214 Mechanics of Composite Materials,Second Edition _MLM.-ML+ abc P Pm and the volume fraction of voids then is ==1-1M+M-M (3.20) abc abc Ps Alternative Solution The preceding problem can also be solved by using Equation(3.16).The theoretical density of the composite is Pa=P/V+Pm(1-V), (3.21) where V/is the theoretical fiber volume fraction given as volume of fibers volume of fibers+volume of matrix M Pr Vi-ML,M-M (3.22) Pr Pim The experimental density of the composite is Pee= M (3.23) abc Substituting Equation(3.21)through Equation(3.23)in the definition of void volume fractions given by Equation (3.16), (3.24) Experimental determination:the fiber volume fractions of the constituents of a composite are found generally by the burn or the acid digestion tests.These tests involve taking a sample of composite and weighing it.Then the density 2006 by Taylor Francis Group,LLC214 Mechanics of Composite Materials, Second Edition , and the volume fraction of voids then is (3.20) Alternative Solution The preceding problem can also be solved by using Equation (3.16). The theoretical density of the composite is , (3.21) where Vf ′ is the theoretical fiber volume fraction given as (3.22) The experimental density of the composite is (3.23) Substituting Equation (3.21) through Equation (3.23) in the definition of void volume fractions given by Equation (3.16), (3.24) Experimental determination: the fiber volume fractions of the constituents of a composite are found generally by the burn or the acid digestion tests. These tests involve taking a sample of composite and weighing it. Then the density abc M MM v f f c f m = + v − + ρ ρ V v abc abc M MM v v f f c f m = =− + ⎡ − ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1 1 ρ ρ ρρ ρ ct f f m f = V V ′ + − ( ) 1 ′ ′ = + V volume of fibers volume of fibers volume f of matrix ′ = + − V M f M MM f f f f c f m ρ ρ ρ . ρce Mc abc = . V abc M MM v f f c f m =− + ⎡ − ⎣ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ 1 1 ρ ρ . 1343_book.fm Page 214 Tuesday, September 27, 2005 11:53 AM © 2006 by Taylor & Francis Group, LLC