206 Mechanics of Composite Materials,Second Edition from Equation (3.2)as 0r+0m=0c· From the definition of the density of a single material, Wc=rVcr ws=ror,and (3.3a-c) Wm=YmUm Substituting Equation(3.3)in Equation(3.2),the mass fractions and vol- ume fractions are related as vand W= Wm= P碰Vw (3.4a,b) Pe in terms of the fiber and matrix volume fractions.In terms of individual constituent properties,the mass fractions and volume fractions are related by P WI= Pm一Vf' PLV+Vm Pm Wn= 1 Vm (3.5a,b) L(1-Vm)+Vm P One should always state the basis of calculating the fiber content of a composite.It is given in terms of mass or volume.Based on Equation(3.4), it is evident that volume and mass fractions are not equal and that the mismatch between the mass and volume fractions increases as the ratio between the density of fiber and matrix differs from one. 2006 by Taylor Francis Group,LLC206 Mechanics of Composite Materials, Second Edition from Equation (3.2) as . From the definition of the density of a single material, (3.3a–c) Substituting Equation (3.3) in Equation (3.2), the mass fractions and vol￾ume fractions are related as (3.4a, b) in terms of the fiber and matrix volume fractions. In terms of individual constituent properties, the mass fractions and volume fractions are related by . (3.5a, b) One should always state the basis of calculating the fiber content of a composite. It is given in terms of mass or volume. Based on Equation (3.4), it is evident that volume and mass fractions are not equal and that the mismatch between the mass and volume fractions increases as the ratio between the density of fiber and matrix differs from one. w f m + w = wc w r v w r v w r v c c c f f f m m m = = = , , . and f f c W = V f , ρ ρ and m m c W = V m, ρ ρ f f m f m f m W = f V +V V , ρ ρ ρ ρ W V V m V f m m m = m − + 1 1 ρ ρ ( ) 1343_book.fm Page 206 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC