Experimental Study on Bi-Axial Mechanical Properties of Warp-Knitted Meshes with and Without Initial Notches

materials

Article Experimental Study on Bi-Axial Mechanical Properties of Warp-knitted Meshes with and without Initial Notches

Huiqi Shao 1,2, Jianna Li 2, Nanliang Chen 1,2, Guangwei Shao 2, Jinhua Jiang 1,2,* and Youhong Yang 3 1 Engineering Research Center of Technical Textiles, Ministry of Education, Donghua University, Shanghai 201620, China; [email protected] (H.S.); [email protected] (N.C.) 2 College of Textiles, Donghua University, Shanghai 201620, China; [email protected] (J.L.); [email protected] (G.S.) 3 Guangdong Polytechnic, Foshan 528041, China; [email protected] * Correspondence: [email protected]; Tel.: +86-21-67792712

Received: 23 August 2018; Accepted: 12 October 2018; Published: 16 October 2018

Abstract: Warp-knitted meshes have been widely used for structural reinforcement of rigid, semi-rigid, and flexible composite materials. In order to meet the performance requirements of different engineering applications, four typical warp-knitted meshes (rectangular, square, circular, and diamond) were designed and developed. The mechanical behaviors of these meshes under mono-axial and multi-axial tensile loads were compared. The influence of the initial notch length and orientation on the mechanical performance was also analyzed. The results showed that the biaxial tensile behavior of warp-knitted meshes tended to be more isotropic. The anisotropy level of the diamond warp-knitted mesh was the lowest (λ = 0.099), while the rectangular one was the highest (λ = 0.502). The notch on a significantly anisotropic mesh was propagated along the direction of larger modulus, while for a not remarkably anisotropic mesh, notch propagation was probably consistent with the initial notch orientation. The breaking strength of warp-knitted meshes with the same initial notch orientation decreased with the increase in notch length in both the wale and course directions. For warp-knitted meshes with the same initial notch length, the breaking strength in the wale direction was kept stable at different notch orientations, while that in the course direction decreased remarkably with notch orientation from 0◦ to 90◦.

Keywords: warp-knitted mesh; mechanical properties; bi-axial stresses; isotropy; initial notches

1. Introduction Recently, the proportion of industrial textiles in whole textile applications has been rapidly increasing in China, especially warp-knitted textiles, which have been widely used in the geotechnical construction, transportation, aerospace, and health ﬁelds. Warp-knitted mesh fabrics are one of the most promising products that can be used as structural materials such as geogrid [1], composite reinforcement [2,3], construction concrete reinforcement [4,5], and biomaterial patches [6–8], due to their light weight, high porosity, strength, and easy design. Speciﬁc geometric morphologies and mechanical properties of warp-knitted meshes are required for different applications. There are various warp-knitted mesh structures with corresponding properties. Different shapes can be realized through the design of knitting patterns during the fabricating process, typically rectangle, square, round, diamond, hexagon, etc. With the increase of applications, some research has been done on the mechanical properties of warp-knitted mesh structures. Mohammad et al. [9] compared the mechanical properties of several different types of warp knitting

Materials 2018, 11, 1999; doi:10.3390/ma11101999 www.mdpi.com/journal/materials Materials 2018, 11, 1999 2 of 13 meshes used for hernia repair. Zhang et al. [10,11] analyzed the knitting parameters, such as drawing off density and warp run-in, on the mechanical properties of the diamond warp-knitted mesh fabric. However, these researches are mainly under uniaxial loads, which sometimes cannot sufficiently describe the performance when simultaneously subjected to multi-axial stresses in real conditions. Kawabata developed a linear algebraic method for the evaluation of the biaxial tensile behavior, which could be suitable for both woven and knitted fabrics [12]. Extension and propagation of cracks and defects are important characteristics in designing textile-based structural materials [13]. A lot of researchers have looked at the effects of various defects on the mechanical behavior of textile materials. Minami et al. [13,14] found that the initial cracks have an obvious influence on the tensile strengths of PVC-coated woven fabrics under mono- and bi-axial tensile loads. Bigaud et al. [15–18] analyzed the failure mechanisms of notched soft composites reinforced by textile structures. Their studies showed that the failure modes depended on the initial crack length, orientation, and loading ratio in the wale and course directions. Luo et al. [19,20] presented a work on the mechanical properties of PVC-coated bi-axial warp-knitted fabric with initial cracks under multi-axial tensile loads. It was found that the crack propagating direction was irrelevant to the initial cracks’ orientations. Triki et al. [21,22] performed tensile central crack tear tests on plain and twill woven fabrics. The tearing energy was proven to be independent of initial crack configurations. However, most of the above mechanisms of crack propagation are developed to explain the mechanical behavior of woven fabrics, woven composites, and biaxial warp-knitted fabrics, which may not suit warp-knitted meshes. Few investigations have been made on the mechanical performance of mesh materials with cracks under bi-axial tensile loads. In this paper, four typical warp-knitted meshes (rectangular, square, round, and diamond) were prepared that may have great potential in engineering applications. Their mechanical performance was tested under both mono-axial and bi-axial stresses. A comparison of the mechanical behaviors between different knitting structures, as well as the differences under mono-axial and bi-axial tensile test were presented. The influences of initial crack lengths and orientations on the mechanical performance under biaxial stresses were also investigated.

