which can be rewritten as: Yer YeVm+Yevr @+① @ ① Gm tuvj 1 Gu=Gm a-叨+号 (10.5)3 10.5 THERMOELASTIC PROPERTIES 10.5.1 Isotropic Material:Recall When the influence of temperature is taken into consideration,Hooke's law for the case of no temperature influence: e=1z-营ace(21 is replaced by the Hooke-Dubamel law: e=z-首ace(②I+aaTI (10.6 where g=Strain tensor Σ=Stress tensor I=Unity tensor E,v Elastic constants for the considered material a Coefficient of thermal expansion' AT=Change in temperature with respect to a reference temperature at which the stresses and strains are nil 10.5.2 Case of Unidirectional Composite The coefficient of thermal expansion of the matrix is usually much larger (more than ten times)than that of the fiber.'In Figure 10.4,one can imagine that even in the absence of mechanical loading,a change in temperature AT will produce a 3A few values of the shear modulus are shown in Section 3.3.1. See Section 16,"Principal Physical Properties." 2003 by CRC Press LLCwhich can be rewritten as: (10.5) 3 10.5 THERMOELASTIC PROPERTIES 10.5.1 Isotropic Material: Recall When the influence of temperature is taken into consideration, Hooke’s law for the case of no temperature influence: is replaced by the Hooke–Duhamel law: (10.6) where e = Strain tensor S = Stress tensor I = Unity tensor E, n = Elastic constants for the considered material a = Coefficient of thermal expansion 4 DT = Change in temperature with respect to a reference temperature at which the stresses and strains are nil 10.5.2 Case of Unidirectional Composite The coefficient of thermal expansion of the matrix is usually much larger (more than ten times) than that of the fiber. 4 In Figure 10.4, one can imagine that even in the absence of mechanical loading, a change in temperature DT will produce a 3 A few values of the shear modulus Gf are shown in Section 3.3.1. 4 See Section 1.6, “Principal Physical Properties.” g
t m + f g
tVm m g
tVf f = + t
t G
t ------- t
t Gm -------Vm t
t Gf = + -----Vf 1 G
t ------- Vm Gm ------- Vf Gf = + ----- G
t Gm 1 1 – Vf ( ) Gm Gf + -------Vf = ------------------------------------ e 1 + n E ------------S n E = – -- trace( ) S I e 1 + n E ------------S n E = – -- trace( ) S I + aDT I TX846_Frame_C10 Page 219 Monday, November 18, 2002 12:25 PM © 2003 by CRC Press LLC