto wood previously obtained using optical microscopy [3]

576 Exp Mech (2011) 51:575–589

interferometric techniques like marker techniques [4, 5] anddigital image correlation [6]. Moire interferometry [7–10],holographic interferometry [11, 12] and speckle interferom-etry [7, 8, 13–18] have been employed extensively fornanoscale and microscale deformation measurements. Amajor disadvantage of interferometric techniques is the levelof surface preparation required to ensure reflection andinterference, which can be extremely challenging formaterials like Palmetto wood [19]. Marker methods haveproven to be more useful for deformation measurements atmultiple length scales. In these approaches, a pre-marked (bygrid or dot) specimen is used for the experiments and themarks on the specimens are tracked to obtain the deformationfield [20, 21].

Digital Image Correlation (DIC) is another full-fielddeformation measurement technique that has been suc-cessfully applied at multiple length scales. The DICmethod has been widely accepted and frequently used forplanar full-field deformation measurement. Since the DICmethod employs both optical imaging and digital imageprocessing, it is oftentimes considered a hybrid techniquecoupling optical imaging with numerical computing. DICcompares the digitized images of an undeformed (refer-ence) specimen to multiple images of deforming speci-men to yield full-field displacement and strain fields [22,23]. DIC can be applied at the microscale and nanoscalewith an appropriate speckle pattern [24]. Generally, arandom speckle pattern that does not include a very highdensity of only high or low grey levels (well-spread) isconsidered appropriate for DIC. Also, DIC can be used atmultiple length scales by using cameras with sufficientlyhigh resolution.

DIC has been used for characterizing inhomogeneousdeformations at different length scales in many applica-tions. For example, it has been previously used for inter-and intra-granular deformation measurements [25]. It hasalso been found to be particularly suitable for strainmeasurement in inhomogeneous, anisotropic, non-linearmaterials [26]. For example, Gonzalez and Knauss [27]used the DIC technique to capture local strain inhomoge-neity in a particulate composite due to an applied globallyhomogeneous strain. DIC has also been used to capturenonuniform deformation fields in a variety of materialsincluding concrete [28], polymeric foam under compression[29], plastic deformation of binary aluminum alloy [30] andclosed-cell aluminum alloy foam [31], among their appli-cations. DIC has been found to be useful in strainmeasurement [2, 32] and fracture studies [33] in wood.For example, DIC has been used to measure strains arounda knot in wood during three-point bend test [2]. In thatparticular case, the natural texture of wood can serve as thespeckle pattern for DIC. Thus, DIC is a proven opticalmeasurement technique for nonuniform strain analysis in

materials such as wood, and would be highly suitable forthe mechanical characterization of Palmetto wood atmultiple length scales.

In this paper, a more detailed understanding of failuremechanisms in Palmetto wood at several length scales isinvestigated at multiple length scales using DIC. Testing isconducted using quasi-static three-point bending in order tocharacterize the microstructural failure mechanisms in amore complex stress state that can initiate multiple failuremechanisms. These measurements are then used to identifyand quantify the evolution of the failure mechanisms ofPalmetto wood at the microscale in order to relate them tothe macroscopic response. Thus, for the first time it will bepossible to understand how these failure mechanismstranslate across multiple length scales in a naturalhierarchically-structured material that may serve as atemplate for biologically-inspired polymer composites. Inprevious work, a model laminated composite structureinspired by Palmetto wood was reported and the effects ofthe bioinspired hierarchical structure on the mechanicalbehavior was characterized [3]. The bioinspired laminatedcomposite exhibited higher flexural energy density and itsWeibull failure statistics were enhanced and found to becloser to those of Palmetto wood.

