Characterization and Analysis of In-Plane Shear Behavior of Glass Warp-Knitted Non-Crimp Fabrics Based on Picture Frame Method

materials

Article Characterization and Analysis of In-Plane Shear Behavior of Glass Warp-Knitted Non-Crimp Fabrics Based on Picture Frame Method

Ali Habboush 1,2,3 ID , Noor Sanbhal 4, Huiqi Shao 1,3, Jinhua Jiang 1,3,* ID and Nanliang Chen 1,3,*

1 Engineering Research Center of Technical Textiles, Ministry of Education, Donghua University, Shanghai 201620, China; [email protected] (A.H.); [email protected] (H.S.) 2 Mechanical Textile Engineering, Aleppo University, Aleppo, Syria 3 College of Textiles, Donghua University, Shanghai 201620, China 4 Department of Textile Engineering, Mehran University of Engineering and Technology Jamshoro, Sindh 76062, Pakistan; [email protected] * Correspondence: [email protected] (J.J.); [email protected] (N.C.); Tel.: +86-21-6779-2712 (J.J.)

Received: 20 June 2018; Accepted: 22 August 2018; Published: 28 August 2018

Abstract: Glass warp-knitted fabrics have been widely used as complex structural reinforcements in composites, such as wind turbine blades, boats, vehicles, etc. Understanding the mechanical behavior and formability of these textiles is very necessary for the simulation of forming processes before manufacturing. In this paper, the shear deformation mechanics of glass warp-knitted non-crimp fabrics (WKNCF) were experimentally investigated based on a picture frame testing apparatus equipped to a universal testing machine. Three commercially available fabrics of WKNCFs were tested for four cycles by the picture frame method. The aim was to characterize and compare the shear behavior of relatively high areal density fabrics during preform processing for composites. The energy normalization theory was used to obtain the normalized shear force from the testing machine data; then, the shear stress against the shear angle was ﬁtted by cubic polynomial regression equations. The results achieved from the equations demonstrated that the in-plane shear rigidity modulus was associated with the shear angle. The effect of the shearing cycles and stitching pattern on shear resistance was also analyzed.

Keywords: glass fabrics; warp knitting; in-plane shear rigidity; picture frame test; tricot and chain stitches

1. Introduction Recently, increasing importance has been placed on composites and their promising future, according to recent market shares and many predictions [1,2]. The attractive advantage is not just their unique combination of strength and light weight [3], it is also based on the plentiful options for reinforcement and matrix [4]. During the forming process, the textile preforms (whether they are wet or dry) undergo compound in-plane and out-of-plane deformations. Better understanding the mechanical behavior, especially for the relatively new fabrics, can help in many applications, particularly for the forming simulation [5]. There are many deformation modes that can occur in the fabric in the draping process, and the entire deformation can be one or any combination of these modes [6]. Consequently, several tests are required to characterize all of those deformation mechanisms. The most signiﬁcant mode of deformation is the in-plane shear through the fabric during draping it over double-curvature surfaces [7], and wrinkling is one of the extreme cases during the fabric formation [8]. However, there are different methods to characterize fabric shear resistance, although there is not yet a standard

Materials 2018, 11, 1550; doi:10.3390/ma11091550 www.mdpi.com/journal/materials Materials 2018, 11, 1550 2 of 18 one [9]. The main sources of shear resistance are the in-plane sheer between yarns and the lateral yarn compression [10,11].

1.1. Picture Frame (PF) Test Picture frame (PF) or (trellis shear frame) is a popular apparatus that is essentially adopted to characterize the in-plane shear behavior of textile fabrics [5], especially for dry fabrics and preforms, to produce composites [12–19]. By this simple method of performing testing, pure shear is triggered by the kinematics of the frame [16], which provides reasonably repeatable results if it is carefully implemented, and produces valuable experimental data for analytical and numerical research on two-dimensional (2D) woven fabrics [9], three-dimensional (3D) woven fabrics [12,20], 2D warp-knitted fabrics [15], and 3D spacer knitted fabrics [14]. Moreover, it can be used for unidirectional non-crimp fabrics (UD-NCFs) [16] as well as biaxial non-crimp fabrics (NCFs) [19]. Until now, there has not yet been a standard testing method using the picture frame; there is just a benchmarking effort on the material testing of woven composites fabrics. This effort has proven that the normalization results obtained from this method could be compared to other research results, even if they use different samples and frame sizes [9]. There are three normalization methods reported in the literature: normalizing data by frame length, fabric area, and the energy method. The latter one was proposed by Harrison et al. [21] and developed by Peng et al. [22]. The energy method for normalization has been used because it is the best method for normalizing the shear data of picture frame test to date [9,19]. Lomov et al. demonstrated that the first shear cycle diagrams showed irregular behavior and evidence of tension in the fibers in the frame [23]. Nonetheless, from the second cycle, the sample is mechanically conditioned [22], and the sample behavior becomes much more stable because the fibers were realigned in the frame [19]. Since there is a small difference in the measured force between the second and third cycle, this can significantly improve the repeatability of the test results [9].

1.2. Warp Knitted Non-Crimp Fabrics (WKNCFs) Some of the key advantages of knitted fabrics for composite reinforcement over woven ones are: the improvement of fabric handling and matrix injection during composite processing [4], the acceptable processability of high-performance ﬁbers [24], the faster manufacturing of knitted fabrics for reinforcements [25] and controlled anisotropy (capability of in laying yarns in the preferential angle) [4,26]. Non-crimp fabrics can be produced by different techniques [27], but the warp-knitting technique is the most ﬂexible and versatile. WKNCFs have a wide range of areal densities from light to quite heavy fabrics with any staking sequence desired to the application [28]. The essential difference in fabric architecture between NCFs and woven materials makes defect formation mechanisms rather different due to the existence of stitching yarn [10]. So, their behavior should be deeply investigated. In-plane shear is the change of angle between yarns, and is also known as trellising shear [29]. Woven fabrics have been investigated in many studies [9,11,12,17,21,29,30], as have the relatively light carbon NCFs [5,10,16,19], but glass WKNCFs need much more attention for a deeper understanding of their shear behavior, especially with relatively heavy areal densities. Thus, to our knowledge, no work has been done to investigate heavy glass fabrics of about 1200 g/m2 using the picture frame. The objective of this work was to characterize and analyze the in-plane shear behavior of relatively heavy areal density glass WKNCF fabrics based on a picture frame experiment. The in-plane shear rigidity moduli of fabrics were determined for four shearing cycles. For this purpose, a picture frame apparatus was set up, and three types of different glass WKNCFs were tested. The effect of the stitching pattern on the shear deformation mechanism was also observed. Materials 2018, 11, 1550 3 of 18 Materials 2018, 6, 20 FOR PEER REVIEW 3 of 18

2.2. Materials Materials and and Methods Methods

2.1.2.1. Materials Materials ® GlassGlass warp-knitted warp-knitted non-crimp non-crimp fabrics fabrics (glass-WKNCFs) (glass-WKNCFs) from from PGTEX PGTEX® companycompany (Changzhou, (Changzhou, China;China; product product codes codes TM-L1250-7, E-LT1100-7,E-LT1100-7, and and E-DB1200-6) E-DB1200-6) were were used used for for the the experiments experiments in thisin 2 thisstudy. study. Fabrics Fabrics with with heavy heavy areal areal densities densities (about (about 1200 1200 g/m g/m) and2) and typical typical stitching stitching patterns patterns (tricot (tricot for forUD UD (unidirectional) (unidirectional) and and LT (longitudinal-transverse)LT (longitudinal-transverse) and and chain chain stitching stitching for DBfor (double-bias))DB (double-bias)) were werecharacterized characterized here. here. The photographsThe photographs of NCF of NCF fabrics fabrics on both on both faces faces are presented are presented in Figure in Figure1. 1.

® FigureFigure 1. 1. PGTEXPGTEX® glassglass warp-knitted warp-knitted non-crimp non-crimp fabrics fabrics (WKNCFs) (WKNCFs) architecture: architecture: ( (aa)) technical technical face; face; (b) (btechnical) technical back back (colored (colored ﬁgure figure in thein the web web version version of thisof this article). article).

