A multiple field image analysis procedure for characterisation of fibrealignment in composites

C.J. Creightona, M.P.F. Sutcliffeb, T.W. Clynea,*aDepartment of Materials Science and Metallurgy, University of Cambridge, Pembroke Street, Cambridge, CB2 3QZ, UK

bDepartment of Engineering, University of Cambridge, Trumpington Street, Cambridge, CB2 1PZ, UK

Received 18 February 1999; revised 29 May 2000; accepted 1 June 2000

Abstract

A novel method is presented for the characterisation of fibre misalignment in composite specimens. The method is based on analysis of lowmagnification images in which the local fibre direction can be inferred from the orientation of elongated features in the image. Specimenpreparation procedures and the image analysis algorithm employed are presented and their usage is illustrated by application to two types ofcarbon fibre composite, one of which showed a high degree of alignment while the other exhibited noticeable fibre waviness. Factorsaffecting the choice of certain image analysis parameters are briefly explored. Comparisons are presented with results obtained usingconventional sectioning, followed by measurement of the aspect ratios exhibited by individual fibres. It is shown that the proposed methodis robust, sensitive and experimentally convenient. It is particularly well suited to the characterisation of specimens exhibiting significantvariations in fibre alignment direction over large distances, i.e. pronounced fibre waviness, and the potential utility of such measurements forthe prediction of compressive strength is highlighted.q 2001 Elsevier Science Ltd. All rights reserved.

Keywords: A. Fibres; E. Pultrusion; A. Polymer-matrix composites (PMCs)

1. Introduction

Systematic characterisation of fibre alignment is animportant objective in the science and technology ofcomposite materials. While this is required for a variety ofpurposes, it is particularly useful in study of the axialcompressive strength. Most models for compressive failureof long-fibre composites focus on shear failure parallel tothe fibre axis, which occurs more readily with increasingmisalignment between this direction and the loading axis.The presence of a region in which the fibres are misorientedwith respect to the loading axis by an anglef tends topromote failure via formation of akink band (some-times termed amicrobuckle) at an applied stresss kp,which can be related to a critical interfacial shear stresson planes parallel to the fibre axis,t 12p. Writing f asthe sum of an original misorientationf 0 and the elasticshear strain,g 12, arising from the shear stresst 12p, leadsafter some rearrangement to the following expression

for the compressive strength.

sk p 1G12c 1f0t12p

� �211

where G12c is the shear modulus of the composite.An analysis of this type has been presented by Budiansky

and Fleck [1]. The above equation reduces to expressionsderived earlier by Argon [2] and by Rosen [3] for the respec-tive limiting cases of a rigid-plastic materialG12c! ∞and no initial fibre misalignmentf0 ! 08: The equationpredicts a value fors kp which falls sharply with increasingf0 from G12c (typically several GPa for a polymer-matrixcomposite) atf0 08 to about 1–2 GPa atf0 < 2–38, for atypical composite shear strength,t12p, of around 50–100 MPa. The model has apparently given fairly good quan-titative agreement between prediction and measurementwhen applied to a range of polymer composites [4–10],although it should be noted that there has often been consid-erable uncertainty surrounding the definition and measure-ment of the appropriate misalignment angle. There havealso been several studies [11–13] in which the basic prin-ciples involved in prediction of this type of shear instabilityhave been incorporated into numerical models, allowinginvestigation of the effects of variables such as the sizeand shape of the initially misoriented region.

Composites: Part A 32 (2001) 221–229

1359-835X/01/$ - see front matterq 2001 Elsevier Science Ltd. All rights reserved.PII: S1359-835X(00)00115-9

www.elsevier.com/locate/compositesa

* Corresponding author. Tel.:144-1223-334332; fax:144-1223-334567.

E-mail address:twc10@cam.ac.uk (T.W. Clyne).