2. Experimental

2.1. Materials Polypropylene monofilament for warp-knitted meshes was provided by the State Key Laboratory for Modification of Chemical Fibers and Polymer Materials (Donghua University, Shanghai, China). Its specifications are shown in Table1.

Table 1. Polypropylene ﬁlament speciﬁcation parameters.

Linear Density Modulus Breaking Strength Breaking Elongation dtex cN/dtex cN/dtex % 169 32.0 5.20 25.4

2.2. Fabrication of Warp-Knitted Meshes Four typical warp-knitted meshes with different mesh shapes were designed and prepared, which were rectangular, square, circular, and diamond-shaped. The lapping diagrams and the loop pictures of the warp-knitted mesh are shown in Figure1. The device used for this fabrication was an E12 Raschel knitting machine (Changzhou Runyuan Warp Knitting Machinery Co., Ltd., Changzhou, China). The knitting parameters of the warp-knitted meshes are shown in Table2. The information of fabricated meshes is shown in Table3, where the density was weighted by a WT2102 electron balance (Changzhou Yi Textile Instrument Co., Ltd., Changzhou, China) with a sample size of 100 mm × 100 mm, the thickness was measured by a YG141N digital fabric thickness gauge (Nantong Materials 2018, 11, x FOR PEER REVIEW 3 of 12

Table 2. Knitting parameters of the warp-knitted meshes.

Warp Run-in Draw off Density Mesh (mm/480 Courses) Let-off Ratio (Loops/cm) Materials 2018, 11, 1999 GB1 GB2 3 of 13 Rectangular 6.8 2620 920/1280 2.32 Square 6.8 2700 2700 3.89 Hongda ExperimentalCircular Instrument Co., Nantong,6.8 China),2850 and2860 the porosity4.06 was calculated with the software Image J (NationalDimond Institutes of Health,6.8 Bethesda,2840 MD,2840 USA). 4.22

FigureFigure 1.1. FourFour typicaltypical warp-knittedwarp-knitted meshmesh samplessamples (right(right side)side) andand theirtheir lappinglapping diagramsdiagrams (left(left side):side): ((aa)) rectangular,rectangular, ( b(b)) square, square, ( c()c) round, round, and and ( d(d)) diamond-shaped. diamond-shaped.

Table 2. Knitting parameters of the warp-knitted meshes. Table 3. Structural parameters of four typical warp-knitted mesh samples. Warp Run-in Draw off DensityArea Density Thickness Porosity Mesh Structures (mm/480 Courses) Let-off Ratio (Loops/cm)g/m2 mm % Rectangle 32.2 GB10.693 GB2 72.1 RectangularSquare 6.820.8 26200.621 920/128074.9 2.32 SquareRound 6.827.6 27000.528 270067.8 3.89 CircularDiamond 6.821.7 28500.488 286077.9 4.06 Dimond 6.8 2840 2840 4.22 2.3. Testing Conditions Table 3. Structural parameters of four typical warp-knitted mesh samples. The mono-axial tensile test was performed on a WDW-20 universal testing machine (Hualong Testing Instrument Co., Shanghai,Area China) Density with a tensileThickness speed of 50 Porositymm/min and a specimen size of Structures 2 100 mm × 100 mm. Five valid experimentalg/m data pointsmm each were obtained% in the wale (x) direction and course (y) dirRectangleection, and the mean 32.2 value was taken 0.693 as the experimental 72.1 result. As shown in Figure 2, the bi-axial tensileSquare testing was carried 20.8 out on an X 0.621‒Y multi-axial electronic 74.9 strength tester (Darong Round 27.6 0.528 67.8 Textile Machinery Co., Wenzhou, China). The tensile speed in both the x and y direction was 50 Diamond 21.7 0.488 77.9 mm/min. Five valid data points were obtained for both the wale (x) direction and course (y) direction, and the mean value was taken as the experimental result. 2.3. Testing Conditions The shape and size of the bi-axial tensile specimen are shown in Figure 3, in which Figure 3a is a nonThe-destructive mono-axial warp tensile-knitted testwas mesh performed and Figure on a3b WDW-20 is a notched universal warp testing-knitted machine mesh. (HualongThe load Testingdirections Instrument were along Co., the Shanghai, wale direction China) ( withx) and a tensilecoursespeed direction of 50 (y mm/min). The initial and notch a specimen with length size of L 100and mm orientation× 100 mm. α relating Five valid to the experimental x-axis was datalocated points at the each center were of obtained the specimen. in the waleIn order (x) direction to study andthe effect course of( yinitial) direction, notch length and the on mean the mechanical value was properties taken as theof warp experimental-knitted meshes, result. three As shown kinds inof Figurenotched2, thespecimens bi-axial with tensile different testing notch was carried lengths out (L = on 1, an3, 5 X-Y mesh) multi-axial and a notch electronic orientation strength of 0° tester were (Darongprepared. Textile For the Machinery influence Co.,of crack Wenzhou, orientation China)., three The specimens tensile speed with in the both same the crackx and lengthy direction (L = 3 wasmesh) 50 but mm/min. different Five crack valid orientations data points (a were= 0°, 45°, obtained 90°) were for both selected. the wale (x) direction and course (y) direction, and the mean value was taken as the experimental result. The shape and size of the bi-axial tensile specimen are shown in Figure3, in which Figure3a is a non-destructive warp-knitted mesh and Figure3b is a notched warp-knitted mesh. The load directions were along the wale direction (x) and course direction (y). The initial notch with length L and orientation α relating to the x-axis was located at the center of the specimen. In order to study the effect of initial notch length on the mechanical properties of warp-knitted meshes, three kinds Materials 2018, 11, 1999 4 of 13

of notched specimens with different notch lengths (L = 1, 3, 5 mesh) and a notch orientation of 0◦ were prepared. For the inﬂuence of crack orientation, three specimens with the same crack length Materials(L = 3 mesh) 2018, 11 but, x FOR different PEER REVIEW crack orientations (a = 0◦, 45◦, 90◦) were selected. 4 of 12 MaterialsMaterials 2018 2018, 11, ,11 x ,FOR x FOR PEER PEER REVIEW REVIEW 4 of4 of12 12

FigureFigure 2. 2.Bi Bi-axial-axial tensile tensile testing testing device. device. Figure 2. BiBi-axial-axial tensile testing device.

