Surface topography evolution of woven thermoplastic composites under deformation

Journal Pre-proof Surface topography evolution of woven thermoplastic composites under deformation John Holmes, Youssef Hafiz, Zbigniew Stachurski, Raj Das, Shankar Kalyanasundaram

PII: DOI: Reference:

S1359-8368(19)36224-9 https://doi.org/10.1016/j.compositesb.2020.107880 JCOMB 107880

To appear in:

Composites Part B

Received date : 19 November 2019 Revised date : 23 January 2020 Accepted date : 12 February 2020 Please cite this article as: J. Holmes, Y. Hafiz, Z. Stachurski et al., Surface topography evolution of woven thermoplastic composites under deformation. Composites Part B (2020), doi: https://doi.org/10.1016/j.compositesb.2020.107880. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier Ltd.

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Surface topography evolution of woven thermoplastic composites under deformation John Holmesa,∗, Youssef Hafiza , Zbigniew Stachurskia , Raj Dasb , Shankar Kalyanasundarama a Research

School of Electrical, Energy and Materials Engineering, Australian National University, North Road, ACT 2601, Australia b Aerospace Engineering and Aviation, RMIT University, Plenty Road, VIC 3082, Australia

Abstract

The evolution of architectural distortion of woven composites can significantly influence the deformation behaviour but is challenging to measure experimentally. In this paper, two techniques are proposed to examine the out-of-plane topography of composites under deformation measured using stereo digital image correlation (DIC). The primary method relies on fitting a surface to the data to compensate for global sample distortion and reveal local topography while the supplementary method uses local curvatures calculated for each data point on the surface. These methods have been applied to thermoplastic composites with different weave architectures, matrix and fibre materials. Topography results show good agreement in magnitude and form with mesoscale finite element analysis (FEA). The methods improve existing experimental techniques to examine local effects with multiple applications regarding deformation, defect detection and failure analysis of composites.

Keywords: A. Thermoplastic resin, C. Finite Element Analysis (FEA), E. Weaving, Digital Image

∗ Corresponding

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Correlation (DIC), Surface topography

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author Email addresses: [email protected] (John Holmes), [email protected] (Youssef Hafiz), [email protected] (Zbigniew Stachurski), [email protected] (Raj Das), [email protected] (Shankar Kalyanasundaram)

Preprint submitted to Composites: Part B

January 23, 2020

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1. Introduction

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With the growth in composite materials usage, new experimental methods are required to detect

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defects in manufacturing and to improve failure investigation. Digital Image Correlation (DIC) is a

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powerful tool for examining deformation and surface strains of composite materials, which is useful for

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identifying defects and examining local phenomena. DIC has experienced rapid growth in usage in the

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past decade, with the necessity of additional surface speckle pattern eclipsed by the benefit of full-field

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strain and displacement measurements [1]. Consequently, DIC is increasingly used for materials testing

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and for monitoring strains during component forming [2, 3]. A challenge is to distinguish the local

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out-of-plane motion in capturing the deformation behaviour of the sample. Changes in architecture

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and consequently, surface topography are significant for materials such as fabrics and composites. The

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small body of work on topography of these materials during deformation has primarily used the out-of-

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plane displacement (dz ). This displacement measurement becomes difficult if there is any rigid body

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motion or distortion of the sample, such as twisting or bending [4, 5]. Further, in some cases, out-

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of-plane displacement is a necessary part of the testing procedure, including in tension-torsion testing

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[6]. These factors can dominate local weave based deformations, defects and wrinkling, preventing or

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substantially reducing their ability to be examined.

For woven fabric, studies [7, 8] have been conducted that combine chromatic confocal microscopy

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with fast Fourier transform (FFT) filtering for detailed analysis of topological characteristics. This

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topography aided in understanding the wettability of the fabric in polymer impregnation for composite

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consolidation [7, 8]. However, the measuring method is not instantaneous as the whole sample needs to

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be scanned, making it unsuitable for deformation measurements. Further, the quality of FFT filtering

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is dependent on sampling parameters (such as cut-off length and resolution) which is found to be

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strongly dependent on the type of material [8]. Other work examining surface topography of partially

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processed carbon fibre / SiC matrix composite makes use of DIC [9]. Scanning the sample in 12 sections

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and then combining the results increases the overall resolution but implies that the characterisation

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needs to be at a single load case. To increase the ability to differentiate local topography from the

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reported panel curvature, height is compared to the average height over the unit cell. However, this

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method requires the isolation of unit cells and is discontinuous which presents difficulties for rapid

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changes in global curvature.

