Table 3.1 Common Fiber Volume Fractions in Different Processes Molding Process Fiber Volume Fraction Contact Molding 30% Compression Molding 40% Filament Winding 60%-85% Vacuum Molding 50%-80% 3.2.2 Fiber Volume Fraction Fiber volume fraction is defined as = Volume of fiber Total volume As a result,the volume of matrix is given as Vm= Volume of matrix Total volume withs Vm=1- Note that one can convert from mass fraction to volume fraction and vice versa.If p,and p are the specific mass of the fiber and matrix,respectively,we have =M+匹 Pr ViPL My=Vrpr+Vupm Py P Depending on the method of fabrication,the common fiber volume fractions are as shown in Table 3.1. 3.2.3 Mass Density of a Ply The mass density of a ply can be calculated as p=total mass total volume 5In reality,the mixture of fiber/matrix also includes a small volume of voids,characterized by the porosity of the composite.One has then V+V+Ve=1,in which V denotes the percentage of"volume of void/total volume."V is usually much less than 1 (See Exercise 18.1.11). 2003 by CRC Press LLC
3.2.2 Fiber Volume Fraction Fiber volume fraction is defined as As a result, the volume of matrix is given as with5 Note that one can convert from mass fraction to volume fraction and vice versa. If rf and rm are the specific mass of the fiber and matrix, respectively, we have Depending on the method of fabrication, the common fiber volume fractions are as shown in Table 3.1. 3.2.3 Mass Density of a Ply The mass density of a ply can be calculated as Table 3.1 Common Fiber Volume Fractions in Different Processes Molding Process Fiber Volume Fraction Contact Molding 30% Compression Molding 40% Filament Winding 60%–85% Vacuum Molding 50%–80% 5 In reality, the mixture of fiber/matrix also includes a small volume of voids, characterized by the porosity of the composite. One has then Vm + Vf + Vp = 1, in which Vp denotes the percentage of “volume of void/total volume.” Vp is usually much less than 1 (See Exercise 18.1.11). Vf Volume of fiber Total volume = ---------------------------------------- Vm Volume of matrix Total volume = -------------------------------------------- Vm = 1 – Vf Vf Mf rf ---- Mf rf ---- Mm r m + ----- = ----------------- Mf Vfrf Vfrf + Vmrm = ------------------------------ r total mass total volume = ------------------------------- TX846_Frame_C03 Page 34 Monday, November 18, 2002 12:05 PM © 2003 by CRC Press LLC
Table 3.2 Ply Thicknesses of Some Common Composites M H E glass 34% 0.125mm R glass 68% 0.175mm Kevlar 65% 0.13mm H.R.Carbon 68% 0.13mm The above equation can also be expanded as p=mass of fiber mass of matrix total volume total volume volume of fiber erpvolume of matrix Pm total volume total volume or P=prVr+puVm 3.2.4 Ply Thickness The ply thickness is defined as the number of grams of mass of fiber mor per m of area.The ply thickness,denoted as b,is such that: b×l(m)=total volume=total volume× mof fiber volume x p or b= mof Vres One can also express the thickness in terms of mass fraction of fibers rather than in terms of volume fraction. =m[】 Table 3.2 shows a few examples of ply thicknesses 3.3 UNIDIRECTIONAL PLY 3.3.1 Elastic Modulus The mechanical characteristics of the fiber/matrix mixture can be obtained based on the characteristics of each of the constituents.In the literature,there are theoretical as well as semi-empirical relations.As such,the results from these relations may not always agree with experimental values.One of the reasons is 2003 by CRC Press LLC