Such work points the way towards simulations allowingprediction of the strength expected with an arbitrary spatialdistribution of fibre alignment angles. However, progresstowards this goal has in practice been severely hamperedby difficulties surrounding the experimental characterisationof fibre misalignment in a composite material. Substitutionof typical data into Eq. (1) highlights the sensitivity ofpredicted strength,s kp, to misalignment angle,f0, particu-larly for low angles. The method most commonly usedhitherto to establishf0 is the simple sectioning procedureoutlined by Vincent and Agassant [14] and by Yurgartis[15], among others. This involves examination of sectionslying at a selected angle to the nominal fibre alignmentdirection. The aspect ratios exhibited by individual fibresin such sections are measured, usually with image analysissoftware. These values are then transformed into angular

misalignments, assuming the fibres to be of circular cross-section and hence elliptical in the viewed section. It is alsopossible, by noting the angle between a reference directionand the major axis of the ellipse, to obtain information aboutthe three-dimensional (3D) orientation distribution.However, this method is extremely cumbersome and canonly give information about the orientation of a relativelysmall number of fibres at a few locations within the material.Furthermore, any attempt to record changes in the alignmentof individual fibres along their length, for example by serialsectioning [16], renders the technique even more time-consuming and is also prone to large errors [17]. Finally,the method is inherently destructive and is unsuited to qual-ity control requirements during monitoring of productionoperations. The use of confocal scanning laser microscopyto image material below the surface, while it can give some

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Fig. 1. (a) Optical micrograph of a pultruded composite, with a domain and pixel array highlighted; (b) schematic depiction of a set of domains (Aj, centred atxj, yj) within which the average fibre orientationf is to be measured.

3D alignment information without the need for serialsectioning [18], also suffers from most of thesedisadvantages.

In the current paper, a novel specimen preparation andimage analysis procedure is presented, which allows rapidacquisition of fibre alignment data in a form, which is wellsuited to use in models for the prediction of compressivestrength.

2. Image acquisition and analysis

2.1. Specimen preparation

In order to characterise spatial variations in fibre align-ment, relatively low magnification micrographs are used, inwhich individual fibres are not very well resolved. The workdescribed here was carried out on: (a) epoxy-67 vol%carbon fibre composite, produced by a pultrusion process;(b) epoxy-61 vol% carbon fibre composite, produced by towinfiltration to form prepreg sheets and subsequent hot press-ing. In the pultruded material, the nominal fibre alignmentdirection is parallel to the pultrusion axis, while in theprepregged sheet it is parallel to the side of the sheet. Fibresin the pultruded material are in general very well aligned,while the prepreg route sheets exhibit a noticeable degree ofwaviness — at least in some regions. Two grades ofpultruded material were examined, one of which was effec-tively free of any pores, while the other contained quitesignificant porosity levels (,3.5%), in the form of elongatedpores parallel to the extrusion axis. Further details of themicrostructures of the two materials are given elsewhere[19].

Specimens were prepared by sectioning and grindingdown to 1200 grit SiC paper. They were then polishedusing 15 and 6mm diamond. The resulting surface washighly reflective when viewed under an optical micro-scope. This surface was then flooded with acetone andrubbed with wire wool parallel to the fibre direction,using light fingertip pressure, for a period of a fewminutes. This process removed some of the epoxymatrix and established good contrast between the fibreand matrix, when viewed under the optical microscope.An example image is shown in Fig. 1a. Slight variationsto this procedure may be needed for different compositesystems, but in general it should not be difficult toproduce suitable levels of contrast for a wide range ofmaterials.

2.2. Image analysis algorithm

Fibre alignment angles could in principle be measuredmanually on such images. However, in practice, this proce-dure must be automated in order to obtain the necessary datawithin acceptable time and precision constraints. The fieldof interest is first divided up into a number of domains,Aj. An example is shown in Fig. 1b. These domainsmay cover the entire field or they may, as in Fig. 1b,cover only a fraction of the total area but be sized anddistributed so as to allow characterisation of the overalltrends in fibre orientation. In other words, the co-ordi-nates of the centroid of each domain, and its dimen-sions, should be specified in such a manner that arepresentative region is being sampled. In order tomeasure the fibre orientation angle,f , in a givendomain, an image analysis algorithm is needed.