TheThe fabrics fabrics were were made made from from more more than than one one set set of of yarns. yarns. Each Each yarn yarn set set (longitudinal, (longitudinal, transverse, transverse, andand bias bias directions) directions) was was approximately approximately straight straight in its in layer its layer in the in fabric the fabric plane. plane. The stitching The stitching yarn with yarn smallerwith smaller linear lineardensity density connected connected the layers the throug layersh through the fabric the thickness fabric thickness and held and adjacent held adjacent layers together.layers together. The other The fabric other fabricdetails details were werelisted listed in Table in Table 1, and1, and the the roving roving properties properties and and fabric fabric manufacturingmanufacturing details details are are shown shown in in Appendix Appendix A.A. The The three three fabrics had had two layers with different parameters,parameters, but but for for UD, the oneone onon thethe technical technical back back was was only only to to support support the the structural structural cohesion cohesion and andfacilitate facilitate the manufacturingthe manufacturing process proc [16ess], [16], and itand was it justwas aboutjust about 6% of 6% the of total the arealtotal density.areal density. The fabrics The fabricshad approximate had approximate areal densities areal densities (~10% (~10% difference difference for LT-t). for LT-t). The naming system abbreviations used by the manufacturing company for these fabrics are as following: UD denotes unidirectional,Table 1. Summary L denotes of PGTEX the® glasslongitudinal WKNCF speciﬁcations.orientation of the fabric (0°), which is the machine production direction, T stands for the transverse orientation (90°) or cross-machine ◦ ◦ ◦ ◦ ◦ direction, andSpeciﬁcation DB denotes the double-bias Unidirectional where 0 the yarnsBiaxial are at 0 a/90 specific angleBiaxial from +45 the/ −machine45 productionMaterial direction, designation which is mainly (+45°/–45°). L1250-7 According LT1100-7 to this naming system, DB1200-6 the codes UD, 1250 (1236) * 1100 (1116) * 1200 (1235) * LT, andFabric DB areal become density clear. (g/m The2) small letter “t” stands for tricot stitching, and “c” stands for chain (0◦ = 1156/90◦ = 80) (0◦ = 606/90◦ = 491) (45◦ = 601/−45◦ = 601) stitching; these were added to the original name of the fabric for easily distinguishing the stitching Stitch yarn Polyester Polyester Polyester type Linearassociated density with of stitchingeach fabric. Moreover, all of the other fabric details are listed in Table 1. The 100 100 100 fabrics’ 3D geometryyarn (D) was modeled by TexGen software (textile geometric modeler, TexGen 3.5.0) [31]. BothStitch sides pattern and (face–back) the stitching patterns Tricot-chain are shown in Figure Tricot-chain 2. Chain-Chain Stitch areal density (g/m2) 12 11 7 Material code in this paper UD-t 1 LT-t 2,3 DB-c 4 1: UD = Unidirectional; 2: L = Longitudinal; 3: T = Transverse; 4: DB = Double-Bias; t = tricot, c = chain; and *: measured areal density.

The naming system abbreviations used by the manufacturing company for these fabrics are as following: UD denotes unidirectional, L denotes the longitudinal orientation of the fabric (0◦), which is the machine production direction, T stands for the transverse orientation (90◦) or cross-machine direction, and DB denotes the double-bias where the yarns are at a speciﬁc angle from the machine production direction, which is mainly (+45◦/−45◦). According to this naming system, the codes UD,

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LT, and DB become clear. The small letter “t” stands for tricot stitching, and “c” stands for chain stitching; these were added to the original name of the fabric for easily distinguishing the stitching type associated with each fabric. Moreover, all of the other fabric details are listed in Table1. The fabrics’ 3D geometry was modeled by TexGen software (textile geometric modeler, TexGen 3.5.0) [31]. Both sides andMaterials the stitching 2018, 6, 20 patterns FOR PEER are REVIEW shown in Figure2. 4 of 18

FigureFigure 2. Three-dimensional 2. Three-dimensional (3D) (3D) geometric geometric model model of fabricof fabric structures structures by TexGenby TexGen software: software: (a) technical(a) face;technical (b) technical face; ( back;b) technical and ( cback;) the and stitching (c) the patternstitching and pattern its notationand its notation at the corner.at the corner.

® 2.2. Methods Table 1. Summary of PGTEX glass WKNCF specifications. Specification Unidirectional 0° Biaxial 0°/90° Biaxial +45°/−45° Studying the deformation mechanisms of fabrics, especially shear behavior by picture frame, Material designation L1250-7 LT1100-7 DB1200-6 needs a lot of attention in order to be1250 done (1236) carefully. * For1100 all (1116) of the * material1200 characterization (1235) * tests Fabric areal density (g/m2) described in the following sections,(0° a= universal1156/90° = 80) testing (0° machine = 606/90° (WDW-20,= 491) (45° Shanghai = 601/−45° Hualong = 601) Test Instrument Co.,Stitch Ltd., yarn Shanghai, China) Polyester provided by the Engineering Polyester Research Polyester Center of Technical TextilesLinear was used.density The of stitching frame was mounted in a load cell (WDW-20, Shanghai Hualong Test Instrument 100 100 100 Co., Ltd., Shanghai,yarn ( China)D) for measuring the ampliﬁer frame displacement force, as shown in Figure3. All of theStitch tests pattern were (face–back) performed at room Tricot-chain temperature and a Tricot-chain constant crosshead displacement Chain-Chain rate of 10 mm/min.Stitch Hence, areal density the strain (g/m rate2) of fabric12 shearing increased as 11the ampliﬁcation factor 7 of the device 1 2,3 4 increased.Material The code specimens in this paper of each type of UD-t fabric were tested inLT-t the frame for four cycles.DB-c At least three 1: UD = Unidirectional; 2: L = Longitudinal; 3: T = Transverse; 4: DB = Double-Bias; t = tricot, c = chain; repeats should be conducted under identical conditions, according to Harrison [32], and the average and *: measured areal density. valuesMaterials of three 2018 repeats, 6, 20 FORfor PEER each REVIEW fabric were presented in the results. 5 of 18 2.2. Methods Studying the deformation mechanisms of fabrics, especially shear behavior by picture frame, needs a lot of attention in order to be done carefully. For all of the material characterization tests described in the following sections, a universal testing machine (WDW-20, Shanghai Hualong Test Instrument Co., Ltd., Shanghai, China) provided by the Engineering Research Center of Technical Textiles was used. The frame was mounted in a load cell (WDW-20, Shanghai Hualong Test Instrument Co., Ltd., Shanghai, China) for measuring the amplifier frame displacement force, as shown in Figure 3. All of the tests were performed at room temperature and a constant crosshead displacement rate of 10 mm/min. Hence, the strain rate of fabric shearing increased as the amplification factor of the device increased. The specimens of each type of fabric were tested in the frame for four cycles. At least three repeats should be conducted under identical conditions, according to Harrison [32], and the average values of three repeats for each fabric were presented in the results. The manufactured picture frame(a) for this study was used( bto) test in-plane shear behavior on cruciform fabric samples, where the length of the fabric was less than that of the frame (Lfabric < Lframe) Figure 3. The picture frame: (a) the manufactured frame with the clamps and connectors; (b) a inFigure order3. to Theavoid picture corner frame: buckling. (a) The the manufactureddesign of the frame frame apparatus with the resembled clamps and that connectors; used by UML (b) a SOLIDWORKS 3D design. (UniversitySOLIDWORKS of Massachusetts 3D design. Lowell, Lowell, MA, USA,) [14], but with a slight difference in dimensions.The slotted The designguide (sliding details andlink) dimens had twoions functions: are illustrated the first in one Figure was 3. connecting one corner of the small amplifier frame to the crosshead of the tensile testing machine (WDW-20, Shanghai Hualong Test Instrument Co., Ltd., Shanghai, China), and the second one was to limit the fabric frame motion between the starting position and final deformed position i.e., between 0° and 60° (1.05 rad) of shear angle. This frame was connected to the crossheads of the tensile machine by two connectors. In addition, an extra two connectors were manufactured in order to use the same frame to other tensile testing machines. The amplifier itself would be helpful if the crosshead displacement and/or the crosshead velocity of the testing machine is limited. From the illustrations in Figure 4, when the amplifier frame is deformed from the starting position by δa displacement due to applying the tensile force , the fabric frame is deformed by αδa, where α is the device amplification factor; it can be calculated by the following equation:

256 mm (1) α= = =4 64 mm

(a) (b) (c)

Figure 4. Schematic diagram of the frame design: starting position (a); shearing position (b); and shear angle (c).