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Numerical methods underpin both DIC and FEA. The data gathered from DIC measurements

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provides a discrete set of points on the sample surface which is used to calculate strain and surface

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deformation. Combining DIC with discrete curvature algorithms allowes the examination of asymmetry

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in membrane bulge tests [10]. Similarly, simulations in conjunction with experimental DIC are a

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common technique to discover underlying deformation and failure mechanisms. Mesoscale simulations

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are favoured where a unit cell is modelled with the yarns and matrix as separate materials [11].

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Meso level simulations have been shown to capture local experimental effects from DIC measurements

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[12, 13].

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The evolution of surface topography is valuable in understanding phenomena including defects,

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wrinkling and strain concentrations, which relate to damage and failure. In woven composites, the

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heterogeneous strain field caused by the yarn crimp architecture correlates to failure location [13, 14].

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These strain concentrations occur in resin-rich regions between yarns of woven composites [15, 16]. 3D

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woven composites with more complex architecture also have strain concentrations, here corresponding

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to the interlacement of the z-binder fibre bundles [17]. However, these previous studies have not been

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able to capture the local topographic changes corresponding to these strain concentrations. Changes in

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surface topography have been used to determine the onset of failure for unidirectional composites with

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defects caused by fibre waviness [18], but it requires manual selection of a cross-section for evaluation.

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Delamination defects between layers in woven composites have been evaluated by topography and strain

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contours [6] but need to be of a sufficient size to differentiate defect from overall sample twisting.

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Phenomena such as buckling in composites under in-plane shear [19] and wrinkling in composites

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and unconsolidated fabrics [5] are other areas where DIC has been used to measure topographic

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characteristics, but local phenomena at the weave level are obscured by global sample movement.

To overcome the limitations of existing experimental techniques in measuring changes in local

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topography using DIC, two methods are proposed in section 2. The first one relies on fitting polynomial

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surfaces to the sample, which counteract the global distortion allowing weave based deformation to be

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examined. The second, supplementary, technique relies on examination of differences in local curvature

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to explore sub-weave scale features. The composite materials, which the techniques are applied to,

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are described in section 3 and the accuracy of the techniques and DIC data is evaluated in section 4.

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Finally, the application of these techniques to woven composites are discussed in section 5. Here, the

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techniques are able to capture the evolution of surface topography under deformation and allow local

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topography changes to be linked to local phenomena including strain concentrations.

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2. Techniques

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The proposed techniques provide an easily implementable method of evaluating changes in weave

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height at multiple deformation stages. The first technique, the surface compensation method, is well

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suited to examining changes in topography of woven architecture. The supplementary technique,

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the curvature method, provides additional details using differences in local curvature to distinguish

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topographical features, including yarn edges and cracks. These two techniques in conjunction allow

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for examination of weave scale and sub-weave scale features.

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2.1. Surface compensation method

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The surface compensation method uses fitted surfaces to compensate for the global sample form.

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The sample form is the overarching shape of the surface which can be greatly influenced by even minor

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motions of the testing apparatus (Figure 1a). If uncompensated, this form dominates deformation

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results (Figure 1b). The fitted surface compensates for the sample form and allows the local weave

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height changes to be observed. The surface model used in this work is a fifth-order polynomial model,

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which was found to have an acceptable balance between accuracy of fit for the tensile test and algebraic

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complexity with 21 parameters. Polynomial models are simple to implement and computationally

(a)

dz

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Tensile load Small motion of test fixture

DIC points found from stochastic pattern

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Figure 1: Surface compensation method. (a) Motion of the test fixtures adds global displacement to local composite displacement. (b) Z displacement (dz ) is dominated by global displacements. (c) Applying the surface compensation method allows for the global motion between planes S1 (original global fitted plane) and S2 (deformed global fitted plane) to be removed. (d) Local change in surface height (Zchange ) shows topographic change linked to the weave.

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efficient and have previously been used to remove sample form in surface topography [20, 21]. Other

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global parametric models can also easily be implemented and may be more appropriate for some

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mechanical tests such as spherical or ellipsoidal surfaces for dome forming tests. Figure 1c illustrates

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the method and the fundamental steps are enumerated below where k represents a single point in x

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and y:

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1. A polynomial surface (S1) is fitted to the undeformed point coordinates (zk,undef ormed ) via

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regression. The standard MATLAB® fitting function (fit with poly55) is used to achieve a least-

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square fit to the polynomial surface points (ˆ zk,undef ormed ), by minimising the sum of surface

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residuals (SSR) for the n data points. This is achieved by changing the weights of the coefficients

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to the polynomial creating a parametric description of the sample surface.

