JOURNAL OFC OM P O S I T EM AT E R I A L SArticle

Uncertainty in geometry of fibre preformsmanufactured with Automated Dry FibrePlacement and its effects on permeability

MY Matveev1, FG Ball2, IA Jones1, AC Long1, PJ Schubel3 andMV Tretyakov2

Abstract

Resin transfer moulding is one of several processes available for manufacturing fibre-reinforced composites from dry

fibre reinforcement. Recently, dry reinforcements made with Automated Dry Fibre Placement have been introduced into

the aerospace industry. Typically, the permeability of the reinforcement is assumed to be constant throughout the dry

preform geometry, whereas in reality, it possesses inevitable uncertainty due to variability in geometry. This uncertainty

propagates to the uncertainty of the mould filling and the fill time, one of the important variables in resin injection.

It makes characterisation of the permeability and its variability an important task for design of the resin transfer moulding

process. In this study, variability of the geometry of a reinforcement manufactured using Automated Dry Fibre Placement

is studied. Permeability of the manufactured preforms is measured experimentally and compared to stochastic simula-

tions based on an analytical model and a stochastic geometry model. The simulations showed that difference between

the actual geometry and the designed geometry can result in 50% reduction of the permeability. The stochastic geometry

model predicts results within 20% of the experimental values.

Keywords

Polymer matrix composites, permeability, uncertainty quantification, statistical properties/methods, Monte Carlo

simulations

Introduction

Automated methods of fibre deposition are in highdemand by the composites industry owing to their abil-ity to reduce waste and increase deposition rate whencompared to hand lay-up.1 Automated Fibre Placement(AFP) and Automated Dry Fibre Placement (ADFP)are designed to place several narrow fibre tows (prepregslit tapes or dry fibre slit tapes with a binder) simultan-eously by applying heat to the tows and consolidatingthem with a roller.1 An inherent feature of AFP andADFP preforms is the presence of gaps and overlapsbetween the tows. Gaps and overlaps can be consideredto be defects as they introduce resin-rich or fibre-richareas and can lead to reduction of mechanicalproperties of the composite.2 In some preforms, gapsare deliberately introduced to avoid overlaps, which arecaused by variable tow width, defects in ADFP processor tow steering. The programmed gaps can also beused to control permeability and resin infusion

as implemented in production of wings and wingboxof MS-21 aircraft.3 However, presence of variabilityin the ADFP lay-up and gap widths in particular,which is clearly visible in a sample lay-up shown inFigure 1, results in uncertainty in the permeabilityof the preform. This uncertainty in the permeability isknown to propagate into variability of the fill time aswell as to be the source of the defects such as dry spotsor incomplete impregnation.4,5 For preforms manufac-tured with ADFP, no data are available on the variabil-ity of either the preform geometry or the permeability.

1Composites Research Group, Faculty of Engineering, University of

Nottingham, UK2School of Mathematical Science, University of Nottingham, UK3Centre for Future Materials, University of South Queensland, Australia

Corresponding author:

MY Matveev, Composites Research Group, Faculty of Engineering,

University of Nottingham, University Park, Nottingham, UK.

Email: Mikhail.Matveev@nottingham.ac.uk

Journal of Composite Materials

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DOI: 10.1177/0021998317741951

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This article presents the first detailed study of an ADFPpreform geometry with a particular focus on variabilityof gap width and associated variability of permeability.

The key objective of resin injection is to achieve thecomplete impregnation of a preform with no dry spotswithin the target time.4 Costly ‘trial and error’ proced-ures can be avoided and the scrap rate can be reduced byemploying numerical simulations for the optimisationof the filling time, pattern and design of resin injectionstrategies, i.e. position of vents and gates. However,practical experience of composite manufacturingshows that the time to fill the preform and outcomesof resin injection can be variable even for a single geom-etry and injection strategy, owing to uncertainty of thepreform and the process. The uncertainty of permeabil-ity can be attributed to the imperfect lay-up, race-track-ing, variability within the preform and human errors.6

While all of these sources of variability remain relevantfor composite manufacturing, this article focuses onvariability of preform permeability owing to geomet-rical variability. The variability of geometry of a non-crimp fabric7 and various woven textiles8–15 has beenstudied by means of image analysis. Most of those stu-dies attempted to describe the amplitude and the correl-ation length of the variability. Experimental data fromthose studies were used in the models of textilereinforcements with variability in the geometry andused for prediction of probability of draping outcomes,8

distribution of mechanical properties12 and permeabil-ity.7,16–20 In particular, it was demonstrated that themould fill time can be several times longer than the filltime in the deterministic case.18

The geometry of a dry reinforcement can bedescribed by a model where tow position, tow widthand other details are described by a set of random vari-ables, which may be mutually independent or can becorrelated. Both uncorrelated and correlated models ofthe geometry variability have been used to predict dis-tribution of permeability of dry reinforcements.7,17–21

The uncorrelated model of the geometry used

by Wong et al.19 predicted the coefficient of variation(CoV, the ratio of the standard deviation to the meanvalue expressed as a percentage) of permeability to be3%, which is lower than the variability observed inexperiments. However, for the case of a non-crimpfabric, it was shown that the correlation length of theyarn path has a significant effect on the average perme-ability as well as its variability.7 It was shown that theaverage permeability can be significantly different fromthe permeability of an idealised reinforcement. Similarconclusions were drawn by Park and Tretyakov20 forthe 2D flow through reinforcement with variability inpermeability. In addition, it was shown that the shapeof the correlation function also has an effect on the filltime and its variance. It can be concluded that charac-terisation of the geometry of a reinforcement is requiredbefore permeability can be reliably predicted. Thedetailed characterisations of textile reinforcements,including correlation lengths, can be found in the lit-erature.8–12,14 However, no such data are available forADFP preforms which are inherently different fromwoven reinforcements.