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The manufactured picture frame for this study was used to test in-plane shear behavior on cruciform fabric samples, where the length of the fabric was less than that of the frame (Lfabric < (a) (b) Lframe) in order to avoid corner buckling. The design of the frame apparatus resembled that used by UMLFigure (University 3. Theof picture Massachusetts frame: (a) Lowell,the manufactured Lowell,MA, frame USA,) with [the14], clamps but with and a connectors; slight difference (b) a in dimensions.SOLIDWORKS The design 3D design. details and dimensions are illustrated in Figure3. The slotted guide (sliding link) had two functions: the first one was connecting one corner of theThe small slotted amplifier guide frame(sliding to link) the crossheadhad two functions: of the tensile the first testing one was machine connecting (WDW-20, one corner Shanghai of the Hualongsmall amplifier Test Instrument frame to Co.,the Ltd.,crosshead Shanghai, of the China), tensile and testing the secondmachine one (WDW-20, was to limit Shanghai the fabric Hualong frame motionTest Instrument between the Co., starting Ltd., Shanghai, position andChina), final and deformed the second position one i.e.,was between to limit the 0◦ and fabric 60◦ frame(1.05 rad)motion of shearbetween angle. the Thisstarting frame position was connected and final deformed to the crossheads position of i.e., the between tensile machine0° and 60° by (1.05 two rad) connectors. of shear Inangle. addition, This anframe extra was two connectorsconnected wereto the manufactured crossheads of in the order tensile to use machine the same by frame two toconnectors. other tensile In testingaddition, machines. an extra Thetwo amplifierconnectors itself were would manufactured be helpful in iforder the crossheadto use the same displacement frame to other and/or tensile the crossheadtesting machines. velocity ofThe the amplifier testing machine itself would is limited. be helpful if the crosshead displacement and/or the crossheadFrom the velocity illustrations of the testing in Figure machine4, when is the limited. amplifier frame is deformed from the starting position by δa Fromdisplacement the illustrations due to applying in Figure the tensile4, when force theP ,amplifier the fabric frame frame is deformeddeformed byfromαδa ,the where startingα is theposition device by amplification δa displacement factor; due it canto applying be calculated the tensile by the force following , the equation:fabric frame is deformed by αδa, where α is the device amplification factor; it can be calculated by the following equation: Lframe 256[mm] α = 256 mm= = 4(1) (1) α= La = 64[mm=4] 64 mm

(a) (b) (c)

FigureFigure 4. 4.Schematic Schematic diagram diagram of of the theframe frame design: design:starting startingposition position ( a(a);); shearing shearing position position ( b(b);); and and shear shear angleangle ( c(c).).

The power applied to the frame P is dissipated in the shearing zone. By simple kinematic analysis of the frame, shear angle γ and be given as a function of the ampliﬁer frame displacement δa by Equation (3): √ ! √ ! L 2 + δ 2 δ θ = cos−1 a a = cos−1 + a (2) 2La 2 2La √ ! π π 2 δ γ = − 2θ = − 2 cos−1 + a (3) 2 2 2 2La where a subscript notation denotes ampliﬁer. Materials 2018, 6, 20 FOR PEER REVIEW 6 of 18

Materials 2018, 6, 20 FOR PEER REVIEW 6 of 18 The power applied to the frame is dissipated in the shearing zone. By simple kinematic analysisThe powerof the frame, applied shear to theangle frame γ and be is given dissipated as a function in the ofshearing the amplifier zone. Byframe simple displacement kinematic δ a by Equation (3): analysis of the frame, shear angle γ and be given as a function of the amplifier frame displacement δa by Equation (3): √2 +δ √2 δ (2) θ = cos = cos + 2 2 2 √2 +δ √2 δ (2) θ = cos = cos + 2 2 2 π π √2 δ γ = −2θ = − 2 cos + (3) 2 2 2 2 π π √2 δ γ = −2θ = − 2 cos + (3) 2 2 2 2 Materialswhere a2018 subscript, 11, 1550 notation denotes amplifier. 6 of 18 whereFrom a subscript the free notation body diagram denotes of amplifier. the amplifier frame as shown in Figures 5 and 6a, the shear force of theFrom amplifier the free can body be calculated:diagram of the amplifier frame as shown in Figures 5 and 6a, the shear force From the free body diagram of the ampliﬁer frame as shown in Figures5 and6a, the shear force of the amplifier can be calculated: (4) of the ampliﬁer can be calculated: = 2cosθ P (4) F= = (4) where is the force measured by the load cellsa 2cos in 2the cosθ crosshead.θ wherewhere P is is thethe forceforce measuredmeasured byby thethe loadloadcell cell in in the the crosshead. crosshead.

Figure 5. Free body diagram of the amplifier shear frame. FigureFigure 5. 5. FreeFree body body diagram diagram of of th thee amplifier ampliﬁer shear shear frame. frame.

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, where is the force on joint between link and link and is the shear force applied(a) to the fabric sample by the(b )link . Then, from the free (bodyc) diagram of link , ∑ =

0: (a) (b) (c) FigureFigure 6.6. SchematicSchematic diagramdiagram ofof thethe frame:frame: ((aa)) shearingshearing positionposition atat θθ;(; (bb)) freefree bodybody diagramdiagram ofof À B;`; andand sin2θ − sin2θ =0 (6) Figure((cc)) freefree 6. bodybody Schematic diagramdiagram diagram ofof thethe linkageof linkage the frame: CBÀ. .( a) shearing position at θ; (b) free body diagram of ; and (c) free bodywhere diagram of isthe the linkage moment at. point B, is the length of link , is the shear force applied on The free body diagrams of the link fabric frame and are shown in Figure 6b. The hinge The free bodythe amplifier diagrams offrame the linkfrom fabric the tensile frameÀ machine,B` and CBÀ and are θ shown is the inangle Figure between6b. The link hinge À to the vertical is free to move. From geometrical symmetry, it can be determined that the force applied on joint is freeThe to free move. bodydirection. From diagrams geometrical of the link symmetry, fabric frame it can be determinedand are that shown the forcein Figure applied 6b. The on jointhingeB` isfrom free linksto move.` ` Fromand` geometrical is zero. Therefore, symmetry, by it a canstatic be anal determinedysis using that the the free force body applied diagram on of joint link` from links CB and ÀSolvingB is zero. Equation Therefore, (6) for by a static , and analysisaccording using to Equation the free (1) body by diagramincluding of the link amplification ÀB, factor: from, it can links be concluded and that: is zero. Therefore, by a static analysis using the free body diagram of link it can be concluded that: , it can be concluded that: = = (7) Fshear== (5)(5) α `= (5) where is the forceBy on substituting joint À between in Equation link ÀB (4), and the link net CBÀ, shear and forceFshear appliedis the on shear the forcefabric applied can be toobtained by: the fabric sample by the link ÀB.` Then, from the free body diagram of link CBÀ, ∑ MB = 0: − (8) = 2 α cosθ Lframe sin(2θ) − FsaLa sin(2θ) = 0 (6) Since the fabric sample is crucified, the sheared region by frame is square (180 × 180 mm2) with where MB is thefour-sided moment atarms point connecting B, Lframe is it the to the length clamping of link Aareas` B,` Fsa inis the the frame. shear forceThe 2D applied geometrical on the details of the ampliﬁer frameframe from are the illustrated tensile machine, in Figure and 4.θ isThe the kinematics angle between of the link testA` leadsB` tothe to a vertical perfect direction. pure shear zone in the Solving Equationfabric sample, (6) for assuming, and according that the yarns to Equation are non-extensible, (1) by including and there the ampliﬁcationis no slippage factor:within the sample [6]. The two principal orientations of the fibers in the sample are connected to the clamping areas of F L F the frame, so that the frame can= besa useda = tosa characterize only unidirectional and biaxial(7) fabrics, not L α triaxial or quadriaxial fabrics. frame

2.3. Test Setups The fabric samples were fixed in the frame under zero tension, because zero pre-tension eliminated the tension–shear coupling and gave the most accurate response [33]. The fabric samples’ orientation in relation to the fabric frame sides was illustrated in Figure 7. Since the fabric specimens with the tricot stitch pattern (LT) were symmetrical in shearing behavior, there was no difference in shearing behavior related to the rovings orientation inside the frame (SS = stitch-shear [19]). However, this case was not the same for the DB fabric due to the chain stitch pattern; the shearing was asymmetrical according to the chain stitch orientation in relation to the shearing direction. On one shearing direction, the stitches were under compression (SC = stitch- compression [19]) during the shear cycle, whereas in the other shearing direction, the stitches suffered from tension (ST = stitch-tension [19]). So, that DB chain stitch was tested in two directions separately. One set of samples was tested in the stitch-compression direction (SC), and the other set was tested in the stitch-tension direction, as shown in Figure 7.