Consider the dark elongated features (which might repre-sent fibres, or matrix between fibres, or bundles of fibres)oriented at an anglef to the reference (horizontal) directionin Fig. 2. For a pixel array inclined at an angleu to thehorizontal, the variation in light intensity,I, with distancealong the array will be as depicted schematically for the twocases shown, corresponding tou being close to, or signifi-cantly different from, f . When the array is orientedalong the axis of the fibrous featureu f; the mini-mum in light intensity corresponding to the dark featurehas a width equal to the length of the array (or, moreprecisely, to that length of the fibrous structure forwhich the contrast in the image is uniform). At allother orientations, the trough representing the fibrousfeature is expected to be narrower than this.

An intensity variation parameter,d , is now defined as theaverage of the absolute differences between the intensityI0at the midpoint of the linescan and the intensities within asuitable distanceL/2 on either side of the mid-position (i.e.for pixel numbers between̂ m). If the intensities aresampled along the pixel array, for an array inclined at an

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Fig. 2. Schematic depiction of a 1D array of pixels within an image,inclined at an angleu to the reference direction, showing typical intensitydistributions along the length of the array, for two values ofu , one of whichis equal to and the other greater than the fibre misalignment anglef .

angleu , the corresponding value ofd can be obtained from

du 12m1 1Xi1 m

i2 mI P02 I Pij j 2

where the intensitiesI Pi are sampled at 2m1 1 pointsregularly spaced along the length of the pixel array. Themagnitude ofdu is a measure of the extent to which theintensity varies along the direction concerned, with smallvalues indicating little variation. The orientation of thefibrous feature corresponds to the angleu for which themagnitude ofdu has a minimum value.

The above operation is carried out at a specified point,defined, as shown in Fig. 1b, by the co-ordinatesxj ; yj;which is the location of the centroid of the pixel array (P0)for all values of the orientationu . In order to characterisethe average alignment within a domain,Aj, the operation isrepeated at a series of points located withinAj — see Fig.1b. These points lie on a grid,xjk; yjk; k 1! N; locatedin the vicinity of xj ; yj:

duj 1NXkNk1

du 3

This leads to an average value ofd , within the domainAj,for each of a series of anglesd to the reference direction. Aplot of d againstu leads to curves of the form shown in Fig.3. The value off , representative of the alignment directionwithin the domain, is taken as equal to the value ofu wherethe minimum occurs in the curve. It can be seen from thecurves in Fig. 3 that the deduced value off is not sensitiveto the length of the array of pixels. This is discussed belowin Section 2.3. The averaging procedure described wasfound to give very similar results to those from morecomplex auto-correlation and Fourier analysis techniques,

and in fact is to be preferred to such methods since it appearsto be a more robust, reliable and accurate technique for thisapplication.

In summary, the following sequence of operations wascarried out in order to implement the analysis:

• A photograph of the microstructure is scanned at a suita-ble size and resolution (or a digital image could beobtained directly). In the current work, the image wastypically of a field with linear dimensions of a few mm,although larger areas can be examined by stitchingtogether several images. The magnification used wastypically such that each pixel was a square of sideabout 3mm. This leads to approximately 500,000 pixelsper image, each of which is assigned one of 256 greyscale levels.

• A set of square domains,Aj, is defined in terms of the co-ordinates of the centroid,xj ; yj; the length of the side,h,and the number of points,N, within the domain at whichanalysis is to be carried out. In the present work, this set ofpoints formed a square grid,xjk; yjk; k 1! N, with Nequal to the number of scanned pixels in the domain.