This work presents statistical characterisationof ADFP cross-ply preforms including acquisition ofmeso-scale geometry, experimental characterisation ofpermeability and stochastic modelling of the permeabil-ity. The article aims to understand the relationshipbetween the variability of the meso-scale geometryand the permeability of the preform. ‘Characterisationof ADFP preform’ section presents manufacturing anddata acquisition methodologies, the statistical descrip-tion of the ADFP geometry and permeability experi-ments. Since the geometry of the ADFP preform isrelatively simple when compared to a woven preform,the problem reduces to characterisation of the flowchannels, or gaps, between the tapes. This assumptionis used in ‘Permeability modelling’ section where ananalytical permeability model of a deterministicADFP geometry, based on the available models,22–24

is described. The model simplifies the problem of the

Figure 1. Programmed and unintended gaps in ADFP preform.

ADFP: Automated Dry Fibre Placement.

2 Journal of Composite Materials 0(0)

flow through the ADFP preform, utilising the concept ofparallel-series connections. This permeability model isthen used in ‘Variability modelling’ section as the basisfor Monte Carlo simulations of permeability of ADFPpreforms with geometry variability using the statisticalgeometry descriptions from ‘Characterisation of ADFPpreform’ section. In ‘Discussion’ section, modellingresults from ‘Variability modelling’ section arecompared with the results of permeability experiments,limitations of the considered model are discussed andspecial attention paid to practical aspects of the designof ADFP preforms. Conclusions are given in the finalsection.

Characterisation of ADFP preform

Materials and experimental programme

The material used in this study was dry 24K carbonfibre tows with areal weight 194 g/m2, width 6.35mmand nominal thickness 0.25mm. The tows are coatedon one side with a proprietary thermoplastic binder.This material was used to produce two fibre preformsas described in ‘Experimental setup’ section. The man-ufactured preforms were characterised by mouldingseveral small samples and taking micrographs of theircross-sections. The preforms were also characterisedduring the manufacturing process by taking opticalimages of every layer (‘Optical characterisation of pre-form geometry’ section) and analysing its statisticalproperties (‘Statistical properties of preform geometry’section). Finally, the permeability of the preforms wasmeasured as well (‘Experimental characterisation of in-plane permeability’ section).

Experimental setup

Two identical dry fibre ADFP preforms were manufac-tured using a Coriolis AFP machine using the dry towsdescribed before. The machine was set to lay downstraight tapes of eight tows each of 1-m length andwith a programmed gap of 1mm between tapes toavoid possible overlaps. The tapes, when laid parallel,formed layers which formed a preform. A cross-plydesign of 16 layers (0�/90�)8 was chosen for ease ofmanufacturing, characterisation and modelling. Eachlayer had a regular shift of 3.5 tow widths relative tothe previous layer of the same direction as shown inFigure 2. Thermoplastic binder on tows was meltedusing a laser system mounted on the lay-up head andtows were consolidated with 200N force applied via asoft roller. The laser power was set to 800W which gavea surface temperature of around 200�C at lay-up speedof 0.8m/s and around 320�C at lay-up speed of 0.4m/s.The first layer of each preform was laid down at a speed

of 0.4m/s to ensure good tack and conformancebetween the tapes and substrate. All other layers werelaid down at 0.8m/s (except layers 2, 3 and 4 in Preform1, which were laid down at 0.6m/s). The effect of thelay-up speed is not studied in this article. The size of thetwo preforms was 1� 1m which ensures that a suffi-ciently large part of the lay-up is free from edge effects.

Optical characterisation of preform geometry

Samples from Preform 1 were infused with Prime 20 LVresin using resin transfer moulding (RTM), cast intopolyester resin and prepared for optical microscopy.Distinctive programmed gaps, small gaps betweentows within tapes and an unintended overlap of towscan be seen in Figure 2. Note that the programmed gaphas a height lower than the tow thickness due to com-paction of the material into the gap. The gap height wasmeasured at the minimum distance between the tows inthe gap and the average of the 25 measurementsresulted in an average gap height of 0.16mm. A scatterplot of the gap height against gap width as measured onthe micrographs is shown in Figure 3. It can be seenthat there is a tendency for wider gaps to have lowergap height but some of the narrow gaps also exhibitedlow gap height. It can also be noted that the variance ofthe gap height seems to be larger for narrow gaps. Theabsence of more detailed data makes it difficult toassume an adequate mathematical model for the gapheight.

Characterisation of geometry of fibre reinforcementcan be performed using various methods such as opticalimaging. A detailed image of each layer of both pre-forms was acquired by pausing the AFP machine,mounting a 24 MPix DSLR camera on a robotic armand taking 84 images covering the entire area of the1� 1m preform with some overlaps. Resolution ofraw images was around 35 mm per pixel. The firstimage of each sequence included an image of a coord-inate marker (checkboard pattern fixed at the lay-uptable during all experiments) and the calibrationtarget with checkboard pattern. After images of thelayer surface were acquired, the AFP lay-up processwas continued until the next layer was finished.

