journal of reinforced plastics meso-scale study of non-linear tensile · 2016. 3. 2. · meso-scale...

Original Article

Meso-scale study of non-linear tensileresponse and fiber trellising mechanismsin woven composites

Behrad Koohbor, Suraj Ravindran and Addis Kidane

Abstract

The non-linear deformation response of plain woven carbon fiber-reinforced composites is experimentally studied at

meso-scales. Stereovision digital image correlation is utilized to capture the full-field strain distribution over a

10� 10 mm2 area of interest located at the center of the specimens. The evolution of local strains on the fiber bundlesand matrix-rich regions as a function of loading is extracted. The effect of fiber orientation angle on fiber bundles stretch

ratio and their angle of rotation (fiber trellising) and the related underlying failure mechanisms are analyzed using the

measured full-field displacement data. The results indicate that the local load-bearing mechanisms are different in on-axis

and off-axis loading conditions, whereas the larger global failure strain noticed in off-axis conditions is attributed to the

occurrence of fiber rotation. The fiber trellising is also shown to promote high local shear strain and consequently leads

to the protrusion of the matrix material on the deformed specimen surface.

Keywords

Carbon fiber, mechanical properties, meso-scale, digital image correlation

Introduction

It is well established that fiber composites exhibit non-linear stress–strain response under off-axis loading.This non-linearity is often observed in the global tensilestress–strain curves of off-axis specimens and is the con-sequence of complex load-bearing mechanisms resultedfrom interactions between the reinforcing fibers and thematrix.1 It is also understood that the global mechan-ical response of off-axis fiber composites has a strongsensitivity to the angle between the loading directionand the orientation of the fibers. The fiber orientationangle affects the degree of the non-linearity in the con-stitutive response of the composite.2–4

Although detailed studies of micro- and macroscopicbehavior of fiber composites are currently available inthe literature, there are only few studies dealing withthe meso-scale response of fiber composites, particu-larly from the experimental perspective.5–12 Theseexperimental-base investigations have generally beencarried out in a more qualitative sense to understandthe yarn interaction mechanisms,9,10 the nature of

deformation inhomogeneity in fiber composites,5,12

detection of damage initiation,11 to provide correlationbetween the macro-scale deformation and failureresponse to the meso-scale behavior of the material,7

and to validate finite element (FE) simulations.6 It isinteresting to note that the application of digital imagecorrelation (DIC) is the common method in the major-ity of the research conducted in the fields of meso-scaledeformation and damage response studies in wovencomposites. This is due to the capability of thistechnique to capture accurate full-field deformationresponse of materials, as well as the availability ofplug-and-play commercial systems.13 This powerful

Department of Mechanical Engineering, University of South Carolina,

Columbia, SC, USA

Corresponding author:

Addis Kidane, Department of Mechanical Engineering, University of

South Carolina, 300 Main Street, Columbia, SC 29208, USA.

Email: [email protected]

Journal of Reinforced Plastics

and Composites

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optical technique has been successfully practiced in thedeformation and failure analyses of fiber composites ata wide range of time and length scales.14,15

A more detailed survey in the available literatureon woven fiber composites reveals that the local deform-ation mechanisms, as well as the origin of the non-lineardeformation response are not yet well understood. Theunderlying mechanisms behind this orientation depend-ence are believed to be due to the occurrence of fibertrellising mechanism in the off-axis specimens subjectedto in-plane tension.8 Fiber trellising has so far only beeninvestigated either at macroscales or through the use ofcomplex finite element analyses. However, fiber trellis-ing is a local mechanism and no evidence on the meso-scale experimental study of this phenomenon is found inthe literature. In light of this, the present work attemptsto experimentally study the meso-scale deformationresponse of a plain woven carbon fiber-reinforced com-posite and to provide quantitative information on thenature of deformation non-linearity in tensile behaviorof off-axis composite specimens. In this regard, stereo-vision 3D DIC was utilized to capture full-field strainmaps at submillimeter length scales. Theoretically, forflat samples loaded in-plane, the use of a single camerasystem and 2D DIC are sufficient. However, the accur-acy of 2D DIC is highly affected by the out-of-planedeformation. The use of 3D DIC has been establishedto allow for a substantially more accurate evaluation ofthe full-field displacement and strain distributions, par-ticularly when significant out-of-plane displacement ispresent within the field of interest.16 The presence ofsuch out-of-plane motions was confirmed in this studyas a direct result of fiber trellising, which causes the pro-trusion of soft matrix material on the surface of the spe-cimen. Hence, 3D DIC is successfully implemented in thiswork, and the principal mechanisms behind the non-linear

response of off-axis woven composite specimens, i.e.fiber trellising and individual fiber bundle stretch werestudied. The authors strongly believe that the currentresearch is the first of its kind to deal with a detailedstudy of underlying mechanisms in the fiber trellisingphenomenon from an experimental perspective.

