Composites Analysis 2011

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COMPOSITES ANALYSIS


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Composites

a composite material is a material which is

composed of at least two elements working together

to produce a material which properties are different

to the properties of those elements on their own.


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Composites

two components: reinforcement + matrix

reinforcements = fibres (glass, carbon etc)

matrix = resin (polyester, epoxy etc)


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Composites

three components: reinforcement + matrix+ core

reinforcements = fibres: glass, carbon etc

matrix = resin: polyester, epoxy etc

CORE = foam, wood, Soric, etc


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Composites

Strength vs Stiffness

strength is about breaking stiffness is about bending


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Composites




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Composites


strength is about breaking

strong enough

not strong enough

strong enough


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Composites




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Composites



stiff enough

not stiff enough


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Composites



strong enough but not stiff enough

compare :

STRONG & STIFFstrong & stiff enough

not stiff and not strong enough


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Composites

Stiffness depending on :

- Material

- Shape

- Thickness


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Several methods have been used to

predict the mechanical properties ofcomposites material such asexperimental (mechanical testing)and

calculation of mechanics of material

(theory).

INTRO


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Maximum composites strength;

a) The total strength is provided by the

fiber reinforcement, hence the fiberstrength is greater that the matrix strength

b) Using high volume fraction, Vf of fiberreinforcement


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REMEMBER.

Composites failures

Usually resulted from fiber debonding, voids, fiber damage etcproducing micro cracks

Micro cracks spreads through the matrix and moving along the fiber-matrix interface until reaching the fiber surfaces

Finally resulted in catastropic failure / total penetration damage


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INTRO (Cont.)

Fiber strength is base on;

1.Mechanical properties of the fibers

2.Orientation of fibers

3.Volume of fibers

4.Surface interaction (Fiber matrix)


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EXPERIMENTAL : MECH.PROPERTIES


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TYPICAL STRESS-STRAIN GRAPH (Cont.)

*Ductility : Easily pulled or deform; hard buteasily broken


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EXAMPLE: STRESS-STRAIN GRAPH

Question:

Q1: Which material is stronger?

Q2: Which material is more brittle?

Q3: Which material is tough?


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TYPICAL DIRECTION OF FORCE


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EXPERIMENTAL : TENSILE TESTING


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TENSILE TESTING (Cont.)


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Modulus of elasticity, E onlyin the elastic region

A stressstrain curve

typical of structural steel

1. Ultimate Strength

2. Yield Strength

3. Rupture

4. Strain hardening

region

5. Necking region.

elastic Material

returning to its normal

size or shape after being

pulled or pressed (Rubber

base like)

plastic The shape

changes permanently(composites)
http://upload.wikimedia.org/wikipedia/commons/0/00/Stress_v_strain_A36_2.pnghttp://upload.wikimedia.org/wikipedia/commons/0/00/Stress_v_strain_A36_2.pnghttp://upload.wikimedia.org/wikipedia/commons/0/00/Stress_v_strain_A36_2.pnghttp://upload.wikimedia.org/wikipedia/commons/0/00/Stress_v_strain_A36_2.png


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EXAMPLE

*Resilience: The capability of material formingback to its original form after being bent,stretched or crushed


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Maximum stress @material ultimatestrength

(plastics deformation occurs)


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*Toughness: material that is not easilycut, broken or worn


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Poissons Ratio

Poisson's ratio (), is the ratio, when a sample object is stretched (Changes in dimension)

When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to

the direction of compression. This phenomenon is called the Poisson effect. Poisson's ratio (nu) is a measure of thePoisson effect.

The Poisson's ratio of a stable, isotropic, linearelastic material cannot be less than 1.0 nor greater than 0.5.

Most materials have Poisson's ratio values ranging between 0.0 and 0.5.

A perfectly incompressible material deformed elastically at small strains would have a Poisson's ratio of exactly 0.5.

Most steels and rigid polymers when used within their design limits (before yield) exhibit values of about 0.3,

increasing to 0.5 for post-yield deformation (which occurs largely at constant volume.)

Rubber has a Poisson ratio of nearly 0.5. Some materials, mostly polymer foams, have a negative Poisson's ratio; ifthese material are stretched in one direction, they become thicker in perpendicular directions.

