Appendixes A.1 WOVEN FABRIC TERMINOLOGY Basic woven fabrics consist of two sets of yarns interlaced at right angles to create a single layer.Such biaxial or 0/90 fabrics are characterized by the following nomenclature: 1.Yarn construction:May include the strand count as well as the number of strands twisted and plied together to make up the yarn.In case of glass fibers,the strand count is given by the yield expressed in yards per pound or in TEX,which is the mass in grams per 1000 m.For example,if the yarn is designated as 150 2/3,its yield is 150 X 100 or 15,000 yd/lb.The 2/after 150 indicates that the strands are first twisted in groups of two, and the/3 indicates that three of these groups are plied together to make up the final yarn.The yarns for carbon-fiber fabrics are called tows.They have little or no twist and are designated by the number of filaments in thousands in the tow.Denier(abbreviated as de)is used for designating Kevlar yarns,where 1 denier is equivalent to 1 g/9000 m of yarn. 2.Count:Number of yarns (ends)per unit width in the warp (lengthwise) and fill (crosswise)directions (Figure A.1.1).For example,a fabric count of 60 X 52 means 60 ends per inch in the warp direction and 52 ends per inch in the fill direction. 3.Weight:Areal weight of the fabric in ounces per square yard or grams per square meter. 4.Thickness:Measured in thousandths of an inch (mil)or in millimeters. 5.Weave style:Specifies the repetitive manner in which the warp and fill yarns are interlaced in the fabric.Common weave styles are shown in Figure A.1.2. (a)Plain weave,in which warp and fill yarns are interlaced over and under each other in an alternating fashion. (b)Basket weave,in which a group of two or more warp yarns are interlaced with a group of two or more fill yarns in an alternating fashion. (c)Satin weave,in which each warp yarn weaves over several fill yarns and under one fill yarn.Common satin weaves are crowfoot satin or four-harness satin,in which each warp yarn weaves over three and under one fill yarn,five-harness satin (over four,under one),and eight-harness satin (over seven,under one). 2007 by Taylor&Francis Group.LLC
Appendixes A.1 WOVEN FABRIC TERMINOLOGY Basic woven fabrics consist of two sets of yarns interlaced at right angles to create a single layer. Such biaxial or 0=90 fabrics are characterized by the following nomenclature: 1. Yarn construction: May include the strand count as well as the number of strands twisted and plied together to make up the yarn. In case of glass fibers, the strand count is given by the yield expressed in yards per pound or in TEX, which is the mass in grams per 1000 m. For example, if the yarn is designated as 150 2=3, its yield is 150 3 100 or 15,000 yd=lb. The 2= after 150 indicates that the strands are first twisted in groups of two, and the =3 indicates that three of these groups are plied together to make up the final yarn. The yarns for carbon-fiber fabrics are called tows. They have little or no twist and are designated by the number of filaments in thousands in the tow. Denier (abbreviated as de) is used for designating Kevlar yarns, where 1 denier is equivalent to 1 g=9000 m of yarn. 2. Count: Number of yarns (ends) per unit width in the warp (lengthwise) and fill (crosswise) directions (Figure A.1.1). For example, a fabric count of 60 3 52 means 60 ends per inch in the warp direction and 52 ends per inch in the fill direction. 3. Weight: Areal weight of the fabric in ounces per square yard or grams per square meter. 4. Thickness: Measured in thousandths of an inch (mil) or in millimeters. 5. Weave style: Specifies the repetitive manner in which the warp and fill yarns are interlaced in the fabric. Common weave styles are shown in Figure A.1.2. (a) Plain weave, in which warp and fill yarns are interlaced over and under each other in an alternating fashion. (b) Basket weave, in which a group of two or more warp yarns are interlaced with a group of two or more fill yarns in an alternating fashion. (c) Satin weave, in which each warp yarn weaves over several fill yarns and under one fill yarn. Common satin weaves are crowfoot satin or four-harness satin, in which each warp yarn weaves over three and under one fill yarn, five-harness satin (over four, under one), and eight-harness satin (over seven, under one). 2007 by Taylor & Francis Group, LLC
Warp FIGURE A.1.1 Warp and fill directions of fabrics. Plain weave fabrics are very popular in wet layup applications due to their fast wet-out and ease of handling.They also provide the least yarn slippage for a given yarn count.Satin weave fabrics are more pliable than plain weave fabrics and conform more easily to contoured mold surfaces. In addition to the biaxial weave described earlier,triaxial (0/60/-60 or 0/45/90)and quadraxial (0/45/90/-45)fabrics are also commercially avail- able.In these fabrics,the yarns at different angles are held in place by tying them with stitch yarns. Common weave styles Plain Crowfoot satin 5 Hamess satin FIGURE A.1.2 Common weave styles.(Courtesy of Hexcel Corporation.With permission.) 2007 by Taylor Francis Group,LLC