Figure 7. Schematic diagrams of fabric samples’ arrangement inside the frame: (a) technical face; (b) technical back. SS = stitch-shear, SC = stitch-compression, ST = stitch-tension.

Materials 2018, 6, 20 FOR PEER REVIEW 7 of 18 where is the force on joint between link and link , and is the shear force applied to the fabric sample by the link . Then, from the free body diagram of link , ∑ = 0:

sin2θ − sin2θ =0 (6) where is the moment at point B, is the length of link , is the shear force applied on the amplifier frame from the tensile machine, and θ is the angle between link to the vertical direction. Materials 2018, 11, 1550 7 of 18 Solving Equation (6) for , and according to Equation (1) by including the amplification factor:

(7) By substituting in Equation (4), the net= shear force= applied on the fabric can be obtained by: α

By substituting in Equation (4), the net shearP force− appliedPempty on the fabric can be obtained by: F = load (8) shear 2α cos θ − (8) = Since the fabric sample is cruciﬁed, the sheared2 α cos regionθ by frame is square (180 × 180 mm2) with four-sidedSince the arms fabric connecting sample is it crucified, to the clamping the shea areasred region in the by frame. frame The is 2Dsquare geometrical (180 × 180 details mm2) ofwith the four-sidedframe are arms illustrated connecting in Figure it to4 .the The clamping kinematics areas of in the the test frame. leads The to 2D a perfect geometrical pure sheardetails zone of the in framethe fabric are illustrated sample, assuming in Figure that 4. The the kinematics yarns are non-extensible,of the test leads andto a thereperfect is pure no slippage shear zone within in the the fabricsample sample, [6]. assuming that the yarns are non-extensible, and there is no slippage within the sample [6]. TheThe two two principal principal orientations orientations of of the the fibers ﬁbers in inth thee sample sample are are connected connected to the to the clamping clamping areas areas of theof theframe, frame, so that sothat the theframe frame can canbe used be used to characterize to characterize only onlyunidirectional unidirectional and biaxial and biaxial fabrics, fabrics, not triaxialnot triaxial or quadriaxial or quadriaxial fabrics. fabrics.

2.3.2.3. Test Test Setups Setups TheThe fabric samplessamples were were ﬁxed fixed in thein framethe frame under under zero tension, zero tension, because zerobecause pre-tension zero pre-tension eliminated eliminatedthe tension–shear the tension–shear coupling and coupling gave the and most gave accurate the most response accurate [33 response]. [33]. TheThe fabric fabric samples’ samples’ orientation orientation in in relation relation to to the the fabric fabric frame frame sides sides was was illustrated illustrated in in Figure Figure 7.7. SinceSince the the fabric fabric specimens specimens with with the the tricot tricot stitch stitch pattern pattern (LT) (LT) were were symmetrical symmetrical in in shearing shearing behavior, behavior, therethere was was no no difference difference in in sheari shearingng behavior behavior related related to to the the rovings rovings orientation orientation inside inside the the frame frame (SS(SS = = stitch-shear stitch-shear [19]). [19]). However, However, this this case case was was not notthe same the same for the for DB the fabric DB fabric due to due the tochain the stitch chain pattern;stitch pattern; the shearing the shearing was asymmetrical was asymmetrical according according to the chain to the stitch chain orientation stitch orientation in relation in relation to the shearingto the shearing direction. direction. On one Onsheari oneng shearing direction, direction, the stitches the stitcheswere under were compression under compression (SC = stitch- (SC = compressionstitch-compression [19]) during [19]) the during shear the cycle, shear whereas cycle, whereas in the other in the shearing other shearingdirection, direction, the stitches the suffered stitches fromsuffered tension from (ST tension = stitch-tension (ST = stitch-tension [19]). So, that [19 DB]). So, chain that stitch DB chainwas tested stitch in was two tested directions in two separately. directions Oneseparately. set of samples One set was of samples tested in was the tested stitch-compres in the stitch-compressionsion direction (SC), direction and the (SC), other and set the was other tested set inwas the tested stitch-tension in the stitch-tension direction, as direction, shown in as Figure shown 7. in Figure7.

FigureFigure 7. 7. SchematicSchematic diagrams diagrams of of fabric fabric samples’ samples’ arrangement arrangement inside inside the the frame: frame: (a (a) )technical technical face; face; (b (b) ) technicaltechnical back. back. SS SS = = stitch-shear, stitch-shear, SC SC = = st stitch-compression,itch-compression, ST ST = = stitch-tension. stitch-tension.

Special attention should be taken to make sure that the fiber yarns were orientated properly to the edges. Any small misalignment will produce tensile or compressive forces in the fiber directions, and as a consequence, a large scatter in the measured force readings will appear [21]. However, the first shear cycle for fabrics showed extremely irregular behavior and evidence of tension in the fibers in the frame [19]; this type of behavior was labeled in [19,34] as ‘bad tests’, and normally, such tests were discarded from the data processing. In addition, when repeating the test for the same fabric, we came Materials 2018, 6, 20 FOR PEER REVIEW 8 of 18

Special attention should be taken to make sure that the fiber yarns were orientated properly to the edges. Any small misalignment will produce tensile or compressive forces in the fiber directions, and as a consequence, a large scatter in the measured force readings will appear [21]. However, the first shear cycle for fabrics showed extremely irregular behavior and evidence of tension in the fibers Materials 2018, 11, 1550 8 of 18 in the frame [19]; this type of behavior was labeled in [19,34] as ‘bad tests’, and normally, such tests were discarded from the data processing. In addition, when repeating the test for the same fabric, we upcame with up some with extremesome extreme irregular irregular cases from cases the from general the general trend, which trend, were which not were included not included in the analysis in the inanalysis this paper. in this paper.

2.4. Testing Protocol (Data(Data Processing,Processing, Normalization,Normalization, andand Fitting)Fitting) In the beginning, a piece of fabric was cut from the roll carefully, andand thethe markingmarking lines were drawn by a metallic ink marker pen (suitable for glassglass ﬁbers).fibers). The cutting of samples was done by “electric“electric scissor”scissor” (shown(shown in FigureFigure8 8)) toto easeease thethe cutting cutting process,process, preventprevent thethe normalnormal problemsproblems ofof using ordinaryordinary scissors, scissors, such such as ﬁberas fiber slippage slippage and local and pull-out, local pull-out, and consequently and consequently reduce preparation reduce misalignmentspreparation misalignments and increase and test increase reproducibility. test reproducibility.

Figure 8. A sample of UD-t after cutting by “e-scissor” with the marking lines.

Firstly, the frame was tested when it was empty, and the displacement-force data were recorded. Firstly, the frame was tested when it was empty, and the displacement-force data were recorded. Then, the fabric samples were fixed in the frame with zero tension, and the displacement-force data for Then, the fabric samples were ﬁxed in the frame with zero tension, and the displacement-force data for the frame and fabric together were recorded. Then, the net shear force can be calculated by Equation (8) the frame and fabric together were recorded. Then, the net shear force can be calculated by Equation above. (8) above. However, this force cannot be directly compared to the results from the other picture frame However, this force cannot be directly compared to the results from the other picture frame arrangements or to the results from the other shear behavior characterization methods (similar to arrangements or to the results from the other shear behavior characterization methods (similar to UBE UBE (uniaxial bias extension). However, the benchmark effort [9] referred to the capability of (uniaxial bias extension). However, the benchmark effort [9] referred to the capability of comparing comparing different picture frame results by using a normalization method. According to the different picture frame results by using a normalization method. According to the researchers [21,22], researchers [21,22], normalization of the shear force based on the energy approach was the best normalization of the shear force based on the energy approach was the best method for the picture method for the picture frame test. It had been used when the length of the fabric sample was not frame test. It had been used when the length of the fabric sample was not necessarily equal to the necessarily equal to the length of the frame, similar to the situation that we had in this study. So, the length of the frame, similar to the situation that we had in this study. So, the shear force data could be shear force data could be normalized using the following equation, which was also used by [10]: normalized using the following equation, which was also used by [10]: (9) = × L F = F ×frame (9) normalized shear L2 From this equation, the normalized shear force was a functionfabric of the frame shear angle (θ), and in orderFrom to thiscalculate equation, the shear the normalized stress, we shearsimply force divide was the a function normalized of the shear frame force shear by anglethe thickness (θ), and inof orderthe fabric: to calculate the shear stress, we simply divide the normalized shear force by the thickness of the fabric: (10) τ= F τ = normalized (10) t where t was the thickness of the fabric, assuming the fabric thickness was constant during the test [6]. The where t was the thickness of the fabric, assuming the fabric thickness was constant during the test [6]. measured thicknesses according to the ASTM D1777-2015 “Standard test method for thickness of The measured thicknesses according to the ASTM D1777-2015 “Standard test method for thickness of textile materials” [35] are given in Table 2. textile materials” [35] are given in Table2.