Characterisation of the geometry of textile reinforce-ment preforms has been performed using various meth-ods, e.g. microcomputed tomography (micro-CT) forsmaller samples when high precision is needed15 andoptical imaging for large samples.11 Development ofthe high-rate deposition processes such as AFP/ADFP require faster inspection techniques for onlineevaluation of the layup quality, e.g. laser profilometersand video-optical methods.25 However, an optical ima-ging technique was selected as neither profilometers norvideo-optical measurements provide greater precision

Matveev et al. 3

and might require longer calibration. The images of thepreform were used to extract exact positions of the tapeedges in order to measure the gaps between them. Rawcamera images were processed using a range of MatLab

tools. The processing algorithm for images of eachlayer was as follows:

1. Remove lens distortion from all images;26

2. Calibrate images in each layer into a plane parallelto the tool surface using the calibration target andcalculate the scale of each layer;

3. Find exact image overlaps, i.e. relative shifts usingFourier correlation of images;

4. Perform edge detection algorithms11,12 on eachimage separately to extract tape edges;

5. Combine detected tape edges together using infor-mation from Step 3.

An example of the image and automatic detection ofthe gap edges is shown in Figure 4. The contrastbetween tows belonging to current and previouslayers was achieved by placing a powerful source oflight perpendicular to the fibre direction in the currentlayer. However, binder veil, which is used for tow

Figure 2. Typical cross-section of RTM sample in the 0� direction (top); an example of overlap between two tows in vacuum bagged

sample (bottom).

RTM: resin transfer moulding.

0

0.05

0.1

0.15

0.2

0.25

0.4 0.6 0.8 1 1.2

Gap

hei

ght,

mm

Gap width, mm

Figure 3. Scatter plot of gap width against gap height.

4 Journal of Composite Materials 0(0)

coating, reflects light in every direction, so adjacenttows blend together on the images. Therefore, precisedetection of the edges between adjacent tows was notpossible. Owing to the use of the directed light sources,the images had significant non-uniformity of bright-ness, which resulted in systematic variation of the gapwidth measurement. The regions obscured by system-atic errors or susceptible to large errors were discarded,still leaving a large set of data for the analysis.

Statistical properties of preform geometry

It was noted in ‘Introduction’ section that the perme-ability of a preform is affected mainly by the width ofthe channels within the preform as it affects porosity,which is related to permeability as described by theKozeny-Carman model.27 The gap width registeredwithin the ADFP preform represents the cumulativevariability of the tow width, unintended gaps betweentows and imprecision of the lay-up. Two representativelayers from each of the two ADFP preforms areconsidered. Layers of the preforms are referenced asPkLl-m, where k is the preform number (1 or 2), l isthe layer number (1 or 3) and m is a subset (correspondsto a column of images) within the layer. A diagram ofthe images and subset positions is shown in Figure 5.The data set for each layer consists of seven subsetswith measurements of width of 17 gaps with 80-mmlength each.

The mean and standard deviation of gap widthswithin two of the subsets of set P1L1, together withstandard errors, are given in Figure 6. Note that theasymmetric confidence intervals of standard deviationsare a consequence of the fact that, for an independentsample of size n, n� 1ð Þs2=�2 follows a chi-squared dis-tribution with n�1 degrees of freedom, which is notsymmetric. Here s2 and �2 are the sample and popula-tion variances, respectively. The mean gap width in thefirst and last subsets exhibits a decreasing trend, whichcan be attributed to a systematic error in image analysis

(see discussion in ‘Experimental setup’ section) or edgeeffects. Consequently, the first and last subsets areexcluded from further analysis and the overall averagegap width and standard deviation are given withoutthem in Figure 7. The width of the 95% confidenceinterval for the mean gap width is close to 0.035mm(1 pixel on the image), i.e. the error is comparable to theresolution of the image. In addition, a straight line par-allel to the x-axis can be put within the confidence inter-val. Thus, it is plausible to assume that the variability ofgap width is weakly stationary, i.e. it has a constantmean value and standard deviation over the entirelength of the tape.

Probability distributions of the gap width distribu-tions in the data sets are shown in Figures 8 and 9,together with normal and lognormal fits for which par-ameters are given in Tables 1 and 2, respectively. TheShapiro–Wilk test28 did not reject (at the 5% signifi-cance level) the hypotheses of the data being from thesedistributions for most of the data sets. From these two

Figure 4. Example of the gap edge detection using automatic image analysis system.

Figure 5. Scheme of the images and subset of images for

characterisation of preform geometry.

Matveev et al. 5

distributions, the lognormal distribution was selectedfor the description of the gap width since, by contrastwith the normal distribution, lognormal random vari-ables take only positive values.

Representative autocorrelation functions (correl-ation along the length) of gap widths after removingthe linear trend, using the MatLab function ‘detrend’,are shown in Figure 10, along with the average

Figure 6. Gap widths in set P1L1 (shaded areas corresponds to 95% confidence interval).

Figure 7. Average gap width, standard deviation of gap width (shaded areas corresponds to 99% confidence interval), ‘all sets’

consist of subsets P1L1-2–P1L1-6, P1L3-2–P1L3-6, P2L1-2–P2L1-6, P2L3-2–P2L3-6.

