composites mechanics micro macro

7/29/2019 Composites Mechanics Micro Macro

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Module 4


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M4.2 Micromechanics of Laminae

M4.1 Micromechanics of Laminae

Learning Units of Module 4


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Note:

So far we have talked on apparent

homogenized properties of a fiber reinforcedlamina.

Now we will examine how we can calculate the

homogeneous lamina properties from theheterogeneous composite material constituentproperties


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Definition of MicromechanicsDefinition of Micromechanics


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Definition

The term micromechanics does notrefer to mechanical behavior at the

molecular level. Looks at components of acomposite, the matrix and the fiber, andtries to predict the behavior of theassumed homogeneous composite material.The behavior or the lamina is calledmacro-mechanics.Study of mechanical behavior of a

composite material in termsof its constituent materials


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Micromechanics


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- Fibers, matrix

- Fiber/matrix interfaces- Microcracks

Continuum

Homogenization

Microscale

Composite representative

volume element

Mesoscale

Macroscale

Composite

structure

Constitutive relations

Evolution laws

Finite element analysis


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Uses of Micromechanics

Predict composite properties from fiber andmatrix data.

Extrapolate existing composite property datato different fiber volume fraction or voidcontent.Check experimental data for errors.Determine required fiber and matrixproperties to produce a desired compositematerial.

The relation between ply uniaxial strengths andconstituent properties of structure is obtainedthrough the composite micromechanics.


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Limitations of Micromechanics

Predicted composite properties are only as goodas fiber and matrix properties used.

Simple theories assume isotropic fibers manyfiber reinforcements are orthotropic.

Some properties are not predicted well by simpletheories more accurate analyses are timeconsuming and expensive.

Predicted strengths are upper bounds


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Lamina (or Ply): It is a single layer (planeor curved) of unidirectional or woven

fabric in a matrix.

Definition of Lamina


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Laminate: Two or more unidirectional laminae or a plystacked together at various orientations is called Laminate.

The laminae (plies) can be of various thicknesses

and consists of different or same materials. Ex: (0/90/0),(0/0/0/0) = (04)

Definition of Laminate


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Hybrid Composites: A composite made up of 2 or moredifferent types of materials. Ex: (0k/0k/45c/90c)

Inter-ply Hybrid Composites: Laminate made up of plies ofGlass/Epoxy, Carbon/Epoxy & Aramid/Epoxy.

Intra-ply Hybrid Composites: A ply made up of two ormore fibers intermingled.

Intra-Interplay Hybrid Composites: Combination ofIntraply and Interply hybrid.

Lay-up: Configuration of a laminate that defines plycomposition. (0/45/90)

Stacking sequence: Configuration of a laminate that definesply composition and the exact sequence of ply orientation and

its thickness.

Continued


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Different Types Laminate Sequences


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Methods Of Micromechanics


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Micromechanics and Assumptions

Approach: mechanics of materials approach,semi-empirical

Assumption: the lamina is looked at as amaterial whose properties are different invarious directions, but not different from one

location to another.


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Continued


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Evaluation of Four Elastic Moduli

There are four elastic moduli of aunidirectional lamina:

Longitudinal Modulus - E1Transverse Modulus - E2

Shear Modulus -G12

Poissons Ratio - n12 Interlaminar Shear Modulus


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Mechanics of Materials Method


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Determination of


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Determination of


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Determination of


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Determination of

2m

f

2m


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Continued


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Inverse Rule of Mixtures

Shear Modulus of fiber in 12-plane

Shear Modulus of matrix

f m

12 f 12 m

f 12

m

v v1

G G G

G

G

= +==


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m f 1212

m f 12 f m

12

m mm f

f 12

G GG

v G v G

G 1G G

v vG

=+

= +

Inverse Rule of Mixtures


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Strength of Materials Approach

Assumptions are made in the strength of materialsapproach:

The bond between fibers and matrix is perfect. The elastic moduli, diameters, and space between

fibers are uniform. The fibers are continuous and parallel. The fiber and matrix follow Hookes law (linearly

elastic). The fibers possess uniform strength.

The composites is free of voids.


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Micromechanics of Strength ModelsPrincipal Strength Parameters of a Lamina


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Laminate Theory

- which layers?- how many layers?

- how thick?

>>> Laminate Properties


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Laminate Properties>>> Behaviour Under Loads

(Strains, Stresses,

Curvature, Failure Mode)


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Figure: Cross-

sectionaldeformations of

unit cell of

graphite-

reinforced materialdue to applied

fiber-direction

strain

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