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2. The out-of-plane Z component of the undeformed raw datapoint (zk,undef ormed ) is compared to

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the corresponding surface coordinate (ˆ zk,undef ormed ) to find the difference: d1k = zk,undef ormed −

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zˆk,undef ormed

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3. A second polynomial surface (S2) is fitted to the deformed stage of interest in the same manner as step 1.

4. The out-of-plane Z component of the deformed point coordinate (zk,def ormed ) is compared to the corresponding point on the second surface (ˆ zk,def ormed ): d2k = zk,def ormed − zˆk,def ormed

5. The difference between the point to surface distances d2 and d1 results in the local out-of-plane

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change in Z without the global change in sample form: Zchange,k = d2k −d1k shown in Figure 1d.

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The techniques can be applied to multiple deformation states of a sample allowing the changes in

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topography (Zchange ) to be compared with the evolution of strains. Results of the technique can be

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analysed in three ways: surface contours, cross-sectional slices and height metrics. Contours of the

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whole sample surface provide a visualisation of the regular topographic behaviour linked to the weave

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pattern. Cross-sectional profiles provide more detail about topography shape at yarn edges and allow

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for comparison to simulations. Height from the minimum to maximum value of Zchange provides a

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topography metric which can be plotted over time. Hence, Zchange of a deforming surface provides

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significant new topographic results which were not previously available using existing techniques.

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2.2. Curvature method

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For each deformation state, the curvature method is also applied to the data to provide a contour

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map of features with sharp gradient changes. This allows sub-weave scale features to be visualised.

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Locating these high curvature features relative to the previous Zchange topography determines if they

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are a sharp change at a yarn edge or a feature within the yarn itself. Given curvature is related to the

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second-order derivative of position, algorithms will magnify the small variations in the material giving 5

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Figure 2: Curvature method. (a) Regions of high mean curvature. (b) Small region of surface showing triangulation. (c) A typical vertex (V ) and the adjacent surface normals (N 1 − N 5). (d) Resulting principal curvatures (k1 and k2 ).

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rise to some noise in the results [22]. However, when interpreted in conjunction with the previous

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method, it highlights key sub-weave scale features enhancing the previous results (Figure 2a).

An algorithm using methods of discrete differential geometry allows an approximation of curvature

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to be calculated for every data point. First, the points are connected in a triangular mesh (Figure 2b),

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then the normals of the faces connected to the data point (vertex) are found (Figure 2c). Next, the

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normals are weighted by area, and the average resulting vertex normal is calculated. Finally, the

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principal curvatures and directions are calculated (Figure 2d). From the principal curvatures (k1 , k2 ),

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the mean curvature (H), the average of the principal curvatures, can then be found. This algorithm is

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based on MATLAB® functions created for characterisation of porous microstructures [23] and based

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on a prior algorithmic approach [24]. This new application of existing tools provides valuable additional

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results to enhance the interpretation of the existing dataset.

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2.3. Applications of the techniques

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The techniques are developed for use in conjunction with DIC measurements for standard mechan-

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ical tests. DIC is becoming increasingly popular due to its ability to provide data in-situ for multiple

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deformation states [25]. These new techniques provide additional information for tests where the data

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is already commonly available, including tension, bending, torsion, and forming tests. Further, the

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techniques themselves compare well against other potential alternatives previously published. The

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methods do not require the segmentation of unit cells [9] and require less user discretion than the FFT

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filtering method for picking parameters [8]. FFT filtering cut-off values need to be altered for different

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woven composites due to changing unit-cell and surface properties. The proposed techniques are as

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easily programmable as FFT filters due to inbuilt and preexisting MATLAB® functions, namely, fit

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using poly55. Similarly, computational time is not an issue as for a dataset of ∼ 120,000 points a fit

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of poly55 takes 1.17 s, and 1000 by 1000 FFT filter takes 2.95 s, with two required in each case for the

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initial and deformed state. Therefore a popular measuring method has been combined with techniques

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which can be applied directly to multiple datasets without the manual selection of parameters.

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3. Materials and methods

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3.1. Material

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Four woven thermoplastic composites are studied which provide a selection of different continuous fibre reinforcements, matrix materials and weave architectures:

• Aramid / polyetherimide (A/PEI), trademarked TC1000 CETEX® and manufactured by Toray Advanced Composites [26].

• Self reinforced polypropylene (SRPP), trademarked CURV® and manufactured by Propex Fabrics from extruded PP tapes [27].