6 Journal of Composite Materials 0(0)

autocorrelation and its error bounds. The average auto-correlation function exhibits some oscillations and isnegative in some regions. Instead of exponentialapproximation, as was performed in other stu-dies,8,9,11,12 the autocorrelation function was analysedusing the power spectral density of the detrended seriesand extracting frequencies corresponding to its peaks.29

The detrending was required to avoid zero frequencywhich appears due to either decreasing or increasingtrends in the measured gap widths. The power spectraldensity of the gap width from the data sets is given inFigure 10. This function has several peaks which cor-respond to frequencies present in the measured gapwidths. The most powerful peak corresponds to a wave-length of 40.7mm, and the next major frequency has awavelength of 16.3mm. Other peaks correspond toshorter wavelengths and have lower power. The longest

autocorrelation length of 40.7mm corresponds to thelower end of the range of correlation lengths reportedfor textile composites, 30–120mm,8,14 and is likely to berelated to behaviour of the dry tows as elastic beams,which respond to perturbations. Furthermore, this canbe related to the spring back effect owing to the drytows being uncoiled from a spool onto a flat surface.Visual examination of the ADFP preforms suggeststhat the second representative wavelength of 16.3mmcorresponds to waviness of the tow edges, which isprobably related to tow slitting.

The average autocorrelation function also indicatesthe appropriate size of representative volume element(RVE), which should be used for the variability study.It can be seen that the autocorrelation function reachesa value near zero for a length greater than 60mm,which means that there is no long-range correlationof the gap widths. The value of 60mm was chosen asthe minimum size of RVE for subsequent studies.

Dependence of the gap width in the other direction,i.e. between adjacent gaps, was also analysed. It wasexpected that adjacent gap widths would be stronglycorrelated because a large gap between two tapes

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4

PD

F

Histogram of gap width in P1L1

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4

PD

F

Histogram of gap width in P1L1

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4

PD

F

Histogram of gap width in P2L1

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4

PD

F

Histogram of gap width in P2L3

Figure 9. Histogram of gap width in the data sets (lognormal

distribution fitted).

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4P

DF

Histogram of gap width in P1L1

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4

PD

F

Histogram of gap width in P1L1

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4

PD

F

Histogram of gap width in P2L1

0 0.5 1 1.5

Gap width, mm

0

1

2

3

4

PD

F

Histogram of gap width in P2L3

Figure 8. Histogram of gap width in the data sets (normal

distribution fitted).Table 2. Results of the Shapiro–Wilk test assuming lognormal

distribution, significance level 5% (only section at x¼ 10.5 mm

and x¼ 72 mm were used for the tests of experimental

distribution).

Set �a �a

Null hypothesis

(Shapiro–Wilk

test)

p-value

(Shapiro–Wilk

test)

P1L1 �0.21 0.21 Not rejected 0.07

P1L3 �0.09 0.22 Not rejected 0.14

P2L1 �0.28 0.18 Not rejected 0.17

P2L3 �0.17 0.20 Not rejected 0.18

All sets �0.25 0.22 Rejected 0.04

aThese values correspond to the mean and std.dev. from Table 1

Table 1. Results of the Shapiro–Wilk test assuming normal

distribution, significance level 5% (only section at x¼ 10.5 mm

and x¼ 72 mm were used for the tests of experimental

distribution).

Set

Mean

(all data),

mm

Std.dev.

(all data),

mm

Null hypothesis

(Shapiro–Wilk

test)

p-value

(Shapiro–

Wilk test)

P1L1 0.83 0.18 Not rejected 0.07

P1L3 0.94 0.20 Not rejected 0.62

P2L1 0.77 0.14 Not rejected 0.19

P2L3 0.86 0.17 Rejected 0.04

All sets 0.80 0.18 Rejected <0.01

Matveev et al. 7

might result in the next gap being smaller. However, aruns test,30 which tests the hypothesis that values froma sequence are independent, on the gap widths showedthat the independence hypothesis cannot be rejected atthe 5% significance level for any of the data sets,making it is plausible to assume that adjacent gapsare independent.

Experimental characterisation of in-planepermeability

Permeability of the preforms, described in‘Experimental setup’ section, was measured using anexperimental setup, which simulates linear flow in apreform during RTM as proposed in Vernet et al.31

with a sample size of 290� 115mm (Figure 11). Thesize of the samples required for the testing and thedesirability of obtaining as many samples as possiblefrom a square preform were among the reasons forchoosing a rectilinear flow testing rig instead of a cir-cular flow rig as the latter requires larger samples.Specimens were cut in two orthogonal directions coin-ciding with the fibre orientations, which were assumedto be the principal flow directions owing to the simplegeometry of the preform. The rig was fitted with twopressure sensors, one at the gate and another at thevent. Specimens were placed into the cavity of 3.2mmdepth, closed with a transparent mould top, made of25-mm Perspex sheet, and injected with synthetic Trentoil at a constant pressure and temperature 18� 1�C.The fluid viscosity � is 0.115 Pa�s at 18�C. The pressureat each sensor was recorded during the entire experi-ment. The arrival time was defined as the instant whenpressure at the second sensor exceeded the pressurethreshold Pthr¼ 0.05 bar. The permeability of the

reinforcement with porosity, ’, was then calculatedassuming ideal linear Darcy’s flow using the arrivaltime, t, and injection pressure, P