Figure 3. Test samples without initial cracks (a) and with initial notch (b). FigureFigure 3. 3 3.T.est TTestest samples samples without without initial initial cracks cracks (a ) ( aand) and with with initial initial notch notch (b (()b. ).). 3. Results Results and and Discussion 3. 3.Results Results and and Discussion Discussion 3.1. Mechanical Behaviors under Mono Mono-Axial-Axial and Multi Multi-Axial-Axial Tensile Tests 3.1.3.1. Mechanical Mechanical Behaviors Behaviors under under Mono Mono-Axial-Axial and and Multi Multi-Axial-Axial Tensile Tensile Tests Tests

3.1.1. Mono Mono-Axial-Axial Tensile Properties 3.1.1.3.1.1. Mono Mono-Axial-Axial Tensile Tensile Properties Properties Similarities werewere observedobserved in in the the deformation deformation process process of warp-knittedof warp-knitted meshes meshes during during a mono-axial a mono- SimilaritiesSimilarities were were observed observed in in the the deformation deformation process process of of warp warp-knitted-knitted meshes meshes during during a monoa mono- - axialtensile tensile test. test. At theAt the beginning beginning of stretching,of stretching, the the yarns yarn slippeds slipped at at the the crossing crossing points points ofof looploop unit unitss axialaxial tensile tensile test. test. At At the the beginning beginning of of stretching, stretching, the the yarn yarns slippeds slipped at atthe the crossing crossing points points of of loop loop unit units s overcoming small friction frictionss and contact forces [23] [23].. Then Then the the mesh mesh extended extended along along the the direction direction of overcomingovercoming small small friction frictions ands and contact contact forces forces [23] [23]. Then. Then the the mesh mesh extended extended along along the the direction direction of of force, andand aa largelarge deformation deformation occurred, occurred mainly, mainly with with the the “necking” “necking phenomenon” phenomenon [24]. [24] Finally,. Finally, the yarn the force,force, and and a largea large deformation deformation occurred occurred, mainly, mainly with with the the “ necking“necking” ”phenomenon phenomenon [24] [24]. Finally,. Finally, the the yinarn the in mesh the mesh unit wasunit straightened,was straightened, stretched, stretched and, slippedand slipped until until it broke. it broke. An example An example of mono-axial of mono- yarnyarn in in the the mesh mesh unit unit was was straightened, straightened, stretched stretched, and, and slipped slipped until until it itbroke. broke. An An example example of of mono mono- - axialtensile tensile stretching stretching process process of diamond of diamond warp-knitted warp-knitted mesh mesh is shown is shown in Figure in Figure4. 4. axialaxial tensile tensile stretching stretching process process of of diamond diamond warp warp-knitted-knitted mesh mesh is ishowns shown in in Figure Figure 4. 4.

Figure 4. Deformation process of warp-knitted mesh fabric during mono-axial stretching. FigureFigure 4. 4. Deformation Deformation process process of ofwarp warp warp-knitted-knitted-knitted mesh mesh fabric fabric during during mono mono-axialmono-axi-axial alstretch stretching.stretchinging. . Figure 5 shows the force‒extension curves of four different warp-knitted meshes under mono- FigureFigure 55 shows5 shows shows the the the force force-extension force‒extension‒extension curvescurves curves of of fourof four four different different different warp-knitted warp warp-knitted-knitted meshes meshes meshes under under under mono-axial mono mono- - axial stress. It can be seen from the diagram that the mechanical properties of warp-knitted meshes axialstress.axial stress stress It can. It. Itcan be can seenbe be seen fromseen from thefrom diagramthe the diagram diagram that that the that mechanicalthe the mechanical mechanical properties properties properties of warp-knitted of of warp warp-knitted-knitted meshes meshes meshes in the in the wale and course directions under mono-axial tension were obviously different. Generally, in a inin the the wale wale and and course course direction directions unders under mono mono-axial-axial tension tension were were obviously obviously different. different. Generally, Generally, in in a a warp knitting structure, the number of yarns in the course direction is less than in the wale direction, warpwarp knitting knitting structure, structure, the the number number of of yarns yarns in in the the course course direction direction is isless less than than in in the the wale wale direction, direction, so the warp breaking strength and modulus should be larger than the course direction. However, in soso the the warp warp breaking breaking strength strength and and modulus modulus should should be be larger larger than than the the course course direction direction. However,. However, in in the circular warp-knitted mesh, the weft breaking strength was greater than that of the warp-knitted thethe circular circular warp warp-knitted-knitted mesh mesh, the, the weft weft breaking breaking strength strength was was greater greater than than that that of of the the warp warp-knitted-knitted mesh, which may be due to the fact that its repeated structure unit was composed of tricot stitch and mesh,mesh, which which may may be be due due to to the the fact fact that that its its repeated repeated structure structure unit unit was was composed composed of of tricot tricot stitch stitch and and cord stitch. The loops in the tricot stitch and cord stitch were tightly bound to the underlap. The cordcord stitch. stitch. The The loops loops in in the the tricot tricot st itchstitch and and cord cord stitch stitch were were tightly tightly bound bound to to the the underlap. underlap. The The