Experimental Method

The motivation of choosing three-point bend test as acharacterization technique lies in the versatility of the stressstate in the specimen due to the presence of bothcompressive and tensile axial strains, as well as shearstrain, in the specimen. Three-point bend specimens withdimensions 100×9×9 mm3 were prepared from a harvestedPalmetto tree for the present study with a volume fractionof macro-fibers of 12%. Tests were performed in an Imadamodel MX 500 load frame [Fig. 2 (a)] with a Z2H-4402 kN load cell that has a load resolution of 0.1 kg. The loadon the specimen was obtained using the load cell attachedto the base of the three-point bend test fixture, whilevertical displacement of the load point was determinedusing a dial caliper attached to the load cell with adisplacement resolution of 10 microns. Supports for thethree-point bend test fixture were 62.5 mm apart, and thespecimen was loaded in two different optical configu-rations: (1) images acquired of the central region of thespecimen for macro-scale tests, and (2) images acquiredfocusing on region near the central loading point of thespecimen for microscale tests. The specimen was loadedwith the fibers oriented transverse to the loadingdirection. Quasi-static bending was performed underdisplacement control at a macro-scale flexural strain rate1.6×10−4/sec.

Exp Mech (2011) 51:575–589 577

(a)

(b)

Palmetto Wood Specimen

1 cm

(c)

1 cm

1 mm 200 μm

1 mm

F = MacrofiberM = Matrix

F

F

M

M

MF

Fig. 2 (a) Three-point bend test set up and specimen configuration used to characterize the deformation of Palmetto wood at multiple lengthscales, and (b) Images of deformed Palmetto wood in three-point bending. The natural texture of the wood was determined to be sufficient forDIC analysis (c) Fields of view at several magnifications demonstrating the multiscale deformation measurement methodology where the interfaceis denoted by a dashed line and the matrix and macrofiber by M and F, respectively. The images are of different specimens that were sequentiallytested at several magnifications

578 Exp Mech (2011) 51:575–589

The Palmetto wood surface texture was good enough fortexture image correlation at all length scales, whichobviated the need to apply an artificial speckle pattern. AFlea 2 digital camera (Point Grey Research, Richmond, BC,Canada) with 2.0 Megapixel resolution was used to capturethe images of specimen during the test with a very highsignal-to-noise ratio. The specimen surface was illuminatedby a MI-150 high intensity fiber optic illuminator fromEdmund Optics (Barrington, NJ, USA). The specimen andits failure under three-point bend test are shown in Fig. 2(b). The DIC analysis was performed using a commerciallyavailable software Vic-2D from Correlation Solutions Inc.(Columbia, SC, USA).

Tests were performed sequentially and repeatedly ondifferent samples at several magnifications in order toreliably measure deformations at multiple length scales.The fields of view at multiple length scales are depicted inFig. 2(c). The images demonstrate the multiscale measure-ment methodology. In these images, M and F indicateporous cellulose matrix and macrofiber respectively whilethe interface is denoted by a dashed line. As mentionedearlier, the tests were performed on different specimens andthe images only show the relative magnifications at whichthe deformation measurements were performed. The small-est subset size compatible with the surface texture of theimage was used for image correlation.

Experimental Results

Deformation Measurement at Macro-Scale

Representative flexural stress-strain response of thePalmetto wood specimen in three-point bending and the

fit of a Weibull distribution for the failure response of abundle of fibers are depicted in Fig. 3 [3]. As a first orderapproximation, the flexural stress, flexural strain and strainenergy for a specimen with cross-section 9.5×9.5 mm2

and support span length of 62.5 mm are calculated usingthe classical relations for homogeneous isotropic materialsgiven by:

s ¼ 3PL

2bh2; " ¼ 6dh

L2;U ¼

Z"

0

s d"0 ð1Þ

where P is the applied load, L is the support span, b isspecimen thickness, h is specimen height, and δ is thedeflection. For these specimen dimensions, the cross-sectional area is nearly 400 times the cross-sectional areaof an individual fiber in the macro-fiber bundle, so theglobal behavior should be considered macroscopic. Thebulk flexural modulus of this representative specimen wasdetermined to be approximately 500 MPa, and thespecimen failed at 4% elongation with a correspondingnominal stress of about 10 MPa. The Weibull distributionof the failure response for a bundle of fibers is given by:

s ¼ E" exp � "

"0

� �b" #

; ð2Þ

where ε0 and β are the Weibull parameters and E is elasticmodulus. The Weibull parameters are chosen as ε0=0.05,β=1.5 with elastic modulus (E) as 500 MPa [3]. The strainenergy up to the failure initiation has been determined tobe 3.0 J/cm2.