• Carbon fibre / polyetheretherketone (CF/PEEK), a consolidation of layers of Pipreg® , a composite system developed by Porcher Industries [28].

• Glass fibre / polypropylene (G/PP), trademarked TWINTEX® and manufactured by Owens Corning Co. from commingled yarns [29].

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The geometry of the composites varies significantly and is illustrated in Table 1 and Figure 3. G/PP

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has only a single layer and consequently the largest yarn spacing. CF/PEEK consists of plain-woven

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layers which have the highest crimp, whilst A/PEI has a 4-harness satin weave and consequently has

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the least crimp. Both SRPP and G/PP have a 2/2 twill weave, but due to SRPP being comprised of

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one, albeit aligned, material, the woven structure is less distinct.

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(a)

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Figure 3: Unit cell geometry for weaves generated using TexGen software with surrounding matrix removed showing diverse architectures (a) A/PEI, (b) SRPP, (c) CF/PEEK, and (d) G/PP.

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Property

A/PEI

SRPP

CF/PEEK

G/PP

2

3

4

1

4H Satin

2/2 Twill

Plain

2/2 Twill

Laminate thickness (mm)

0.48

0.9

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Yarn spacing (mm)

1.55

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Layers Weave

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Table 1: Geometric properties of materials

3.2. Method

Tensile tests were conducted to failure on a model 4505 INSTRON® testing machine. The samples

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used in this study are 25 mm by 160 mm, and six repeats are conducted for each. A gauge length of

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50 mm is used and an elongation control of 0.1 mm/s. The strain on the surface of the samples is

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captured using a stereo (three-dimensional) DIC system ARAMIS® version 6.3 [30]. By comparing

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images from two CCD cameras at regular time intervals (1 Hz in this study), a field of surface points

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can be tracked and their displacements and strains calculated. A high contrast stochastic pattern is

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sprayed onto the sample surface to enable the identification and tracking of points. The measuring

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area was ∼ 30 mm by ∼ 25 mm a depth of field of ∼ 10 mm for data capture. The cameras have

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sensors of 2448 by 2048 pixels, which results in a magnification of around 80 pixels/mm. Points are

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found by correlating 20 by 20 pixels (240 µm) subsets and points are generated every 5 pixels (60 µm).

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ARAMIS® points are then exported to MATLAB® for further processing and data visualisation where

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the techniques are applied as described in section 2.

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3.3. Finite element modelling

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Numerical simulations for the change in surface topography of the composites were developed

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in ABAQUS/Standard® finite element software. The models consist of composite unit cells with

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periodic boundary conditions (PBCs) with material properties based on the constituent fibres and

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matrix (table of mechanical properties provided in Appendix A). A micromechanical homogenisation

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model is used to determine the properties of the yarn from the matrix and fibre using an ABAQUS

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plugin module [31]. The yarn properties are used in the woven composite unit cell with the geometry

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created using the software TexGen [32]. Mechanical properties are orientated along the yarn direction,

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and a conformal mesh is created using tetrahedral elements. Initial seeding size of the geometry

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varies between ∼0.05 mm to ∼0.15 mm. The resulting number of elements is between 550,000 and

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1915,000. The meshing of the sides in TexGen is such that opposite faces are identical to allow for the

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application of PBCs. PBCs allow deformation to be locally influenced by the weave while maintaining

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overall continuum compatibility and are widely used for modelling unit cells [33, 34]. The use of PBCs

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is appropriate as the unit-cell is much smaller than the sample width for A/PEI, SRPP and C/PEEK

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and for the unbalanced G/PP crimp discrepancies (discussed in subsection 5.3) are far more significant

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than any free edge effects. PBCs are applied to the unit cell sides through equations linking directly

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opposite nodes. The equations include ‘constraint drivers’ allowing for deformation by strains εx , εy ,

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εz , εxy , εxz , εyz . In this study, εy was applied with results recorded every 0.5% strain.

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4. Accuracy Analysis

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4.1. Measurement Accuracy

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Displacement errors are the primary consideration for the accuracy of topographical results and can

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be categorised into bias and random errors. Bias errors are systematic errors such as lens focus, camera

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angle, and the algorithm’s calibration ability to capture the distortions [2]. Random errors include

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thermal fluctuations and variations in the quality of the speckle pattern [1]. With correct calibration,

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bias errors are far less significant than random errors. Therefore the displacement accuracy can be

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estimated by measuring the noise in a series of static images [35, 36]. The DIC algorithm is run on six

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images of a fixed sample using the same parameters as for the experiment to eliminate the parameters

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influence on the errors [3]. The standard deviation of the displacements is used to determine the uncertainty. This results in an average standard deviation error of 0.21 µm in-plane displacements and

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0.98 µm out-of-plane displacements. As a result of the 25-degree angle necessary to achieve lens focus

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and correlation over the whole field of view, accuracy is less in the z-direction. However, errors are

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still an order of magnitude lower than the topographic changes of the weave.

