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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.cfm8/12/2019 Global Works 30march2012 Frp Ghl
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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.cfm8/12/2019 Global Works 30march2012 Frp Ghl
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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