Experimental

Material and specimen geometry

Quasi-static tensile experiments were conducted onthree-layer orthogonally woven carbon fiber-reinforcedcomposite sheets of 0.8mm thickness. The compositecontains approximately 70 vol.% carbon fibers. Carbonfibers of �7 mm in diameter are processed into towsinterwoven to a plain weave fabric, forming unit cellsof �1.8� 1.8mm2 dimensions. Further details on theproperties of the composite specimens used in the pre-sent work can be found elsewhere.3 Rectangular speci-mens of 25mm wide and 175mm long were cut out ofthe as-received composite sheet in directions of �¼ 0�,15�, 30� and 45�, measured from the vertical principaldirection, as shown in Figure 1(a). The grip length was25mm at both specimen ends, resulting in a gage lengthof 125mm. Specimens were inserted into the tensilemachine with their grip length held inside the hydraulicgrips. To protect against the damage caused by serratedsteel grips, 2mm thick aluminum tabs were epoxied onthe grip section at both ends of the tensile specimens, asshown in Figure 1(b).

Tensile experiments and DIC

Tensile tests were performed using a 250 kN MTSmachine in displacement control mode at a rate of

Figure 1. (a) Schematic view of the off-axis tensile specimens. An actual tensile specimen is illustrated in (b) and the typical speckle

pattern applied on the specimen center can be seen in (c).

2 Journal of Reinforced Plastics and Composites 0(0)



1.5mm/min, which is equivalent to a mean strain rateof 2� 10�4 s�1. Load and cross-head displacement datawere acquired from the load-cell and displacement sen-sors of the tensile frame, respectively, while their sam-pling rates were synchronized with the framing rate ofthe cameras used for the image correlation purpose.

3D DIC was used to study the full-field deformationresponse of specimens at meso-scales. A high-contrast, random and isotropic speckle pattern isrequired to extract full-field deformation responseusing DIC. Taking advantage of the natural blackcolor of the specimens, white speckle patterns contain-ing �20 mm randomly distributed dots were applied ona 10� 10mm2 area at the center of each specimenusing an air brush and a diluted flat white paint (seeFigure 1(b) and (c).

A stereovision camera system containing a pair of5 MP CCD cameras, each equipped with a high-magnification 100mm macro lens was used to capturestereo images of the speckled area during loading. Inthe case of stereovision 3D DIC, the out-of-planemotion will not have any significant contribution tothe in-plane deformation measurement and hence, theaccuracy of the in-plane strain measurements will besubstantially improved.16 The camera system was cali-brated prior to the tensile experiments using 6� 6mm2calibration plates.17 External illumination containinghigh-intensity LED white light source was used to pro-mote uniform illumination of the specimen in theregion of interest. Figure 2 depicts the experimentalsetup used in this work. Calibration details of thestereovision system are listed in Table 1.

Images from the speckled region were takenduring tensile loading at full-field resolution of

2448� 2048 pix2 and at a rate of 1 fps. Images acquiredduring the tensile experiments were used to extract thedisplacement and strain fields using commercial DICsoftware Vic-3D.17 In this software, subset and stepsizes of 81 pix and 9 pix were selected, respectively,and a spatial resolution of 7.21mm/pix was determined,accordingly.

Figure 2. The experimental setup utilized to capture meso-scale deformation response of the specimens in this work.

Table 1. System parameters obtained from calibration of the

stereo camera arrangements.

Parameter Camera 1 Camera 2

Center – x (pixels) 1003 682

Center – y (pixels) 1299 597

Focal length – x (pixels) 52,005 55,023

Focal length – y (pixels) 52,014 55,043

Skew (�) 0.94 �3.39

Alpha (�) �0.34Beta (�) �28.07Gamma (�) 0.00

Tx(mm) 103.77

Ty (mm) 0.42

Tz (mm) 38.75

Koohbor et al. 3



Mathematical analysis of fiber trellising

When woven composites are subjected to off-axis ten-sile loading, the fiber bundles tend to re-orient towardsthe direction of the applied load. This behavior isreferred to as ‘fiber trellising’ and is documented tooccur when the angle between the fiber bundles changesfrom 90�.8,18,19 The highest degree of fiber trellising inwoven composites is observed in 45� off-axis specimenand accounts for the large non-linear deformationresponse observed in the material. In this work, fibertrellising phenomenon was studied and quantitativelyanalyzed at meso-scales, by tracking the local deform-ation and rotation of fiber bundles, as discussed below.