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4.2. Technique Accuracy

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The accuracy of the fit itself also needs to be considered. As a benchmark test of the technique,

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Euler buckling was induced into a 1 mm thick 25 mm wide aluminium sample by gradually reducing

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the 50 mm gauge length. The surface maintains the same local surface topography throughout the

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Z (mm)

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5.6

Sample Polynomial fit

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5.2 -10

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0

0 -0.01

5

-10

10

Y (mm)

Unbuckled

-5

Buckled

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5

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Y (mm)

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Figure 4: Cross-section of polynomial fit captures the global buckling deformation: (a) Sample z position and polynomial fit (b) Local height for unbuckled (d1 ) and buckled (d2 ) surface.

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test. Consequently, it is possible to see how well the fit is able to remove the global sample distortion.

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A good fit is achieved for the deformed surface with the fifth-order polynomial fit. (Figure 4a). The

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residual between the fit and the buckled surface has a standard deviation of 3.5 µm, the same value

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as the unbuckled. There is no major induced shape bias on the residual, therefore the order of the fit

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is suitable for the sample behaviour. Further, the local differences have a similar shape, meaning that

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they are due to the small amount of surface roughness, and the fit can successfully remove the global

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buckling without impacting local features (Figure 4b).

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5. Results and discussion

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The utility of the techniques proposed in this study is examined by analysing the topography of

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woven composite materials under tensile deformation. The tensile test allows the evolution of local

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topography of the composite to be inspected as it progresses to failure. Specifically, topography is

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examined in relation to underlying mechanisms, strain concentrations, fibre waviness, local curvature

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and FEA simulations.

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5.1. Topography

Topographic change during deformation is a significant phenomenon for woven composites. Until

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now, it has been challenging to obtain high-quality experimental results with global displacements

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obscuring local weave changes. Now, however, application of the surface compensation method can

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capture the distinctive Zchange topography for the woven composites. As illustrated in Figure 5: twill

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weaves (G/PP and SRPP) are characterised by continuous valleys 45-degrees inclined to the woven

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yarns, plain weaves (CF/PEEK) have a regular chequerboard pattern, and satin weaves (A/PEI) have

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distinctive peaks (in this case pairs alternating in direction between 45 and -45 degrees).

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The mechanism driving the change in the woven topography is the straightening of the yarns in

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the direction of tensile load (Y-direction). This straightening pushes up the crossing transverse fibre

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bundles causing the comparatively flat surface to have increasingly significant local height variations.

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This interchange of waviness in the yarns is termed crimp interchange and is linked to the weave pattern

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[37]. Height changes in topography for different materials vary significantly. Despite comparable

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thickness, the ultimate height change for CF/PEEK is 0.019 mm (SD = 0.003) whilst G/PP(Weft

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loading) is 0.62 mm (SD = 0.05) immediately prior to failure. This can be attributed to both the

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weave architecture and constituent materials. The multiple layers of CF/PEEK reduce the overall out-

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of-plane motion, and the stiffer carbon fibres result in lower global strain reducing crimp interchange.

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Accurate measurement of the surface height allows for better design choices for composites where good

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surface finish after deformation is essential. A growing application for this is the use of formed woven

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A/PEI SRPP

Principal strain 1 (%)

G/PP(Weft)

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Zchange (mm)

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Surface topography

Figure 5: Topography and strain results prior to failure. Surface topography (left) and face view Zchange (centre) show distinctive patterns closely linked to major principal strain 1 (right). G/PP was tested in each directions as the weave has varying waviness in perpendicular direction leading to differences in topography and strain. Orientation: X horizontal, Y vertical.

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composite sheets for aircraft interiors requiring an excellent surface finish with minimal postprocessing

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[38].

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5.2. Strain concentrations

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While the locations of strain concentrations in woven composites have previously been examined

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[14–16], their association with topography has been difficult to measure experimentally. Now, however,

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the relationship between higher principal strain (1 ) and peaks in topography where the transverse

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fibre bundles are pushed upwards is illustrated (Figure 5). In the case of the satin weave (A/PEI), the

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sharp peaks cause high strain in the matrix rich region at the edge of the transverse fibre bundle as it

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is pushed upwards. For the plain weave (CF/PEEK), the highest strains are more distributed due to

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smaller topographic change but still concentrated in the areas of the surface transverse fibre bundles.