Representative displacement and strain fields obtainedusing DIC at the macro-scale can be seen in Fig. 4 beforethe onset of failure. The specimen in the image was 500pixels in height, and DIC was performed using a subset sizeof 25×25 pixel2 (0.45×0.45 mm2) for image correlation.As can be noted from Fig. 3, the specimen can bearsubstantial load after failure initiation and does not exhibitcatastrophic failure and absorbs significant amount of strainenergy during the multi-step failure response, a responsethat is preferred for engineering applications where energyabsorption is important. Indeed, it was noted in a previousstudy that fiber-bridging is the primary mechanism forPalmetto wood to carry load post-failure [3]. The displace-ment and strain fields shown in Fig. 4 correspond to point Ain the flexural stress-strain response of the specimen (Fig. 3).The macroscopic displacement field is symmetric withrespect to the loading point indicating that at the macroscopicscale, the behavior of the wood appears to be homogeneous.However, the accompanying macro-scale strain fields reveala slight asymmetry with respect to the loading point that mayarise due to inhomogeneity from the macro-fiber distributionin the wood along the specimen length.

Fig. 3 Representative quasi-static macroscopic flexural-stress straincurve for Palmetto wood with a Weibull fit indicating that the failureresponse conforms to a Weibull distribution

Exp Mech (2011) 51:575–589 579

The bending response of the specimen was evaluatedthrough the classical beam bending theory for homogeneousisotropic material. The vertical displacement along the lengthof the specimen is extracted from the DIC analysis as shownin Fig. 5. The displacement field appears to be similar to thatexpected from three-point bending of a homogeneousisotropic material. The flexural strain is calculated from thecurvature-strain relationship in the beam bending of homo-geneous isotropic material through a quadratic fit to thedisplacement. The strain is determined to be 0.007, whichmatches well with the axial strain of 0.006 directly obtainedfrom the DIC displacement field in the tensile region of thespecimen. Thus, it can be concluded at this length scale thatthe behavior of the specimen is primarily homogeneous,

although there can be some slight asymmetry in thedisplacement due to the distribution of macro-fibers.

The degraded modulus of Palmetto wood was alsodetermined by flexural unloading and reloading to evaluatethe nature of the damage evolution. The variation of thedegraded modulus normalized by initial modulus with themaximum elastic curvature of the specimen, evaluated bothfrom theoretical calculations and experimental measure-ments, is shown in Fig. 6 (a), and both the results matchwell. The damage variable (D) based on the elastic energyequivalence given by D ¼ 1� ðE=E0Þ1=2 has been deter-mined, and regression fit using the progressive damageevolution formula given by D ¼ Dlimf1� exp½�að"� "iÞ�gis shown in Fig. 6 (b) [34]. The parameters of the

(a)

(b)

4 6v (pixels)

-0.007 0.02εxy

-0.02 0.002 εyy

εxx-0.01 0.004

1 cm

x

y

Fig. 4 Macroscopic (a)displacement (pixels) and (b)strain fields in Palmetto woodobtained under three-pointbending before the onset offailure. The fields evidencemacroscopically inhomogeneousbehavior of the material. Theload level corresponds to pointA of Fig. 3

580 Exp Mech (2011) 51:575–589

progressive damage evolution are the upper bound limit formaterial damage, Dlim=0.9, threshold strain for damageinitialization εi =0.034, acceleration factor of damageevolution a=20.

