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The role of loops in 3D fabric composites
Composites Science and Technology 60 (2000) 1835±1849
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The role of loops in 3D fabric composites Wen-Shyong Kuo Department of Aeronautical Engineering, Feng Chia University, Taichung 407, Taiwan, ROC Received 5 August 1999; received in revised form 2 March 2000; accepted 21 March 2000
Abstract The role of interlacing loops on the performance of 3D composites has long been overlooked. One possibility is that loops occupy only a small fraction of the volume, yet experiments have shown that their in¯uence can be disproportionate in determining damage behavior. The key lies in the fact that loops not only build the 3D network of reinforcements by connecting through-thickness yarns, they also cover and protect the composites from external attack. In the present work, the role is examined experimentally. Two types of three-axis woven composites were made, one combining solid carbon/epoxy rods along the axial direction, and the other employing carbon yarns in all axes. These composites are identical in loop patterns but distinct in yarn alignment. Composite geometry was ®rst examined by introducing two unit cells that describe internal yarns and surface loops. Two terms describing the coverage of surface loops were de®ned and calculated for the fabrics under investigation. In order to elucidate the in¯uence of loops, some specimens were ground to remove all loops on surfaces. Material characterizations based upon ¯exure and Izod impact tests were then carried out. The loop-retained and loop-removed specimens provide a sharp contrast in the con®guration of damage. On the basis of the comparison, the role of loops has been examined. The results show that loops can provide at least two functions that enhance composite durability and damage tolerance. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Fabrics; A. Loops; C. Microstructure; C. Damage tolerance
1. Introduction In textile fabrics, the interlacing of yarns is a necessity that brings together the otherwise separated ®ber tows. Depending on methods of fabric formation, yarn interlacing can vary widely in the shapes and the patterns of distribution. In two-dimensional (2D) woven and braided fabrics, yarns usually undergo low-angle undulation to obtain the maximum composite stiness and strength. In knitted fabrics, yarns are typically linked together by loop structures, which can provide the resulting composites with a greater extensibility. In three-dimensional (3D) fabrics involving multi-axis reinforcements, the pattern of yarn interlacing can be more complicated. When making complex fabrics, designing the pattern is perhaps the most crucial part of fabric formation. The diculty lies in the requirement that all yarns should be appropriately integrated into the near-net-shape fabric. Thus, making complex 3D fabrics would call for a unique, and often ingenuous, design of the interlacing pattern and the techniques of accomplishing it. In the inverse sense, by examining the interlacing pattern on a E-mail address: [email protected]
fabric, one would be able to perceive its interior structure and even how the fabric was made. It is clear that designing the processes of yarn interlacing plays a central role in fabric formation. One problem with yarn interlacing is that yarns are unable to remain straight at the point of interlacing, causing the so-called yarn crimp. This inevitably lowers the composite stiness and strength. In the literature, numerous researches have been conducted to address the interlacing-related problems in 2D woven-fabric composites [1± 3]. Yet the same studies dedicated to the 3D counterparts of such materials have been essentially absent. For 3D fabrics, interlacing loops, while also causing yarn crimp, can have many interesting implications for the resulting composites because of the most fundamental featureÐ interlacing loops connect through-thickness yarns. Although interlacing loops usually occupy only a small volume fraction in 3D fabrics, their in¯uence can be disproportionate. While little is known about this, an attempt is made in this work for this purpose. Herein, the term loop represents interlacing on 3D woven composites; the term cross-over stands for interlacing in 2D woven fabrics. Interlacing loops in knitted fabrics are substantially different and are not discussed in this work.
0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(00)00075-0
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2. Unique features of loops The underlying goals of loops and cross-overs are the same: to integrate the fabric. Despite this, in many ways loops in 3D fabrics dier from cross-overs in 2D fabrics. First, in 2D weaves and braids, yarns are in a form of low-level undulation, and the yarn crimp due to crossover is generally less than 30 at the highest slope. In comparison, many 3D fabrics require yarns to undergo a high level of directional change. Two- and four-step braided fabrics are characterized by angular orientation of braiding yarns; a more-than-90 degrees directional change is not uncommon [4,5]. For many 3D woven fabrics, such as the present ones, a directional change as high as 180 degrees (namely, a U-turn) is needed. Second, yarns can interlace only on the surface of 2D fabrics. In comparison, yarns can interlace at essentially any part of 3D fabrics. Under most conditions, yarns interlace on outer surfaces. Each interlacing yarn comes out from a surface, makes a turn, and reenters into the fabric, thereby forming a loop. For hollow fabrics, loops are also needed on inner surfaces. Along with surface loops, yarn can also interlace within fabric interior. Angle-interlocked fabrics, if needed, can be an example of this type. There are also a number of uncommon fabrics where interlacing loops simply do not exist. One example is the 3-axis orthogonal fabrics built solely by solid, impregnated rods [6]. There is also a case that after-machining is needed for making composite parts with accurate dimensions. The after-machining, often seen in 3D carbon/carbon composites, can entirely or partly remove the loops. Third, cross-overs occupy a major proportion, measured in area, of 2D fabrics. Indeed, 2D plain weaves can be perfectly assembled by the unit cells of crossover. In contrast, 3D fabrics generally possess only a small proportion, measured in volume, of interlacing loops. Most 3D fabrics have Ð and are desirable to have Ð straight yarns inside the fabrics; yarn interlacing is needed only on fabric surfaces. When the fabric is thick, the volume fraction of surface loops becomes proportionally low. For this reason, according to the rule-of-mixtures, the composite stiness is less aected by the loops. This could be one of the reasons that the importance of loops has long been overlooked. The last is the variability of interlacing patterns. Interlacing patterns in 2D fabrics can be changed rather freely. There are a number of 2D weaves with dierent interlacing patterns, including 1/1 plain, 2/2 twill, 4/1 satin and 7/1 satin [1]. In comparison, surface loops in 3D fabrics are themselves non-separable portions that connect internal yarns. Therefore, surface loops can rarely be varied in a free manner without changing the construction of internal yarns. For 2-step braided fabrics, the loop pattern is determined when the arrangement of axial yarns is given [4,5]. For 3-axis
orthogonal fabrics, it is possible to have such a design freedom to some extent. But making 3D fabrics often involves a complex design of the moving paths of shuttles or carriers, especially when making intricate, nearnet-shape fabrics. The paramount is to achieve the desired external shape and internal yarn structure. In other words, the pattern of surface loops is a determined outcome Ð rather than an independent designing parameter Ð of the process of fabric formation. In addition, from the viewpoint of composite stiness, it appears to be unnecessary to deliberately change the loop pattern, as is the case for 2D weaves. Yet this does not imply that surface loops are also less in¯uential to all composite behaviors. When it comes to composite susceptibility, damage evolution, or energy absorption, the scenario is radically dierent. Many experiments revealed that loops have fascinating implications for damage-related properties [5,8]. Two results in the previous works are reiterated. When conducting compression tests for the 2-step braided composites, it was found that the locations of the yarn buckling were aected by the surface loops [7]. Experiments showed that axial yarns buckled at sites outside the loops. The loops eectively con®ned the movement of axial yarns, thereby preventing the covered portion from collapse by buckling. Second, in the subsequent work aiming at the ¯exural behavior of the 3-axis orthogonal composites, surface loops again played a crucial role in the growth of matrix cracks [8]. The micrographs showed that transverse cracks bypassed the loops before growing into the material, and no loop was fractured due to the cracks. This indicated that the loop-covered portions were free from such cracks. The importance of surface loops can be better understood through the nature of crack initiation and propagation. In general, cracks can be categorized into interior-initiated and exterior-initiated, according to their locations of nucleation. The interior-initiated type is often associated with defects in material, if the worst is embedded in interior. On the other hand, the exteriorinitiated type is often associated with the load that causes stress concentrations on surface. Cracks are likely to originate from outer surfaces and grow inward. Bending, for example, can create cracks of this type. When an exterior-initiated crack appears in a 3D composite, loops on surface tend to be the ®rst reinforcing element to meet the crack. The incoming crack cannot go any further unless it either fractures or circumvents the encountered loop. Loops, in this situation, act as a protective skin that defends the interior portion from outer attacks. With a well-designed loop pattern, the composite would become more impenetrable. The merit of surface loops should not be limited to resisting exterior cracks. According to past experience, 3D composites rarely fail in a catastrophic manner. Loops that
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link to through-thickness yarns and make the composite integrated could be a great contributor to this. In this work, the role of loops is examined with a particular emphasis on composite damage behavior. 3. Preparation of specimens The processing of the specimens was similar to that in the previous work [7]. The orthogonal weaving involves 4 steps in a cycle of fabric formation, as shown in Fig. 1. The axial (z-axis) yarns are arranged in a row-and-column pattern. The 4 steps in turn feed weaving yarns along the +x, +y,ÿx, and ÿy directions, respectively. Shuttles (represented by arrows) were moved manually according to the prescribed moving paths. By varying the paths, there are alternatives to form the 3-axis fabrics with distinct interlacing patterns. Shown in Fig. 1 is the one that allows the outer axial yarns covered by interlacing loops only (not by straight portions of transverse yarns). This feature enables an easier assessment of the in¯uence of loops on the composite. Two types of 3-axis fabrics have been made. The ®rst (labeled YYR) comprises of carbon yarns in the x and y axes, while the solid carbon/epoxy rods are incorporated along the axial (z) direction. The second (labeled as YYY) is a conventional type composed of carbon yarns in all axes. The axial bundles were arranged in a 510 row-and-column pattern, as illustrated in Fig. 2a.
