3.1 Basic Equations 27 Unit Cell Fig.3.2.A unit cell in a hexagonal-packed array of fiber-reinforced composite material where and are Poisson's ratios for the fiber and matrix,respectively. For Young's modulus in the 2-direction (also called the transverse stiffness), we have the following relation: 1 vf vm 瓦可+D (3.4) where E is Young's modulus of the fiber in the 2-direction while Em is Young's modulus of the matrix.For the shear modulus G12,we have the following relation: 1 vf vm (3.5) where G and Gare the shear moduli of the fiber and matrix,respectively. For the coefficients of thermal expansion a and a2 (see Problem 2.9),we have the following relations: afEiv/+amEmym (3.6) EfVf+EmVm g=g-()4a-av网 +e+()a-v (3.7) where of and ag are the coefficients of thermal expansion for the fiber in the 1- and 2-directions,respectively,and am is the coefficient of thermal expansion3.1 Basic Equations 27 Fig. 3.2. A unit cell in a hexagonal-packed array of fiber-reinforced composite material where νf 12 and νm are Poisson’s ratios for the fiber and matrix, respectively. For Young’s modulus in the 2-direction (also called the transverse stiffness), we have the following relation: 1 E2 = V f Ef 2 + V m Em (3.4) where Ef 2 is Young’s modulus of the fiber in the 2-direction while Em is Young’s modulus of the matrix. For the shear modulus G12, we have the following relation: 1 G12 = V f Gf 12 + V m Gm (3.5) where Gf 12 and Gm are the shear moduli of the fiber and matrix, respectively. For the coefficients of thermal expansion α1 and α2 (see Problem 2.9), we have the following relations: α1 = αf 1Ef 1 V f + αmEmV m Ef 1 V f + EmV m (3.6) α2 =  αf 2 − Em E1  νf 1 (αm − αf 1 )V m  V f +  αm +  Ef 1 E1  νm(αm − αf 1 )V f  V m (3.7) where αf 1 and αf 2 are the coefficients of thermal expansion for the fiber in the 1- and 2-directions, respectively, and αm is the coefficient of thermal expansion