Deformation Measurement at Microscale Within ElasticRegime

Since Palmetto wood is a hierarchically structured materialover several length scales, images were taken at multiplemagnifications to elucidate the roles of the porous cellulosematrix and embedded fibers in the failure process. Imageswere captured at magnifications that were 10X higher thanthe macro-scale to better quantify the mechanical behaviorof the Palmetto wood at what is considered to be theintermediate microscale.

At this magnification, the macrofibers are 70–75 pixelswide and separated by approximately 140–150 pixels at20% volume fraction, so a subset size of 50×50 pixel2

(0.11×0.11 mm2) was used for image correlation. Spatially

cyclic strain distribution along the depth (vertical direction)consistent with the fiber distribution starts to becomeevident at this magnification (Fig. 7) and high shear strainbetween fibers can be more easily discerned as shown inFig. 7 (b). The images are acquired at the compressive sideof the specimen approximately 2 mm from the centralsupport at the bottom side of the specimen. The load levelcorresponds to a flexural stress of 1.4 MPa and flexuralstrain of 0.2%, values that are well below the level requiredfor failure initiation. The strain field is consistent with ahighly inhomogeneous material response, with localizedstrain that can lead to fiber-matrix debonding or matrixfailure. It can be noted in the strain fields from highermagnification images that the material is prone to sheardebonding at the macro-fiber-matrix interface and withinthe cellulose matrix, more due to the high shear strainaccumulation than to the tensile failure of the macro-fiber.Furthermore, there is significant localization of normalstrain in between the fibers within the matrix that could

(a)

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.02 0.04 0.06 0.08Total Strain

D

ExperimentalFit

D = 0.9*{1-exp[-20*(ε-0.034)]}

(b)

Fig. 6 (a) The comparison of theoretical calculated and experimentalmeasured maximum elastic curvatures with respect to normalizeddegraded modulus and the upper bound for constant stress, and (b)evolution of the elastic energy equivalent damage, D, with total strainalong with a fit using the formula for progressive damage evolution

(a)

(b)

-10 0v (pixels)

1 cm

x

y

Fig. 5 (a) Vertical displacement field of the Palmetto wood specimenunder quasi-static three-point bend test that resembles typicaldisplacement field in three-point bending for homogeneous isotropicmaterial, (b) vertical displacement of the specimen along the line(shown in (a)) and quadratic fit used to calculate the strain from beambending theory

Exp Mech (2011) 51:575–589 581

potentially lead to pore collapse (i. e., collapse of cellularstructure) and densification of the microstructure into layers(i.e., stratification) as typically seen in ductile, porousmaterials.

Images were also captured on the tensile side (i.e., topside of the specimen) at a distance of approximately 5 mmfrom the center support to elucidate the tensile straindistribution. However, strain analysis on the tensile side

εyy εxx

εxy

-0.002 0.002

x

y

1 mm

Fig. 7 Strain contours inPalmetto wood during three-point bending obtained incompression region of specimenat intermediate microscalemagnification exhibiting moreinhomogeneous shear straindistribution consistent with theporous microstructure of thematrix, and strain distributionalong the depth (along whitedashed line). The shear strainand transverse normal strainvaries cyclically with macro-fiber (MF) and matrixdistribution

εxx

εxy

εyy

-0.01 0.02

x

y

1 mm

Fig. 8 Strain contours inPalmetto wood during three-point bending in tensile regionof the specimen at intermediatemicroscale magnification, andstrain distribution along thedepth (dashed white line) withsimilar variability due tomicrostructure as observed incompression region. Anyvariability in strain magnitudebetween compressive andtensile regions is attributed todifferences in the macro-fiberdistribution

582 Exp Mech (2011) 51:575–589

of the specimen revealed that the strain distribution at themacro-fiber-matrix interface remains the same as wasobserved on compression side at the microscale, as shownin Fig. 8. High shear strain is noted at the macro-fiber-matrix interface and the strains vary cyclically with thelocal distribution of the macro-fiber and cellulose matrix. Itis noted that there is a minor difference between the straindistributions in the tensile and compressive regions whichmight be due to variability in the macro-fiber distributionwithin the Palmetto wood. Nevertheless, the basic micro-structural response is found to be similar. Thus, the highshear strain at the macro-fiber-matrix interface and similar-ity in strain distribution is established irrespective of theglobal deformation state in either the tensile or compressiveregions of the specimen.