Fig. 1. Weaving steps for making the 3-axis fabrics.
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In both fabrics, the axial reinforcements (rod in the YYR and yarn in the YYY) are composed of one 12kcarbon tow, while the weaving yarns (x- and y-axis reinforcements) are composed of two 12k-carbon tows. The rods, made by pultrusion, were 1 mm in diameter and 58.8 vol% in ®ber content [7]. Both fabrics were then impregnated with the epoxy resin by using vacuum-assisted resin transfer molding. The resin used was the Ciba-Geigy LY564, cured at 60 C for 24 h and post-cured at 120 C for 4 h. Fig. 3 shows the typical YYR and YYY composites. Testing specimens were taken by cutting the cured composites normal to the axial direction. To investigate the in¯uence of loops, one half of the specimens were carefully ground to remove all surface loops; this loopremoving process is termed deloop in this work. The delooped YYR and YYY are labeled DL-YYR and DL-YYY, respectively. Thus, there are a total of four composite types in this study; their nominal dimensions are listed in Table 1. Fig. 2b schematically shows the cross-section of the delooped composites. To remove loops completely, the specimen surfaces were ground as precisely as possible so that a half cross-section of each axial bundle lying on the surface was removed, as illustrated in Fig. 2b. After being delooped, all the throughthickness (x- and y-axis) yarns become fragmented.
Fig. 2. Illustration of cross-sections of loop-retained and delooped composites.
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Fig. 3. Composites made in the present work.
Due to the grinding, the cross-sectional area is reduced, and the number of axial bundles is equivalently equal to 36 (49). The cross-section and the number of axial bundles are unequal in the loop-retained and delooped specimens. For this reason, comparisons between dierent types should be made on a per-area or per-bundle base, which can reduce the in¯uence of unequal cross-section to a minimum level. 4. Geometry of loops Each method of fabric formation yields a distinct pattern of surface loops. Although only the 3-axis type is examined, the concept and formulation can be similarly applied to other fabrics. 4.1. Unit cells Two unit cells are introduced for internal yarns and surface loops, as shown in Fig. 4. The representative volume for the internal yarns can be modeled as a cuboid with dimensions Lx, Ly and Lz along the x, y, and z directions, respectively [7,8]. Based on Fig. 4a, the cell dimensions are equal to the sum of the associated bundle sizes:
Lx Uy Uz ;
1
Ly Ux Wz ;
2
Lz Wx Wy ;
3
where Wi and Ui are cross-sectional dimensions of the iaxis yarns. For the YYR, the axial rods are circular with Wz=Uz=1 mm, and the x- and y-axis yarns are closely rectangular. For the YYY, the yarn cross-sections are less regular, often in a form of distorted ellipse. Nevertheless, the use of the unit cell for calculating ®ber distribution (Section 4.2) is appropriate for dierent crosssectional shapes. Fig. 4b illustrates the loop pattern on the yz surface and the unit cell for the loops. The unit cell on the yz surface has dimensions Ly and 2Lz. In the ®gure, Si is the spacing between i-axis yarns. The spacings Sy and Sz are indeed the allocated cross-sectional dimensions for the x-axis yarns (Wx and Ux). For loops on the xz surface, the unit cell is similar. 4.2. Fiber volume fractions For 3D composites, distribution of ®bers in each component is more informative than the overall ®ber
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Table 1 Construction and dimensions of the specimens Label
YYR
DL-YYR
YYY
DL-YYY
x-Axis y-Axis z-Axis Loops Specimen width (mm) Specimen thickness (mm) Lx (mm) Ly (mm) Lz (mm)
24k Yarn 24k Yarn 12k Rod Retained 19.5
24k Yarn 24k Yarn 12k Rod Removed 17.2
24k Yarn 24k Yarn 12k Yarn Retained 25.2
24k Yarn 24k Yarn 12k Yarn Removed 23.7
10.1
7.2
7.5
4.8
1.8 1.9 3.2
1.8 1.9 3.2
1.2 2.6 3.1
1.2 2.6 3.1
content. For the present fabrics, ®bers distribute in four components: x axis, y axis, z axis, and loops. Fiber distribution in the delooped composites is ®rst discussed. Since loops are absent, the delooped composite becomes an assemblage of the unit cell (Fig. 4a), allowing evaluation of the ®ber volume fractions from the unit cell. Because the number of carbon ®laments within a yarn is a constant, the volume of ®bers along each axis can be calculated as long as the unit cell dimensions are known. Thus, the volume fraction of the ®bers along the i axis (V®) can be expressed as Vfi
df 2 li Ni 4Lx Ly Lz
4
where Ni is the number of ®laments within the bundle (Table 1), df is the ®ber diameter (7 mm for the carbon ®bers), and li is the length of the bundle within the unit cell. Assuming the yarns are straight, li is equal to the unit cell dimension Li. The overall ®ber content (Vf) for the delooped composites is thus the sum of the three components: Vf Vfx Vfy Vfz :
5
When loops are involved, the unit cell must be rede®ned to account for the loops. To this end, the smallest representative volume is the volume formed by a cycle of weaving. The volume has a cross-section (w and h) de®ned in Fig. 2a and a depth equal to the pitch length (2Lz) de®ned in Fig. 4b. The ®ber volume fraction in each component can be calculated in a similar manner. Vfi
df 2 li Ni ; 8whLz
6
in which li is the total yarn length of the i-component within the volume. The overall ®ber content (Vf) is the sum of the four components:
Fig. 4. Unit cells for the fabric.
Vf Vfx Vfy Vfz Vfl ;
7
where V¯ is the volume fraction of ®bers in loops. Herein, the x and y-axis yarns are de®ned as the straight portions within the fabric, and the straight portions are indeed those included in the delooped fabric (Fig. 2b). Loops are de®ned as the weaving yarns outside the cross-section of the delooped fabric. Since there are 49 unit cells in the delooped cross-section, and there are two such layers in a pitch length, thus lx =72Lx and ly =72Ly. The yarn length of the z-axis, lz, is 100Lz. Loops are close to a half of an ellipse with the major axis
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(L2y+L2z )0.5 and the minor axis Lx. Loops on the xzsurface can be de®ned similarly. The length of the loops can be calculated by integrating the curve segments. Results of the ®ber volume fractions are listed in Table 2. Loops enlarge the fabric and reduce overall ®ber content. Because the present fabrics are relatively thin (only 5 layers of axial bundles), loops occupy signi®cant amount of ®ber volumeÐabout the same as other three components. The surface layers containing loops are less dense in ®ber content. When loops are removed, the overall ®ber content Vf is about 10% higher than the loop-retained counterparts. The in¯uence of loops on ®ber content should diminish when the number of axial bundles increases. It can be seen that the all-yarn composites are denser than the rod-reinforced counterparts, because yarns are shapeable and thinner than the rods.
fraction of axial yarn covered by loops. Based on the unit cell, the area covered by a loop is found to be AL Sy Wz Sz Wy 3Sy Sz :
According to the de®nition, the coverages become Cs
Sy Wz Sz Wy 3Sy Sz ÿ ; 2 Wz Sz Wy Sy
Cay
Sy Wz Sz Wy 2Sy Sz ÿ : 2 Wz Sz Wy Sy
4.3. Interlacing and intersecting angles At interlacing, each weaving yarn comes out from a surface, changes its direction, and reenters into the fabric, as shown in Fig. 5a. The loop connects two inside portions and makes an angular change , which is de®ned as the interlacing angle. The loop intersects the interlaced axial yarn by an angle de®ned as the intersecting angle y, as shown in Fig. 5b. For the present fabric, the angles are 180
8
Ly : tan Lz
9
ÿ1
These two angles characterize con®guration of a loop. 4.4. Coverage and jamming To characterize the density of loops, two terms are introduced: surface coverage (Cs) and axial-yarn coverage (Cay). Surface coverage, analogous to the conventional de®nition of coverage in 2D woven fabrics, is de®ned as the area fraction of the surface covered by loops. Axial-yarn coverage is de®ned as the length
Table 2 Fiber distribution and loop coverages Label
YYR
DL-YYR
YYY
DL-YYY
Vfx Vfy Vfz V¯ Vf
0.095 0.101 0.117 0.093 0.406
0.151 0.160 0.134 Ð 0.445
0.068 0.149 0.122 0.103 0.442
0.113 0.248 0.146 Ð 0.507
Cs Cay
0.61 0.49
Ð Ð
0.56 0.45
Ð Ð
10
Fig. 5. De®nition of the angles.
