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MECHANICS OF FRP

COMPOSITE LAMINATESStresses, Strains & Failure

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PRESENTOR

PROF.DR. A.KANNI RAJ M.E.(NITT), PH.D.(IITM)AUTHOR - Omni Scriptum GmbH & Co KG - GERMANY

PROFESSORDEPARTMENT OF ARONAUTICAL ENGINEERINGPSN COLLEGE OF ENGINEERING AND TECHNOLOGY

MELATHEDIYOOR-627152TIRUNELVELI DISTRICT

TAMILNADUINDIA

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COMPOSITES

"A composite is a structural material which consists ofcombining two or more constituents. The constituents arecombined at a macroscopic level and are not soluble in eachother. One constituent is called the reinforcing phase and theone in which it is embedded is called the matrix.

Reinforcing phase - Fibres, particles or flakesMatrix- Materials are generally continuous, eg. polymer.A lamina (also called a ply or layer) is a single flat layer of

unidirectional fibers or woven fibers arranged is a matrix.A laminate is a stack of plies of composites. Each layer can belaid at various orientations and can be different materialsystems."

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LAY-UP CODES

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ORTHOTROPY

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HOOKES LAW

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STIFFNESS

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LAMINATES

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NEED FOR STACK

lamina (ply) of FRP is remarkably

strong along the fiber direction

lamina is considerably weaker inall off-fiber directions

So, a laminate constructed by a

number of laminae oriented atdifferent directions is used

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LAMINA THEORY

valid for thin laminates

(span aand b> 10thinckness t)

small displacement win the transversedirection (w

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KIRCHHOFF IDEAS

Normals remain straight (they do not

bend)

Normals remain unstretched (they keepthe same length)

Normals remain normal (they always

make a right angle to the neutral plane)

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GOOD BONDING

The bonding itself is infinitesimally small

(there is no flaw or gap between layers)

The bonding is non-shear-deformable

(no lamina can slip relative to another)

The strength of bonding is as strong as

it needs to be (the laminate acts as a

single lamina with special integratedproperties)

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PLATE THEORY

The classical lamination theory is identical

to the classical plate theory

only difference is in the material properties(stress-strain relations)

In classical plate theory, material is

isotropic, while FRPlaminate with multiple

plies have more complicated

http://www.efunda.com/formulae/solid_mechanics/plates/theory.cfmhttp://www.efunda.com/formulae/solid_mechanics/plates/theory.cfm

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CORNERSTONES

Kinematicequations

Constitutiveequations

force resultantequations

equilibriumequations

http://www.efunda.com/formulae/solid_mechanics/composites/comp_lamina_principal.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_kinematics.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_resultants.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_lamina_principal.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_resultants.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_equilibrium.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_equilibrium.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_equilibrium.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_resultants.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_lamina_principal.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_resultants.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_theory_kinematics.cfmhttp://www.efunda.com/formulae/solid_mechanics/composites/comp_lamina_principal.cfm

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KINEMATICS

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WHERE

u0, v0, and w0are the displacements of themiddle plane in the x, y, and zdirections,

respectively.

Please note that some literature maydefine kxyas the total skew curvature which

eliminates the factor of 2.

Also note that Kirchhoff's assumptions are

introducted to simplify the displacement

fields.

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CONSTITUTIVE

alternatively,

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WHERE

subscript k indicates the kth layer

counting from the top of the laminate

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RESULTANTS

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WHERE

subscript k indicates the kth layer

from the top of the laminate

Nis the total number of layers.

Note that perfect bonding is

assumed so we can move theintegration inside the summation

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EQUILIBRIUM

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[A],[B] & [D]

The plate is homogeneous

Plate is not isotropic material

subjected to both transverse and in-planloadings

Cartesian coordinate system is used

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AGAIN

goal is to develop the relationsbetween the external loadings and the

displacements

relations between the resultants

(forces Nand moments M) and the

strains (strains and curvatures k) areof most interest in practice

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REPALCE F & M

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PLUS

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where

A is called the extensional stiffness

Bis called the coupling stiffness

Dis called the bending stiffness of laminate

COMBINE

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COMPONENTS

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tkis the thickness of thekthlayer

is distance from mid-plan to the centroid ofkthlayer

Forming A ,B, andD, is probably crucial step

WHERE

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TSAI-HILL

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WHERE