CT. Herakovich/Mechanics Research Communications 41(2012)1-20 4.0 MOC-Tl L St Matls Fig 10. Composite laminate. 0,25非 0750 Poisson ratio: Ey Fig 8. Shear modulus predictions for carbon/epoxy Vxy 8x (11) fibers in the kth layer oriented at an angle ek from a global x-axis s depicted in Fig. 10. ix (12) Analysis results in the fundamental equation relating the inplane forces N and moments ( M acting on the laminate to Coefficient of mutual influence the midplane strains E) and curvatures( x) through coefficients [A] [B]and ( D] that are functions of the material properties, layers nxy xei ai1 thickness and stacking sequence of the layers N A B The coefficient of mutual influence(13)quantifies the shear ( 8) strain associated with normal strain; it is non-zero when the lam- inate compliance t The effective engineering properties of symmetric laminates can Specific examples of the range of engineering properties thatcan be predicted from Eq ( 8)through a series of thought experimen be affected through the choice of material and stacking sequence here the laminate is subjected to a series of specified loadings. are presented in Figs 11-13. These figures show the variation in With the laminate compliance defined: axial modulus, Poisson ratio and shear modulus for T300/5208 car- bon/epoxy. la]=2HIAJ-I (9) These three figures show that the effective engineering prop- for the engineering properties of the laminate. Examples are. ons erties of angle-ply laminates are higher than those of the Axial modulus: inates can exhibit values greater than 1.0, and the shear modulus of angle-ply laminates is largest at 45. Ex Another most interesting result for laminated composites (Fig. 14)is the fact that the through-the-thickness P 20.0 0.400 0.200 MOC-TI 0.100 .Mori-Tanaka 含 St matls 0.0 0.00 0.0 0.250 0.750 20.00 8000 Fig. 11. Axial modulus -unidirectional and angle-ply laminates.C.T. Herakovich / Mechanics Research Communications 41 (2012) 1–20 7 Fig. 8. Shear modulus predictions for carbon/epoxy. fibers in the kth layer oriented at an angle k from a global x-axis as depicted in Fig. 10. Analysis results in the fundamental equation relating the inplane forces {N} and moments {M} acting on the laminate to the midplane strains {ε◦} and curvatures { } through coefficients [A], [B] and [D] that are functions of the material properties, layers thickness and stacking sequence of the layers.  N M  =  A B B D  ε◦  (8) The effective engineering properties of symmetric laminates can be predicted from Eq. (8) through a series of thought experiments where the laminate is subjected to a series of specified loadings. With the laminate compliance defined: [a∗] ≡ 2H[A] −1 (9) The results of these thought experiments provide expressions for the engineering properties of the laminate. Examples are: Axial modulus: Ex = ¯ x ε◦ x = 1 a∗ 11 (10) Fig. 9. Poisson’s ratio predictions for carbon/epoxy. Fig. 10. Composite laminate. Poisson ratio: xy = −ε◦ y ε◦ x = −a∗ 12 a∗ 11 (11) Shear modulus: Gxy = ¯xy ◦ xy = 1 a∗ 66 (12) Coefficient of mutual influence: xy,x = ◦ xy ε◦ x = a∗ 16 a∗ 11 (13) The coefficient of mutual influence (13) quantifies the shear strain associated with normal strain; it is non-zero when the lam￾inate compliance term a∗ 16 is non-zero. Specific examples ofthe range of engineering properties that can be affected through the choice of material and stacking sequence are presented in Figs. 11–13. These figures show the variation in axial modulus, Poisson ratio and shear modulus for T300/5208 car￾bon/epoxy. These three figures show that the effective engineering prop￾erties of angle-ply laminates are higher than those of the corresponding laminae. Further, Poisson’s ratio of angle-play lam￾inates can exhibit values greater than 1.0, and the shear modulus of angle-ply laminates is largest at 45◦. Another most interesting result for laminated composites (Fig. 14) is the fact that the through-the-thickness Poisson’s ratio Fig. 11. Axial modulus – unidirectional and angle-ply laminates.