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Two non-dimensional ratios are introduced: ly
Sy ; Wy
lz
Sz : Wz
13
Physically, li characterizes the packing of the i-axis bundles. Using the ratios, the coverages can be expressed as ly lz 3ly lz ; Cs ÿ 2 1 ly 1 lz
14
ly lz 2ly lz : Cay ÿ 2 1 ly 1 lz
15
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the upper bound of the coverage, occurs within the range Cs=0.5±0.625. The calculated results of Cay are shown in Fig. 7. The Cay also increases with the ratios. The upper bound for Cay, independent of the ratios, is equal to 0.5, meaning that for each axial yarn at the outside, at least a half of its length will not be covered by loops. The coverages of the present fabrics are marked in the ®gures and also listed in Table 2. 4.5. Loop-caused deformation
Loop jamming is likely to occur when the bundles are thin and when bundle spacings are wide. If jamming occurs, the loop should be remodeled and the equations should be reformulated. Fig. 6 shows the calculated Cs as a function of ly and lz. The Cs increases with ly and lz until jamming occurs. Jamming of loops, representing
During fabric formation, applying tension to yarns is needed in order to straighten the yarns and compact the fabric. When an interlacing yarn changes its direction, a resultant force is created. For 2D weaves, the resultant force caused by the warp yarns can be counter-balanced by that caused by the weft yarns, since both are undulated. Unfortunately, the counter-balancing force does not exist in 3D fabrics. The interlaced yarns, usually the axial yarns designed to be straight, must be deformed in response to the resultant force. Fig. 8 is a micrograph of the 3-axis composite showing deformation of axial yarns. Fig. 9 illustrates how the deformation is formed. At each loop, the resultant force pushes the interlaced yarn toward the inward direction. As shown in the ®gure, steps 1 and 3 push the axial yarns to undulate in the x direction. In the same manner, steps 2 and 4 push the axial yarns to undulate in the y direction. Thus, the axial yarns are actually deformed in a helical form. The period of the helical de¯ection is, therefore, equal to the pitch length. In general, deformation of yarns due to interlacing in 3D fabrics is complex but perceivable through the processes of fabric formation. It is clear that interlacing loops not only deform the interlaced yarns on exterior,
Fig. 6. Calculated surface coverage as a function of the ratios (solid square: YYR, solid circle: YYY).
Fig. 7. Calculated axial-yarn coverage as a function of the ratios (solid square: YYR, solid circle: YYY).
It should be noted that the loop area [Eq. (10)] and thus the coverages are calculated under an assumption that loops do not overlap with each other Ð a condition otherwise known as jamming. According to Fig. 4b, neighboring loops overlap when Sz cot > Wy :
16
Combining Eqs.(9), (13) and (16), the condition for loop jamming becomes ly lz > 1:
17
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Fig. 8. Cross-section of the YYY showing loop-caused deformation in the axial yarns. Fig. 9. Illustration of loop-caused deformation.
they also aect yarns in interior. For this reason, although loops generally occupy only a tiny fraction of the overall volume, their in¯uence on the composite stiness can be disproportionate Ð not because of the crimp in themselves but because of the induced deformation in internal yarns. 5. Material characterization 5.1. Flexure test For the three-point bending tests, the specimen length was 100 mm, and the testing span was 70 mm. Four specimens were tested for each composite type. The specimens were placed with the axial direction normal to the loading edge. The cross-head speed was set at 2 mm/min and was halted after apparent damage had developed in the specimen. Both the cross-head displacement and the load were digitally acquired. After the test, each damaged specimen was immersed into a box containing low-viscosity, unsaturated polyester (UP) resin, which was then cured under a vacuum condition. The UP resin in®ltrated the crack openings and ®xed the originally developed damage, thereby allowing the subsequent slicing, grinding and polishing of the desired cross-sections.
5.1.1. Rod-reinforced composites The acquired load-de¯ection curves of the same type are generally very close in the slope, peak load, and shape of the non-linear portion; typical curves are shown in Fig. 10. Both the YYR and the DL-YYR are approximately linear at the initial loading. The curves become nonlinear beyond about 3 mm of de¯ection, entering a region in which the load drops and occasionally regains with the de¯ection. The YYR stays at a rather long plateau region before it eventually falls. In comparison, after reaching its peak load, the DL-YYR declines almost constantly with the de¯ection. Fig. 11 shows typical damaged specimens under the 3-point bending test. For both loop-retained and delooped specimens, compression-related failures are less apparent. The dominant damage modes are rupture of the rods and transverse matrix cracking Ð both initiating from the middle of the bottom surface, where the tensile strain is the highest (Fig. 11a). The eect of loops can be seen from Fig. 11b. Separation of the axial rods is common on the DL-YYR. When loaded in bending, the rods under tension tend to debond and slide. If this happens, the debonded rod can leave the surface Ð a mode termed as pop-out in this work. This mode is more pronounced in the impacted DL-YYR. For the loop-retained
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Fig. 11. Damage in the rod-reinforced composites due to the ¯exural load (left:YYR, right:DL-YYR).
Fig. 10. Typical load-de¯ection curves of the composites.
specimens, in comparison, pop-out of rods is impossible, since loops can ®rmly hold the rods. Another apparent mode of damage is transverse cracking, due to the tensile stress. Two types of transverse cracking have been observed. One is the dominant transverse crack that originates at the middle of the tensile side and penetrates nearly throughout the thickness. The dominant transverse crack causes extensive ruptures of the rods. The crack propagates along a socalled weaker-plane, which will be discussed. The other type is the multiple matrix cracks that run across the specimen surface in a parallel manner, as shown in the
YYR of Fig. 11a. These cracks, usually stop when they meet the ®ber bundles, are less harmful to the composite. 5.1.2. All-yarn composites Typical loading curves of the all-yarn composites are shown in Fig. 10b. The curves drop sharply after reaching the peak loads, in contrast to the YYR that has a long plateau in the nonlinear region. Fig. 12 shows typical damaged specimens. The damage con®gurations are similar to the rod-reinforced counterparts except that the pop-out of axial bundle is absent. The reason is attributed to the loop-caused deformation in axial yarns. An undulated bundle is more eective in transferring load to contiguous elements Ð through both normal and shear stresses on the bundle interface Ð than is a straight bundle. In the DL-YYY, large-scale
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Fig. 12. Tensile surfaces of the all-yarn composites due to the ¯exural load (left:YYY, right:DL-YYY).
debonding and sliding of undulated axial yarns are suppressed, thus ruling out the possibility of yarn popout. Since debonding and sliding consume energy and extend damaged zone, the lack of pop-out can lead to more detrimental damage in a smaller region. 5.2. Izod-impact test The Izod-impact test is illustrated in Fig. 13. The specimen, 50 mm in length, was clamped vertically with 30 mm above the support. The pendulum hit the specimen at 22 mm above the support (or 8 mm below the free end). Three specimens were tested for each composite type. The specimens were not notched. Although the Izod and Charpy impact tests are most commonly used for notched metals, they are also suitable for 3D composites. In contrast to metallic specimens that often break from the notch in a brittle manner, 3D composites can develop complex but nondisintegrated types of damage. Thus, while the test yields fracture toughness for metals, it provides the capability of energy absorption for the 3D composites. Moreover, this test readily reveals the role of loops in resisting exterior-initiated cracks. To compare the results of dierent composite types, the term unit absorbed-energy, de®ned as the absorbedenergy divided by the cross-sectional area of the specimen, is introduced. The results are shown in Fig. 14. The delooped specimens are notably lower than the corresponding loop-retained ones. Even normalized by
Fig. 13. Illustration of the Izod-impact test.
