The constants A and 42 are given by the following expressions: [(am-a)△22-(am-a)△12】 A1= △T △11△22-△21△12 T(am-a6)△1l-(am-a)△21 △7 △11△22-△21△12 where a=2+》 Ym+ 1 △2=-EaEa/ △21=- [I-m+ 1-m),(1+vm) EfrVf Em EmVf 1 △2=2Au △T =temperature change,which is negative for cooling E =modulus Poisson's ratio 9 =coefficient of linear thermal expansion volume fraction fl,fr,m=subscripts indicating fiber (longitudinal and radial)and matrix, respectively Figure A.2.2 shows the variation of residual stresses for a carbon fiber-epoxy lamina with ve =0.5.The largest stress in the matrix is the longitudinal stress, 0.2 4=0.5 Longitudinal Hoop 0.1 Fiber Matrix 0 Hoop -0.1 Radial Longitudinal -0.2 0.5 1.0 1.5 rir FIGURE A.2.2 Thermal stresses in the fiber and the matrix as a function of radial distance in a 50 vol%AS carbon fiber-reinforced epoxy matrix.(Adapted from Nairn, J.A.,Polym.Compos.,6,123,1985.) 2007 by Taylor Francis Group,LLC.The constants A1 and A2 are given by the following expressions: A1 ¼ (am
af1)D22
(am
afr)D12 D11D22
D21D12  DT A2 ¼ (am
afr)D11
(am
af1)D21 D11D22
D21D12  DT where D11 ¼ 2 nm Em þ nf1 Efl vm vf
D12 ¼
vm Eflvf þ 1 Em
D21 ¼
(1
nfr)vm Efrvf þ (1
nm) Em þ (1 þ nm) Emvf   D22 ¼ 1 2 D11 DT ¼ temperature change, which is negative for cooling E ¼ modulus n ¼ Poisson’s ratio a ¼ coefficient of linear thermal expansion v ¼ volume fraction fl, fr, m ¼ subscripts indicating fiber (longitudinal and radial) and matrix, respectively Figure A.2.2 shows the variation of residual stresses for a carbon fiber–epoxy lamina with vf ¼ 0.5. The largest stress in the matrix is the longitudinal stress, Longitudinal Longitudinal 0.5 0.2 0.1 0 0.1 0.2 1.0 r/rf 1.5 Hoop Hoop Matrix Radial Fiber Stress (MPa) per C vf = 0.5 FIGURE A.2.2 Thermal stresses in the fiber and the matrix as a function of radial distance in a 50 vol% AS carbon fiber-reinforced epoxy matrix. (Adapted from Nairn, J.A., Polym. Compos., 6, 123, 1985.)
2007 by Taylor & Francis Group, LLC.