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530.418 Aerospace Structures and Materials

Lecture 22: Laminate Design

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Composite lay up:

Lamina orthotropic

properties

Laminate Isotropic/anisotropic

properties determined bycomposite design

Fiber orientation used to specify composite lay up,e.g. [0/90/+45/-45/0/-45/+45/90/0]

n

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Laminate Ply Orientation Code

Each ply accounted for Start at top Angles between -90 and +90 Repeat plies by subscript

[02 90 02] = [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]

045-45

90

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Influence of individual laminates

[0 45 -45 90 90 -45 45 0]

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Lay up effect on strength and stiffness

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Elastic behavior and constants

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Anisotropic laminate behavior

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Key point …

Loading composites can lead to ply coupling

and funny shapes !!!

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Deflection of laminates

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Effect of symmetry

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

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Tailoring ply orientations

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Laminate stress distributions

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Voight Model

A B

Iso-strain

A = B =

Av. = VA A + VB B

Av. E = Av. / = VA A / + VB B /

Ecomposite = VA EA + VB EB

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Reuss Model

A B

Iso-stress

A = B =

Av. = VA A + VB B

Av. = VA A + VB B

1 / Ecomposite = VA / EA + VB / EB

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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

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Extrenal loading and deflections

• External loading• N1 = Nx = in-plane axial load• N2 = Ny = in-plane transverse load• N3 = Nz = N4 = Nxz = N5 = Nyz = 0• N6 = Nxy = in-plane shear load • M1 = axial bending load• M2 = transverse bending load• M6 = 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

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Hooke’s law

i = Cij j

xx C11 C12 C13 C14 C15 C16 xx

yy C21 C22 C23 C24 C25 C26 yy

zz = C31 C32 C33 C34 C35 C36 zz

yz C41 C42 C43 C44 C45 C46 yz

xz C51 C52 C53 C54 C55 C56 xz

xy C61 C62 C63 C64 C65 C66 xy

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Hooke’s law

i = Cij j

xx C11 C12 C13 C14 C15 C16 xx

yy C21 C22 C23 C24 C25 C26 yy

= C31 C32 C33 C34 C35 C36

C41 C42 C43 C44 C45 C46

C51 C52 C53 C54 C55 C56

xy C61 C62 C63 C64 C65 C66 xy