the cross-sectional area, the delooped specimens are still about 35% lower than the loop-retained counterparts. For both rod-reinforced and all-yarn composites, retaining surface loops is important in preserving the
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of the excessive defection. The third mode, rod pull-in, is visible from the surface of the DL-YYR (marked by the arrow in Fig. 15a). Rod pull-in is a sub-critical mode that combines debonding and sliding of rods, both consuming energy and contributing to impact tolerance. Loops can do very little in resisting rod pull-in. The DLYYR specimens were intensively damaged. Along with the aforementioned modes, rod pop-out is also apparent. Without being supported by loops, the rods on surface become likely to move apart from the surface. 5.2.2. All-yarn composites Fig. 16 shows the typical impacted YYY and DLYYY. For both types of composites, the damaged region is relatively smaller. The axial yarns were signi®cantly ruptured at the crack opening. The DL-YYY was the only type that can be completely fractured apart. Pull-in and pop-out of axial bundles, commonly seen in the rod-reinforced types, are absent in these types. Because of the loop-caused deformation, the axial yarns are undulated, and large-scale debonding and sliding are inhibited. Consequently, the majority of impact energy was absorbed by the tensile rupture of axial yarns. The brittle carbon yarns, under tensile rupture, can absorb a relatively small amount of energy. Due to the lack of yarn pull-in, no axial bundle was used to bridge the crack opening. Compared with the complex damage con®guration in the DL-YYR, the DL-YYY has developed a rather clean and regular transverse crack along the weaker-plane. This single and simple damage con®guration signi®cantly suppresses the potential for energy absorption, as revealed in the results of the unit absorbed-energy. 6. Role in damage resistance Fig. 14. Results of energy absorption of the impacted specimens.
capability of energy absorption. It is of interest to compare the YYR with the YYY (or the DL-YYR with the DL-YYY) Ð a comparison that manifests the eect of the rods. The rod-reinforced specimens are two times more capable in absorbing the impact energy. 5.2.1. Rod-reinforced composites When impacted, the specimens were fractured from the base, at which the bending moment was the highest. A dierence from the ¯exure test is that the specimens were excessively de¯ected at a much higher speed. Fig. 15 compares the impacted YYR and DL-YYR. The YYR was damaged in three modes: rod rupture, matrix cracking, and rod pull-in. Rod ruptures were extensive at the dominant crack. Compared with the 3-point bending tests, the crack opening is much wider because
6.1. Reinforcing weaker-planes No plane is truly weak in 3D composites that are multi-directionally reinforced. Yet these materials are macroscopically non-uniform, and inevitably some planes are relatively weaker. According to experimental observations, the weaker-planes locate at the interfacial planes between x- and y-axis yarns. Cracks along weaker-planes can avoid ®bers in the x- and y-axis yarns. Both the ¯exure and the impact tests result in bending, which causes tensile stress in one side and compressive stress in the other. All specimens showed that the dominant crack was initiated from the tensile side along a weaker-plane. Fig. 17 illustrates the locations of weaker-planes (marked by arrows), assuming that tensile side is on the right. Fig. 18 is a micrograph of the YYY specimen after the ¯exural test, showing a crack along the weaker-plane. The compressive side is on the top, at which the axial yarn was buckled, and a
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Fig. 15. Impacted specimens of the YYR (left) and the DL-YYR (right); the arrow indicating pull-in of the rods.
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Fig. 16. Impacted specimens of the YYY (left) and the DL-YYY (right).
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Fig. 18. A fractured YYY specimen under ¯exural load, showing a crack along the weaker-plane (compressive side on the top). Fig. 17. Locations of weaker-planes marked by arrows.
kink band was formed (indicated by the arrow). All other axial yarns were fractured due to tension. The crack grew along the plane without encountering ®bers in the x- and y-axis yarns. On surface, the x- and y-axis yarns are the loops, which can block the growth of the crack. The experiments showed that when a crack meets a loop, the crack is either stopped or de¯ected. In no case can a crack fracture the encountered loop. This suggests
that loops on the surface can cover the otherwise weaker-planes. When covered by loops, the weakerplanes are reinforced. For the present fabrics, loops cover a half of weaker-planes. Still, cracks can grow into the uncovered weaker-planes. To be more eective in resisting cracks, allowing fewer weaker-planes to outer attacks can be helpful. To this end, the weaving processes must be redesigned to obtain a loop pattern that covers more of the weaker-planes.
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6.2. Holding axial yarns In response to loads, 3D composites can develop complex deformation and stresses. The induced stresses could push apart the axial yarns that lie on outer surfaces. An example is the pop-out of rods seen in the DLYYR. Once an axial yarn tends to move apart, the transverse yarns must respond to prevent disintegration. In a loop-retained composite, the loops can ®rmly hold axial yarns. If loops are absent, on the other hand, separation of damaged yarns can take place rather easily. Holding axial yarns on outer surfaces appears to be an important function for the composite to remain integrated; a cascade of succeeding damage mechanisms could otherwise be triggered. From the viewpoint of energy absorption, preventing the composite from disintegration is bene®cial even when damage has developed in the interior. Another function of loops Ð related to holding axial yarns Ð is the transfer of loads into through-thickness yarns. To fully exploit 3D integrity, yarns in all directions should be able to carry load eectively. If loops on the surface are removed, the through-thickness yarns become fragmented. As a result, the through-thickness yarns become less eective in load-transfer, and the reinforcing eciency is also reduced. 7. Conclusions Four composite types display distinct damage con®gurations under the ¯exural and impact loads. The rodreinforced composites undergo more complex failure mechanisms and absorb more energy than do the allyarn counterparts. The all-yarn composites are damaged in a smaller region, in part because of the loop-caused deformation in axial yarns that inhibit large-scale debonding and sliding. Despite the specimens responding dierently to the loads, interlacing loops show the same importance for the 3D composites. Based on the damage con®gurations, two major functions of loops have been identi®ed. Loops act as a protective skin for 3D composites. They can defend the internal yarns from outer attacks through crack termination or de¯ection. The key lies in the fact that they cover the otherwise weaker-planes, along which cracks can penetrate into the interior. The number of weaker-planes in the delooped specimens is two times denser than that in the loop-retained composites. With a proper design of the weaving process, it is
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possible to achieve a loop pattern that covers more of weaker-planes. This is a topic of interest to pursue. Loops are also eective in holding axial yarns and in preventing disintegration. Were loops removed, the outer axial yarns are left unsupported, giving rise to the possibility of failure. Most important, the originally continuous through-thickness yarns become fragmented, thus lowering the load-transfer eciency and adversely aecting the 3D integrity. This function makes it clear that loops should be retained whenever possible, and a near-net-shape design without aftermachining is preferable. Two coverages describing the density of loops have been introduced. Although yet to be proved, the link between the coverages and the two functions could exist. A further quantitative study for the link is needed. Although loops appear to be favorable in terms of damage resistance, attention should be paid to the loopcaused deformation in internal yarns, which can lower the composite stiness and strength. Acknowledgements The author wishes to thank the Feng Chia University (FCU-RD-87-01) and the National Science Council of Taiwan, ROC (NSC 89-2216-E-035-002) for the support of this research. References 1 Chou TW. Microstructural design of ®ber composites. Cambridge, UK: Cambridge University Press, 1992. (p. 374±422). 2 Tan P, Tong L, Steven GP. Modelling for predicting the mechanical properties of textile composites Ð a review. Composites Part A 1997;28A:903±22. 3 Naik N.K. Woven fabric composites. Technomic Publishing Company, Lancaster: Basel, 1994. 4 Kuo WS, Chen HI. Fabrication and microgeometry of two-step braided composites incorporating pultruded rods. Composite Science and Technology 1997;57:1457±67. 5 Kuo WS, Ko TH, Chen HI. Elastic moduli and damage mechanisms in 3-D braided composites incorporating pultruded rods. Composites Part A 1998;29A:681±92. 6 Fitzer E. The future of carbon±carbon composites. Carbon 1987;25:163±90. 7 Kuo WS, Cheng KB. Processing and microstructures of 3-D woven fabric composites incorporating solid rods. Composites Science and Technology 1999;59:1833±46. 8 Kuo WS, Lee LC. Elastic and damage behavior of 3-D woven composites incorporating solid rods. Composites Part A 1999;30A:1135±48.