The above equation can also be expanded as or 3.2.4 Ply Thickness The ply thickness is defined as the number of grams of mass of fiber mof per m2 of area. The ply thickness, denoted as h, is such that: or One can also express the thickness in terms of mass fraction of fibers rather than in terms of volume fraction. Table 3.2 shows a few examples of ply thicknesses. 3.3 UNIDIRECTIONAL PLY 3.3.1 Elastic Modulus The mechanical characteristics of the fiber/matrix mixture can be obtained based on the characteristics of each of the constituents. In the literature, there are theoretical as well as semi-empirical relations. As such, the results from these relations may not always agree with experimental values. One of the reasons is Table 3.2 Ply Thicknesses of Some Common Composites Mf H E glass 34% 0.125 mm R glass 68% 0.175 mm Kevlar 65% 0.13 mm H.R. Carbon 68% 0.13 mm r mass of fiber total volume -------------------------------- mass of matrix total volume = + ------------------------------------- volume of fiber total volume ---------------------------------------rf volume of matrix total volume = + -------------------------------------------- rm r r = fVf + rmVm h ¥ 1 m2 ( ) total volume total volume mof fiber volume ¥ rf = = ¥ ------------------------------------------- h mof Vfrf = --------- h mof 1 rf ---- 1 rm ------ 1 – Mf Mf -------------- Ë ¯ Ê ˆ = + TX846_Frame_C03 Page 35 Monday, November 18, 2002 12:05 PM © 2003 by CRC Press LLC
Table 3.3 Fiber Elastic Modulus Glass Carbon Carbon E Kevlar H.R. H.M. fiber longitudinal modulus in e direction Efe (MPa) 74.000 130,000230,000 390.000 fiber transverse modulus in t direction Ef (MPa) 74,000 5400 15,000 6000 fiber shear modulus Gfa (Mpa) 30,000 12,000 50,000 20,000 fiber Poisson ratio via 0.25 0.4 0.3 0.35 Isotropic Anisotropic because the fibers themselves exhibit some degree of anisotropy.In Table 3.3, one can see small values of the elastic modulus in the transverse direction for Kevlar and carbon fibers,whereas glass fiber is isotropic. With the definitions in the previous paragraph,one can use the following relations to characterize the unidirectional ply: Modulus of elasticity along the direction of the fiber E is given by? E ErVt+EmVm or Ee=E'+Em(1-月 In practice,this modulus depends essentially on the longitudinal mod- ulus of the fiber,E because E<<E (as Em resin/Eglss6%). Modulus of elasticity in the transverse direction to the fiber axis,E: In the following equation,E represents the modulus of elasticity of the 6This is due to the drawing of the carbon and Kevlar fibers during fabrication.This orients the chain of the molecules. Chapter 10 gives details for the approximate calculation of the moduli E.E Ge and v which lead to these expressions. 2003 by CRC Press LLC
because the fibers themselves exhibit some degree of anisotropy. In Table 3.3, one can see small values of the elastic modulus in the transverse direction for Kevlar and carbon fibers, whereas glass fiber is isotropic. 6 With the definitions in the previous paragraph, one can use the following relations to characterize the unidirectional ply: Modulus of elasticity along the direction of the fiber El is given by 7 E = Ef Vf + EmVm or In practice, this modulus depends essentially on the longitudinal modulus of the fiber, Ef , because Em << Ef (as Em resin/Ef glass # 6%). Modulus of elasticity in the transverse direction to the fiber axis, Et: In the following equation, Eft represents the modulus of elasticity of the Table 3.3 Fiber Elastic Modulus Glass Carbon Carbon E Kevlar H.R. H.M. fiber longitudinal modulus in direction Ef (MPa) 74,000 130,000 230,000 390,000 fiber transverse modulus in t direction Eft (MPa) 74,000 5400 15,000 6000 fiber shear modulus Gft (Mpa) 30,000 12,000 50,000 20,000 fiber Poisson ratio vft 0.25 0.4 0.3 0.35 Isotropic 6 This is due to the drawing of the carbon and Kevlar fibers during fabrication. This orients the chain of the molecules. 7 Chapter 10 gives details for the approximate calculation of the moduli E, Et , Gt and ut which lead to these expressions. Anisotropic Ï Ô Ô Ô Ô Ô Ì Ô Ô Ô Ô Ô Ó E EfVf Em 1 – Vf = + ( ) TX846_Frame_C03 Page 36 Monday, November 18, 2002 12:05 PM © 2003 by CRC Press LLC