Microscale strain measurements shown in Fig. 9 andobtained when imaging at a higher magnification, indicatesubstantially higher strain at the matrix-macro-fiber inter-

face than within the macro-fiber. In fact, the strain in thefiber is an order of magnitude smaller due to the higherrigidity of the fiber. The strain fields are shown for aflexural stress of approximately 2.1 MPa and a globalflexural strain of 0.3% flexural strain, which is in thenominally elastic regime. The displacement field in thespecimen, the vertical displacement profile and straindistributions are shown in Fig. 9 (a) and (b). The bendingappears qualitatively similar to the classical bending of astiff fiber in a compliant matrix, however with the caveat ofasymmetry along the fiber. The asymmetry might occur dueto inhomogeneity in matrix stiffness. The curvature of themacro-fiber in local bending at the microscale is used tocalculate microscale strain level, and is consistent with theaxial strain of 0.003 measured from the microscale DICdisplacement fields. The curvature of the specimen at themacro-scale and that of the macro-fiber at the microscaleare found to be approximately similar at equivalent macro-

R2 = 0.9866

-1

-0.8

-0.6

-0.4

-0.2

0

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

x/L

V d

isp

lace

men

t (p

ixel

s)

VQuadratic fit

(a)

(b)

εxx εyy

εxy

-0.003 0.003

-1 0 v (pixels)

1 mm

x

y

Fig. 9 (a) Local bending ofmacro-fiber (dashed white lineindicates the fiber-matrixinterface) (b) Strain fields inPalmetto wood at secondintermediate microscaleobtained near fiber-matrixinterface

Exp Mech (2011) 51:575–589 583

scale flexural strain level, which is approximately0.001 mm−1. Thus, the flexural response translates fromthe macro-scale to the microscale through the mechanicalbehavior of the macro-fiber rather than through the porouscellulose matrix. However, a positive transverse strainoccurs in the fiber that might result from the debonding ofmicrofibers within the macro-fiber due to local bending ofthe macro-fiber as depicted in Fig. 9 (a).

High interfacial shear strain makes the material prone todebonding. The strain fields in the fibers were morehomogeneous and smaller in magnitude as compared tothat in the matrix. This difference is not unexpected, sincethe mechanical properties of the macro-fiber such asstiffness are greater than those of the porous cellulosematrix, and therefore the response is nearly rigid. To betterelucidate the interfacial strain distribution, images werecaptured at 20X magnification. A subset size of 35×35pixel2 (0.028×0.028 mm2) was used for image correlation.The strain fields in Fig. 10 help to understand the differencein strain level in macro-fiber and matrix. The strain fieldsindicate high shear strain at the macro-fiber-matrix interfaceand the normal strains are found to be much higher in thematrix. However, the interfacial mechanics were found to bethe same as elucidated at the lower magnification, except thehigh shear strain and compressive strain associated with pore

collapse is more clearly evident in the matrix at the interfaceusing higher magnification.

Deformation Measurement at Microscale Within FailureRegime

To understand failure initiation, the strain field wasevaluated from the images captured just after the maximumstress level had been reached (Fig. 11). The global stressstrain behavior obtained from homogeneous isotropicassumption is shown. Comparing the strain fields obtainedat the microscale with observations of failure initiation inthe images [Fig. 11 (a), (b)], it would appear that crackinitiation within the cellulose matrix is dominated by shearstrain. The strain field in the pre-failure image can be usedto predict the failure initiation. The images correspond to aglobal flexural stress of 11 MPa and flexural strain of 3%.As can be noted from the strain fields, the shear strain at thefailure initiation site is much higher (6%) than the normalstrains (1%).