www.elsevier.com/locate/compscitech
The role of loops in 3D fabric composites Wen-Shyong Kuo Department of Aeronautical Engineering, Feng Chia University, Taichung 407, Taiwan, ROC Received 5 August 1999; received in revised form 2 March 2000; accepted 21 March 2000
Abstract The role of interlacing loops on the performance of 3D composites has long been overlooked. One possibility is that loops occupy only a small fraction of the volume, yet experiments have shown that their in¯uence can be disproportionate in determining damage behavior. The key lies in the fact that loops not only build the 3D network of reinforcements by connecting through-thickness yarns, they also cover and protect the composites from external attack. In the present work, the role is examined experimentally. Two types of three-axis woven composites were made, one combining solid carbon/epoxy rods along the axial direction, and the other employing carbon yarns in all axes. These composites are identical in loop patterns but distinct in yarn alignment. Composite geometry was ®rst examined by introducing two unit cells that describe internal yarns and surface loops. Two terms describing the coverage of surface loops were de®ned and calculated for the fabrics under investigation. In order to elucidate the in¯uence of loops, some specimens were ground to remove all loops on surfaces. Material characterizations based upon ¯exure and Izod impact tests were then carried out. The loop-retained and loop-removed specimens provide a sharp contrast in the con®guration of damage. On the basis of the comparison, the role of loops has been examined. The results show that loops can provide at least two functions that enhance composite durability and damage tolerance. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: A. Fabrics; A. Loops; C. Microstructure; C. Damage tolerance
1. Introduction In textile fabrics, the interlacing of yarns is a necessity that brings together the otherwise separated ®ber tows. Depending on methods of fabric formation, yarn interlacing can vary widely in the shapes and the patterns of distribution. In two-dimensional (2D) woven and braided fabrics, yarns usually undergo low-angle undulation to obtain the maximum composite stiness and strength. In knitted fabrics, yarns are typically linked together by loop structures, which can provide the resulting composites with a greater extensibility. In three-dimensional (3D) fabrics involving multi-axis reinforcements, the pattern of yarn interlacing can be more complicated. When making complex fabrics, designing the pattern is perhaps the most crucial part of fabric formation. The diculty lies in the requirement that all yarns should be appropriately integrated into the near-net-shape fabric. Thus, making complex 3D fabrics would call for a unique, and often ingenuous, design of the interlacing pattern and the techniques of accomplishing it. In the inverse sense, by examining the interlacing pattern on a E-mail address: [email protected]
fabric, one would be able to perceive its interior structure and even how the fabric was made. It is clear that designing the processes of yarn interlacing plays a central role in fabric formation. One problem with yarn interlacing is that yarns are unable to remain straight at the point of interlacing, causing the so-called yarn crimp. This inevitably lowers the composite stiness and strength. In the literature, numerous researches have been conducted to address the interlacing-related problems in 2D woven-fabric composites [1± 3]. Yet the same studies dedicated to the 3D counterparts of such materials have been essentially absent. For 3D fabrics, interlacing loops, while also causing yarn crimp, can have many interesting implications for the resulting composites because of the most fundamental featureÐ interlacing loops connect through-thickness yarns. Although interlacing loops usually occupy only a small volume fraction in 3D fabrics, their in¯uence can be disproportionate. While little is known about this, an attempt is made in this work for this purpose. Herein, the term loop represents interlacing on 3D woven composites; the term cross-over stands for interlacing in 2D woven fabrics. Interlacing loops in knitted fabrics are substantially different and are not discussed in this work.
0266-3538/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(00)00075-0
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2. Unique features of loops The underlying goals of loops and cross-overs are the same: to integrate the fabric. Despite this, in many ways loops in 3D fabrics dier from cross-overs in 2D fabrics. First, in 2D weaves and braids, yarns are in a form of low-level undulation, and the yarn crimp due to crossover is generally less than 30 at the highest slope. In comparison, many 3D fabrics require yarns to undergo a high level of directional change. Two- and four-step braided fabrics are characterized by angular orientation of braiding yarns; a more-than-90 degrees directional change is not uncommon [4,5]. For many 3D woven fabrics, such as the present ones, a directional change as high as 180 degrees (namely, a U-turn) is needed. Second, yarns can interlace only on the surface of 2D fabrics. In comparison, yarns can interlace at essentially any part of 3D fabrics. Under most conditions, yarns interlace on outer surfaces. Each interlacing yarn comes out from a surface, makes a turn, and reenters into the fabric, thereby forming a loop. For hollow fabrics, loops are also needed on inner surfaces. Along with surface loops, yarn can also interlace within fabric interior. Angle-interlocked fabrics, if needed, can be an example of this type. There are also a number of uncommon fabrics where interlacing loops simply do not exist. One example is the 3-axis orthogonal fabrics built solely by solid, impregnated rods [6]. There is also a case that after-machining is needed for making composite parts with accurate dimensions. The after-machining, often seen in 3D carbon/carbon composites, can entirely or partly remove the loops. Third, cross-overs occupy a major proportion, measured in area, of 2D fabrics. Indeed, 2D plain weaves can be perfectly assembled by the unit cells of crossover. In contrast, 3D fabrics generally possess only a small proportion, measured in volume, of interlacing loops. Most 3D fabrics have Ð and are desirable to have Ð straight yarns inside the fabrics; yarn interlacing is needed only on fabric surfaces. When the fabric is thick, the volume fraction of surface loops becomes proportionally low. For this reason, according to the rule-of-mixtures, the composite stiness is less aected by the loops. This could be one of the reasons that the importance of loops has long been overlooked. The last is the variability of interlacing patterns. Interlacing patterns in 2D fabrics can be changed rather freely. There are a number of 2D weaves with dierent interlacing patterns, including 1/1 plain, 2/2 twill, 4/1 satin and 7/1 satin [1]. In comparison, surface loops in 3D fabrics are themselves non-separable portions that connect internal yarns. Therefore, surface loops can rarely be varied in a free manner without changing the construction of internal yarns. For 2-step braided fabrics, the loop pattern is determined when the arrangement of axial yarns is given [4,5]. For 3-axis
orthogonal fabrics, it is possible to have such a design freedom to some extent. But making 3D fabrics often involves a complex design of the moving paths of shuttles or carriers, especially when making intricate, nearnet-shape fabrics. The paramount is to achieve the desired external shape and internal yarn structure. In other words, the pattern of surface loops is a determined outcome Ð rather than an independent designing parameter Ð of the process of fabric formation. In addition, from the viewpoint of composite stiness, it appears to be unnecessary to deliberately change the loop pattern, as is the case for 2D weaves. Yet this does not imply that surface loops are also less in¯uential to all composite behaviors. When it comes to composite susceptibility, damage evolution, or energy absorption, the scenario is radically dierent. Many experiments revealed that loops have fascinating implications for damage-related properties [5,8]. Two results in the previous works are reiterated. When conducting compression tests for the 2-step braided composites, it was found that the locations of the yarn buckling were aected by the surface loops [7]. Experiments showed that axial yarns buckled at sites outside the loops. The loops eectively con®ned the movement of axial yarns, thereby preventing the covered portion from collapse by buckling. Second, in the subsequent work aiming at the ¯exural behavior of the 3-axis orthogonal composites, surface loops again played a crucial role in the growth of matrix cracks [8]. The micrographs showed that transverse cracks bypassed the loops before growing into the material, and no loop was fractured due to the cracks. This indicated that the loop-covered portions were free from such cracks. The importance of surface loops can be better understood through the nature of crack initiation and propagation. In general, cracks can be categorized into interior-initiated and exterior-initiated, according to their locations of nucleation. The interior-initiated type is often associated with defects in material, if the worst is embedded in interior. On the other hand, the exteriorinitiated type is often associated with the load that causes stress concentrations on surface. Cracks are likely to originate from outer surfaces and grow inward. Bending, for example, can create cracks of this type. When an exterior-initiated crack appears in a 3D composite, loops on surface tend to be the ®rst reinforcing element to meet the crack. The incoming crack cannot go any further unless it either fractures or circumvents the encountered loop. Loops, in this situation, act as a protective skin that defends the interior portion from outer attacks. With a well-designed loop pattern, the composite would become more impenetrable. The merit of surface loops should not be limited to resisting exterior cracks. According to past experience, 3D composites rarely fail in a catastrophic manner. Loops that
W.-S. Kuo / Composites Science and Technology 60 (2000) 1835±1849
link to through-thickness yarns and make the composite integrated could be a great contributor to this. In this work, the role of loops is examined with a particular emphasis on composite damage behavior. 3. Preparation of specimens The processing of the specimens was similar to that in the previous work [7]. The orthogonal weaving involves 4 steps in a cycle of fabric formation, as shown in Fig. 1. The axial (z-axis) yarns are arranged in a row-and-column pattern. The 4 steps in turn feed weaving yarns along the +x, +y,ÿx, and ÿy directions, respectively. Shuttles (represented by arrows) were moved manually according to the prescribed moving paths. By varying the paths, there are alternatives to form the 3-axis fabrics with distinct interlacing patterns. Shown in Fig. 1 is the one that allows the outer axial yarns covered by interlacing loops only (not by straight portions of transverse yarns). This feature enables an easier assessment of the in¯uence of loops on the composite. Two types of 3-axis fabrics have been made. The ®rst (labeled YYR) comprises of carbon yarns in the x and y axes, while the solid carbon/epoxy rods are incorporated along the axial (z) direction. The second (labeled as YYY) is a conventional type composed of carbon yarns in all axes. The axial bundles were arranged in a 510 row-and-column pattern, as illustrated in Fig. 2a.
