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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
Strength vs Stiffness
strength is about breaking stiffness is about bending
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Composites
Strength vs Stiffness
strength is about breaking
strong enough
not strong enough
strong enough
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Composites
Strength vs Stiffness
strength is about breaking stiffness is about bending
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Composites
Strength vs Stiffness
strength is about breaking stiffness is about bending
stiff enough
not stiff enough
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Composites
Strength vs Stiffness
strength is about breaking stiffness is about bending
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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TENSILE TESTING (Cont.)
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TENSILE TESTING (Cont.)
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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TENSILE TESTING (Cont.)
EXAMPLE
*Resilience: The capability of material formingback to its original form after being bent,stretched or crushed
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TENSILE TESTING (Cont.)
Maximum stress @material ultimatestrength
(plastics deformation occurs)
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TENSILE TESTING (Cont.)
*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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LONGITUDINAL & TRANSVERSE PROPERTIES OF COMPOSITES
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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LONGITUDINAL & TRANSVERSE PROPERTIES OF COMPOSITES
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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LONGITUDINAL & TRANSVERSE PROPERTIES OF COMPOSITES
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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LONGITUDINAL & TRANSVERSE PROPERTIES OF COMPOSITES
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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