Materials 2018, 6, 20 FOR PEER REVIEW 9 of 18 Materials 2018, 11, 1550 9 of 18 Table 2. Fabric thicknesses.

TableFabric 2. Fabric Code thicknesses. t (mm) UD-t 1.25 FabricLT-t Code t 1.36(mm) UD-tDB-c 1.251.2 LT-t 1.36 DB-c 1.2 The cubic polynomial function was chosen; it had potential benefits within a finite element model, and its derivative can be easily calculated and implemented into a mode [11]. By fitting the shearThe stress cubic curves polynomial using function polynomial was chosen; cubic itfitting had potential from the benefits origin within point a(start finite elementfrom (0,0)), model, the andexpression its derivative of shear can bestress easily as calculateda function andof shear implemented angle can into be aobtained mode [11 [using]. By fitting fitting the in shearthis stage stress is curvesmore usingaccurate]: polynomial cubic fitting from the origin point (start from (0,0)), the expression of shear stress as a function of shear angle can be obtained [using fitting in this stage is more accurate]: τγ = +γ +γ +γ (11) 2 3 where A = 0; then, the shear modulusτ(γ G) 12= canA + beB γcalculated+ Cγ + fromDγ the derivative of the fitting equation(11) determined from the data points on the curve of the shear stress versus the shear angle; the shear whereangleA unit= 0; is then, in radians. the shear modulus G12 can be calculated from the derivative of the fitting equation determined from the data points on the curve of the shear stress versus the shear angle; the shear angle unit is in radians. γ =+2γ +3γ (12) 2 In our measurement for WKNCFs,G12(γ) =theB + tricot2Cγ + st3itchDγ pattern for biaxial fabric could(12) be mechanicallyIn our measurement conditioned’, for WKNCFs,and it could the tricotbe experimentally stitch pattern proved for biaxial that fabric the second could be and mechanically third cycle conditioned’,were much more and it stable could in be characterizing experimentally the proved in-plane that shear the second behavior. and thirdOn the cycle other were hand, much the more chain stablestitch in pattern characterizing for biaxial the fabric in-plane could shear be behavior.conditioned On thejust otherin the hand, SC direction, the chain stitchbut not pattern in the for ST biaxialdirection, fabric because could besome conditioned stitches will just inbe thebroken SC direction, in the first but cycle. not in Still, the ST the direction, next shear because cycles some were stitchesimplemented will be brokenon the fabric in the to first investigate cycle. Still, the the change next shearin shear cycles behavior. were implemented on the fabric to investigate the change in shear behavior. 3. Experimental Results 3. ExperimentalIn this study, Results four shearing cycles were executed for each fabric sample. For each cycle, diagrams duringIn this the study, loading four phase shearing were cycles registered, were executedwhile the fordiagram each fabric during sample. the unloading For each cycle,phase diagrams(returning duringthe frame the loadingto the starting phase wereposition) registered, were not while registered. the diagram during the unloading phase (returning the frame”Bad to tests” the starting data were position) discarded were notfrom registered. the processing, which indicates the test with extremely irregular”Bad tests”behavior data and were the discardedevidence of from tension the processing,of the fibers which in the indicatesframe. The the normalized test with extremelyshear force irregularfor fabrics behavior is given and in Figure the evidence 9. of tension of the fibers in the frame. The normalized shear force for fabrics is given in Figure9.

(a) (b)

Figure 9. Cont.

Materials 2018, 6, 20 FOR PEER REVIEW 10 of 18 Materials 2018,, 611, 20, 1550 FOR PEER REVIEW 1010 of of 18 18

(c) (d) (c) (d) Figure 9. Normalized shear force: (a) UD-t in SS = stitch-shear; (b) LT-t in SS = stitch-shear; (c) DB-c Figure 9. Normalized shear force:force: ((aa)) UD-tUD-t inin SS SS = = stitch-shear; stitch-shear; ( b(b)) LT-t LT-t in in SS SS = stitch-shear;= stitch-shear; (c )(c DB-c) DB-c in in SC = stitch-compression; andd (d) DB-c in ST = stitch-tension. Error bars indicate standard deviation inSC SC = stitch-compression;= stitch-compression; and and ( )(d DB-c) DB-c in in ST ST = stitch-tension.= stitch-tension. Error Error bars bars indicate indicate standard standard deviation deviation in threein three tests. tests. in three tests. Considering the thickness of fabric samples, the shear stress curves against the shear angle Considering thethe thicknessthickness of of fabric fabric samples, samples, the the shear shear stress stress curves curves against against the shear the angleshear wouldangle would be obtained. By fitting these curves using cubic polynomial regression, the values of Equations wouldbe obtained. be obtained By ﬁtting. By fitting these curvesthese curves using using cubic cubic polynomial polynomial regression, regression, the values the values of Equations of Equations (11) (11) and (12) would be obtained. The details were shown in Appendix B. (11)and and (12) (12) would would be obtained. be obtained. The The details details were were shown shown in Appendix in AppendixB. B. Then, by the derivation of these curves, the shear modulus G12 has been determined. The curves Then, by the derivation of these curves, the shear modulus G 12 hashas been been determined. determined. The The curves curves were illustrated in Figure 10, and the values of the equation coefficients12 are provided in Appendix B. were illustrated in Figure 10,10, and the values of the equation coefficients coefﬁcients are provided in Appendix B B..

(a) (b) (a) (b)

(c) (d) (c) (d) Figure 10. In-plane shear rigidity modulus: (a) UD-t in SS = stitch-shear; (b) LT-t in SS = stitch-shear; Figure 10. In-plane shear rigidity modulus: (a) UD-t in SS = stitch-shear; (b) LT-t in SS = stitch-shear; Figure(c) DB-c 10. inIn-plane SC = stitch-compression; shear rigidity modulus: (d) DB-c (a )in UD-t ST = in stitch-tension. SS = stitch-shear; (b) LT-t in SS = stitch-shear; (c) DB-c in SC = stitch-compression; stitch-compression; ( (d)) DB-c DB-c in in ST ST = stitch-tension. stitch-tension.

Materials 2018, 11, 1550 11 of 18 MaterialsMaterials 2018 2018, ,6 6, ,20 20 FOR FOR PEER PEER REVIEW REVIEW 1111 of of 18 18

FromFrom thethe curvescurves inin FigureFigure 1010,10,, forfor thethe tricottricot pattern,pattepattern,rn, thethe fabricfabric shearshear rigidityrigidity generallygenerally increasedincreased withwith thethe shear shear angleangle andand hadhad a a similar similar trend trend inin all all of of the the cycles. cycles. Besides, Besides,Besides, for for th thethee chain chainchain stitching stitchingstitching pattern patternpattern underunder compression, compression, the the the shear shear shear modulus modulus modulus had had had the the the same same same tren tren trenddd as as the asthe thetricot tricot tricot pattern pattern pattern in in the the in first thefirst ﬁrstcycle,cycle, cycle, and and decreasedanddecreased decreased inin thethe in thefollowingfollowing following cycles.cycles. cycles. However,However, However, forfor for chainchain chain stitchingstitching stitching inin in tension,tension, tension, thethe shear shearshear modulusmodulus increasedincreased andand thenthen decreaseddecreased rapidlyrapidly rapidly afterafter after somesome some stitchesstitches stitches werewere were broken.broken. broken.