Fig. 1. Weaving steps for making the 3-axis fabrics.
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In both fabrics, the axial reinforcements (rod in the YYR and yarn in the YYY) are composed of one 12kcarbon tow, while the weaving yarns (x- and y-axis reinforcements) are composed of two 12k-carbon tows. The rods, made by pultrusion, were 1 mm in diameter and 58.8 vol% in ®ber content [7]. Both fabrics were then impregnated with the epoxy resin by using vacuum-assisted resin transfer molding. The resin used was the Ciba-Geigy LY564, cured at 60 C for 24 h and post-cured at 120 C for 4 h. Fig. 3 shows the typical YYR and YYY composites. Testing specimens were taken by cutting the cured composites normal to the axial direction. To investigate the in¯uence of loops, one half of the specimens were carefully ground to remove all surface loops; this loopremoving process is termed deloop in this work. The delooped YYR and YYY are labeled DL-YYR and DL-YYY, respectively. Thus, there are a total of four composite types in this study; their nominal dimensions are listed in Table 1. Fig. 2b schematically shows the cross-section of the delooped composites. To remove loops completely, the specimen surfaces were ground as precisely as possible so that a half cross-section of each axial bundle lying on the surface was removed, as illustrated in Fig. 2b. After being delooped, all the throughthickness (x- and y-axis) yarns become fragmented.
Fig. 2. Illustration of cross-sections of loop-retained and delooped composites.
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Fig. 3. Composites made in the present work.
Due to the grinding, the cross-sectional area is reduced, and the number of axial bundles is equivalently equal to 36 (49). The cross-section and the number of axial bundles are unequal in the loop-retained and delooped specimens. For this reason, comparisons between dierent types should be made on a per-area or per-bundle base, which can reduce the in¯uence of unequal cross-section to a minimum level. 4. Geometry of loops Each method of fabric formation yields a distinct pattern of surface loops. Although only the 3-axis type is examined, the concept and formulation can be similarly applied to other fabrics. 4.1. Unit cells Two unit cells are introduced for internal yarns and surface loops, as shown in Fig. 4. The representative volume for the internal yarns can be modeled as a cuboid with dimensions Lx, Ly and Lz along the x, y, and z directions, respectively [7,8]. Based on Fig. 4a, the cell dimensions are equal to the sum of the associated bundle sizes:
Lx Uy Uz ;
1
Ly Ux Wz ;
2
Lz Wx Wy ;
3
where Wi and Ui are cross-sectional dimensions of the iaxis yarns. For the YYR, the axial rods are circular with Wz=Uz=1 mm, and the x- and y-axis yarns are closely rectangular. For the YYY, the yarn cross-sections are less regular, often in a form of distorted ellipse. Nevertheless, the use of the unit cell for calculating ®ber distribution (Section 4.2) is appropriate for dierent crosssectional shapes. Fig. 4b illustrates the loop pattern on the yz surface and the unit cell for the loops. The unit cell on the yz surface has dimensions Ly and 2Lz. In the ®gure, Si is the spacing between i-axis yarns. The spacings Sy and Sz are indeed the allocated cross-sectional dimensions for the x-axis yarns (Wx and Ux). For loops on the xz surface, the unit cell is similar. 4.2. Fiber volume fractions For 3D composites, distribution of ®bers in each component is more informative than the overall ®ber
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Table 1 Construction and dimensions of the specimens Label
YYR
DL-YYR
YYY
DL-YYY
x-Axis y-Axis z-Axis Loops Specimen width (mm) Specimen thickness (mm) Lx (mm) Ly (mm) Lz (mm)
24k Yarn 24k Yarn 12k Rod Retained 19.5
24k Yarn 24k Yarn 12k Rod Removed 17.2
24k Yarn 24k Yarn 12k Yarn Retained 25.2
24k Yarn 24k Yarn 12k Yarn Removed 23.7
10.1
7.2
7.5
4.8
1.8 1.9 3.2
1.8 1.9 3.2
1.2 2.6 3.1
1.2 2.6 3.1
content. For the present fabrics, ®bers distribute in four components: x axis, y axis, z axis, and loops. Fiber distribution in the delooped composites is ®rst discussed. Since loops are absent, the delooped composite becomes an assemblage of the unit cell (Fig. 4a), allowing evaluation of the ®ber volume fractions from the unit cell. Because the number of carbon ®laments within a yarn is a constant, the volume of ®bers along each axis can be calculated as long as the unit cell dimensions are known. Thus, the volume fraction of the ®bers along the i axis (V®) can be expressed as Vfi
df 2 li Ni 4Lx Ly Lz
4
where Ni is the number of ®laments within the bundle (Table 1), df is the ®ber diameter (7 mm for the carbon ®bers), and li is the length of the bundle within the unit cell. Assuming the yarns are straight, li is equal to the unit cell dimension Li. The overall ®ber content (Vf) for the delooped composites is thus the sum of the three components: Vf Vfx Vfy Vfz :
5
When loops are involved, the unit cell must be rede®ned to account for the loops. To this end, the smallest representative volume is the volume formed by a cycle of weaving. The volume has a cross-section (w and h) de®ned in Fig. 2a and a depth equal to the pitch length (2Lz) de®ned in Fig. 4b. The ®ber volume fraction in each component can be calculated in a similar manner. Vfi
df 2 li Ni ; 8whLz
6
in which li is the total yarn length of the i-component within the volume. The overall ®ber content (Vf) is the sum of the four components:
Fig. 4. Unit cells for the fabric.
Vf Vfx Vfy Vfz Vfl ;
7
where V¯ is the volume fraction of ®bers in loops. Herein, the x and y-axis yarns are de®ned as the straight portions within the fabric, and the straight portions are indeed those included in the delooped fabric (Fig. 2b). Loops are de®ned as the weaving yarns outside the cross-section of the delooped fabric. Since there are 49 unit cells in the delooped cross-section, and there are two such layers in a pitch length, thus lx =72Lx and ly =72Ly. The yarn length of the z-axis, lz, is 100Lz. Loops are close to a half of an ellipse with the major axis
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(L2y+L2z )0.5 and the minor axis Lx. Loops on the xzsurface can be de®ned similarly. The length of the loops can be calculated by integrating the curve segments. Results of the ®ber volume fractions are listed in Table 2. Loops enlarge the fabric and reduce overall ®ber content. Because the present fabrics are relatively thin (only 5 layers of axial bundles), loops occupy signi®cant amount of ®ber volumeÐabout the same as other three components. The surface layers containing loops are less dense in ®ber content. When loops are removed, the overall ®ber content Vf is about 10% higher than the loop-retained counterparts. The in¯uence of loops on ®ber content should diminish when the number of axial bundles increases. It can be seen that the all-yarn composites are denser than the rod-reinforced counterparts, because yarns are shapeable and thinner than the rods.
fraction of axial yarn covered by loops. Based on the unit cell, the area covered by a loop is found to be AL Sy Wz Sz Wy 3Sy Sz :
According to the de®nition, the coverages become Cs
Sy Wz Sz Wy 3Sy Sz ÿ ; 2 Wz Sz Wy Sy
Cay
Sy Wz Sz Wy 2Sy Sz ÿ : 2 Wz Sz Wy Sy
4.3. Interlacing and intersecting angles At interlacing, each weaving yarn comes out from a surface, changes its direction, and reenters into the fabric, as shown in Fig. 5a. The loop connects two inside portions and makes an angular change , which is de®ned as the interlacing angle. The loop intersects the interlaced axial yarn by an angle de®ned as the intersecting angle y, as shown in Fig. 5b. For the present fabric, the angles are 180
8
Ly : tan Lz
9
ÿ1
These two angles characterize con®guration of a loop. 4.4. Coverage and jamming To characterize the density of loops, two terms are introduced: surface coverage (Cs) and axial-yarn coverage (Cay). Surface coverage, analogous to the conventional de®nition of coverage in 2D woven fabrics, is de®ned as the area fraction of the surface covered by loops. Axial-yarn coverage is de®ned as the length
Table 2 Fiber distribution and loop coverages Label
YYR
DL-YYR
YYY
DL-YYY
Vfx Vfy Vfz V¯ Vf
0.095 0.101 0.117 0.093 0.406
0.151 0.160 0.134 Ð 0.445
0.068 0.149 0.122 0.103 0.442
0.113 0.248 0.146 Ð 0.507
Cs Cay
0.61 0.49
Ð Ð
0.56 0.45
Ð Ð
10
Fig. 5. De®nition of the angles.