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In the case of the twill weaves (SRPP and G/PP), the higher strains are distributed by cracking,

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running along the transverse yarn or tape. For G/PP, the consolidation of the yarn is not consistent,

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with regions of varying fibre volume fraction. Regions with lower volume fraction have lower transverse

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yarn stiffness and consequently experience higher strain and eventually cracking. For SRPP higher

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overall strain and local differences in the polymer consolidated properties similarly lead to varying

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strain. Therefore, topography, along with material defects, is closely linked to strain concentrations

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and needs to be considered when interpreting strain contours of woven composites.

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5.3. Fibre waviness disparity

An especially useful application of these new topography techniques is for analysing composites

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with a disproportionate amount of fibre bundle waviness observable in the two weave directions. The

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G/PP has such a disparity which significantly influences its topography, mechanical properties and

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failure behaviour. These phenomena in regards to fibre bundle waviness disparity, causing variations in

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damage onset, failure load and final elongation have been previously observed in woven composites and

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are an essential consideration for manufacture [39–41]. However, previously, it has not been possible

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to measure the changes in topography evolution, linked with these differences. These new methods of

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topographic characterisation are well suited to assess these changes. The G/PP composites were consolidated with one direction tensioned (Warp) and hence had

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straighter yarns compared to greater waviness in the perpendicular direction (Weft). The compos-

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ite was manufactured from woven commingled glass and PP fibres which were consolidated with a

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hot press. Tests were conducted by applying load in both the warp and weft directions with these

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samples denoted G/PP(Warp) and G/PP(Weft). The reduced crimp in the warp direction of load for

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G/PP composites corresponds to shallow topography maximum height change of 0.43mm (SD = 0.08),

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compared to loading the weft direction with 0.62 mm (SD = 0.05). Further warp loading produces less

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0.8 G/PP (Warp) G/PP (Weft)

G/PP (Warp) G/PP (Weft)

0.6

Height (mm)

Load (N)

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6000 4000

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2000 0

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1

2

3

4

5

6

0

Elongation (mm) (a)

1

2

3

4

5

6

Elongation (mm) (b)

Figure 6: Evolution of topography and load for G/PP with distinct behaviour when loaded in warp and weft directions. (a) Load elongation response (error bars for maximum load), and (b) Topographic height between Zchange maximum and minimum over time (error bars for maximum height).

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average global strain, 4.6% (SD = 0.4) compared to weft loading 6.0% (SD = 1.0). The weft loading

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strain at failure has a more significant component of fibre straightening in addition to strain of the

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fibres themselves.

In addition to differences in global strain, differences are present in mechanical load (Figure 6a).

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Greater crimp and additional in-plane fibre waviness for weft fibre bundles require more severe yarn

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motion (larger displacement) and hence larger strain to straighten. This motion causes earlier onset of

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damage and delamination between the longitudinal and transverse yarns, which concurs with previous

272

studies [39, 40]. The delamination also results in fibre damage reducing composite stiffness and leading

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to a lower failure load in the weft case, 4843 N (SD = 172) compared to 8518 N (SD = 889) in the warp

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case. The load elongation curve for the G/PP(Warp) experiences non-linearity and divergence from

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the G/PP(Weft) curve around 2 kN (1 mm elongation) corresponding to audible damage far earlier

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than that for G/PP(Warp). The initial similarity between the curves is due to the straighter warp

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fibre bundles still having some crimp which like the weft can straighten. Immediately prior to failure,

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G/PP(Weft) samples experience a flattening of the load due to progressive damage accumulation in

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contrast to the relative linearity and catastrophic failure in the G/PP(Warp).

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268

Along with the load elongation response, the evolution of topography provides insight into the

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materials’ response to deformation and eventual failure (Figure 6b). G/PP(Warp) has a distinct change

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in height evolution trend. Initially, it exhibits a rapid increase in height with global strain caused by a

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reduction in crimp. However, as fibre bundles start to become straight, mechanical fibre strain becomes

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the primary contributor to global displacement. As a result, height increase becomes less prominent

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as further straightening, pushing up transverse yarns, is no longer possible. In contrast, G/PP(Weft) 13

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exhibits a singular trend attributed to more initial crimp. Additionally, damage and weakening of

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the matrix between the longitudinal and transverse yarns mean that out-of-plane displacement is not

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as restricted as it is for G/PP(Warp). The trend is not as steep, due to in-plane fibre waviness,

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simultaneous straightening of which has a far more limited impact on out-of-plane height.