Anisotropic materials can have Poisson ratios above 0.5 in some directions.

Anisotropic material Material properties that have different properties in differentdirection. Example: Composites; longitudinal direction @ transverse direction
http://en.wikipedia.org/wiki/Materialshttp://en.wikipedia.org/wiki/Nu_%28letter%29http://en.wikipedia.org/wiki/Isotropichttp://en.wikipedia.org/wiki/Elastichttp://en.wikipedia.org/wiki/Yield_%28engineering%29http://en.wikipedia.org/wiki/Yield_%28engineering%29http://en.wikipedia.org/wiki/Elastichttp://en.wikipedia.org/wiki/Isotropichttp://en.wikipedia.org/wiki/Nu_%28letter%29http://en.wikipedia.org/wiki/Materials


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Poissons Ratio (Cont.)Ratio of the transversestrain (normal to theapplied load),x dividedby axial strain (in the

direction of the appliedload), y.(-) ve is to counter the negativecontraction strain


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EXAMPLE: STRESS/STRAIN DIAGRAM PLOT

Tensile specimen with tab

Given;

Specimen length = 8.0 inch

Specimen width = 1.0 inch

Plot the stress/strain graph:

Load (Ib) Elongation (inch) Stress (psi) Strain

1000 0.010

? ?

2000 0.020

3000 0.0504000 0.100

5000 0.200

6000 Failure


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TYPICAL FAILURE MODE IN COMPOSITES TENSILE TEST


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TYPICAL FAILURE MODE IN COMPOSITES TENSILE TEST

Failure @ middle

Failure @ grip

Failure @ lateral gage


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THEROETICAL APPROACH


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REMEMBER.

Composites

(denoted by c)

Fiber reinforcement

(denoted by f)

Matrix system

(denoted by m)= +

Remember: Most of thestrength of composites isprovided by the fiber!!!

A composite is a structural material which consist of combining 2 or 3or more elements in a system


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MECHANICS TERMINOLOGY

Isotropic material Material that has same properties inall direction if applying load. Example: SteelAnisotropic material Material properties that havedifferent properties in different direction. Example:Composites; longitudinal direction @ transversedirection

Homogeneous body Has properties that are the sameat all points in the body

Inhomogeneous body Has non uniform propertiesover the body

Lamina Single flat layer of a unidirectional OR wovenfibers in a matrixLaminate Stack of plies of composites with variousorientation


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EXPERIMENT vsTHEORY

Composite behaviour

Experiment micro/makro mechanics

Tensile Compression Others Rule of

mixture

(ROM)

Voids

content

Longitudinal/Transverse

properties

Others

Prediction of composites density

Prediction of composites weight fraction

Prediction of composites volume fraction

Prediction of Youngs Modulus

Others


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Both concepts of micro and macro

mechanics allows the tailoring/modification

of a composites components to meetspecifics structural requirement.


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Composites

Micromechanics


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Micromechanical Analysis

A simplified composites model is

considered consisting of a fiber

surrounded by matrix phase.

This composites elements is

embended in a homogeneousmedium @ matrix


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Fiber dominated strength


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Matrix dominated strength


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ANALYSIS USING RULE OF MIXTURE (ROM)

Composites obey the rule-of-mixture

ROM States that the composites

mechanical properties can be calculatedas the sum of the value of property ofeach element/constituent by its respective

volume fraction OR weight fraction in

the composites system


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Calculation of composites mech. properties using rule of mixture will requireyou to determine the volume fraction OR weight fraction of each elements.

RULE OF MIXTURE (Cont.)

The volume fraction of fiber & matrix is determine by;

Vfiber= vfiber

vcomposites

Vmatrix= vmatrix

vcompositesWhere; Vf is the volume of fiber & Vm is the volume of matrixVc is the volume of composites


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ROM - The sum of volumefraction of ALL elements in a

composites must be equal to 1;

vcomposites = vfiber + vmatrix = 1


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The weight fraction of fiber & matrix is determine by;

Wfiber = wfiber

wcomposites

Wmatrix = wmatrix

wcomposites

Where; Wfis the weight of fiber & Wm is the weight of matrix

Wc is the volume of composites

RULE OF MIXTURE (Cont.)