4.4. Discussion Discussion

4.1.4.1. Shear Shear Deformation Deformation Mechanics Mechanics an andandd Effect Effect of of the the Shearing Shearing CyclesCycles

4.1.1.4.1.1. Unidirectional Unidirectional with with Tricot Tricot StitchStitch FabricFabric inin in StitchStitch Stitch ShearShear Shear (UD-t(UD-t (UD-t inin in SS)SS) SS) FigureFigure9 9aa9a presented presentedpresented the thethe curves curvescurves of the ofof normalizedthethe normalnormalized shearized shearshear force (expressedforceforce (expressed(expressed in units inin of units N/mm)units ofof againstN/mm)N/mm) againsttheagainst shear the the angle shear shear (in angle angle radian) (in (in forradian)radian) UD-t for for fabric. UD-t UD-t The fabric. fabric. chart The The of chart thechart first of of the shearthe first first cycle shear shear showed cycle cycle showed theshowed same the the trend same same as trendthetrend next as as the shearingthe next next shearing shearing cycles, which cycles, cycles, means which which that means means there that that was there there no was evidencewas no no evidence evidence of fiber of of tension fiber fiber tension tension inside theinside inside frame; the the frame;thereby,frame; thereby,thereby, zero pre-tension zerozero pre-tensionpre-tension was achieved. waswas achieved.achieved. The shear TheThe behavior shearshear behavior inbehavior the second, inin thethe third, second,second, and third, fourththird, andand cycles fourthfourth was cyclesalmostcycles was was the almost samealmost due the the tosame same the due smalldue to to differencesthe the small small differenc differenc in the sheareses in in forcethe the shear shear among force force the among among cycles. the the Therefore, cycles. cycles. Therefore, Therefore, the tricot thepatternthe tricot tricot induced pattern pattern the induced induced same effectsthe the same same on effects theeffects shear on on mechanismsthethe shear shear mechanisms mechanisms by different by bycycles. different different cycles. cycles. Essentially,Essentially, the the graphs graphs startedstarted fromfrom from thethe the origin,origin, origin, butbut but generally,generally, generally, thethe the WKNCFWKNCF WKNCF fabricsfabrics fabrics werewere were easyeasy easy toto deform.todeform. deform. At At the Atthe first thefirst firststage stage stage of of shearing shearing of shearing (~0.17 (~0.17 (~0.17 rad), rad), th rad),thee curves curves the curves were were near near were to to nearthe the zero, zero, to the because because zero, becausethe the applied applied the forceappliedforce waswas force justjust was makingmaking just rovingsmakingrovings torovingsto bebe closercloser to be totocloser eaeachch other. toother. each Consequently,Consequently, other. Consequently, thethe spacesspaces the betweenbetween spaces between rovingsrovings wererovingswere diminishing diminishing were diminishing without without any any without lateral lateral anycompaction. compaction. lateral compaction. Then, Then, in in the the next next Then, stage, stage, in thewhich which next starts starts stage, from from which (~0.17 (~0.17 starts rad) rad) offromof shearingshearing (~0.17 angle, rad)angle, of thethe shearing laterallateral angle, compactioncompaction the lateral betweenbetween compaction neighboringneighboring between rovingsrovings neighboring waswas arisingarising rovings graduallygradually was arising upup toto ~0.26gradually~0.26 rad.rad. After upAfter to that, ~0.26that, aa rad. rapidrapid After riserise in that,in thethe a loadload rapid resistanceresistance rise in the ofof loadthethe fabricfabric resistance samplesample of was thewas fabric observedobserved sample becausebecause was rovingsobservedrovings beganbegan because toto squeezesqueeze rovings within beganwithin tothethe squeeze layer.layer. However,However, within the thethe layer. effecteffect However, ofof thethe transversetransverse the effect roving ofroving the transverse layerlayer waswas neglected.rovingneglected. layer was neglected. FromFrom visualvisual observations,observations, betweenbetween the the starting starting and and finalfinalfinal position,position, asas shownshown inin FigureFigure 11,1111,, therethere werewere nonono wrinkles wrinkleswrinkles up upup to toto 1.05 1.051.05 rad radrad of ofof the thethe shear shearshear angle, anglangle, bute, butbut there therethere was waswas local locallocal out-of-plane out-out-of-planeof-plane buckling bucklingbuckling due duedue to the toto thelateralthe lateral lateral compaction compaction compaction in the in in shearedthethe sheared sheared region, region, region, as illustrated as as illustrated illustrated in Figure in in Figure Figure 12. 12. 12.

((aa)) ((bb))

FigureFigure 11. 11. UD-t UD-t sample sample in inin the thethe picture picturepicture frame frameframe apparatus; apparatus;apparatus; th thethee region region subjected subjected to to pure pure shear shear is is in in green. green. ((aa)) StartingStarting position;position; ((bb)) at at 1.05 1.05 rad rad shearing shearing angleangle angle (colored(colored (colored ﬁgurefigu figurere inin in thethe the webweb web versionversion version ofof of thisthis this article).article). article).

FigureFigure 12. 12. Schematic SchematicSchematic diagram diagram of of local local roving roving buckling buckling due due to to lateral lateral compaction. compaction.

4.1.2.4.1.2. Biaxial Biaxial 0°/90° 0°/90° Tricot Tricot Stitch Stitch Fabric Fabric in in Stitch Stitch Shearing Shearing (LT-t (LT-t in in SS) SS) AtAt the the initial initial stage stage of of shearing, shearing, the the normalized normalized sh shearear force force was was very very low low due due to to the the free free rotation rotation ofof rovings rovings inside inside the the tricot tricot pattern, pattern, as as a a curve curve was was shown shown in in Figure Figure 9b. 9b. Then, Then, the the shear shear force force increased increased

Materials 2018, 11, 1550 12 of 18

4.1.2. Biaxial 0◦/90◦ Tricot Stitch Fabric in Stitch Shearing (LT-t in SS) At the initial stage of shearing, the normalized shear force was very low due to the free rotation Materials 2018, 6, 20 FOR PEER REVIEW 12 of 18 of rovings inside the tricot pattern, as a curve was shown in Figure9b. Then, the shear force increased gradually as the spacing between the rovings was vanishing, and the compaction between them start to occur, causing the force to increase rapidly. However,However, inin the next shearing cycles, the fabric became easier to be sheared because of the mechanical cond conditioningitioning or or “softening” of of the the tricot tricot structure. structure. Having a similar trend of shear force by the next cycles was evidence that the zero pre-tension was achieved. Moreover, thethe valuesvalues of of the the shearing shearing force forc ine in the the following following cycles cycles were were lower lower because because of the of strainedthe strained tricot tricot pattern pattern in the in ﬁrstthe first cycle. cycle. In the comparison of shear behavior between LT-t and UD-tUD-t fabric, there were nono out-of-planeout-of-plane wrinkling, and and even even no nolocal local buckling buckling occurred occurred in LT-t in fabric LT-t until fabric the until end theof the end shearing of the test shearing (~1.05 rad), test (~1.05as in the rad), photograph as in the photograph in Figure 13. in The Figure distribution 13. The distribution of fabric weight of fabric between weight the between layers was the layersthe reason was thefor this reason difference for this differencein wrinkle information. wrinkle formation. In the LT-t In fabric, the LT-t the fabric, areal density the areal was density distributed was distributed between betweenthe longitudinal the longitudinal and transverse and transverse layer nearly layer in nearly an equal in an manner, equal manner, but the butweight the weightin the UD-t in the fabric UD-t fabricwas mostly was mostly in just in one just layer. one layer. Therefore, Therefore, the LT-t the LT-tstructure structure had hadmore more spaces spaces between between the therovings rovings in ineach each layer. layer. Consequently, Consequently, it was it waseasier easier to be to defo bermed deformed by shearing, by shearing, which which was apparent was apparent in the curves in the curvesof Figure of 9a,b. Figure 9a,b.

Figure 13. LT-tLT-t in the deformed position sample (1.05 rad shearing angle).