Materials 2018, 11, 1999 5 of 13 wale and course directions under mono-axial tension were obviously different. Generally, in a warp knitting structure, the number of yarns in the course direction is less than in the wale direction, so the warp breaking strength and modulus should be larger than the course direction. However, in the circular warp-knitted mesh, the weft breaking strength was greater than that of the warp-knitted mesh, whichMaterials may 2018,be 11, duex FOR to PEER the factREVIEW that its repeated structure unit was composed of tricot stitch and5 cordof 12 stitch. The loops in the tricot stitch and cord stitch were tightly bound to the underlap. The friction offriction the underlaps of the underlap was largers was than larger the than wale the direction wale direction when there when was there stress was in the stress course in the direction. course Thedirection. warp strengthThe warp of strength the rectangular of the rectangular warp-knitted warp mesh-knitted was aboutmesh threewas about times three that oftimes other that structures. of other Becausestructures. its structure Because was its structure three-bar wasknitting, three the-bar plaiting knitting chain, the and plaiting stuffer chainweft yarn andincreased stuffer weft the warp yarn bindingincreased force. the warp The warp binding breaking force. elongationThe warp breaking was less thanelongation in other was structures, less than since in other there structures, was only stuffersince there weft was yarn only in the stuffer course weft direction. yarn in Thethe course mono-axial direction. tensile The properties mono-axial of square tensile and properties diamond of warp-knittedsquare and diamond meshes werewarp similar,-knitted but meshes the breaking were similar, strength but and the elongationbreaking strength of diamond and elongation meshes were of aboutdiamond 50% meshes higher were than thoseabout of50% square higher meshes. than those of square meshes.

FigureFigure 5. MonoMono-axial-axial and and multi multi-axial-axial tensile tensile curves curves of (a) of rectangular, (a) rectangular, (b) square, (b) square, (c) round (c), and round, (d) anddiamond (d) diamond-shaped-shaped warp-knitted warp-knitted meshes. meshes. 3.1.2. Bi-Axial Tensile Properties 3.1.2. Bi-Axial Tensile Properties Warp-knitted meshes are mostly subjected to different directional forces. Therefore, it is of Warp-knitted meshes are mostly subjected to different directional forces. Therefore, it is of practical signiﬁcance to study the bi-axial mechanical properties. In the case of bi-axial stretching, practical significance to study the bi-axial mechanical properties. In the case of bi-axial stretching, the the warp-knitted mesh will ﬁrst quickly overcome the friction of the crossing points between the yarns, warp-knitted mesh will first quickly overcome the friction of the crossing points between the yarns, then the mesh unit is evenly stretched and expanded along both the wale and course directions until then the mesh unit is evenly stretched and expanded along both the wale and course directions until the yarn is stretched to breaking point. the yarn is stretched to breaking point. From the bi-axial tensile curves of warp-knitted meshes, as shown in Figure5, it can be seen that From the bi-axial tensile curves of warp-knitted meshes, as shown in Figure 5, it can be seen that the differences in bi-axial tensile breaking strength of the four meshes were remarkable. The wale and the differences in bi-axial tensile breaking strength of the four meshes were remarkable. The wale course breaking strength of rectangular warp-knitted mesh were the highest, and the course breaking and course breaking strength of rectangular warp-knitted mesh were the highest, and the course strength was much higher than that under mono-axial stretching. The wale and course breaking breaking strength was much higher than that under mono-axial stretching. The wale and course strength of the other three meshes were similar, with the diamond warp-knitted mesh a little higher. breaking strength of the other three meshes were similar, with the diamond warp-knitted mesh a little higher. Similar to those under mono-axial tension, the course breaking strength of circular warp- knitted mesh under bi-axial was slightly larger than the wale direction. The wale and course elongation of the four warp-knitted meshes under bi-axial stretching were much smaller than those in mono-axial tension.

Materials 2018, 11, 1999 6 of 13

Similar to those under mono-axial tension, the course breaking strength of circular warp-knitted mesh under bi-axial was slightly larger than the wale direction. The wale and course elongation of the four warp-knitted meshes under bi-axial stretching were much smaller than those in mono-axial tension.

E = ∆σ/∆ε. (1)

The results of tensile modulus of four different warp-knitted meshes under mono-axial and bi-axial stresses are shown in Table4. ET and EL are the asymptotic modulus in the wale and course direction, respectively. The orthogonal anisotropy degree λ [9,25] of the warp-knitted mesh can be characterized by the ratio of the modulus in the wale and course directions, where λ = 0 means ideal isotropy, while λ = 1 indicates full anisotropy.

λ = 1 − min(ET, EL)/max(ET, EL). (2)

Table 4. Asymptotic modulus of the warp-knitted meshes.