Kexp ¼�’L2

2Ptð1Þ

where the flow length, L � 1þ Pthr=Pð ÞLsensor, is thedistance from the injection gate to the second pressuresensor, Lsensor, corrected with respect of the pressurethreshold Pthr as described in Matveev et al.32

Permeability measurements using a rectilinear injec-tion tool are prone to being affected by race trackingalong the sides of the tool. Therefore, a transparentmould top was used in order to observe the experimentsusing a video camera enabling experiments exhibitingrace tracking to be discarded. The nominal fibre volumefraction was calculated as �A �N=ð� � tÞ, where �A is theareal density of the tows, N¼ 16 is the number of layersin the preform, �¼ 1800 kg/m3 is the density of carbon

Figure 10. Autocorrelation (detrending applied), shaded area shows 95% confidence interval (left); power spectral density of gap

widths (right).

Figure 11. Scheme of the experimental rig.

8 Journal of Composite Materials 0(0)

fibre and t is the thickness of the preform. Then, for thepreform consisting of 16 layers and compacted to athickness of 3.2mm the nominal fibre volume fractionwas predicted to be equal to 54%. Measured permeabil-ity values for a nominal fibre volume fraction of 54%are given in Table 3. The sample distribution of thepermeabilities is given in Figure 12. The hypothesisthat the distribution follows a lognormal distribution

was not rejected by the Shapiro–Wilk test at the 5%significance level for any of the data sets.

Examples of the flow patterns, observed in the pre-form and recorded using a video camera, are shown inFigure 13. As expected, the flow in the gaps was fasterthan the flow in the tapes, which greatly distortsthe flow front. However, the gaps did not act as race-tracking channels owing to the complexity of the geom-etry of preform where the gaps are placed in thestaggered pattern and form a network of the channels.This network of the channels homogenises the flow andas a result creates a more uniform flow front than in thecase of pure race-tracking.

The distorted flow front observed in the experimentsalso introduces error in the permeability measurements.In the present experimental setup, the arrival time ismeasured by a single pressure sensor placed at thecentreline of the tool close to the vent. Therefore, thepositions of gaps in the bottom layer affect the regis-tered arrival time, e.g. by triggering early arrival whenthe entire mould is not yet filled, resulting in overesti-mation of the permeability. These overestimated valuescontribute to the right tail of the distribution shown inFigure 13. The effect of the flow front unevenness canbe reduced by performing the saturated flow experi-ments by measuring the flow rate after the porousmedium is fully saturated. It is expected that thiswould reduce the error and also yield permeabilityvalues slightly higher than those measured with the pre-sent setup.

The other source of uncertainty in the experiments isrelated to the potential deformation of the mould top.The effect of this uncertainty was kept to a minimum byusing a low injection pressure. It was estimated thatdeflection of the mould top was up to 0.15mm accord-ing to the plate theory,33 resulting in a fibre volumefraction change of 3%.

Figure 13. Flow patterns in ADFP preform.

ADFP: Automated Dry Fibre Placement.

Figure 12. Distribution of measured permeability, lognormal fit

in red.

Table 3. Results of permeability measurements.

Entire domain

Number of

samples

Permeability

(std.dev.), 10�11 m2

Direction 1Panel 1 13 1.46 (0.11)

Panel 2 6 1.79 (0.21)

Direction 2Panel 1 9 1.44 (0.19)

Panel 2 3 2.16 (1.02)

Matveev et al. 9

Permeability modelling

A fibre preform during resin injection is often assumedto behave as a saturated porous medium and flowthrough it is described by Darcy’s law. Most of theapproaches for permeability prediction7,19,23,24 arebased on the multi-scale homogenisation procedure,which assumes separation of the scales to simplify themodelling of the flow, e.g. flow in a unidirectional (UD)fibre bundle (micro-scale) is considered separately fromthe meso-scale flow and then homogenised. Then thehomogenised permeability of the micro-scale fibre bun-dles is implemented intro the meso-scale model.Homogenisation approaches have proved their effective-ness and accuracy for various reinforcements. For exam-ple, analytical homogenisation of flow was applied topredict the permeability of UD multi-layer preforms,22

plain weaves23 and multi-layer triaxial braid.24 Allapproaches divided the geometry of reinforcementsinto elementary volumes and channels, which are thenreconnected assuming series and/or parallel flow. Thesame approach is chosen here given the simple meso-scale geometry of the ADFP preform. In this case, thegeometry at the meso-scale is viewed as a layered struc-ture with each layer consisting of homogeneous tapeswith rectangular gaps between them. The homogenisa-tion procedure for the saturated permeability of the pre-form becomes viable because of the distributed nature ofthe gaps, which create a more uniform flow as discussedin ‘Statistical properties of preform geometry’ section. Itshould be noted that this approach of modelling alayered structure neglects the through-thickness fluidexchange by the adjacent layers. This assumption isbased on the consideration that individual layers arerelatively thin and the flow front in a layer with lowerpermeability is levelled out by two adjacent layers eachwith a higher permeability. In addition, the design of theADFP preform contains a limited number of gaps andthe remainder of the preform consists of densely packedfibres, which makes difference between the local perme-abilities of adjacent layers relatively insignificant.