4.1.3. Biaxial +45°/−45° Chain Stitch Fabric in Stitch Compression (DB-c in SC) 4.1.3. Biaxial +45◦/−45◦ Chain Stitch Fabric in Stitch Compression (DB-c in SC) For biaxial chain stitch fabric +45°/−45°, the chain-stitching pattern made the fabric behavior For biaxial chain stitch fabric +45◦/−45◦, the chain-stitching pattern made the fabric behavior asymmetrical in shearing. In this case, the chain stitch would suffer from compression in one direction asymmetrical in shearing. In this case, the chain stitch would suffer from compression in one direction and from tension in the other direction. Thus, different modes of deformation were observed in the and from tension in the other direction. Thus, different modes of deformation were observed in the stitch compression direction for the DB-c fabric. The +45° and −45° rovings rotated toward the loading stitch compression direction for the DB-c fabric. The +45◦ and −45◦ rovings rotated toward the loading direction and therefore, they were forced to slide through the stitch loops. This sliding led to frictional direction and therefore, they were forced to slide through the stitch loops. This sliding led to frictional resistance between the stitches and rovings. The sliding of rovings as they rotated was the reason for resistance between the stitches and rovings. The sliding of rovings as they rotated was the reason for the low load resistance. the low load resistance. In the curve of the first cycle in Figure 9c, the normalized shear force started to rise gradually up In the curve of the ﬁrst cycle in Figure9c, the normalized shear force started to rise gradually to ~0.5 rad. The rovings became close to each other due to rotating and sliding between rovings inside up to ~0.5 rad. The rovings became close to each other due to rotating and sliding between rovings the stitches. After 0.5 rad, the lateral compaction led to a rapid increase in the shear force and the inside the stitches. After 0.5 rad, the lateral compaction led to a rapid increase in the shear force and rovings would be squeezed together within the fabric. This action would not break the stitches in the the rovings would be squeezed together within the fabric. This action would not break the stitches chains, but it was responsible for the rapid increase in the load resistance. However, in the next cycles, in the chains, but it was responsible for the rapid increase in the load resistance. However, in the there was just a slight increase in the shear force within the cycle, which means that the stitches were next cycles, there was just a slight increase in the shear force within the cycle, which means that the strained by the compressed rovings during the first cycle, and became “mechanically conditioned” stitches were strained by the compressed rovings during the ﬁrst cycle, and became “mechanically or “softer”, which have made the resistance lower in the next cycles. In addition, from visual conditioned” or “softer”, which have made the resistance lower in the next cycles. In addition, from observations, there were no wrinkles up to 1.05 rad of the shear angle, as shown in Figure 14. Only visual observations, there were no wrinkles up to 1.05 rad of the shear angle, as shown in Figure 14. small local buckling in some rovings occurred at a large deformation angle due to the restrictions of chain stitches during the compaction.

Materials 2018, 11, 1550 13 of 18

Materials 2018, 6, 20 FOR PEER REVIEW 13 of 18 Only small local buckling in some rovings occurred at a large deformation angle due to the restrictions Materialsof chain 2018 stitches, 6, 20 FOR during PEER the REVIEW compaction. 13 of 18

Figure 14. DB-c sample at a 1.05 rad shearing angle.

4.1.4. Biaxial +45°/−45° ChainFigure Stitch 14. Fabric DB-c sample in Stitch at a Tension 1.05 rad shearing (DB-c in angle.ST) A different mechanism of deformation was detected in stitch tension direction for the DB-c 4.1.4. Biaxial +45°/ +45◦/−45°−45 Chain◦ Chain Stitch Stitch Fabric Fabric in inStitch Stitch Tension Tension (DB-c (DB-c in in ST) ST) fabric; where the direction of loading made the stitches under tension, this arrangement applied very A different mechanism of deformation was detected in stitch tension direction for the DB-c high Afixation different to mechanismthe rovings. of Therefore, deformation addition was detectedal rotations in stitch were tension limited, direction and global for the out-of-plane DB-c fabric; fabric; where the direction of loading made the stitches under tension, this arrangement applied very wherewrinkling the directioncould be observed of loading at madean earlier the stitchesstage in undercomparison tension, to thisstitch arrangement compression applied (SC), as veryshown high in high fixation to the rovings. Therefore, additional rotations were limited, and global out-of-plane ﬁxationFigure 15. to Continuing the rovings. the Therefore, test would additional result in rotations more noticeable were limited, wrinkles, and global especially out-of-plane near the wrinkling center of wrinkling could be observed at an earlier stage in comparison to stitch compression (SC), as shown in couldthe sheared be observed zone. Stitch at an earliertension stage was inthe comparison reason for tothe stitch steep compression increase of the (SC), shearing as shown force, in Figure up to an15. Figure 15. Continuing the test would result in more noticeable wrinkles, especially near the center of Continuing~0.87 rad shear the test angle. would This result fast inincrease more noticeable of the shear wrinkles, force especiallycould be nearclarified the centerby tensile of the modulus sheared the sheared zone. Stitch tension was the reason for the steep increase of the shearing force, up to an zone.stitching Stitch chains tension being was several the reasontimes higher for the than steep th increasee friction of and the compaction shearing force, modulus up to of an the ~0.87 rovings rad ~0.87 rad shear angle. This fast increase of the shear force could be clarified by tensile modulus shear[19]. Then, angle. the This shear fast force increase would of the not shear be increased, force could because be clariﬁed so many by tensile stitches modulus would stitchingbe broken, chains and stitching chains being several times higher than the friction and compaction modulus of the rovings beingthere was several nothing times holding higher the than rovings the friction together and, as compactionthe curves were modulus shown ofin theFigure rovings 9d. [19]. Then, the [19]. Then, the shear force would not be increased, because so many stitches would be broken, and shearThe force first would break not of stitches be increased, under becausetension appeared so many stitchesat an ~0.5 would rad shear be broken, angle, andas illustrated there was in nothing Figure there was nothing holding the rovings together, as the curves were shown in Figure 9d. holding15a. After the that, rovings many together, local wrinkles as the curvesappeared were between shown the in Figureunbroken9d. loops, as shown in Figure 15b. The first break of stitches under tension appeared at an ~0.5 rad shear angle, as illustrated in Figure 15a. After that, many local wrinkles appeared between the unbroken loops, as shown in Figure 15b.

(a) (b)

Figure 15. DB-c( in a) ST: (a) atat ~0.5~0.5 rad; ( b) at 1.05 rad. (b)

By comparing the shearFigure force 15. DB-cbetween in ST: the(a) attwo ~0.5 dirad;rections (b) at 1.05 for rad. the same fabric, it could be The ﬁrst break of stitches under tension appeared at an ~0.5 rad shear angle, as illustrated in concluded that the shear behavior was anisotropic. This matter should be considered in establishing FigureBy 15 comparinga. After that, the manyshear localforce wrinklesbetween appearedthe two di betweenrections thefor unbrokenthe same loops,fabric, asit showncould be in a good material model for such type of fabrics in order to accurately predict their total shear behavior. concludedFigure 15b. that the shear behavior was anisotropic. This matter should be considered in establishing For the samples of UD-t, LT-t, and DB-c in SC, the in-plane shearing behavior could be analyzed a goodBy material comparing model the shearfor such force type between of fabrics the in two or directionsder to accurately for the predict same fabric, their ittotal could shear be concluded behavior. from the second cycle, since the second cycle reflected the pure in-plane shear behavior, as many that theFor shearthe samples behavior of UD-t, was anisotropic.LT-t, and DB-c This in SC, matter the in-plane should be shearing considered behavior in establishing could be analyzed a good studies considered [9,19]. However, for DB-c in ST, just the first cycle should be analyzed to frommaterial the modelsecond for cycle, such since type ofthe fabrics second in cycle order refl to accuratelyected the pure predict in-plane their total shear shear behavior, behavior. as many investigate the shear behavior in the stitch tension direction, due to the breakage of some stitches studiesFor considered the samples [9,19]. of UD-t, However, LT-t, and for DB-c DB-c in SC, in theST, in-planejust the shearing first cycle behavior should could be analyzed be analyzed to during the first cycle of shearing. investigatefrom the second the shear cycle, behavior since the in secondthe stitch cycle tension reﬂected direction, the pure due in-plane to the breakage shear behavior, of some as stitches many during the first cycle of shearing.

Materials 2018, 11, 1550 14 of 18 studies considered [9,19]. However, for DB-c in ST, just the ﬁrst cycle should be analyzed to investigate the shear behavior in the stitch tension direction, due to the breakage of some stitches during the ﬁrst cycle of shearing.