Warp-knitted Mono-Axial Stretch Bi-Axial Stretch Mesh ET/MPa EL/MPa ET/MPa EL/MPa Rectangular 13.317 0.654 16.845 8.385 Square 3.298 1.570 3.813 2.879 Circular 3.447 1.190 2.894 3.862 Dimond 3.894 1.400 5.344 4.812

Figure6 shows the anisotropy levels of four warp-knitted meshes under mono-axial and bi-axial stresses. The larger the value of λ, the more anisotropic the mesh will be. It is obvious that the level of orthogonal anisotropy under mono-axial stress is much higher than under bi-axial stresses, because the yarn in load-bearing meshes is more well-distributed and uniform when suffering from multi-directional constraints [26]. So the biaxial tensile behavior of warp-knitted meshes tends to be more isotropic. In the case of bi-axial stresses, the least anisotropic mesh was diamond warp-knitted mesh (λ = 0.099), which means its mechanical behavior in the wale and course directions tended to be relatively close. The anisotropy levels of square warp-knitted mesh (λ = 0.245) and circular warp-knitted mesh (λ = 0.251) were similar, slightly higher than that of diamond. The anisotropy level of the rectangular warp-knitted mesh was the highest (λ = 0.502), so the mechanical properties would exhibit remarkable anisotropy. Materials 2018, 11, x FOR PEER REVIEW 6 of 12

3.1.3. Mechanical Anisotropy Properties As shown in Figure 5, after a range of non-linear deformation, which may be about 20–60% of the extension to failure, the relationships between force and extension of warp-knitted meshes become linear in both mono-axial and bi-axial tests. This linear deformation is during the process of stretching the yarns, where most of the applications are working in this range of strain. Therefore, when we assume that the thickness of the meshes does not change after stretching, the asymptotic modulus can be obtained according to the slope of the linear section using the ordinary least squares method: E = /  . (1) The results of tensile modulus of four different warp-knitted meshes under mono-axial and bi- axial stresses are shown in Table 4. ET and EL are the asymptotic modulus in the wale and course direction, respectively. The orthogonal anisotropy degree λ [9,25] of the warp-knitted mesh can be characterized by the ratio of the modulus in the wale and course directions, where λ = 0 means ideal isotropy, while λ = 1 indicates full anisotropy.

 =−1 min(EEEETLTL , ) / max( , ) . (2)

Table 4. Asymptotic modulus of the warp-knitted meshes.

Figure 6 shows the anisotropy levels of four warp-knitted meshes under mono-axial and bi-axial stresses. The larger the value of λ, the more anisotropic the mesh will be. It is obvious that the level of orthogonal anisotropy under mono-axial stress is much higher than under bi-axial stresses, because the yarn in load-bearing meshes is more well-distributed and uniform when suffering from multi-directional constraints [26]. So the biaxial tensile behavior of warp-knitted meshes tends to be more isotropic. In the case of bi-axial stresses, the least anisotropic mesh was diamond warp-knitted mesh (λ = 0.099), which means its mechanical behavior in the wale and course directions tended to be relatively close. The anisotropy levels of square warp-knitted mesh (λ = 0.245) and circular warp- knitted mesh (λ = 0.251) were similar, slightly higher than that of diamond. The anisotropy level of Materialsthe rectangular2018, 11, 1999 warp-knitted mesh was the highest (λ = 0.502), so the mechanical properties would7 of 13 exhibit remarkable anisotropy.

Figure 6. Degree of orthogonalorthogonal anisotropy for different warp-knittedwarp-knitted meshes under mono-axialmono-axial and bi-axialbi-axial tensile loads.

3.2. Mechanical Behavior with Initial Cracks During the knitting process, the phenomena of skipping a stitch, missing a stitch, and the breakage of the knitting yarns when rubbing against metal needles all lead to visible or invisible defects or cracks in the meshes. Furthermore, minor damage may also occur when the meshes are exposed to sharp objects during transportation and utilizations. These kinds of local damage have a significant influence on the performance of composite materials, such as mesh-reinforced concrete [5]. Therefore, research on the influence of cracks on the mechanical properties of warp-knitted mesh is of great significance for various applications.

3.2.1. Notch Propagation Analysis Due to the appearance of notches, the failure mode of warp-knitted mesh under bi-axial stresses seems to be different. During bi-axial stretching of the warp-knitted mesh with initial notch, the stress concentration points were mainly around the notch and near the clamps. The failure process can generally be divided into four stages. Firstly, under the bi-axial loads, the notch in the warp-knitted mesh opened and expanded gradually from the closed state until the edges of the notch were straightened. Then, the deformation was caused by the slippage of the yarns, including the transfer of the top arc to the loop pillar and the extraction of broken yarns from the notch. When the applied loads continued to increase and reached a critical value, the yarns were stretched to breaking point. The notch extended to the next mesh unit. Figure7 shows the notch propagations of four kinds of warp-knitted meshes with notches (L = 3, α = 0◦) located in the center. By observing the mechanical behavior of different warp-knitted meshes with initial notches, it was found that the direction of notch propagation was related to the anisotropy. For warp-knitted meshes with signiﬁcant anisotropy, the notches usually propagated along the direction of the larger modulus, such as the rectangular warp-knitted mesh shown in Figure7a. For a not remarkably anisotropic mesh, notch propagation was probably consistent with the initial notch orientation and the shapes of notch expansion were generally elliptical or circular, as shown in Figure7b–d. Materials 2018, 11, x FOR PEER REVIEW 7 of 12

3.2. Mechanical Behavior with Initial Cracks During the knitting process, the phenomena of skipping a stitch, missing a stitch, and the breakage of the knitting yarns when rubbing against metal needles all lead to visible or invisible defects or cracks in the meshes. Furthermore, minor damage may also occur when the meshes are exposed to sharp objects during transportation and utilizations. These kinds of local damage have a significant influence on the performance of composite materials, such as mesh-reinforced concrete [5]. Therefore, research on the influence of cracks on the mechanical properties of warp-knitted mesh is of great significance for various applications.