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Two non-dimensional ratios are introduced: ly
Sy ; Wy
lz
Sz : Wz
13
Physically, li characterizes the packing of the i-axis bundles. Using the ratios, the coverages can be expressed as ly lz 3ly lz ; Cs ÿ 2 1 ly 1 lz
14
ly lz 2ly lz : Cay ÿ 2 1 ly 1 lz
15
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the upper bound of the coverage, occurs within the range Cs=0.5±0.625. The calculated results of Cay are shown in Fig. 7. The Cay also increases with the ratios. The upper bound for Cay, independent of the ratios, is equal to 0.5, meaning that for each axial yarn at the outside, at least a half of its length will not be covered by loops. The coverages of the present fabrics are marked in the ®gures and also listed in Table 2. 4.5. Loop-caused deformation
Loop jamming is likely to occur when the bundles are thin and when bundle spacings are wide. If jamming occurs, the loop should be remodeled and the equations should be reformulated. Fig. 6 shows the calculated Cs as a function of ly and lz. The Cs increases with ly and lz until jamming occurs. Jamming of loops, representing
During fabric formation, applying tension to yarns is needed in order to straighten the yarns and compact the fabric. When an interlacing yarn changes its direction, a resultant force is created. For 2D weaves, the resultant force caused by the warp yarns can be counter-balanced by that caused by the weft yarns, since both are undulated. Unfortunately, the counter-balancing force does not exist in 3D fabrics. The interlaced yarns, usually the axial yarns designed to be straight, must be deformed in response to the resultant force. Fig. 8 is a micrograph of the 3-axis composite showing deformation of axial yarns. Fig. 9 illustrates how the deformation is formed. At each loop, the resultant force pushes the interlaced yarn toward the inward direction. As shown in the ®gure, steps 1 and 3 push the axial yarns to undulate in the x direction. In the same manner, steps 2 and 4 push the axial yarns to undulate in the y direction. Thus, the axial yarns are actually deformed in a helical form. The period of the helical de¯ection is, therefore, equal to the pitch length. In general, deformation of yarns due to interlacing in 3D fabrics is complex but perceivable through the processes of fabric formation. It is clear that interlacing loops not only deform the interlaced yarns on exterior,
Fig. 6. Calculated surface coverage as a function of the ratios (solid square: YYR, solid circle: YYY).
Fig. 7. Calculated axial-yarn coverage as a function of the ratios (solid square: YYR, solid circle: YYY).
It should be noted that the loop area [Eq. (10)] and thus the coverages are calculated under an assumption that loops do not overlap with each other Ð a condition otherwise known as jamming. According to Fig. 4b, neighboring loops overlap when Sz cot > Wy :
16
Combining Eqs.(9), (13) and (16), the condition for loop jamming becomes ly lz > 1:
17
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Fig. 8. Cross-section of the YYY showing loop-caused deformation in the axial yarns. Fig. 9. Illustration of loop-caused deformation.
they also aect yarns in interior. For this reason, although loops generally occupy only a tiny fraction of the overall volume, their in¯uence on the composite stiness can be disproportionate Ð not because of the crimp in themselves but because of the induced deformation in internal yarns. 5. Material characterization 5.1. Flexure test For the three-point bending tests, the specimen length was 100 mm, and the testing span was 70 mm. Four specimens were tested for each composite type. The specimens were placed with the axial direction normal to the loading edge. The cross-head speed was set at 2 mm/min and was halted after apparent damage had developed in the specimen. Both the cross-head displacement and the load were digitally acquired. After the test, each damaged specimen was immersed into a box containing low-viscosity, unsaturated polyester (UP) resin, which was then cured under a vacuum condition. The UP resin in®ltrated the crack openings and ®xed the originally developed damage, thereby allowing the subsequent slicing, grinding and polishing of the desired cross-sections.
5.1.1. Rod-reinforced composites The acquired load-de¯ection curves of the same type are generally very close in the slope, peak load, and shape of the non-linear portion; typical curves are shown in Fig. 10. Both the YYR and the DL-YYR are approximately linear at the initial loading. The curves become nonlinear beyond about 3 mm of de¯ection, entering a region in which the load drops and occasionally regains with the de¯ection. The YYR stays at a rather long plateau region before it eventually falls. In comparison, after reaching its peak load, the DL-YYR declines almost constantly with the de¯ection. Fig. 11 shows typical damaged specimens under the 3-point bending test. For both loop-retained and delooped specimens, compression-related failures are less apparent. The dominant damage modes are rupture of the rods and transverse matrix cracking Ð both initiating from the middle of the bottom surface, where the tensile strain is the highest (Fig. 11a). The eect of loops can be seen from Fig. 11b. Separation of the axial rods is common on the DL-YYR. When loaded in bending, the rods under tension tend to debond and slide. If this happens, the debonded rod can leave the surface Ð a mode termed as pop-out in this work. This mode is more pronounced in the impacted DL-YYR. For the loop-retained
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Fig. 11. Damage in the rod-reinforced composites due to the ¯exural load (left:YYR, right:DL-YYR).
Fig. 10. Typical load-de¯ection curves of the composites.
specimens, in comparison, pop-out of rods is impossible, since loops can ®rmly hold the rods. Another apparent mode of damage is transverse cracking, due to the tensile stress. Two types of transverse cracking have been observed. One is the dominant transverse crack that originates at the middle of the tensile side and penetrates nearly throughout the thickness. The dominant transverse crack causes extensive ruptures of the rods. The crack propagates along a socalled weaker-plane, which will be discussed. The other type is the multiple matrix cracks that run across the specimen surface in a parallel manner, as shown in the
YYR of Fig. 11a. These cracks, usually stop when they meet the ®ber bundles, are less harmful to the composite. 5.1.2. All-yarn composites Typical loading curves of the all-yarn composites are shown in Fig. 10b. The curves drop sharply after reaching the peak loads, in contrast to the YYR that has a long plateau in the nonlinear region. Fig. 12 shows typical damaged specimens. The damage con®gurations are similar to the rod-reinforced counterparts except that the pop-out of axial bundle is absent. The reason is attributed to the loop-caused deformation in axial yarns. An undulated bundle is more eective in transferring load to contiguous elements Ð through both normal and shear stresses on the bundle interface Ð than is a straight bundle. In the DL-YYY, large-scale
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Fig. 12. Tensile surfaces of the all-yarn composites due to the ¯exural load (left:YYY, right:DL-YYY).
debonding and sliding of undulated axial yarns are suppressed, thus ruling out the possibility of yarn popout. Since debonding and sliding consume energy and extend damaged zone, the lack of pop-out can lead to more detrimental damage in a smaller region. 5.2. Izod-impact test The Izod-impact test is illustrated in Fig. 13. The specimen, 50 mm in length, was clamped vertically with 30 mm above the support. The pendulum hit the specimen at 22 mm above the support (or 8 mm below the free end). Three specimens were tested for each composite type. The specimens were not notched. Although the Izod and Charpy impact tests are most commonly used for notched metals, they are also suitable for 3D composites. In contrast to metallic specimens that often break from the notch in a brittle manner, 3D composites can develop complex but nondisintegrated types of damage. Thus, while the test yields fracture toughness for metals, it provides the capability of energy absorption for the 3D composites. Moreover, this test readily reveals the role of loops in resisting exterior-initiated cracks. To compare the results of dierent composite types, the term unit absorbed-energy, de®ned as the absorbedenergy divided by the cross-sectional area of the specimen, is introduced. The results are shown in Fig. 14. The delooped specimens are notably lower than the corresponding loop-retained ones. Even normalized by
Fig. 13. Illustration of the Izod-impact test.