Plain weave fabrics are very popular in wet layup applications due to their fast wet-out and ease of handling. They also provide the least yarn slippage for a given yarn count. Satin weave fabrics are more pliable than plain weave fabrics and conform more easily to contoured mold surfaces. In addition to the biaxial weave described earlier, triaxial (0=60=60 or 0=45=90) and quadraxial (0=45=90=45) fabrics are also commercially available. In these fabrics, the yarns at different angles are held in place by tying them with stitch yarns. Warp Fill FIGURE A.1.1 Warp and fill directions of fabrics. Common weave styles Plain Crowfoot satin 5 Harness satin FIGURE A.1.2 Common weave styles. (Courtesy ofHexcel Corporation.With permission.) 2007 by Taylor & Francis Group, LLC
A.2 RESIDUAL STRESSES IN FIBERS AND MATRIX IN A LAMINA DUE TO COOLING [1] The following equations,derived on the basis of a composite cylinder model (Figure A.2.1),can be used to calculate the residual stresses in fibers and matrix in a unidirectional composite lamina developed due to differential thermal shrinkage as it cools down from the high processing temperature to the ambient temperature: =40+) 0m=A2, ==4-》 =4(-》 where =radial distance from the center of the fiber rr =fiber radius Im =matrix radius in the composite cylinder model,which is equal to (ri/ve) m,f =subscripts for matrix and fiber,respectively r,0,z=subscripts for radial,tangential (hoop),and longitudinal directions, respectively. Radial Fiber Matrix FIGURE A.2.1 Cross section of a composite cylinder model. 2007 by Taylor Francis Group.LLC
A.2 RESIDUAL STRESSES IN FIBERS AND MATRIX IN A LAMINA DUE TO COOLING [1] The following equations, derived on the basis of a composite cylinder model (Figure A.2.1), can be used to calculate the residual stresses in fibers and matrix in a unidirectional composite lamina developed due to differential thermal shrinkage as it cools down from the high processing temperature to the ambient temperature: srm ¼ A1 1 r2 m r2 , sum ¼ A1 1 þ r2 m r2 , szm ¼ A2, srf ¼ suf ¼ A1 1 r2 m r2 f , szf ¼ A2 1 r2 m r2 f , where r ¼ radial distance from the center of the fiber rf ¼ fiber radius rm ¼ matrix radius in the composite cylinder model, which is equal to (rf=vf 1 2) m,f ¼ subscripts for matrix and fiber, respectively r,u,z ¼ subscripts for radial, tangential (hoop), and longitudinal directions, respectively. Fiber Matrix rf r m Radial Tangential q FIGURE A.2.1 Cross section of a composite cylinder model. 2007 by Taylor & Francis Group, LLC.
The constants A and 42 are given by the following expressions: [(am-a)△22-(am-a)△12】 A1= △T △11△22-△21△12 T(am-a6)△1l-(am-a)△21 △7 △11△22-△21△12 where a=2+》 Ym+ 1 △2=-EaEa/ △21=- [I-m+ 1-m),(1+vm) EfrVf Em EmVf 1 △2=2Au △T =temperature change,which is negative for cooling E =modulus Poisson's ratio 9 =coefficient of linear thermal expansion volume fraction fl,fr,m=subscripts indicating fiber (longitudinal and radial)and matrix, respectively Figure A.2.2 shows the variation of residual stresses for a carbon fiber-epoxy lamina with ve =0.5.The largest stress in the matrix is the longitudinal stress, 0.2 4=0.5 Longitudinal Hoop 0.1 Fiber Matrix 0 Hoop -0.1 Radial Longitudinal -0.2 0.5 1.0 1.5 rir FIGURE A.2.2 Thermal stresses in the fiber and the matrix as a function of radial distance in a 50 vol%AS carbon fiber-reinforced epoxy matrix.(Adapted from Nairn, J.A.,Polym.Compos.,6,123,1985.) 2007 by Taylor Francis Group,LLC
The constants A1 and A2 are given by the following expressions: A1 ¼ (am af1)D22 (am afr)D12 D11D22 D21D12 DT A2 ¼ (am afr)D11 (am af1)D21 D11D22 D21D12 DT where D11 ¼ 2 nm Em þ nf1 Efl vm vf D12 ¼ vm Eflvf þ 1 Em D21 ¼ (1 nfr)vm Efrvf þ (1 nm) Em þ (1 þ nm) Emvf D22 ¼ 1 2 D11 DT ¼ temperature change, which is negative for cooling E ¼ modulus n ¼ Poisson’s ratio a ¼ coefficient of linear thermal expansion v ¼ volume fraction fl, fr, m ¼ subscripts indicating fiber (longitudinal and radial) and matrix, respectively Figure A.2.2 shows the variation of residual stresses for a carbon fiber–epoxy lamina with vf ¼ 0.5. The largest stress in the matrix is the longitudinal stress, Longitudinal Longitudinal 0.5 0.2 0.1 0 0.1 0.2 1.0 r/rf 1.5 Hoop Hoop Matrix Radial Fiber Stress (MPa) per C vf = 0.5 FIGURE A.2.2 Thermal stresses in the fiber and the matrix as a function of radial distance in a 50 vol% AS carbon fiber-reinforced epoxy matrix. (Adapted from Nairn, J.A., Polym. Compos., 6, 123, 1985.) 2007 by Taylor & Francis Group, LLC.
which is tensile.If it is assumed that the lamina is cured from 177C to 25C, the magnitude of this stress will be 29.3 MPa,which is ~25%of the ultimate strength of the matrix.The hoop stress in the matrix is also tensile,while the radial stress is compressive. REFERENCE 1.J.A.Nairn,Thermoelastic analysis of residual stresses in unidirectional high- performance composites,Polym.Compos.,6:123 (1985). 2007 by Taylor Francis Group.LLC
which is tensile. If it is assumed that the lamina is cured from 1778C to 258C, the magnitude of this stress will be 29.3 MPa, which is ~25% of the ultimate strength of the matrix. The hoop stress in the matrix is also tensile, while the radial stress is compressive. REFERENCE 1. J.A. Nairn, Thermoelastic analysis of residual stresses in unidirectional highperformance composites, Polym. Compos., 6:123 (1985). 2007 by Taylor & Francis Group, LLC