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5.4. Curvature

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Curvature provides additional topographical information at a smaller length scale relative to weave.

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The curvature results for the materials are distinctly different (Figure 7). A/PEI has high curvature

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in a concentrated region corresponding to high strain. SRPP has no discernible changes in curvature

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because, with less distinction in properties of the woven structure, there are no rapid topographical

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changes. Similarly, whilst CF/PEEK does have a curvature contour corresponding to the woven

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topography, the stiff fibres and limited out-of-plain movement serve to create a surface without sharp

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height changes and distinct features. G/PP(Warp) has curvature in distinct lines through transverse

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bundles corresponding to the high principal strain (1 ) caused by varying fibre volume fraction. For

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G/PP(Weft), curvature shows the edges of the transverse fibre bundles as they form sharp rises when

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partially debonding from the longitudinal yarns beneath.

H

(b)

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(a)

(d)

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(c)

Figure 7: Local mean curvature (H) of composites prior to failure. (a) A/PEI (b) CF/PEEK (c) G/PP(Warp) and (d) G/PP(Weft). SRPP has low local curvature hidden by noise. Orientation: X horizontal, Y vertical.

301

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The curvature method opens up several applications. In the case of G/PP(Warp), it is possible to

identify the direction and movement of individual misaligned fibre bundles. Also, the method is sensi14

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tive to sudden discontinuities of the surface, which can occur with cracking. While previous research

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had to rely on strains [42], topography provides another approach to aid in identifying the location,

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direction and quantity of cracking. Similarly, in the case of A/PEI and G/PP(Weft), curvature high-

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lights regions where there is a very sharp topographic change at the edge of the transverse bundles,

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which corresponds to strain concentrations and in the G/PP(Weft) case debonding. Both the curva-

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ture method and the surface compensation method are particularly useful for examining defects and

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monitoring damage of structures with few separate plies. For thicker structures with high ply numbers

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the techniques are a useful additional tool to examine surface phenomena in conjunction with other

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techniques such as X-ray Computed Tomography (CT) to examine internal damage.

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5.5. Finite element comparison

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FEA has been widely used to understand deformation and failure of woven composites. However,

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previous studies have been limited to strain comparisons when compared to experimental results [12–

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15, 43–45]. With accurate experimental measurements, it is possible to compare topography with a

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widely used mesoscale simulation approach (Figure 8).

SRPP

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A/PEI

G/PP

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CF/PEEK

Figure 8: Zchange (mm) for FEA mesoscale simulation. Unit cell is repeated to provide contours at a comparable scale to experimental results and show a high degree of similarity to experimental topography pattern and magnitude.

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The topological changes of the surface of experimental DIC and FEA results show similar magni-

318

tude and behaviour for the balanced composites: A/PEI, SRPP and CF/PEEK. However, comparing

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sections in the direction of tensile load (Y) highlights some variations. In the case of A/PEI (Figure 9a)

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Z change (mm)

0.02 0 -0.02

0.04

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Z change (mm)

0.04

0.02

0

-0.02

-0.04 -10

-5

0

Y (mm) (a) A/PEI

0.01 0 -0.01 -10

10

-10

-5

0

Y (mm) (c) CF/PEEK

-5

0

5

10

5

10

Y (mm)

(b) SRPP

Z change (mm)

Z change (mm)

0.02

5

5

0.2 0

-0.2

-0.4 -10

10

-5

0

Y (mm)

(d) G/PP

Figure 9: Typical sections along Y direction for weaves. Simulations and experiments show good agreement for balanced weaves but significant differences for G/PP which has the discrepancy in fibre waviness. Solid black line FEA simulation, blue square marker line DIC data, red diamond marker line perpendicular loading G/PP(Weft).

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differences are attributed to material variability; in the case of SRPP (Figure 9b) these material differ-

321

ences are further exaggerated when subjected to high strains. For CF/PEEK (Figure 9c) variations are

322

due to both a higher initial level of surface roughness and smaller topographic magnitude, increasing

323

the influence of measurement errors discussed in subsection 4.1.