Let us consider a single fiber bundle with initial lengthli and initial angle �i, relative to the horizontal axis asshown in Figure 3. Upon exertion of the tensile load, thesection is stretched to a length lf and rotated towards theloading direction. The angle between the principalbundle axis and horizontal axis is increased to �f atthis point. The variables li and lf can be quantified bytracking the displacement fields at positions A and B, as

li ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixB � xAð Þ2þ yB � yAð Þ2

qð1aÞ

lf ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixB0 � xA0ð Þ2þ yB0 � yA0ð Þ2

q

¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffixB � xAð Þ þ uB � uAð Þ½ �2

þ yB � yAð Þ þ vB � vAð Þ½ �2

vuut ð1bÞ

where xk and yk represent the original coordinates atpoint k, respectively, and uk and vk are the horizontaland vertical displacement components at the same

point, respectively. Similarly, the angle �, inundeformed (�i) and deformed (�f) states can be calcu-lated as

�i ¼ tan�1yB � yAxB � xA

� �ð2aÞ

�f ¼ tan�1yB0 � yA0xB0 � xA0

� �

¼ tan�1 yB � yAð Þ þ vB � vAð ÞxB � xAð Þ þ uB � uAð Þ

� � ð2aÞ

All the variables shown in equations (1) and (2)can be obtained from the results of meso-scale DICanalyses. Obtaining the local fiber stretch magnitudeand its angle change facilitates a quantitative ana-lysis of fiber trellising occurred in different off-axisspecimens.

Results and discussion

Global stress–strain curves

Global stress–strain curves of the off-axis specimenswere obtained using two methods. First, followingthe conventional procedure, load and displacementin the gauge area were measured from the machineload-cell and cross-head motion, respectively, andthe global flow curves were plotted. In the secondapproach, the load measured by the machine load-cell was used to determine the global stress value.However, the strain developed in the specimen wasobtained by spatial averaging of the full-field verticalstrain maps captured by DIC.2,3 Figure 4 shows theglobal true stress–strain curves obtained using the twoapproaches. Close agreement between the two sets ofcurves indicates that the field of view (10� 10mm2)used in the DIC analysis has been large enough tobe statistically representative of the global responseof the material.8,20

Global mechanical properties of the off-axis speci-mens were extracted from the global flow curves andare listed in Table 2.

The off-axis specimens exhibit significantly differentmechanical response in terms of elastic modulus,Poisson’s ratio and strain-to-failure. The failure strain("f) at global scale was found to be one order of mag-nitude larger for the case of �¼ 45� compared with�¼ 0�. Such substantial variation observed in theglobal mechanical response of composite specimenscan be further investigated considering the differencesin the underlying load-bearing mechanisms in eachspecimen.

Figure 3. Schematic configurations of a single longitudinal tow,

before and after application of the tensile load.




Meso-scale deformation response

Typical contours showing the evolution of full-fieldvertical strain on a 5� 5mm2 area at the center of45� off-axis specimen are plotted in Figure 5. The con-tour maps show highly non-homogeneous strain fields,with noticeably large vertical strain componentlocalized in multiple parallel inclined strips. Such het-erogeneous full-field strain response agrees with theprevious observations by Ivanov et al.6 Note that themaximum local strain values shown here are consider-ably higher than the corresponding global strain in eachimage. This local non-homogeneous deformationresponse has also been observed in the case of otheroff-axis specimens, however, with different degrees ofnon-homogeneity.

Figure 6 demonstrates the local non-homogeneity ofthe vertical strain at the instant of failure, for differentoff-axis specimens. Considering the locations of max-imum and minimum local vertical strains, it is observedthat for �¼ 0� the largest magnitude of local strain isdeveloped within the areas containing mostly fiber bun-dles oriented parallel to the direction of the tensile load(see Figure 6(a)). This indicates that the longitudinaltows undergo the tensile deformation in �¼ 0�, andaccordingly, it can be expected that the tensile load ismostly carried by these tows. Similar strain patternswere found experimentally and also by using FE mod-eling in literature.9,21 On the other hand, for off-axisspecimens, i.e. �¼ 15�, 30� and 45�, the largest localstrain is developed in epoxy-rich areas confinedbetween longitudinal and transverse tows, as seen inFigure 6(b) and (c). Note that the degree of strainlocalization significantly increases in �¼ 45� specimen

Figure 4. Global stress–strain curves obtained for the off-axis

specimens.