3.2.1. Notch Propagation Analysis Due to the appearance of notches, the failure mode of warp-knitted mesh under bi-axial stresses seems to be different. During bi-axial stretching of the warp-knitted mesh with initial notch, the stress concentration points were mainly around the notch and near the clamps. The failure process can generally be divided into four stages. Firstly, under the bi-axial loads, the notch in the warp-knitted mesh opened and expanded gradually from the closed state until the edges of the notch were straightened. Then, the deformation was caused by the slippage of the yarns, including the transfer of the top arc to the loop pillar and the extraction of broken yarns from the notch. When the applied loads continued to increase and reached a critical value, the yarns were stretched to breaking point. The notch extended to the next mesh unit. Figure 7 shows the notch propagations of four kinds of warp-knitted meshes with notches (L = 3, α = 0°) located in the center. By observing the mechanical behavior of different warp-knitted meshes with initial notches, it was found that the direction of notch propagation was related to the anisotropy. For warp-knitted meshes with significant anisotropy, the notches usually propagated along the direction of the larger modulus, such as the rectangular warp-knitted mesh shown in Figure 7a. For a not remarkably anisotropic mesh, notch propagation was probably consistent with the initial notch orientation and the shapes of notch Materials 2018, 11, 1999 8 of 13 expansion were generally elliptical or circular, as shown in Figure 7b–d.

Figure 7. CrackCrack propagation propagation images images of ( (aa)) rectangular, rectangular, ( b) square, ( c) round round,, and (d) diamond diamond-shaped-shaped ◦ warp-knittedwarp-knitted meshes with initial notch of L = 3, α = 0° 0 underunder bi bi-axial-axial tensile tensile loads. loads. 3.2.2. Effect of Initial Notch Length on Mechanical Properties 3.2.2. Effect of Initial Notch Length on Mechanical Properties The tensile curves of warp-knitted meshes with the same orientation initial notch (α = 0◦) and The tensile curves of warp-knitted meshes with the same orientation initial notch (α = 0°) and without a notch are shown in Figure8. In this figure, (a), (b), (c), and (d) correspond to the rectangle, without a notch are shown in Figure 8. In this figure, (a), (b), (c), and (d) correspond to the rectangle, square, circular, and diamond-shaped warp-knitted meshes, respectively. It can be seen from Figure8 square, circular, and diamond-shaped warp-knitted meshes, respectively. It can be seen from Figure that there are differences in the shape of tensile curves between the specimen with and without notches. The difference is mainly in the tensile modulus and breaking strength, indicating that the existence of an initial notch significantly influenced the mechanical properties of the warp-knitted mesh. The influence was decided by the mesh structures and the notch configurations. The tensile processes of the four warp-knitted meshes were similar. When the yarn broke and the crack expanded, it showed obvious multi-peak characteristics, indicating that other mesh units were not structurally raveled after the breaking notch. This is because the warp-knitted meshes have good resistance to raveling [6]. Comparing the tensile curves of the four warp-knitted meshes, it was found that the influence of initial notches on the tensile modulus of rectangular, square, and circular warp-knitted meshes was more significant than on the diamond mesh. According to the failure process and tensile curves in Figure8, when the load reached a critical value, the warp-knitted mesh began to break and the maximum value was called the tensile strength. In this paper, the first load peak was regarded as the breaking strength of the warp-knitted mesh in this direction. Figure9 shows the bi-axial breaking force of four warp-knitted meshes with different crack lengths. The same trend of the breaking strength and initial notch length was observed in all four warp-knitted meshes, when the notch orientation kept the same (α = 0◦). With the increase in notch length, the breaking strength of the warp-knitted mesh decreased in both the wale and course directions. The reason may be that the initial notches were caused by cutting the yarn, which results in a reduction of effective yarn amount within the clamping distance. However, the sensitivity of breaking strength to the notch length was different for knitted structures. Among the four mesh structures, the variation in breaking strength of the diamond warp-knitted mesh with the change of notch length was minimal, as shown in Figure9d. In the same warp-knitted mesh, the decrease of breaking strength with the notch length in the wale direction was more remarkable than the weft. Because the warp knitting method determines that the overall direction of the yarns is along the wale direction of the fabric [27,28], generally the wale mechanical properties of the warp-knitted fabric are better than the course direction. Therefore, the length of the initial notch had a greater impact on the wale strength. When the notch was very small (L = 1), the tensile curves of notched warp-knitted mesh Materials 2018, 11, x FOR PEER REVIEW 8 of 12

8 that there are differences in the shape of tensile curves between the specimen with and without notches. The difference is mainly in the tensile modulus and breaking strength, indicating that the existence of an initial notch significantly influenced the mechanical properties of the warp-knitted Materialsmesh.2018 The, 11 influence, 1999 was decided by the mesh structures and the notch configurations. The tensile9 of 13 processes of the four warp-knitted meshes were similar. When the yarn broke and the crack expanded, it showed obvious multi-peak characteristics, indicating that other mesh units were not werestructurally not significantly raveled different after the frombreaking those notch. without This initial is because notches, the as warp well-knitted as the differencemeshes have of breaking good strength.resistance This to phenomenon raveling [6]. Comparing is in accordance the tensile with curves the multi-axial of the four warp-knitted warp-knitted fabricsmeshes, [ 20it was] and found woven fabricsthat [the13]. influence However, of withinitial the notches increase on the in notch tensile size, modulus the influence of rectangular, on the mechanicalsquare, and circular properties warp of- the warp-knittedknitted meshes mesh was becomes more significant more significant. than on the diamond mesh.

