Chapter 15: Composites

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Chapter 15 Composites
Many engineering components are composites
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Chapter 15 Composites
ISSUES TO ADDRESS...
What are the classes and types of composites?
Why are composites used instead of metals,
ceramics, or polymers?
How do we estimate composite stiffness
strength?
What are some typical applications?
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Classification of Composites
Composites - Multiphase material
w/significant proportions of ea. phase.
Matrix - The continuous phase -
Purpose is to transfer stress to other
phases protect phases from environment
- Classification MMC, CMC, PMC
metal
ceramic
polymer
Dispersed phase -Purpose enhance matrix
properties. MMC increase sy, TS, creep
resist. CMC increase Kc PMC
increase E, sy, TS, creep resist.
-Classification Particle, fiber, structural
From D. Hull and T.W. Clyne, An Intro to
Composite Materials, 2nd ed., Cambridge
University Press, New York, 1996, Fig. 3.6, p. 47.
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COMPOSITE SURVEY Particle-I
Particle-reinforced
Examples
Adapted from Fig. 10.10, Callister 6e.
Adapted from Fig. 16.4, Callister 6e.
Adapted from Fig. 16.5, Callister 6e.
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COMPOSITE SURVEY Particle-II
Particle-reinforced
Elastic modulus, Ec, of composites -- two
approaches.
Fig. 15.3
Application to other properties --
Electrical conductivity, se Replace E by se.
-- Thermal conductivity, k Replace E by k.
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COMPOSITE SURVEY Fiber-I
Fiber-reinforced
Aligned Continuous fibers
Ex
--Metal g'(Ni3Al)-a(Mo) by eutectic
solidification.
--Glass w/SiC fibers formed by glass slurry
Eglass 76GPa ESiC 400GPa.
(a)
From F.L. Matthews and R.L. Rawlings, Composite
Materials Engineering and Science, Reprint ed.,
CRC Press, Boca Raton, FL, 2000. (a) Fig. 4.22,
p. 145 (photo by J. Davies) (b) Fig. 11.20, p.
349 (micrograph by H.S. Kim, P.S. Rodgers, and
R.D. Rawlings).
(b)
From W. Funk and E. Blank, Creep deformation of
Ni3Al-Mo in-situ composites", Metall. Trans. A
Vol. 19(4), pp. 987-998, 1988.
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COMPOSITE SURVEY Fiber-II
Fiber-reinforced
Discontinuous, random 2D fibers
Example Carbon-Carbon --process
fiber/pitch, then burn out at up to
2500C. --uses disk brakes, gas
turbine exhaust flaps, nose cones.
(b)
(a)
Other variations --Discontinuous, random
3D --Discontinuous, 1D
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Elasticity of Composites

• Stress-strain response depends on properties of
• reinforcing and matrix materials (carbon,
  polymer, metal, ceramic)
• volume fractions of reinforcing and matrix
  materials
• orientation of fibre reinforcement (golf club,
  kevlar jacket)
• size and dispersion of particle reinforcement
  (concrete)
• absolute length of fibres, etc.

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Families of Composites particle, fibre,
structural reinforcements
ceramics
Twisting, Bending
Orientation dependence
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Two simplest cases Iso-load and Iso-strain
Isostrain Load Reinforcements
Aligned Isoload Load Reinforcements
Perpendicular (Isostress below)
Strain or elongation of matrix and fibers are the
same!
Volume fraction
F
Load (Stress) across matrix and fibers is the
same!
F
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Isostrain Case in Ideal Composites
Isostrain Case
strain
forces
Load is distributed over matrix and fibers, so
?cAc ?mAm ?fAf.
if the fibers are continuous, then volume
fraction is easy.
For Elastic case
Composite Property
like law of mixtures
Properties include elastic moduli, density, heat
capacity, thermal expansion, specific
heat, ...
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Iso-Load Case for Ideal Composites
Isoload Case
strain
forces
Without de-bonding, loads are equal, therefore,
strains must add, so
if the fibers are continuous or planar, then
area of applied stress is the same.
elastic case
Composite Property
like resistors in parallel.
Properties include elastic moduli, density, heat
capacity, thermal expansion, specific
heat, ...
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ISOSTRAIN Example Suppose a polymer matrix (E
2.5 GPa) has 33 fibre reinforcements of glass (E
76 GPa). What is Elastic Modulus?
26.7 GPA
25 GPA
Stiffness of composite under isostrain is
dominated by fibers.
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ISOLOAD Example Suppose a polymer matrix (E 2.5
GPa) has 33 fibre reinforcements of glass (E
76 GPa). What is Elastic Modulus?
Rearrange
3.8 GPA
Elastic modulus of composite under isoload
condition strongly depends on stiffness of
matrix, unlike isostrain case where stiffness
dominates from fibers.
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Modulus of Elasticity in Tungsten Particle
Reinforced Copper

• Particle reinforcements usually fall in between
  two extremes.