4.2. In-Plane Shear Rigidity Modulus From the mentioned procedure in Section 2.2 to determine the in-plane shear rigidity modulus expression as a function of the shear angle in radians, the following equations can be written for the ﬁrst cycle of UD-t, LT-t, DB-c-SC, and DB-c-ST, respectively:

2 G12(γ)UD = 0.23078 + 0.69608γ − 0.13284γ (13)

2 G12(γ)LT = 0.36923 − 1.54978γ + 3.26637γ (14) 2 G12(γ)BD in SC = 1.13072 − 4.38108γ + 6.28908γ (15) 2 G12(γ)DB in ST = −0.1446 + 8.53802γ − 7.76553γ (16) These equations have been plotted, and the values of coefﬁcients for all of the cycles are given in AppendixB.

5. Conclusions The in-plane shear rigidity modulus for glass WKNCFs fabrics based on picture frame test data were evaluated. The procedure was just depending on the picture frame shear experiment. The force-displacement results during the tests were used to obtain the normalized shear force, shear stress, and in-plane shear rigidity modulus. This modulus was a very important feature in characterizing the mechanical behavior of the reinforcement fabrics for forming the simulation of composites. The simple procedure of defining the shear modulus equation was presented based on the pure shear mechanism of the picture frame apparatus. Three types of warp-knitted non-crimp fabrics (WKNCFs) were investigated. The fabrics had two different stitching patterns, namely, tricot and chain. The cubic polynomial approximation was used to determine the shear stress equation against the shear angle; then, shear rigidity had been calculated from the derivative of the shear stress fitting equations. It was also found that the shear rigidity for fabrics with a tricot pattern increased with the shear angle, and showed the same trend in cycles with a lower shearing force. For the “chain stitching pattern under compression”, the shear rigidity was decreased in the initial stage of shearing, and afterwards, it increased rapidly in the first cycle, while it generally decreased in the next cycles. On the other hand, for the “chain stitching pattern under tension”, the shear rigidity increased up to the stage of some stitches being broken, at which point it decreased rapidly.

Author Contributions: All of the authors designed and contributed to this study. Conceptualization, A.H. and J.J.; Methodology, A.H., J.J. and N.C.; Software, A.H. and H.S.; Validation, A.H. and H.S.; Formal Analysis, S.N. and N.C.; Investigation, A.H. and H.S.; Resources, J.J. and N.C.; Data Curation, A.H.; Writing–Original Draft Preparation, A.H. and H.S.; Writing–Review & Editing, J.J., N.C. and S.N.; Visualization, A.H.; Supervision, J.J. and N.C.; Project Administration, J.J. and N.C.; Funding Acquisition, J.J. and N.C. Funding: This work was funded by National Natural Science Foundation of China (NSFC 11472077), the National Key Research and Development Program of China (2016YFB0303300), and the Fundamental Research Funds for the Central Universities (2232018G-06). Acknowledgments: The authors thank PGTEX® company (Changzhou, China) for providing various fabrics testing materials. Conﬂicts of Interest: The authors declare no conﬂict of interest. Materials 2018, 11, 1550 15 of 18

Appendix A

Table A1. Fabric manufacturing details and roving properties.

Speciﬁcation Uni-Directional 0◦ Bi-Axial 0◦/90◦ Bi-Axial +45◦/−45◦ Material designation L1250-7 LT1100-7 DB1200-6 Machine gauge E5 E5 E5 Run-in length per rack (m) 6.9 5.5 4.6 Course density per cm 2.5 3.5 4.6 Wale density per cm 2.8 2.8 1.9 Stitch length (mm) 14.4 11.5 9.6 Material code in this paper UD LT DB

Roving tensile strength = 0.46 N/tex according to GB/T 7690.3 (ISO 3341) testing standard [36], and ﬁlament diameter = 17 µm according to GB/T 7690.5 (ISO 1888) [37].

Appendix B

Fitting Data of Stress Curves For each fabric and each cycle, the average shear force was calculated, and then used to find the shear stress. The shear stress was fitted using OriginPro® software (2017) into a cubic polynomial function, and the coefficients with their corresponding standard error for all of the fabrics and cycles are given in Table A2 below.

Table A2. Cubic polynomial regression coefﬁcients of all of the fabrics and cycles in this study.

Cubic Polynomial Regression Shear Stress (MPa) Versus Shear Angle (Radian) Equation y = A + Bx + Cx2 + Dx3 Model UD-t in SS Plot 1st cycle 2nd cycle 3rd cycle 4th cycle A 0 0 0 0 B 0.23078 0.19699 0.21942 0.15659 C 0.69608 0.20446 0.17528 0.16253 D −0.13284 0.04723 0.04658 0.03754 Reduced Chi-Sqr. 5.16 × 10−3 5.95 × 10−3 6.30 × 10−3 3.76 × 10−3 R-Square (COD *) 0.92309 0.78099 0.76775 0.78099 Adj. R-Square 0.92303 0.78082 0.76757 0.78082 Model LT-t in SS Plot 1st cycle 2nd cycle 3rd cycle 4th cycle A 0 0 0 0 B 0.36923 −0.01327 −0.12329 −0.15442 C −0.77489 −0.04628 0.22919 0.32619 D 1.08879 0.29004 0.01397 −0.09504 Reduced Chi-Sqr. 5.49 × 10−4 4.66 × 10−4 5.04 × 10−4 4.69 × 10−4 R-Square (COD *) 0.98362278 0.905371738 0.752072267 0.618709869 Adj. R-Square 0.983609879 0.905297198 0.751876971 0.618409523 Materials 2018, 11, 1550 16 of 18

Table A2. Cont.

Cubic Polynomial Regression Shear Stress (MPa) Versus Shear Angle (Radian) Equation y = A + Bx + Cx2 + Dx3 Model DB-c in SC Plot 1st cycle 2nd cycle 3rd cycle 4th cycle A 0 0 0 0 Materials 2018, 6B, 20 FOR PEER REVIEW1.13072 0.91366 0.53815 0.26212 16 of 18 C −2.19054 −1.62744 −0.83705 −0.27092 Adj.D R-Square 2.096360.992204642 0.899170.814631248 0.578541313 0.37458 0.570250134 0.06045 Reduced Chi-Sqr. 4.90 × 10−4 2.27 × 10−4 2.16 × 10−4 1.23 × 10−4 Model DB-c in ST R-Square (COD *) 0.992211058 0.814794067 0.578948913 0.570669812 Adj. R-SquarePlot 0.992204642 1st cycle 0.814631248 2nd cycle 0.578541313 3rd cycle 0.570250134 4th cycle ModelA 0 DB-c 0 in ST 0 0 B −0.1446 0.34435 0.22025 0.28696 Plot 1st cycle 2nd cycle 3rd cycle 4th cycle A C 04.26901 − 00.52362 −0.26056 0 −0.43635 0 B D −0.1446−2.58851 0.34435 0.32061 0.22025 0.15463 0.26718 0.28696 ReducedC Chi-Sqr. 4.26901 8.54 × 10−4 −0.52362 3.00 × 10−4 − 1.290.26056 × 10−4 2.08−0.43635 × 10−4 R-SquareD (COD *) −2.588510.996806629 0.320610.83340502 0.887601356 0.15463 0.83340502 0.26718 Reduced Chi-Sqr. 8.54 × 10−4 3.00 × 10−4 1.29 × 10−4 2.08 × 10−4 Adj. R-Square 0.996804122 0.833274255 0.887513131 0.833274255 R-Square (COD *) 0.996806629 0.83340502 0.887601356 0.83340502 Note:Adj. *—CoefficientR-Square of determination; 0.996804122 x is the0.833274255 shear angle in radian, 0.887513131 y is the in-plane 0.833274255 shear rigidity Note:modules, *—Coefficient and A, ofB,determination; C and D are coefficientsx is the shear of angle the in polynomial radian, y is thefunction. in-plane shear rigidity modules, and A, B, C and D are coefficients of the polynomial function. Shear stress curves and the corresponding fitted curves of UD fabric, for example, are illustrated in FigureShear stressA1. The curves resultant and thefunctions corresponding were derived fitted to curves obtain of the UD in-plane fabric, for shear example, rigidity are modulus. illustrated in Figure A1. The resultant functions were derived to obtain the in-plane shear rigidity modulus.

FigureFigure A1. A1.Shear Shear stress stress curves curves for for four four cycle cycle of of UD UD fabric. fabric.

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