• The grid of points within each domain is rotated to anangleu relative to the reference direction. This is illu-strated in Fig. 1a. The light intensity along the 1D-pixelarrays produced in this way is calculated from the originalpixel array of the scanned image using a cubic interpola-tion procedure. The value ofd corresponding to this angleu for a single pixel array is obtained using Eq. (2) and theaverage value ofd for the set of pixel arrays lying at thisangle,du j, is obtained using Eq. (3). Padding of the data isused at the edges of the domain, taking the intensitiesoutside the domain equal to the values at the nearestpixel inside the domain.

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Fig. 3. Image analysis data obtained from a prepregged sheet material. Plots are shown of the measured value of the intensity variation parameter,d , as a ratioto the minimum value obtained, as a function of the inclination,u , of the pixel array to the reference direction. The curves correspond to different values ofL,the length of the pixel array.

• By rotating the grid through a series ofu values andrepeating the operation, a plot ofdu j againstu is gener-ated and the value ofu corresponding to the minimum inthis plot is taken as thef value characteristic of thedomain.

Details of the cubic interpolation algorithm used are asfollows. In order to determinedu j for an arbitrary domainrotation, u , a rotated, but still square, array of grey scaleintensity dataI Px0;y0 is necessary. The position in 2Dspacex0; y0 of the intensity data required was determinedusing the transformation equations

x0 x cosu 1 y sinu 4

y0 y cosu 2 x sinu 5where (x, y) are the spatial co-ordinates of the intensityfunction I Px;y and the origin is taken at the top lefthand corner of the image. The functionI Px;y and thelocal gradient functions 2I Px;y=2x; 2I Px;y=2yand22I Px;y=2x 2y were determined, then a third orderpolynomial was fitted to approximately satisfy all localconditions. The local intensity gradients were determinedusing a central finite difference expression of the form

2I Px;y2x

{ I Px11;y} 2 { I Px21;y}x 1 12 x 2 1 6

Once the coefficients of the polynomial had been ascer-tained (using the “MATLAB” software package), the grey-scale intensity of the point concerned was determined bycubic interpolation between the values for the adjacentpixels. Of course, alternative interpolation algorithmscould have been used. It is also worth noting that it wouldhave been possible to rotate the specimen and take a seriesof pictures, which would have removed the necessity forimage rotation. However, this would introduce problemsof retaining the same field coverage, ensuring precisely

controlled rotation intervals and raising appreciably theimage storage requirements.

The complete procedure was then repeated for eachdomain in the field. Using the parameter values outlinedabove, the complete operation typically took about 3 h ona standard workstation, for a set of domains covering atypical image field.

2.3. Precision and sensitivity

Two parameters central to the analysis are chosen arbi-trarily. These are the length of the pixel array,L, and thelength of the side of the domains,h. The effect of varyingthe value ofL was shown in Fig. 3. It can be seen thatthe deduced value off (, 2 1.58 in this case) is notsensitive to the chosen value ofL. As long asL is notmuch less than the characteristic length of features inthe image (,100mm in this case), the outcome shouldbe insensitive to the value chosen. It may be noted thatthere are some anomalous data aroundu 08; particu-larly for the shortest value ofL (32mm). This is aconsequence of certain characteristics of the cubic inter-polation procedure. Errors in the deduced value offdue to this effect can be avoided by ensuring that thepixel orientation in the scanned image does not coincidewith the fibre orientation.

Of course, there is also the issue of the pixel sizerelative to the scale of the features in the microstruc-ture. A pixel size well below the feature size willgenerate noise in these algorithms, while clearly alarge size will mean that important contrast informationwill be lost. The basic underlying feature in these mate-rials is clearly the fibre, although (depending on speci-men preparation and imaging conditions) the contrast inthe image may actually arise from bundles of fibres,rather than individual fibres. In any event, it has beenfound in the present work that a pixel size somewhatsmaller than the fibre diameter gives the best discrimi-nation, although the sensitivity is not very high. Someexperimentation is probably advisable for each combi-nation of specimen preparation procedure and imagingconditions.