The process of shear cracking in the matrix wasevaluated at the highest magnification level of 20X fromthe macro length scale. While debonding takes place in thematrix-fiber interface due to shear strain, compressivefailure at the micro-scale level is noted (Fig. 12) due to

εxx εyy

εxy

-0.006

200 μm

y

x

0.006

Fig. 10 Strains measured200 μm into matrix at micro-scale indicating concentration ofshear strains very close(~0.25df) to the fiber-matrixinterface with associated porecollapse which may allow theshear strain to build up at theinterface (dashed white line)

584 Exp Mech (2011) 51:575–589

pore collapse (i.e., crushing) of the matrix. At lower globalstrain levels, the matrix begins to undergo localizedcompressive strain and shear strain at discrete locations.However, as the global strain increases these strains beginto coalesce into a band due to pore collapse, and a shearcrack begins to form as evidenced by the high levels ofshear strain along this band. The evolution of shearcracking can be seen in Fig. 12.

Figure 12 demonstrates that compressive failure growsfaster than the tensile failure site, leading to a macro-crack.Also, it is noted that higher compressive strain isaccumulated faster than the shear strain, as indicated bythe second strain contours in Fig. 12, where compressivestrain reaches 0.09% while shear strain is approximately0.06%. The compressive strain was also evidenced to someextent in larger length scale deformation measurements asshown in Fig. 10. The collapse of the porous matrix

increases the local shear strain which generates potentialsites for the initiation of shear cracks as the global strainincreases. Hence, it is believed that the pore collapsemechanism leads to shear accumulation. Furthermore, it ismost likely the mechanism by which the flexural responsecan translate uniformly from the macro-scale to themicroscale in the macro-fiber, as was previously discussed.

To map the microscopic-to-macroscopic behavior of thePalmetto wood, the strains at each length scale werecompared. The evolution of microscale local strainsobtained by DIC from the 10X magnification imagescaptured on the tensile and compressive side of thespecimen are tracked over the quasi-static bending processwith respect to the macro-scale flexural strain. Theevolution is depicted in Fig. 13. The microscale strainsare found to increase steadily with the macro-scale flexuralstrain. The microscale transverse and shear strain increased

(a)

(b)

ΔεΔε = 0.001

εxy

εyyεxx

-0.01

High shearstrain

Failure initiation atHigh shearstrain site

x

y

1 mm

0.06

Fig. 11 (a) Strain fields in thePalmetto wood specimen underquasi-static three-point bendbefore failure initiation and (b)failure initiation by shearcracking in the cellulose matrixafter a macro-scale flexuralstrain increment, Δε, of 0.001.The failure initiationcorresponds to the high shearstrain site

Exp Mech (2011) 51:575–589 585

at rates similar to the macro-scale flexural strain afterfailure, and faster than the microscale axial strain, whichwas approximately half the rate of the macro-scale flexuralstrain. Therefore, the faster increase in transverse and shearstrains is consistent with their dominance in failureinitiation. Furthermore, the accumulation of microscaletransverse strain is nearly identical in the compressive andtensile regions. Since this strain is compressive, it isresponsible for the pore collapse mechanism and indicatesthat pore collapse is independent of the global bendingstate, most likely due to the local macro-fiber bendingpreviously characterized in Fig. 9. The evolution of themicroscale strain components at a different location on theimage is shown in Fig. 13 (e). The microscale strain isshown to increase at slightly different rate than the previous

location, with a change in sign for shear strain due toinhomogeneity of the specimen at the microscale.