The homogenisation procedure for the ADFP pre-form is shown schematically in Figure 14. The hom-ogenisation starts by defining the permeabilities of itssimplest sub-structures: tows and gaps. Permeability oftows (i.e. dry fibre bundles) are homogenised using theGebart formulae34 for direction along, Ky,k, and trans-verse to fibres, Ky,?

Ktow,k ¼8R2

53

1� Vf

� �3V2

f

ð2Þ

Ktow,? ¼16

9�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

6

Vf:max

Vf� 1

� �2:5s

ð3Þ

where R is the fibre radius, Vf is the fibre volume frac-tion within the tow and Vf:max is the maximum fibrevolume fraction in hexagonal packing.

The permeability of a gap along its length, Kgap, isgiven by a series35

Kgap ¼b2

121�

192

�5b

a

X1i¼1

tanh ð2i�1Þ�a2b

� �ð2i� 1Þ5

0@

1A ð4Þ

where a and b are the dimensions of the cross-section ofthe gap. The infinite series (4) was truncated to 10terms, which gave errors of less than 1%.

The permeability of a single layer along thefibre direction can be calculated using a weighted aver-aging approach,24 assuming parallel flow in the gapsand tows

Klayer,k ¼ �Kgap þ ð1� �ÞKtow,k ð5Þ

where � is the volume fraction of the gaps in thepreform.

Assuming that flow across the gaps makes a negli-gible contribution to the total flow, the transverse per-meability of a single layer can be calculated usingweighted averaging

1

Klayer,?¼

1� �ð Þ

Ktow,?þ

�

Kgap�

1� �ð Þ

Ktow,?ð6Þ

Using the derived values of the permeability alongand across the fibres, the permeability tensor of a layer,Klayer, in the reference frame aligned with the fibreorientation can be given as

Klayer ¼Klayer,k 0

0 Klayer,?

� �ð7Þ

The flow in a multi-layer preform is represented as anumber of parallel flows through the layers. Then the

Figure 14. Homogenisation approach.

10 Journal of Composite Materials 0(0)

overall in-plane permeability of the preform can bewritten as

Kin ¼XNi¼1

tiTRð�iÞ � K

ðiÞlayer � R

Tð�iÞ ð8Þ

where KðiÞlayer is permeability of i-th layer calculated

using equations (2) to (6), ti is the thickness of i-thlayer, T is the overall thickness, R is rotation matrixand �i is the orientation of i-th layer in a chosen refer-ence coordinate system.

The proposed model for saturated in-plane perme-ability was validated by fluid dynamics simulationperformed in ANSYS CFX using a model for asteady-state flow in four orthogonal gaps (i.e. four-layer preform) shown in Figure 15. The analyticalin-plane model yielded results within 10% of thenumerical model for all the considered cases as shownin Figure 15. The closest agreement was achieved forthe models with low porosities, when the approxima-tion of the gaps as slender non-interacting channels ismost reasonable.

Saturated permeability of the preform was calcu-lated using the presented approach and two preformmodels, referred as ‘designed’ and ‘averaged’, with theparameters given in Table 4. The first preform modelcorresponded to the nominal preform geometry withthe programmed value of the gap width. The secondpreform model accounted for the reduction of the gapwidth and height and used their averaged values asdescribed in ‘Characterisation of ADFP preform’ sec-tion. The fibre radius in equation (2) was equal to3.5� 10�6 m. The fibre volume fraction within a towin equations (2) and (3) was set to 0.7. However, theeffect of this parameter on the total permeability is notsignificant (permeability changes by 3% when the par-ameter changed by 15%). The ‘designed’ preformmodel predicted a permeability of 2.81� 10�11m2,

which is twice the permeability measured from thereal preform (as described in ‘Statistical properties ofpreform geometry’ section). The ‘average’ preformmodel yielded a permeability value of 1.81� 10�11

m2, which is 16% higher than the mean measuredvalue and within the 99% confidence interval for allof the experimental measurements, except forDirection 1, Preform 1.

The permeability model with the more precise geom-etry of the ADFP preform, which accounts for thereduction of the gap width and height, predicts perme-ability which is in good agreement with the experimen-tal results but does not provide any information on thevariability of the permeability. In the next section, thepreform model with variability of the gap width isdescribed.

Variability modelling

The gap widths and correlation properties measured,described in ‘Optical characterisation of preform geom-etry’ section, can be implemented into a preform modelwith randomly variable gaps. Prior to the use of theexperimental data described in ‘Optical characterisa-tion of preform geometry’ section, several assumptionsneed to be made. It should be noted that the width ofthe gaps was measured during the lay-up stage, which isthen followed by a compaction before RTM. The com-paction can introduce variations to the measured geom-etry, e.g. it is known that the compaction of 3D woven

Figure 15. Model of four orthogonal gaps (left); comparison of theoretical and numerical predictions of in-plane permeability of a

four-layer orthogonal preform (right).

Table 4. Geometrical parameters of the permeability model.