Geometric differences arising from material not confroming to idealised unit cells lead to distinct

325

differences for G/PP (Figure 9d). As the simulation has balanced crimp, results fall somewhere

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between G/PP(Warp) and G/PP(Weft) in terms of overall topography. G/PP(Warp) shows a reduced

327

periodicity of the repeating element due to the closer packing of transverse yarns. This suggests that

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standard balanced architecture in unit cells is inadequate when a significant discrepancy in fibre crimp

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exists. Sections through G/PP(Weft) show sharper and larger changes at edges of the fibre bundle - a

330

square wave rather than a sinusoidal wave. These locations correspond to high principal strains (1 )

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and an indication of previously discussed damage and delamination of the bond between the transverse

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and longitudinal yarns. Therefore, topography results (Zchange ) are an effective tool in understanding

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how well FE models can predict composite behaviour during deformation. Experimental topography

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data can be used to refine crimp in mesoscale models to better capture unbalanced material architecture

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and increase accuracy of results. Hence, topography in addition to strain should be considered when

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evaluating and refining mesoscale FE models of woven composites.

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6. Conclusion

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Two methods have been developed in this work which improve experimental topography measure-

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ments. The first method relies on using a fitted surface to compensate for global sample distortion

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during deformation, while the second examines local curvature variations to find sub-weave scale fea-

341

tures. These methods have been applied to a variety of weaves (plain, twill and satin), single and

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multilayer composites with different matrices (PP, PEI, and PEEK) and fibres (carbon, glass, and

343

aramid). Results can be gathered even for small topographical changes and prove useful for evaluating

344

mesoscale finite element simulations. Results also improve understanding of composites with unbal-

345

anced crimp and its relation to mechanical properties and failure. These methods have potential for

346

application to other mechanical testing procedures beyond the tensile test. In these cases, the methods

347

may improve results by isolating local topological changes from global curvature, sample distortion or

348

movement of test fixtures. There is also significant potential in thin structures to use topographic

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characterisation for topographic defect detection and examination of failure mechanisms.

350

7. Acknowledgements

FEA simulations were undertaken with the supercomputer from the National Computational In-

352

frastructure (NCI), under the ANU Merit Allocation Scheme (ANUMAS). The first author would

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like to acknowledge the support of the Australian Government Research Training Program (RTP)

354

Scholarship.

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Appendix A. Material properties for finite element modelling

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The table provides details of the constituent matrix and fibre materials for the composites and

357

used in the finite element models. In the case of A/PEI, C/PEEK and G/PP fibre and matrix

358

are homogenised into yarn properties for TexGen simulation. For SRPP, tape properties are used

359

directly as the yarn. Laminate properties are additional information about consolidated properties

360

from manufacturer specifications.

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Property

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Table A.2: Mechanical properties of materials

Units

Matrix

A/PEI

SRPP∗

C/PEEK

G/PP∗∗

[26, 46]

[27, 43, 47]

[48–50]

[29, 51, 52]

Density (pm )

Kg/m3

1270

911

1300

911

Modulus (Em )

GP a

3.28

1.2

3.72

1.2

Poisson’s ratio (νm )

-

0.36

0.3

0.37

0.3

Fibre / Tape Density

Kg/m3

1440

920

1760

2619

E1f

GP a

112

8

230

73.1

ν12f , ν13f

-

0.35

0.4

0.25

0.22

E2f , E3f

GP a

4.14

1

40

-

ν23f

-

0.3

0.63

0.2

-

G12f , G13f

GP a

2.9

0.85

24

-

G23f

GP a

1.6

0.307

16.7

-

Average diameter

µm

12

-

7

17

Failure strain

%

2.4

-

1.5

4.8

50

-

50

35

-

4.2

67

14

650

920

1377

1458

Laminate Volume fraction (V f )

%

Modulus (E11 )

GP a g/m

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Areal Weight

2

* The SRPP properties are a product of the manufacturing method and architecture and do not originate from two different constituents ** Glass properties are considered isotropic

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New technique for measuring topographic change from deformation of woven composites Composites examined include matrices: PEEK, PEI, PP and fibres: carbon, aramid, glass Insight into strain concentrations, unbalanced architectures and defect detection

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Experimental topography is a tool to validate quality of FEA mesoscale models

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Potential application to a wide range of mechanical testing procedures using DIC

Tensile load Small motion of test fixture

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dz

✗

Zchange

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DIC points found from stochastic pattern

New Technique d2

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d2

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Zchange d1

Z

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Declaration of interests

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☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

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None

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John Holmes: Conceptualization, Investigation, Writing – Original Draft Youssef Hafiz: Writing Review & Editing Zbigniew Stachurski: Writing - Review & Editing Raj Das: Writing - Review & Editing Shankar Kalyanasundaram: Supervision, Writing - Review & Editing