The effect of domain size can be seen in Fig. 4, whichshows the dependence of the estimated fibre misalignmentanglef on the domain side lengthh. For very small valuesof h (,200mm), there are insufficient data to extract areliable estimate of f . At intermediate values(200mm , h , 400mm), there is a region wheref changeslittle with domain size. For larger values than this, averagingis now being done over a region within whichf changessignificantly with position, so that the deduced value startsto vary again. Hence the spatial resolution of the method isabout 200mm. This is more than adequate to capture thevariation in fibre misalignment angle with position seen inFig. 1b. The eye can clearly discern a directionality in thesmall region outlined in Fig. 1a, with side lengthh equal to

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Fig. 4. Image analysis data obtained from the prepregged sheet, showing theeffect of altering the length of the domain side on the deduced value of theaverage fibre misalignment angle,f , within the domain.

530mm. However, it is clear that there is insufficient detailin the image to extract an accurate orientation direction for aregion with side length one eighth of this region(h < 54mm). Hence the resolution of the method is limitedby the resolution of the image. Of course, it should benoted that altering the domain size will in many caseslead to a change in the actual average fibre misalign-ment angle within the domain and, indeed, it may beuseful to obtain some such information systematically.In general, there may be an incentive to identify sets ofimage analysis conditions, which are well suited toparticular types of investigation, which might facilitatecomparisons between results obtained by differentresearch teams.

Probably the most powerful feature of the analysis isthe fact that alignment information can be obtained as afunction of position over relatively large regions of agiven composite material. Such information is poten-tially useful from the point of view of understandingthe compressive failure of specimens and componentsmade from the material concerned. It is also possiblefor correlations to be established between measuredmisalignment distributions and the processing conditionsunder which the composite was produced. Some workhas already been carried out [19] in which such correla-tions have been established. The results given below areconfined to illustrations of the type of misalignmentdata, which can be obtained.

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Fig. 5. Images from pore-free pultruded material, used for characterisation of the degree of fibre alignment: (a) SEM micrograph of a section cut at an angle of68 to the nominal extrusion direction, for measurement of the aspect ratios of elliptical fibre sections according to the Yurgartis method; (b) optical micrographof a section cut parallel to the pultrusion direction, for application of the proposed procedure.

3. Application of the technique

3.1. Well-aligned composite material

The pultruded composite material exhibits a high degreeof alignment, with little or no variation apparent to the eyebetween different specimens or different regions of the samespecimen. Quantitative studies of fibre alignment werecarried out on both the porous and pore-free grades, usingthe fibre sectioning (Yurgartis) method and the proposed(multiple field image analysis, MFIA) technique. Typicalimages used for the two procedures are presented in Fig.5, which shows optical micrographs of the pore-free mate-rial. The Yurgartis method obviously involves study ofmuch smaller regions of the material than does the proposedmethod.

Results obtained from analysis of images such as those inFig. 5 are shown in Fig. 6. Fig. 6a shows data from theYurgartis method, while Fig. 6b relates to the MFIA proce-dure. It can be seen that both methods indicate that the fibresare well aligned, with measured misalignments ranging upto about 18 from the nominal fibre alignment direction. TheYurgartis method appears to have picked up some slightlyhigher values of misalignment angle than the MFIA techni-que. This might be expected on the grounds that there may

be the odd stray fibre, which has become slightly moremisaligned than its neighbours and this would only bepicked up by a single fibre method. It might be arguedthat such single fibre effects are of limited interest, sincethey are unlikely to affect the macroscopic failure beha-viour. Moreover, there is evidence in the data of Fig. 6that the MFIA technique is picking up an effect not detectedby the Yurgartis method, since the data in Fig. 6b suggestthat the porous material is slightly less well-aligned than thepore-free material. This is consistent with the fact that someslight fibre waviness was observable on careful inspectionof regions in the immediate vicinity of the voids. It is notreally surprising that this was not detected with the Yurgar-tis method, since there are inherent experimental difficultiesin trying to ensure that large, representative volumes ofmaterial are examined, particularly when there is interestin material close to free surfaces (including pores).