Designed Averaged

Gap width (mm) 1.0 0.8

Gap height (mm) 0.2 0.16

Gap volume fraction 0.02 0.0155

Matveev et al. 11

textile reinforcement can distort gap measurements sig-nificantly.36 However, in the case of preforms manufac-tured by ADFP, prior to the lay-up each tape is alreadycompacted to a high fibre volume fraction and thenfurther compacted by a roller during the lay-up stage.This, together with the binder activated during the lay-up stage, creates a preform which is denser, and muchmore rigid and stable, than conventional dry reinforce-ments. Research on consolidation of prepregs and pre-preg AFP tapes has shown that the tapes with lowthickness to width ratio do not exhibit squeezing flowand do not fill the gaps.37 These considerations allow usto assume that the tows are not significantly disturbedduring the compaction phase. The other possiblechange of the geometry is lateral expansion of the com-pacted tows. However, the overall change of thicknessduring compaction was no more than 5% and this pro-cess is expected to increase of the fibre volume fractionwithin the tows rather than cause lateral expansion.These arguments make it possible to assume that thewidth of the gap measured on a dry non-compactedpreform is still applicable to the compacted preformduring the RTM stage.

The permeability of the preform with randomly vari-able gaps can be calculated by extending the modelpresented in ‘Permeability modelling’ section. Eachvariable channel in the model is assumed to consist ofmany sections, each having its own constant channelwidth and height. These sections are then assumed tobe connected in series and the total permeability of agap is given by

Kgap ¼XNi¼1

1

Kgapðai, bÞ

!�1ð9Þ

where ai is the width of the gap in the i-th section and Nis the total number of sections.

The model of the ADFP prefrom geometry withvariable gaps is based on the assumptions that a gapwidth along the fibre direction, x, is modelled as a sta-tionary lognormal random function, aðxÞ, having cor-relation function cðxÞ given by the averageautocorrelation function in Figure 10. All the adjacentgaps in a preform are assumed to be independent fromeach other. Realisations of the random gaps were simu-lated as follows. First, a gap is divided into N sections,whose centre-points are regularly spaced and given bya vector xif g. Then, the correlation matrix C is com-posed using the correlation function cðxÞ, so thatCij ¼ c xi � xj

� �. Finally, a vector of gap widths,

a ¼ aif g, where ai ¼ aðxiÞ, is sampled at points xif g asshown below

a ¼ exp �JN,1 þ �2UR

� �ð10Þ

Here � and � are the sample mean and standarddeviation from Table 2, JN,1 is an N� 1 vector ofones, U is the upper triangle matrix found from theCholesky decomposition UUT ¼ C and R is a vectorof independent normally distributed random variableseach having zero mean and unit variance. Note that thetrend discussed in ‘Optical characterisation of preformgeometry’ section is neglected.

The model of the ADFP preform was sampled usingthe parameters measured in ‘Characterisation of ADFPpreform’ section and employed for permeability simu-lations using the Monte Carlo method. First, the effectof the number of sections N on the permeability wasassessed. As expected, the Monte Carlo simulationsshowed that for the small N, the permeability hashigh standard deviation, which converges to a constantvalue with increase of N. The converged values of themean and standard deviation at the total length of63mm (N¼ 360, distance between the sampling pointwas kept constant and equal to 0.175 mm) were foundto be 1.35� 10�11 m2 and 0.05� 10�11 m2, respectively(Table 5). The permeabilities are given in Table 5. Thesimulated distribution of the permeability is shown inFigure 16. In contrast to the deterministic model(‘Permeability modelling’ section) which overestimatedthe permeability, the variability model predicted thepermeability to be 14% lower than the experimentalvalues. Comparison between the models is discussedin the following section.

Discussion

The detailed image analysis of the geometry of manu-factured ADFP preforms resulted in several findings.The average gap width is 20% lower than the designedvalue and its CoV is up to 25%. Micro-imaging ofRTM samples of the ADFP panels showed that thegap height is lower than the layer thickness owing to

Figure 16. Simulated distribution of permeability for RVE

length of 63 mm.

RVE: representative volume element.

12 Journal of Composite Materials 0(0)

compaction effects. Sources of the variation of the gapwidth include precision of the lay-up, variability in towwidth, presence of unintended gaps between tows andpossible measurement errors which stem from the ima-ging and image analysis. The total of the measurementerror is estimated to be within 1–2 pixels on the originalimage (0.035–0.07mm) and is several times lower thanamplitude of the measured variations. With edge defectsfrom tow cutting excluded, the gap width was weaklystationary within the resolution of the images. The gapwidth could be represented by either a normal or a log-normal distribution as the corresponding statisticalhypotheses were not rejected. The lognormal distribu-tion was chosen because gap width cannot take negativevalues. The correlation function of gap widths obtainedfrom the data was found to be different from the correl-ation functions of the woven textiles presented in otherstudies.9,11,14 In particular, several oscillations areclearly visible in the present correlation function, indi-cating the presence of several meso-scale variabilities.The largest wavelength, 40.7mm, of the correspondingpower spectral density was close to the correlationlength found in textile reinforcements with tight weav-ing. The following mechanistic explanation can be pro-posed. Variability in the textiles is more likely to beintroduced by the weaving process, i.e. shuttle move-ments. Variability in the ADFP preforms is introducedby either vibrations of the robotic arm, spring back effectof the uncoiled tows or variability of the material, i.e.non-straight tows or variability of the towwidth. In bothcases, longer correlation lengths can be related to mech-anical constraints – yarns in tight weaving are restrictedfrom movement by other yarns (by both friction andcompression mechanisms) and tows in an ADFP pre-form are restricted from movement by the binder. Thesecond wavelength in the correlation function for theADFP preform is related to the wavy edges of thetows (which are produced by slitting wide tapes).