Table 2. Global mechanical properties of

the off-axis specimens.

� (�) E (GPa) � "f (%)

0 68.1 0.076 1.75

15 35.9 0.487 4.61

30 16.7 0.739 10.42

45 11.9 0.779 17.72

Figure 5. Evolution of vertical strain component at different global strain magnitudes for 45� off-axis specimen. The global strainmagnitude corresponding to each plot is indicated on the top. Far-field load is applied vertically.

Koohbor et al. 5



compared with �¼ 15�. In addition, the fiber-rich areasfor these specimens show substantially lower strainmagnitudes.

The comparison between two extreme cases, i.e.�¼ 0� and �¼ 45� has also been made by plotting thevariation of normalized local vertical strain across threeunit cells, as shown in Figure 7. Note that the curves in

Figure 7 represent the variation of normalized verticalstrain ("yy="f) at the instant of failure for each speci-men, where "f denotes the failure strain of the corres-ponding sample. Figure 7 also confirms the significantlylarger variation of strain across the cells in the case of45�off-axis specimen compared with �¼ 0�. To explainsuch differences, it should be noted that in off-axis

Figure 6. Full-field distribution of normalized vertical strain component ("yy="f ) for (a) �¼ 0� (b) �¼ 15� and (c) �¼ 45�. Directionsof the far-field load and principal fibers are marked.

Figure 7. (a) Variation of normalized vertical strain component ("yy="f ) across three unit cells of width ‘W’, shown schematically in(b), for the specimens with �¼ 0� and �¼ 45�. Note that far-field load is applied vertically.




specimens, i.e. �¼ 15�, 30� and 45�, the application ofan axial tensile load could result in the rotation of thefiber bundles towards the loading direction, in additionto the stretching of the fiber bundles. This tendency ofthe fibers to re-orient towards the loading axis, or theso-called ‘fiber trellising’ phenomenon, attributes to thelarge local plastic deformation observed in off-axis spe-cimens. To confirm and quantify the occurrence of thismechanism, the results from the procedure discussed inMathematical analysis of fiber trellising section are pre-sented below.

The magnitude of fiber stretch was measured foreach specimen, according to equation (1). Figure 8shows the variation of fiber stretch ratio, �l=l0, as afunction of global vertical strain applied on each speci-men. Considering the curves in Figure 8, the followingtwo remarks need to be discussed:

1. It is clearly observed that the value of the fiberstretch ratio in �¼ 0� at any given point duringdeformation is close to the global strain valueapplied on the specimen. This observation is inagreement with the discussion provided earlier onthe more significant role of longitudinal fiber towsin load-bearing mechanism of this specimen. Theslight deviation between the fiber stretch ratio andthe global strain value in �¼ 0� specimen might bedue to the fact that the global strain magnitude ismeasured over a significantly larger area that con-tains both longitudinal and transverse fiber bundles,as well as matrix-rich zones, while the stretch ratio iscalculated locally without including the transverse

bundles and matrix-rich areas. Due to this fact, thedeviation between the fiber stretch ratio and theglobal strain magnitude significantly increases withincreasing the angle between the fiber bundles andthe loading direction.

2. Although the global failure strain magnitudes of thespecimens in the present work were found to beremarkably different, the magnitudes of their corres-ponding fiber stretch ratios upon failure were rela-tively close, being in the range of 1.07% to 1.28%.This agrees well with the fact that when failureoccurs, the fiber stretch cannot be larger than thefailure strain of the fiber, regardless of its tensile-loading angle. On the other hand, the larger valuesof global failure strains measured for specimens with0�

Figure 10. Full-field distribution of shear strain component ("xy) for (a) �¼ 0� and (b) �¼ 45�, at the instant of failure.

Figure 11. High-magnification images showing the surface profile of for (a) �¼ 0� and (b) �¼ 45� off-axis specimens after failure.The magnitudes of the surface elevation along the transverse direction (dashed line marked on (a) and (b)) are plotted in (c).




longitudinal and transverse fiber bundles. The develop-ment of this large shear strain has been exemplified inFigure 10, where the full-field shear strain distributionsfor two extreme cases, i.e. �¼ 0� and �¼ 45�, aredisplayed.