the cross-sectional area, the delooped specimens are still about 35% lower than the loop-retained counterparts. For both rod-reinforced and all-yarn composites, retaining surface loops is important in preserving the
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of the excessive defection. The third mode, rod pull-in, is visible from the surface of the DL-YYR (marked by the arrow in Fig. 15a). Rod pull-in is a sub-critical mode that combines debonding and sliding of rods, both consuming energy and contributing to impact tolerance. Loops can do very little in resisting rod pull-in. The DLYYR specimens were intensively damaged. Along with the aforementioned modes, rod pop-out is also apparent. Without being supported by loops, the rods on surface become likely to move apart from the surface. 5.2.2. All-yarn composites Fig. 16 shows the typical impacted YYY and DLYYY. For both types of composites, the damaged region is relatively smaller. The axial yarns were signi®cantly ruptured at the crack opening. The DL-YYY was the only type that can be completely fractured apart. Pull-in and pop-out of axial bundles, commonly seen in the rod-reinforced types, are absent in these types. Because of the loop-caused deformation, the axial yarns are undulated, and large-scale debonding and sliding are inhibited. Consequently, the majority of impact energy was absorbed by the tensile rupture of axial yarns. The brittle carbon yarns, under tensile rupture, can absorb a relatively small amount of energy. Due to the lack of yarn pull-in, no axial bundle was used to bridge the crack opening. Compared with the complex damage con®guration in the DL-YYR, the DL-YYY has developed a rather clean and regular transverse crack along the weaker-plane. This single and simple damage con®guration signi®cantly suppresses the potential for energy absorption, as revealed in the results of the unit absorbed-energy. 6. Role in damage resistance Fig. 14. Results of energy absorption of the impacted specimens.
capability of energy absorption. It is of interest to compare the YYR with the YYY (or the DL-YYR with the DL-YYY) Ð a comparison that manifests the eect of the rods. The rod-reinforced specimens are two times more capable in absorbing the impact energy. 5.2.1. Rod-reinforced composites When impacted, the specimens were fractured from the base, at which the bending moment was the highest. A dierence from the ¯exure test is that the specimens were excessively de¯ected at a much higher speed. Fig. 15 compares the impacted YYR and DL-YYR. The YYR was damaged in three modes: rod rupture, matrix cracking, and rod pull-in. Rod ruptures were extensive at the dominant crack. Compared with the 3-point bending tests, the crack opening is much wider because
6.1. Reinforcing weaker-planes No plane is truly weak in 3D composites that are multi-directionally reinforced. Yet these materials are macroscopically non-uniform, and inevitably some planes are relatively weaker. According to experimental observations, the weaker-planes locate at the interfacial planes between x- and y-axis yarns. Cracks along weaker-planes can avoid ®bers in the x- and y-axis yarns. Both the ¯exure and the impact tests result in bending, which causes tensile stress in one side and compressive stress in the other. All specimens showed that the dominant crack was initiated from the tensile side along a weaker-plane. Fig. 17 illustrates the locations of weaker-planes (marked by arrows), assuming that tensile side is on the right. Fig. 18 is a micrograph of the YYY specimen after the ¯exural test, showing a crack along the weaker-plane. The compressive side is on the top, at which the axial yarn was buckled, and a
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Fig. 15. Impacted specimens of the YYR (left) and the DL-YYR (right); the arrow indicating pull-in of the rods.
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Fig. 16. Impacted specimens of the YYY (left) and the DL-YYY (right).
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Fig. 18. A fractured YYY specimen under ¯exural load, showing a crack along the weaker-plane (compressive side on the top). Fig. 17. Locations of weaker-planes marked by arrows.
kink band was formed (indicated by the arrow). All other axial yarns were fractured due to tension. The crack grew along the plane without encountering ®bers in the x- and y-axis yarns. On surface, the x- and y-axis yarns are the loops, which can block the growth of the crack. The experiments showed that when a crack meets a loop, the crack is either stopped or de¯ected. In no case can a crack fracture the encountered loop. This suggests
that loops on the surface can cover the otherwise weaker-planes. When covered by loops, the weakerplanes are reinforced. For the present fabrics, loops cover a half of weaker-planes. Still, cracks can grow into the uncovered weaker-planes. To be more eective in resisting cracks, allowing fewer weaker-planes to outer attacks can be helpful. To this end, the weaving processes must be redesigned to obtain a loop pattern that covers more of the weaker-planes.
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6.2. Holding axial yarns In response to loads, 3D composites can develop complex deformation and stresses. The induced stresses could push apart the axial yarns that lie on outer surfaces. An example is the pop-out of rods seen in the DLYYR. Once an axial yarn tends to move apart, the transverse yarns must respond to prevent disintegration. In a loop-retained composite, the loops can ®rmly hold axial yarns. If loops are absent, on the other hand, separation of damaged yarns can take place rather easily. Holding axial yarns on outer surfaces appears to be an important function for the composite to remain integrated; a cascade of succeeding damage mechanisms could otherwise be triggered. From the viewpoint of energy absorption, preventing the composite from disintegration is bene®cial even when damage has developed in the interior. Another function of loops Ð related to holding axial yarns Ð is the transfer of loads into through-thickness yarns. To fully exploit 3D integrity, yarns in all directions should be able to carry load eectively. If loops on the surface are removed, the through-thickness yarns become fragmented. As a result, the through-thickness yarns become less eective in load-transfer, and the reinforcing eciency is also reduced. 7. Conclusions Four composite types display distinct damage con®gurations under the ¯exural and impact loads. The rodreinforced composites undergo more complex failure mechanisms and absorb more energy than do the allyarn counterparts. The all-yarn composites are damaged in a smaller region, in part because of the loop-caused deformation in axial yarns that inhibit large-scale debonding and sliding. Despite the specimens responding dierently to the loads, interlacing loops show the same importance for the 3D composites. Based on the damage con®gurations, two major functions of loops have been identi®ed. Loops act as a protective skin for 3D composites. They can defend the internal yarns from outer attacks through crack termination or de¯ection. The key lies in the fact that they cover the otherwise weaker-planes, along which cracks can penetrate into the interior. The number of weaker-planes in the delooped specimens is two times denser than that in the loop-retained composites. With a proper design of the weaving process, it is
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possible to achieve a loop pattern that covers more of weaker-planes. This is a topic of interest to pursue. Loops are also eective in holding axial yarns and in preventing disintegration. Were loops removed, the outer axial yarns are left unsupported, giving rise to the possibility of failure. Most important, the originally continuous through-thickness yarns become fragmented, thus lowering the load-transfer eciency and adversely aecting the 3D integrity. This function makes it clear that loops should be retained whenever possible, and a near-net-shape design without aftermachining is preferable. Two coverages describing the density of loops have been introduced. Although yet to be proved, the link between the coverages and the two functions could exist. A further quantitative study for the link is needed. Although loops appear to be favorable in terms of damage resistance, attention should be paid to the loopcaused deformation in internal yarns, which can lower the composite stiness and strength. Acknowledgements The author wishes to thank the Feng Chia University (FCU-RD-87-01) and the National Science Council of Taiwan, ROC (NSC 89-2216-E-035-002) for the support of this research. References 1 Chou TW. Microstructural design of ®ber composites. Cambridge, UK: Cambridge University Press, 1992. (p. 374±422). 2 Tan P, Tong L, Steven GP. Modelling for predicting the mechanical properties of textile composites Ð a review. Composites Part A 1997;28A:903±22. 3 Naik N.K. Woven fabric composites. Technomic Publishing Company, Lancaster: Basel, 1994. 4 Kuo WS, Chen HI. Fabrication and microgeometry of two-step braided composites incorporating pultruded rods. Composite Science and Technology 1997;57:1457±67. 5 Kuo WS, Ko TH, Chen HI. Elastic moduli and damage mechanisms in 3-D braided composites incorporating pultruded rods. Composites Part A 1998;29A:681±92. 6 Fitzer E. The future of carbon±carbon composites. Carbon 1987;25:163±90. 7 Kuo WS, Cheng KB. Processing and microstructures of 3-D woven fabric composites incorporating solid rods. Composites Science and Technology 1999;59:1833±46. 8 Kuo WS, Lee LC. Elastic and damage behavior of 3-D woven composites incorporating solid rods. Composites Part A 1999;30A:1135±48.