The stochastic modelling and permeability experi-ments yielded mean values of permeability, which are14% lower that the experimental mean value andwithin its 99% confidence interval. This, however, doesnot apply to the standard deviation of the permeability,which was found to be two to five times lower than theexperimental standard deviation. Distributions of thepermeability measured from the samples and predictedwith the stochastic model were also significantly differ-ent. The experimental distribution is close to a lognor-mal distribution and has a right tail with several highvalues of permeability. However, the simulated distribu-tion of permeability was almost symmetric (though aright tail was present). These discrepancies stem fromseveral assumptions in both modelling and experiments.

The stochastic model of the ADFP preform includedonly variability of the gap width, while the gap height

is also variable and its effect is quite important as canbe seen from comparison of the models of as-designedand averaged geometries. The measurements obtainedfrom the micrographs showed that there is a weak cor-relation between the gap width and gap height but nomathematical model can be assumed at present.Possible underestimation of the gap height, as well asabsence of unintended gaps between the tows, explainthe absence of high values of permeability in the simu-lated distribution (Figure 16). In order to address theseissues, further improvements to the model are plannedfor the future.

As for possible experimental errors, the ADFP pre-form could have non-uniform thickness and hence fibrevolume fraction. The lower thickness could result inadditional artificial flow paths. Furthermore, the per-meability rig was intended to replicate linear flow in theclosed RTM tool with constant cavity depth while thetop mould could have deflection of up to 0.15mm asdiscussed in ‘Optical characterisation of preform geom-etry’ section. Both of these factors can be a source ofhigh permeability values observed in experiments.Another possible source of error, the race-trackingeffect, was ruled out by discarding relevant samplesafter observing the flow front through the transparenttop of the mould. This observation revealed the error inthe permeability measurements owing to the flow frontdistortion and sensor position. It is of interest for futureresearch to estimate the measurement error and reduceits significance. Finally, the differences between themodelling and experiments include the model assump-tion of in-plane flow with no coupling between thelayers and the saturated flow while the experimentswere performed for unsaturated media. The shape ofthe flow front for multi-layer preforms and accuracy ofthe presented homogenisation procedure were shown tobe dependent on the ratio of through-thickness and in-plane permeability.38 However, it is expected that thedifference between the permeabilities in this preform isof an order of magnitude everywhere except for theprogrammed gaps, which should not result in morethan 10% difference between the presented model andmore refined models.

The experimental data presented in this article aremore applicable than merely to this single design of apreform. The variability of the gap width is invariant ofthe programmed gap width, because the tapes areplaced individually, one by one. Therefore, it is possibleto estimate the effect of variability on preforms with anarbitrary gap width and, importantly, to use the widthof the gap as a tool to mitigate the effects of its ownvariability. For example, consider a preform witha programmed gap width of 2mm whose variability isidentical to the one measured in ‘Characterisation ofADFP preform’ section. Repeating the procedures

Matveev et al. 13

described in ‘Variability modelling’ section, reveals thatthe permeability of the preform with variability is only12% lower than that of the as-designed preform withideal geometry. However, increase of the gap widthshould be carefully considered as it can lead to thehigher distortion of the flow front similar to race-track-ing, which can reduce the robustness of the process.The outlined idea is an important step towards fullyengineered materials, which combine both design forperformance and for manufacturing approaches.

Conclusions

For the first time, the geometry of the ADFP preformswas studied in detail by means of image analysis. Theaverage gap width was 20% lower than the designedgap width (0.8mm instead of 1.0mm) and the CoV ofthe gap width was up to 25%. Therefore, the use of theas-designed geometry for modelling purposes isunacceptable.

Experimentally measured permeability was found tobe marginally more than half the predicted permeabilityof the designed preform. Permeability of the ADFPpreforms was found to have a lognormal distributionwith CoV of up to 15%. The permeability predictedusing the averaged geometry parameters and the aver-age permeability predicted with stochastic models werewithin one standard deviation of the experimentalresults and within 20% of their mean values.Predicted CoV of the permeability was found to beonly 3.5%. The presented data on geometry of theADFP preform and its permeability can be used forresin injection simulations to predict the mould fillingtime and flow patterns. Such simulations are of interestfor future studies.

The model presented includes only one type of vari-ability, the width of the programmed gaps between thetows, while in practice, the height of the channel is alsovariable and other sources of variability are present.Furthermore, the flow through the preform was homo-genised using assumptions of series and parallel flow.There is therefore scope for further study of the ADFPgeometry by detailed numerical simulations of mouldfilling. This work demonstrates the importance of con-sidering the real geometry of the fibre preform. It showsthat even small deviations from the designed geometry

can result in large deviations of the permeability. At thesame time, this gives opportunity to mitigate the vari-ability by changing the programmed gap width as out-lined above.

Acknowledgements

The authors would like to express their gratitude to theNational Composite Centre (NCC), Bristol, UK, for help

with experimental ADFP trials and Dr Andreas Endruweit(University of Nottingham) for help with permeabilityexperiments.

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest withrespect to the research, authorship, and/or publication of this

article.

Funding

The author(s) disclosed receipt of the following financial sup-port for the research, authorship, and/or publication of thisarticle: This work was supported by the Engineering andPhysical Sciences Research Council [grant number: EP/

K031430/1], through the ‘‘Robustness-performance optimisa-tion for automated composites manufacture’’ project.

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