The macroscopic shear strain before failure initiation hasbeen measured to be approximately 2% at the failure initiationsite (Fig. 4). However, microscale pre-failure shear strain (inpore collapse) is determined to be as high as 4.5% (Fig. 12).These shear strain magnitudes are plausible given thehierarchical and inhomogeneous structure of the material atmultiple length scales. Since a significant accumulation ofstrain at the microscale is required to initiate macroscopicfailure, the macroscopic stress is limited by the level ofmicroscale strain. Due to the compliance of the cellulosematrix, the micro-scale strain is not completely transferred tothe higher length scale. The collapse of the cellulose matrixhelps it to “absorb” strain locally and redistribute it to

εyy εxy

-0.0005

-0.0009

-0.0025

-0.0005

-0.0009

-0.025 -0.003

0

a

b

c

x

y 200 μm

0.0015 0.045

0.0006 0.0025

0.00060.0006

0.0005 0.0005

-0.0006

Fig. 12 Evolution of shearcracking in cellulose material.The pores collapse (0) andcoalesce together (a) andaccumulate shear strain (b)leading to macro crack (c). Thepore collapse mechanism helpsfor load absorption. The imagescorrespond approximately to thepoints 0, A, B, C in Fig. 13 (c)

586 Exp Mech (2011) 51:575–589

impede the initiation of macroscopic failure of the material.As discussed earlier, the porous media is weaker as opposedto the fiber material and does not transfer strain completelyto the fiber. The matrix material absorbs the strain, requiringhigher strain levels for macroscopic failure to initiate eventhough microscale failure may initiate earlier, which meansmicroscale failure is actually initiating in the elastic regime atthe macroscale.

Discussion of Results

DIC analysis has been performed at multiple length scales tounderstand the failure mechanism in Palmetto wood underthree-point bending with quasi-static load. Several possible

modes of failure are: (i) tensile failure on the tension side, (ii)buckling (wrinkling) on compression side or (iii) inter-layerdelamination due to shear. Multiple length scale deformationmeasurements are performed under quasi-static load. Twotypes of cracking are noted in the specimens, namely macro-fiber-matrix debonding and matrix shear cracking. Both typesof responses are found to be dominated by interlayer shear andtransverse compression.

At the macro-scale, specimens prepared from thePalmetto wood exhibit more homogeneous materialbehavior as evidenced by homogeneous strain fields.The macro-scale bending can be mapped to that of ahomogeneous isotropic material. However, highly inhomo-geneous deformations due to the fiber reinforcement andmatrix response can be distinguished at the microscale. The

(a) (b)

(c) (d)

(e)

x

y

1 mmA1

A2 B1 B2

Fig. 13 Intermediate microscaleshear strain field of interfibermatrix in (a) tensile and (b)compressive regions of thespecimen, (c) macroscopicstress-strain response, and (d)the evolution of the microscalestrains with macro-scale flexuralstrain (right side) in the tensile(solid line) and compressive(dashed line) regions. Thestrains were extracted at theencircled points A1, B1 in (a)and (b). The state of deforma-tion corresponding to the pointsA, B, C and D are shown in thestress-strain response 1:1correspondence between themagnitudes of the microscalestrains and macro-scale flexuralstrain is denoted by the dashedyellow lines, (e) slightlydifferent evolution of the straincomponents at differentlocations (A2, B2 in (a) and (b))in the same image due toinhomogeneity

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periodicity of fiber and matrix is evident from the periodicnature of the shear strain distribution along the depth inspecimen. High shear strain is found at the macro-fiber-matrixinterfaces on both the globally tensile and globally compres-sive sides of the specimen. The fiber, being mechanicallysuperior, does not deform as a porous matrix material (asexpected), giving rise to shear strain concentrations at thefiber-matrix interface.

When obtaining microscale deformation measurement,the macro-fiber level has been noted to deform like a beamembedded in a compliant matrix giving rise to a classicalbending profile. The compressive load is not transferred tothe fiber since the inter-fiber matrix absorbs the loadthrough a collapse mechanism. For this reason, crushingof the material at the loading point does not affect the far-field behavior of the specimen, and also enables thematerial to sustain higher normal load in the directionperpendicular to fiber alignment.

