278 L.N.McCartney 7.3.1 Properties Derived from the Lame Solution By making use of Maxwell's methodology in conjunction with the Lame solution for two bonded concentric cylinders,several properties of a fiber- reinforced composite can be estimated.It has been shown [8]that the following effective properties for the multiphase fiber-reinforced com- posite Transverse bulk modulus: Axial Poisson's ratio: Axial thermalexpansion coefficient: Transverse thermal expansion coefficient:a may be estimated using the formulae 京》 (7.16) 吹吹-好 (7.17) a+听a欧)-a+a+(+) (7.18) where 11 1 1 11 (7.19) 1 i=l - 1 (7.20) 1 11solution for two bonded concentric cylinders, several properties of a fiber￾reinforced composite can be estimated. It has been shown [8] that the T A A T may be estimated using the formulae 1 eff m m T 1T T 1 11 , k k 1 µ ⎛ ⎞ Λ = + ⎜ ⎟ − Λ ⎝ ⎠ (7.16) eff m A A2 m eff T T 1 1 , k ν ν µ ⎛ ⎞ = −Λ + ⎜ ⎟ ⎝ ⎠ (7.17) eff eff eff m m m T AA T A A 3 m eff T T 1 1 ( ) ( ) , k α να α ν α µ ⎛ ⎞ + = + + Λ + ⎜ ⎟ ⎝ ⎠ (7.18) where m eff m TT T T 1 f 1 m meff TT TT 11 1 1 , 11 1 1 N i i i i kk k k V µ µ k k = − − Λ = = + + ∑ (7.19) m meff AA AA 2 f 1 m meff TT TT , 11 1 1 N i i i i V k k νν νν µ µ = − − Λ = = + + ∑ (7.20) L.N. McCartney posite Transverse bulk modulus: k Axial thermalexpansion coefficient:α Transverse thermal expansion coefficient:α Axial Poisson’s ratio:ν eff eff eff eff following effective properties for the multiphase fiber-reinforced com￾By making use of Maxwell’s methodology in conjunction with the Lamé 7.3.1 Properties Derived from the Lamé Solution 278