Materials 2018, 11, x FOR PEER REVIEW 9 of 12

mesh were not significantly different from those without initial notches, as well as the difference of breaking strength. This phenomenon is in accordance with the multi-axial warp-knitted fabrics [20] andFigure wovenFigure 8. Tensile8. fabrics Tensile curves [13]curves. forHowever, for different different with initial initial the notchnotch increas lengthse in undernotch under bisize, bi-axial-axial the tensile tensile influence loads loads:: (ona) ( arectangular,the) rectangular, mechanical properties(b)( square,b) square, of (c the) ( round,c) warpround and-,knitted and (d ()d diamond-shaped) meshdiamond becomes-shaped more warp-knitted warp significant.-knitted meshes.

According to the failure process and tensile curves in Figure 8, when the load reached a critical value, the warp-knitted mesh began to break and the maximum value was called the tensile strength. In this paper, the first load peak was regarded as the breaking strength of the warp-knitted mesh in this direction. Figure 9 shows the bi-axial breaking force of four warp-knitted meshes with different crack lengths. The same trend of the breaking strength and initial notch length was observed in all four warp-knitted meshes, when the notch orientation kept the same (α = 0°). With the increase in notch length, the breaking strength of the warp-knitted mesh decreased in both the wale and course directions. The reason may be that the initial notches were caused by cutting the yarn, which results in a reduction of effective yarn amount within the clamping distance. However, the sensitivity of breaking strength to the notch length was different for knitted structures. Among the four mesh structures, the variation in breaking strength of the diamond warp-knitted mesh with the change of notch length was minimal, as shown in Figure 9d. In the same warp-knitted mesh, the decrease of breaking strength with the notch length in the wale direction was more remarkable than the weft. Because the warp knitting method determines that the overall direction of the yarns is along the wale direction of the fabric [27,28], generally the wale mechanical properties of the warp-knitted fabric are better than the course direction. Therefore, the length of the initial notch had a greater impact on the wale strength. When the notch was very small (L = 1), the tensile curves of notched warp-knitted

FigureFigure 9. 9.Effect Effect of of the the initial initial notch notch length length on on the the breaking breaking force force under under bi-axial bi-axial tensile tensile loads: loads:(a) (a) ectangular,ectangular, ( b)) square, square, ( (cc) )round round,, and and (d ()d diamond) diamond-shaped-shaped warp warp-knitted-knitted meshes. meshes.

3.2.3. Effect of Crack Angle on Mechanical Properties The tensile curves of the warp-knitted meshes with different notch orientations (α = 0°, 45°, 90°) and same notch length (L = 3) are shown in Figure 10; (a), (b), (c), and (d) correspond to the rectangle, square, circular, and diamond-shaped meshes, respectively. The tensile curves vary at different orientations from the figure. Therefore, the mechanical performance of a notched warp-knitted mesh is not only affected by the notch length, but also by the notch orientation. The influence also closely depends on the knitting structure. Similar to the phenomenon of notch length, the diamond warp- knitted mesh had the smallest variation with the change in notch orientation, indicating that the performance of a diamond warp-knitted mesh was more stable at different notch orientations. The breaking strengths of warp-knitted meshes with different notch orientation are shown in Figure 11. It can be observed that the mechanical performance trends of the four warp-knitted meshes with the variation of the notch orientation were different between the wale direction (y direction) and the course direction (x direction). In the wale direction, the change of the breaking strength of the warp-knitted mesh was relatively small, indicating that the effect of notch orientation on the breaking strength of the wale direction was insignificant. When the initial notch length was the same, due to the warp-knitted structure, the number of broken yarns in the wale direction with a notch orientation of 0° and 45° was almost the same. At a notch orientation of 90°, the number of warp broken yarns decreased, but the breaking strength of wale direction will also decrease because of the increase in warp yarn breaking length when under bi-axial stresses. So the breaking strength of the wale direction at the notch orientation of 90° was only slightly larger than that at 0° and 45°. In the course direction, the breaking strength of the warp-knitted mesh decreased linearly with the increase of the notch angle, indicating that the weft breaking strength was more sensitive to notch orientation. Under

Materials 2018, 11, 1999 10 of 13

3.2.3. Effect of Crack Angle on Mechanical Properties The tensile curves of the warp-knitted meshes with different notch orientations (α = 0◦, 45◦, 90◦) and same notch length (L = 3) are shown in Figure 10; (a), (b), (c), and (d) correspond to the rectangle, square, circular, and diamond-shaped meshes, respectively. The tensile curves vary at different Materials 2018, 11, x FOR PEER REVIEW 10 of 12 orientations from the ﬁgure. Therefore, the mechanical performance of a notched warp-knitted meshmono is-axial not onlystresses, affected it was by found the notch that the length, breaking but alsostrength by the of notchwarp- orientation.knitted mesh The was inﬂuence only sensitive also closelyto transverse depends notches, on the not knitting to oblique structure. and longitudinal Similar to the notches phenomenon [11]. This of is notch completely length, different the diamond from warp-knittedthe results under mesh bihad-axial the smallest stresses. variation Therefore, with the the testing change methods in notch must orientation, be selected indicating appropriately that the performanceaccording to ofthe a end diamond use conditions. warp-knitted mesh was more stable at different notch orientations.