Further post-mortem investigations revealed that theoccurrence of large in-plane rotations in off-axis speci-mens can increase surface asperity of the deformedmaterial. Figure 11 depicts the high-magnificationimages taken from the surface of the specimens afterfailure. The degree of the so-called surface asperity issignificantly higher for �¼ 45� and is decreased pro-gressively as � converges to 0�. Also, the 3D profilemeasurements conducted on the specimen surfaceindicate that the peak value of the surface asperity for�¼ 45� is located over the intersection of longitudinaland transverse fiber tows.

The observation of the developed local surface aspe-rities in �¼ 45� can again be explained through thefiber trellising mechanism. As discussed earlier, thelarge rotation of the fibers can exert substantiallylarge values of shear deformation on the epoxy regionsconfined within the orthogonal fiber tows. This largedeformation magnitude may eventually cause the rela-tively softer epoxy to be extruded out of the plane ofthe lamina. This mechanism results in the formation ofsurface asperities over the epoxy-rich regions on thesurface ply, as illustrated earlier in Figure 11.However, the occurrence of such local out-of-planedeformation of the epoxy within the inner plies of thecomposite sheet may give rise to the partial delamin-ation of the plies, yielding in the nucleation of internaldamage. The explained mechanism can be consideredas a possible internal damage mechanism for wovencomposite subjected to off-axis tensile-loading condi-tions and can be a point of interest for future investi-gations on the subject.

Conclusions

Off-axis tensile deformation response of an orthogon-ally woven carbon fiber-reinforced composite was stu-died at mesoscopic scales. Stereovision DIC was used tocapture full-field displacement and strain distributionsover a millimeter-sized area at the center of the speci-mens. The significantly different global mechanicalresponses of the off-axis specimens in this work wereexplained through the load-bearing mechanisms as afunction of fiber orientation, while the experimentaldata were used to validate the proposed mechanisms.Non-linear response observed in specimens with0�

11. Ullah H, Harland AR and Silberscmidt VV.Characterisation of mechanical behaviour and damageanalysis of 2D woven composites under bending.

Compos Part B Eng 2015; 75: 156–166.12. Nicoletto G, Anzelotti G and Riva E. Mesoscopic strain

field in woven composites: experimental vs. finite elementmodeling. Opt Laser Eng 2009; 47: 352–359.

13. Sutton MA, Orteu JJ and Schreier HW. Image correlationfor shape, motion and deformation measurements.New York: Springer, 2009.

14. Canal LP, Gonzalez C, Molina-Aldareguia JM, et al.Application of digital image correlation at micro-scalein fiber-reinforced composites. Compos Part A Appl Sci

2012; 43: 1630–1638.15. Mallon S, Koohbor B, Kidane A, et al. Fracture behavior

of prestressed composites subjected to shock loading: a

DIC-based study. Exp Mech 2015; 55: 211–225.16. Sutton MA, Yan JH, Tiwari V, et al. The effect of out-of-

plane motion on 2D and 3D digital image correlationmeasurements. Opt Laser Eng 2008; 46: 746–757.

17. Correlated Solutions Inc., www.correlatedsolutions.com(accessed 3 December 2008).

18. Xue P, Peng X and Cao J. A non-orthogonal constitutive

model for characterizing woven composites. Compos Part

A Appl Sci 2003; 34: 183–193.19. Xue P, Cao J and Chen J. Integrated micro/macro-

mechanical models of woven fabric composites under

large deformation. Compos Struct 2005; 70: 69–80.20. Kanit T, Forest S, Galliet I, et al. Determination of the

size of the representative volume element for random

composites: Statistical and numerical approach. Int J

Solids Struct 2003; 40: 3647–3679.21. Tabatabaei SA, Swolfs Y, Wu H, et al. Full-field strain

measurements and meso-FE modeling of hybrid carbon/

self-reinforced polypropylene. Compos Struct 2015; 132:

864–873.22. Lussier D and Chen J. Material characterization of

woven fabrics for thermoforming of composites.

J Thermoplast Compos 2002; 15: 497–509.

23. Peng X, Guo Z, Du T, et al. A simple anisotropic hyper-

elastic constitutive model for textile fabrics with applica-

tion of forming simulation. Compos Part A Appl Sci 2013;

52: 275–281.


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