The tensile load is primarily carried by the fibers. Sincethe fibers are both stronger and more rigid than thesurrounding matrix, the tensile region deforms less thanthe compressive zone. Failure at both the macro-fiber-matrix interface and cellulose matrix is seen to bedominated by interlayer debonding due to shear strain.The wavy nature of shear strain across the width of thespecimen indicates high shear in the macro-fiber-matrixinterface. The shear strain at potential failure sites appearsto increase steadily until failure. Strain at the microscale isseen to be higher than measured at the macro-scale. Thisdifference is acceptable at the microscale since local failureinitiation does not immediately lead to macroscopic failureof the specimen because of local redistribution of the loadwithin the multiple-laminate nature of wood.

Damage in the Palmetto wood material occurs via amulti-step failure process. The difference in mechanicalproperties between the compliant matrix and comparativelyrigid macro-fibers results in high shear strain concentrationat the interface. At the highest magnification scale, the porecollapse mechanism and accumulation of strain by porecollapse is observed. The shear cracking is noted to beinitiated by the pore collapse at sites undergoing high shearstrain and compressive strain. From the analysis of damageevolution for this material, the experimental measurementof the degraded modulus with elastic curvature shows asubstantial initial drop. After the initial drop, the responsedoes follow the upper bound for constant stress, indicatinglarge initial load shedding consistent with macroscalefailure followed by a more gradual evolution in microscaledamage. From the damage evolution based on the hypoth-esis of elastic energy equivalence, it appears that theacceleration factor is quite high, indicating a rapidaccumulation of microscale damage with strain throughoutthe Palmetto wood.

Conclusions

Mechanical characterization of Palmetto wood, a hierarchi-cally structured natural material that can serve as a templatefor biologically-inspired polymer composites, has beeninvestigated at multiple length scales using quasi-staticthree-point bend testing with the neutral axis of thespecimen along the fiber orientation. Strain fields weredetermined at the various length scales using DIC across arange of optical magnifications in order to elucidate on thedistinct roles of the porous cellulose matrix and embeddedfibers in the failure process. The natural texture of thespecimens was found to be adequate for image correlationacross the length scales of interest.

It was determined from the quasi-static DIC results atthe macro-scale that the material behaves fairly homoge-neously with a slight asymmetry due to the presence offibers. The macro-scale bending behavior complies wellwith the classical beam bending theory. However,microscale measurements at a magnification differenceof 10X-20X relative to the macro-scale revealed inhomoge-neous deformations due to differences in the properties of themacro-fibers and porous cellulose matrix. The shear andtransverse strains exhibited significantly greater variabilitythan the axial strain. The variability in shear strain coincidedwith debonding at the fiber-matrix interface or crackingwithin the matrix due to shear strain. The variability intransverse strain was primarily within the matrix andcoincided with pore collapse.

It is postulated that the pore collapse mechanism acts as aload absorber that significantly reduces the energy availablefor fiber-matrix debonding, and enables the flexural responseto translate from the macro-scale to the microscale in themacro-fiber. DIC measurements obtained at the highestmagnification revealed that there was no further elucidationthat could be obtained for the load transfer mechanism.However, the pore collapse mechanism and shear strainaccumulation is elucidated. The microscale transversenormal strain and shear strains monotonically increase alongwith the macro-scale flexural strain at a faster rate than thelongitudinal strain, indicating their dominance in the failureprocess. The microscale mechanical behavior was consistentin both the compression and tension regions of the three-point bend specimen, indicating that the failure process wasnot sensitive to the sign of the stress state.

Acknowledgements The financial support of Sandia NationalLaboratory through Sandia Contract PO#551836 and the support ofDr. Bruce LaMattina through ARO# W911NF-06-1-0216 and Dr.Yapa Rajapakse through ONR# N000140910640 are gratefullyacknowledged. In addition, the research support provided by theDepartment of Mechanical Engineering at the University of SouthCarolina is also gratefully acknowledged.

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