FigureFigure 10. 10. TensileTensile curves curves for for different different initial initial notch notch orientations orientations under under bibi-axialaxial tensile tensile loads loads:: (a) (arectangular,) rectangular, (b ()b square,) square, (c) ( cround) round,, and and (d ()d diamond) diamond-shaped-shaped warp warp-knitted-knitted meshes. meshes.

The breaking strengths of warp-knitted meshes with different notch orientation are shown in Figure 11. It can be observed that the mechanical performance trends of the four warp-knitted meshes with the variation of the notch orientation were different between the wale direction (y direction) and the course direction (x direction). In the wale direction, the change of the breaking strength of the warp-knitted mesh was relatively small, indicating that the effect of notch orientation on the breaking strength of the wale direction was insigniﬁcant. When the initial notch length was the same, due to the warp-knitted structure, the number of broken yarns in the wale direction with a notch orientation of 0◦ and 45◦ was almost the same. At a notch orientation of 90◦, the number of warp broken yarns decreased, but the breaking strength of wale direction will also decrease because of the increase in warp yarn breaking length when under bi-axial stresses. So the breaking strength of the wale direction at the notch orientation of 90◦ was only slightly larger than that at 0◦ and 45◦. In the course direction, the breaking strength of the warp-knitted mesh decreased linearly with the increase of the notch angle, indicating that the weft breaking strength was more sensitive to notch orientation. Under mono-axial stresses, it was found that the breaking strength of warp-knitted mesh was only sensitive to transverse notches, not to oblique and longitudinal notches [11]. This is completely different from the results

Figure 11. Effect of the initial notch orientations on the breaking force under bi-axial tensile loads: (a) rectangular, (b) square, (c) round, and (d) diamond-shaped warp-knitted meshes.

Materials 2018, 11, x FOR PEER REVIEW 10 of 12

mono-axial stresses, it was found that the breaking strength of warp-knitted mesh was only sensitive to transverse notches, not to oblique and longitudinal notches [11]. This is completely different from the results under bi-axial stresses. Therefore, the testing methods must be selected appropriately according to the end use conditions.

Materials 2018, 11, 1999 11 of 13 underFigure bi-axial 10. stresses. Tensile Therefore, curves for thedifferent testing initial methods notch must orientations be selected under appropriately bi-axial tensile according loads: (a to) the end userectangular, conditions. (b) square, (c) round, and (d) diamond-shaped warp-knitted meshes.

FigureFigure 11.11. Effect of th thee initial initial notch notch orientations orientations on on the the breaking breaking force force under under bibi-axialaxial tensile tensile loads loads:: (a) (raectangular,) rectangular, (b) ( bsquare,) square, (c) ( cround) round,, and and (d ()d diamond) diamond-shaped-shaped warp warp-knitted-knitted meshes. meshes.

4. Conclusions In this research, the mechanical properties of four typical warp-knitted mesh fabrics under bi-axial tension were studied, and the effects of different types of prefabricated initial notches on their mechanical performance were analyzed. Based on the results of the experiments and analysis, the following conclusions were obtained:

(1) Warp-knitted meshes presented different mechanical behavior under mono-axial and bi-axial stresses. The meshes under biaxial stresses tended to be more isotropic, and the anisotropy level was decided by the fabric structure. The anisotropy degree of the diamond warp-knitted mesh was the lowest (λ = 0.099), while the rectangular one was the most anisotropic (λ = 0.502). (2) The mechanical performance of warp-knitted meshes was affected by notches. The failure mode of the meshes with notches under biaxial stresses was related to the anisotropy level. The notch on a signiﬁcantly anisotropic warp-knitted mesh (rectangular mesh λ = 0.502) usually propagated along the direction of the larger modulus (ET = 16.845 MPa). For a not remarkably anisotropic mesh (λ = 0.099, 0.245, 0.251), notch propagation was probably consistent with the initial notch orientation. (3) The breaking strength of warp-knitted meshes with the same initial notch orientation decreased with the increase of notch length in both the wale and course directions. The effect varied according to the fabric structure. The diamond warp-knitted mesh had a minimal effect on the reduction of the mechanical performance. For warp-knitted meshes with the same initial notch length, the breaking force in the wale direction was stable at different notch orientations, while that in the course direction decreased remarkably with notch orientation from 0◦ to 90◦. Materials 2018, 11, 1999 12 of 13

Author Contributions: Conceptualization, H.S. and G.S.; Methodology, H.S., J.J. and N.C.; Formal Analysis, H.S. and J.L.; Investigation, H.S. and Y.Y.; Resources, Y.Y.; Data Curation, H.S., G.S. and Y.Y.; Writing-Original Draft Preparation, H.S. and J.L.; Writing-Review & Editing, J.J. and N.C.; Supervision, N.C.; Project Administration, J.J. and N.C.; Funding Acquisition, J.J. and N.C. Funding: This research was funded by the National Key Research and Development Program of China (2016YFB0303300), Natural Science Foundation of China (Grant No. NSFC 11472077), Fundamental Research Funds for the Central Universities (Grant No. 2232018G-06), and was funded by China National Textile and Apparel Council (No. J201507). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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