Micromechanical Analysis of a Lamina 213 Wc Pa-Pa (3.15) Poel Pa Substituting Equation (3.13)and Equation (3.15)in Equation (3.11),the volume fraction of the voids is (3.16) =Pa-Pac Pa Example 3.2 A graphite/epoxy cuboid specimen with voids has dimensions of a x b x c and its mass is M After it is put it into a mixture of sulfuric acid and hydrogen peroxide,the remaining graphite fibers have a mass M.From independent tests,the densities of graphite and epoxy are pand P respectively.Find the volume fraction of the voids in terms of a,b,c,MoM Po and P Solution The total volume of the composite v is the sum total of the volume of fiber Ur,matrix v,and voids v: 0e=Ur+0m+0。 (3.17) From the definition of density, L 0- (3.18a) P M.-Mr 0m= (3.18b) Pm The specimen is a cuboid,so the volume of the composite is Ve=abc. (3.19) Substituting Equation(3.18)and Equation(3.19)in Equation(3.17)gives 2006 by Taylor Francis Group,LLCMicromechanical Analysis of a Lamina 213 (3.15) Substituting Equation (3.13) and Equation (3.15) in Equation (3.11), the volume fraction of the voids is (3.16) Example 3.2 A graphite/epoxy cuboid specimen with voids has dimensions of a × b × c and its mass is Mc. After it is put it into a mixture of sulfuric acid and hydrogen peroxide, the remaining graphite fibers have a mass Mf . From independent tests, the densities of graphite and epoxy are ρf and ρm, respectively. Find the volume fraction of the voids in terms of a, b, c, Mf , Mc, ρf , and ρm. Solution The total volume of the composite vc is the sum total of the volume of fiber vf , matrix vm, and voids vv: (3.17) From the definition of density, (3.18a) (3.18b) The specimen is a cuboid, so the volume of the composite is (3.19) Substituting Equation (3.18) and Equation (3.19) in Equation (3.17) gives v w v c ce ct ce ct = ⎛ − ⎝ ⎜ ⎞ ⎠ ⎟ ρ ρ ρ ρ . V v v v v c ct ce ct = = ρ ρ − ρ . vvv v c f mv =++ . v M f f f = ρ , v M M m c f m = − ρ . v abc c = . 1343_book.fm Page 213 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC