1. 1 530.418 Aerospace Structures and Materials Lecture 22: Laminate Design

2. 2 Composite lay up: Lamina orthotropic properties Laminate Isotropic/anisotropic properties determined by composite design Fiber orientation used to specify composite lay up, e.g. [ 0/90/+45/-45/0/-45/+45/90/0] n

3. 3 Laminate Ply Orientation Code Each ply accounted for Start at top Angles between -90 and +90 Repeat plies by subscript [0 2 90 0 2 ] = [0 0 90 0 0] Repeat sub groups also possible [0 (45 -45) 3 0] = [0 45 -45 45 -45 45 -45 0] Entire laminate may be repeated [0 90 0] 3 = [0 90 0 0 90 0 0 90 0] A strike through last ply means it is center but not repeated S = symmetric [0 45 -45 90] S = [0 45 -45 90 90 -45 45 0] Can subscript # and S [0 45 -45 90] 2S = [0 45 -45 90 0 45 -45 90 90 -45 45 0 90 -45 45 0] 0 45 -45 90

4. 4 Influence of individual laminates [0 45 -45 90 90 -45 45 0]

5. 5 Lay up effect on strength and stiffness

6. 6 Elastic behavior and constants

7. 7 Anisotropic laminate behavior

8. 8 Key point … Loading composites can lead to ply coupling and funny shapes !!!

9. 9 Deflection of laminates

10. 10 Effect of symmetry Reduces out-of-plan coupling and distortions associated with Poisson ration mismatch.

11. 11 Tailoring ply orientations

12. 12 Laminate stress distributions

13. 13 Voight Model A B Iso-strain A = B = Av. = V A A + V B B Av. E = Av. / = V A A / + V B B / E composite = V A E A + V B E B

14. 14 Reuss Model ABAB Iso-stress A = B = Av. = V A A + V B B 1 / E composite = V A / E A + V B / E B

15. 15 Terminology Micro mechanics –Interaction between constituents (fiber and matrix) and ply –Too detailed for failure –OK for elasticity -> rule of mixtures Macro mechanics –Relation between plies and laminate –Continuum mechanics, each level homogeneous + orthotropic –Lamination theory principle mathematical tool for relationship –Ply properties measured Laminate theory assumptions –Thin plate or shell (2D stresses) –Plies orthotropic elasticity (4 ind. Const.) –Must transform elastic constants (ply) to laminate axes using law of Cosines

16. 16 Extrenal loading and deflections External loading N 1 = N x = in-plane axial load N 2 = N y = in-plane transverse load N 3 = N z = N 4 = N xz = N 5 = N yz = 0 N 6 = N xy = in-plane shear load M 1 = axial bending load M 2 = transverse bending load M 6 = twisting load External deflections 1 = x = in-plane axial strain 2 = y = in-plane transverse strain 3 = z = 4 = xz = 5 = yz = 0 6 = xy = in-plane shear strain 1 = axial curvature 2 = transverse curvature 6 = twist

17. 17 Hookes law i = C ij j xx C 11 C 12 C 13 C 14 C 15 C 16 xx yy C 21 C 22 C 23 C 24 C 25 C 26 yy zz = C 31 C 32 C 33 C 34 C 35 C 36 zz yz C 41 C 42 C 43 C 44 C 45 C 46 yz xz C 51 C 52 C 53 C 54 C 55 C 56 xz xy C 61 C 62 C 63 C 64 C 65 C 66 xy

18. 18 Hookes law i = C ij j xx C 11 C 12 C 13 C 14 C 15 C 16 xx yy C 21 C 22 C 23 C 24 C 25 C 26 yy = C 31 C 32 C 33 C 34 C 35 C 36 C 41 C 42 C 43 C 44 C 45 C 46 C 51 C 52 C 53 C 54 C 55 C 56 xy C 61 C 62 C 63 C 64 C 65 C 66 xy