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Simplified Examples of Composites
Are these isostrain or isoload? What are some
real life examples?
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Simplified Examples of Composites
Load, F

• Material A and B are different
• e.g., walkway, trapeze bar,

• Fiber reinforced epoxy cylinder
• e.g, pressure cylinder

• welded tubular composite

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Self-Assessment Example isostrain
A platform is suspended by two parallel rods (A
and B). Yielding of either rod of this
composite constitutes failure, such as the
falling (and possible death) of the trapeze
artist, the people using the walkway, etc.
Each rod is 1.28 cm in diameter. Rod A is 4340
steel, with E 210 GPa, ?ys 855 MPa. Rod B is
7075-T6 Al alloy, with E 70 GPa, ?ys 505 MPa.
(a) What uniform load can be applied to the
platform before yielding will occur?
If not elastic, then composite fails, due to
permanent deformation! Hence
(b) Which rod will be first to yield? Justify and
explain your answer.
To justify, consider how much load is carried
FA/FB relative to that expected from the YS.
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COMPOSITE SURVEY Fiber-III
Fiber-reinforced
Critical fiber length for effective stiffening
strengthening
fiber strength in tension
fiber diameter
shear strength of fiber-matrix interface
Ex For fiberglass, fiber length gt 15mm needed
Why? Longer fibers carry stress more
efficiently!
Shorter, thicker fiber
Longer, thinner fiber
Adapted from Fig.15.7
Poorer fiber efficiency
Better fiber efficiency
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COMPOSITE SURVEY Fiber-IV
Fiber-reinforced
Estimate of Ec and TS --valid when
-- Elastic modulus in fiber direction
--TS in fiber direction
efficiency factor --aligned 1D K 1
(anisotropic) --random 2D K 3/8 (2D
isotropy) --random 3D K 1/5 (3D isotropy)
Values from Table 15.3
(aligned 1D)
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COMPOSITE SURVEY Structural
Structural
Stacked and bonded fiber-reinforced sheets
-- stacking sequence e.g., 0/90 -- benefit
balanced, in-plane stiffness
Fig. 15.16
Sandwich panels -- low density, honeycomb
core -- benefit small weight, large bending
stiffness
Fig. 15.17
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Composite Benefits
CMCs Increased toughness
PMCs Increased E/r
MMCs Increased creep
resistance
Adapted from T.G. Nieh, "Creep rupture of a
silicon-carbide reinforced aluminum composite",
Metall. Trans. A Vol. 15(1), pp. 139-146, 1984.
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Laminate Composite (Ideal) Example
Gluing together these composite layers composed
of epoxy matrix (Em 5 GPa) with graphite fibres
(Ef 490 GPa and Vf 0.3). Central layer is
oriented 900 from other two layers.

• Case I - Load is applied parallel to fibres in
  outer two sheets.
• Case II - Load is applied parallel to fibres of
  central sheet.
• What are effective elastic moduli in the two
  case?
• First need to know how individual sheets
  respond, then average.

For isoload case.
For isotrain case.
Case I Elam(2/3)(150.5 GPa) (1/3)(7.1 GPa)
102.7 GPa
Case II Elam(1/3)(150.5 GPa) (2/3)(7.1 GPa)
54.9 GPa
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Mechanical Response of Laminate Complex, NOT
Ideal

• 3 Conditions required consider top and bottom
  before laminated
• strain compatibility- top and bottom must have
  same strain when glued.
• stress-strain relations - need Hookes Law and
  Poisson effect.
• equilibrium - forces and torques, or twisting
  and bending.

Isostrain for load along x-dir
Poisson Effect and Displacements in D

• When glued together displacements have to be
  same!
• Unequal displacements not allowed!
• So, top gets wider (?ytop gt 0) and bottom gets
  narrower (?ybott lt 0).
• Equilibrium Fy 0 (?ybot tbot ?ytop
  ttop)L. (t thickness)

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COMPATIBILITY When glued, displacements have to
be same!
As stress is applied, compatibility can be
maintained, depending on the laminate, only if
materials twists.
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Symmetry of laminate composite dictates properties
Elastic constants are different for different
symmetry laminates.
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Orientation of layers dictates response to
stresses
Want compressive stresses at end of laminate so
there are no tensile stresses to cause
delamination - failure!
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NO delamination - failure!
Apply in-pane Tensile Stress A B 90 45 45 45
45 90 45 90 45 45 90 45 Tensile -gt
delaminate Compressive
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Why Laminate Composite is NOT Ideal

• Depending on placement of load and the
  orientation of fibers internal to sheet and the
  orientation of sheets relative to one another,
  the response is then very different.
• Examples of orientations of laminated sheets
  that provided compressive stresses at edges of
  composite and also tensile stresses there.
  gtgtgtgt Tensile stresses lead to delamination!
• The stacking of composite sheets and their
  angular orientation can be used to prevent
  twisting moments but allow bending moments.
  This is very useful for airplane wings, golf club
  shafts (to prevent slices or hooks), tennis
  rackets, etc., where power or lift comes or is
  not reduced from bending.

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Thermal Stresses in Composites

• Not just due to fabrication, rather also due to
  thermal expansion differences between matrix and
  reinforcements ?Tm and ?Tr.
• Thermal coatings, e.g.
• Material with most contraction (least) has
  positive (negative) residual stress. (For
  non-ceramics, you should consider plastic strain
  too.)
• Ceramic-oxide thermal layers, e.g. on gas turbine
  engines
• ceramic coating ZrO2-based (lower ?Tr)
• metal blade (NixCo1-x)CrAlY (higher ?Tm)
• Failure by delamination without a good design of
  composite, i.e. compatibility maintained.

If forced to be compatible, composite will bend
and rotate
At T1
At T2
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Summary
Composites are classified according to --
the matrix material (CMC, MMC, PMC) -- the
reinforcement geometry (particles, fibers,
layers). Composites enhance matrix
properties -- MMC enhance sy, TS, creep
performance -- CMC enhance Kc -- PMC
enhance E, sy, TS, creep performance
Particulate-reinforced -- Elastic modulus
can be estimated. -- Properties are
isotropic. Fiber-reinforced -- Elastic
modulus and TS can be estimated along fiber dir.
-- Properties can be isotropic or
anisotropic. Structural -- Based on
build-up of sandwiches in layered form.