3.2. Prepreg consolidated sheet

The prepregged material is suited to the study of rela-tively large misalignments, and also of significant spatialvariations in local misalignment angle. It has long beenrecognised that fibre sectioning methods such as the Yurgar-tis technique are not at all well-suited to study of this type ofmaterial, since there are difficulties in choosing representa-tive points for sectioning and there are also significant prac-tical problems in attempting to ensure that a universalreference direction is applied to sections which are remotefrom each other. Hence it has hitherto been virtually impos-sible to obtain reliable misalignment maps over relativelylarge areas of a composite specimen. With the proposedMFIA method, however, these are relatively straightforwardto obtain. An example is presented in Fig. 7, which shows:(a) an image of the free surface of a consolidated sheet,about 20× 5 mm2; (b) a corresponding contour map show-ing how the average misalignment angle varies with posi-tion. This map was obtained by measuring the value off inabout 200 domains, centred on a regular grid of points. Inthis particular example, a noticeably wavy region is appar-ent in the micrograph near the top edge, about one third ofthe way along. This is apparent in the contour map as aregion in whichf varies between about̂ 58. This is thetype of information is needed for comprehensive predictionof the compressive strength of such material, using modelswhich take into account the size, shape and average fibreinclination of misaligned regions.

4. Conclusions

The following conclusions can be drawn from this work.

1. A new technique has been outlined for the measurementof fibre misalignment distributions within a compositematerial. It is based on image analysis of low magnifica-tion micrographs in which the local fibre alignment

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Fig. 6. Histograms showing the measured fibre orientation distributionsobtained for pore-free and porous pultruded composites, using: (a) theYurgartis method (about 180 fibres examined in each case); and (b) theproposed (MFIA) procedure (about 60 domains examined in each case).

direction is indicated by the orientation of elongated lightand dark features.

2. Specimen preparation and microscopy procedures havebeen described which led to the production of suitableimages for two types of carbon fibre composite. Similartechniques are expected to be applicable to a wide rangeof composite types. A relatively simple image-processingalgorithm has been outlined which allows the local fibrealignment direction to be measured on a digitised image.The method is well suited to the characterisation of largevolumes of material without the procedure becomingunduly time-consuming, either experimentally or interms of computing time.

3. Two arbitrarily chosen parameters are involved in theimage analysis procedure. These are the lengths of thepixel array used to determine the fibre orientation and thesize of the domain over which the measured fibre align-ment is averaged. The effects of varying these parametershave been briefly investigated.

4. It is shown that the results obtained are insensitive to thepixel array length, provided it is greater than a character-istic feature length. This is expected to be related to fibrediameter. In the present work, with a fibre diameter ofabout 7mm, the feature length was found to be of theorder of 100mm.

5. In the present work, the domains used have all been

square. Very small domains tend to lead to unreliableresults, particularly if the sides are shorter than the char-acteristic feature length. In the present work, a domainside length of between about 200 and 400mm was foundto give consistent results. The procedures are reliable forlarger domains, but the measured average misalignmentangle tended to fluctuate as a result of significant varia-tions in local fibre alignment within the domain.

6. Similar results are obtained with the proposed methodand with fibre sectioning techniques, when applied towell-aligned (pultruded) material. The proposed methodis particularly well suited to composite specimens exhi-biting long-range spatial variations in fibre alignment(waviness) and it has been shown how contour mapscan be constructed to present misalignment data obtainedover large areas of material.

Acknowledgements

This work was carried out as part of a studentshipsupported by the EPSRC, within a programme involvingHexcel Composites, British Aerospace, DERA and Neptco.The authors are grateful for useful discussions with Mr J.Ellis (Hexcel), Dr J. Ball (British Aerospace) and Prof. N.A.Fleck (Cambridge University).

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Fig. 7. (a) Optical micrograph showing the free surface of prepregged sheet material, with the centroid of each measurement domain marked by a black dot. (b)Corresponding contour map of measured average misalignment angle within each domain, with each grid intersection point corresponding to one of the blackdots in the micrograph.

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