where the transformation matrix is [1-6] 3 n2 2mn [T]= n2 m2 -2mn (2.14) -mn mn m2-n2 and m cos 0 (2.15a) n=sin 0 (2.15b) From Equations (2.12)and (2.13)it is possible to establish the lamina strain-stress relations in the (x,y)coordinate system [1-6] Ex 516 6 Ey 69 (2.16) 56 Sao The S terms are the transformed compliances defined in Appendix A. Similarly,the lamina stress-strain relations become x Q16 y Qu2 y (2.17)） txy] Q16 Q where the overbars denote transformed reduced stiffness elements,defined in Appendix A. 2.1.2 Hygrothermal Strains If fibrous composite materials are processed at elevated temperatures,ther- mal strains are introduced during cooling to room temperature,leading to residual stresses and dimensional changes.Figure 2.4 illustrates dimensional changes of a composite subjected to a temperature increase of AT from the reference temperature T.Furthermore,polymer matrices are commonly hygroscopic,and absorbing moisture leads to swelling of the material.The analysis of moisture expansion strains in composites is mathematically ©2003 by CRC Press LLCwhere the transformation matrix is [1–6] (2.14) and m = cos θ (2.15a) n = sin θ (2.15b) From Equations (2.12) and (2.13) it is possible to establish the lamina strain–stress relations in the (x,y) coordinate system [1–6] (2.16) The Sij terms are the transformed compliances defined in Appendix A. Similarly, the lamina stress–strain relations become (2.17) where the overbars denote transformed reduced stiffness elements, defined in Appendix A. 2.1.2 Hygrothermal Strains If fibrous composite materials are processed at elevated temperatures, ther￾mal strains are introduced during cooling to room temperature, leading to residual stresses and dimensional changes. Figure 2.4 illustrates dimensional changes of a composite subjected to a temperature increase of ∆T from the reference temperature T. Furthermore, polymer matrices are commonly hygroscopic, and absorbing moisture leads to swelling of the material. The analysis of moisture expansion strains in composites is mathematically T = m n mn n m mn mn mn m n [ ] − − −             2 2 2 2 2 2 2 2 x y xy y xy S S S SSS SSS ε ε γ σ σ τ             =                             11 12 16 12 22 26 16 26 66 x x y xy x y xy Q Q Q QQQ QQQ σ σ τ ε ε γ             =                           11 12 16 12 22 26 16 26 66 TX001_ch02_Frame Page 15 Saturday, September 21, 2002 4:48 AM © 2003 by CRC Press LLC