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Composite density is commonly

calculated or predicted using

ROM based on volume fraction(vf & vm) compare to weight

fraction (wf

& wm

)

COMPOSITE DENSITY (cont.)

Composite density, comp = Fiber density, fiber + Matrix density, matrix


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Applying the definition of density

equals to weight fraction to

volume fraction will give;

Composite density, comp = wf / vf+ wm / vm


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Example

Determine the density of a glass epoxy laminate with a 60% fiber volumefraction

Given; density of glass fiber is fiber = 2500 kg/m ; the density of

matrix, matrix= 1200 kg/m

Solution:

The density of composites, comp

= (2500)(0.6) + (1200)(0.4)

= 1980 kg/cm

Composite density, comp = Fiber density, fiber + Matrix density, matrix


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Micromechanics

The design and analysis of laminated

structures are express in stress strain

Failures cause by tensile or compressionstrength are refered to as;

- Longitudinal tensile/compression strength

- Transverse tensile/compression strength


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STRESS

Stress = Force per unit area acting on a material


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STRAIN

Strain = Deformation of materials per unit length (with no unit)


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LONGITUDINAL & TRANSVERSE PROPERTIES OF COMPOSITES

Longitudinal strength

The strength of composites when measured in the direction of thefibers until the samples fails.

As the load increases, the strain increases hence the compositesdeform at equal amount;

OR

Composites strain, comp = Fiber strain,

fiber = Matrix strain, matrix

However load applied is partitioned (divided) between the fiber

and matrix elements giving;

Composites load, Pcomp = Fiber load, Pfiber + Matrix load, Pmatrix


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Composites load, Pcomp = Fiber load, Pfiber + Matrix load, Pmatrix

From;

And;

Stress, = Force @ Load, P

Cross section area, A

Give;

Acompcomp = Afiberfiber + Amatrixmatrix


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Assuming that the length of sample in this determination oflongitudinal composites strength is equal to 1 and in order to replacethe cross sectional area, A of elements to volume fraction then thevolume fraction of each elements can be written as;

Acompcomp =Afiberfiber +Amatrixmatrix

comp =Afiber fiber +Amatrix matrix

Acomp Acomp

comp = Vfiberfiber + Vmatrixmatrix

REMEMBER

Vfiber= vfiber / vcomposites

Vmatrix= vmatrix / vcomposites

Give;


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Prediction of the Youngs modulus using rule-of mixtures for longitudinalfibers.

From;

comp =

Vfiber

fiber +

Vmatrix

matrix

Give;

compEcomp = VfiberfiberEfiber + VmatrixmatrixEmatrix

IMPORTANT NOTE:Youngs modulus, E = /

Thus the Youngs modulus is predicted by;

Ecomp = VfiberEfiber + VmatrixEmatrix

Remember: Composites strain, comp = Fiber strain,

fiber = Matrix strain, matrix

R.O.M for longitudinal fibers


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Example

Find the longitudinal Youngs modulus for a glass epoxy laminate with 60%fiber volume fraction.

Given : Efiber 10 GPa, Ematrix 1 Gpa

Solution:

Ecomp = Vfiber Efiber + Vmatrix Ematrix

Ecomp = (0.6)(10) + (0.4)(1)= 6.4 GPa


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Transverse strength

Refers to properties of the composites Youngs modulus in thedirection normal to the fiber

1 = Vfiber + V matrix

Ecomp Efiber Ematrix

R.O.M for transverse fibers

*Modulus: A measurement of stiffness;where the material is not easily bent, foldedor changed shape


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Example

Find the transverse Youngs modulus of a glass epoxy laminate witha fiber volume fraction of 60%.

Given; Efiber = 10 GPa, Ematrix = 1 Gpa

Solution;

The transverse Youngs modulus,

1 / Ecomp = (0.6) / (10) + (0.4) / (1)

1 / Ecomp = 0.06 + 0.4

= 0.46

Ecomp = 2.17GPa


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Composites Analysis 2011

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