Mechanical Behavior of
Composite Materials
Mimicking Mother Nature
Ashraf F. Bastawros
Fall-2001
Material Sciences and Engineering
MatE271
Week 14-1
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Goals for this unit
4• Survey composite materials (Ch. 14)
4 – Fiber reinforced materials
4
» Natural (wood, foam, coral)
4
» Synthetic (fiber reinforcement, concert, foams)
4 – Large aggregate composites
4 – Several special types
4• Understand properties of composites
4 – Averaging schemes
4 – Mechanical properties
Ø Multifunctional materials (from properties of individual
phases)
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1
Classification of Composites
Composites
Particulate
Fiber
Structural
Laminates
Large Dispersion
Particle Strengthened
Continuous Discontinuous
Aligned
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Sandwich
Panels
Random
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Synthetic Fiber-Reinforced Composites
• One of the most common composite types
– Micron scale reinforcing fibers (stronger/stiffer)
» Glass fibers
» Higher moduli fibers (“advanced composites”)
– Matrix material is frequently a polymer
(weaker/softer/less brittle/inexpensive)
Continuous
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Chopped
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Weaved
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2
Fiberglass Fibers
» Glass fiber-reinforced polymer
» Different compositions of glass (consider electrical,
thermal, chemical and mechanical properties)
- Strong interfacial bond between fibers and matrix to
transfer loads effectively between phases
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Week 14-1
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Advanced Composites
• Higher moduli fibers than glass
• Matrix can be polymer, ceramic or metal
– PMCs, CMCs, MMCs
• Many materials were developed for military
applications (e.g. “stealth” structures)
• Conversion to other markets
– Marine, aviation, civil engineering structures,
automotive components, sporting goods (costs
still quite high)
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3
Parameters
Distribution
Concentration
Size
Shape
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Orientation
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14.3 Property Averaging
• Properties of composite
represent some average of
the constituent properties
• The “average” is extremely
sensitive to geometry
– parallel to fibers
– perpendicular to fibers
– in a uniformly dispersed aggregate
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4
Composite properties are intermediate between two materials
4Stage I - elastic deformation with intermediate
4Stage II - matrix yields
4Failure - Non-catastrophic. When fibers fracture, you now have
new fiber length and matrix is still present
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Week 14-1
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Volume Fraction in Fiber Composites
o Elastic modulus is dependent on the volume
fraction of fibers
o “Rule of mixtures” equation (again)
• E - elastic modulus, V- volume fraction, m- matrix, f- fiber
• upper bound
(isoiso-strain)
• lower bound
(isoiso-stress)
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Ec = EmVm + E fV f
EmE f
Ec =
E fVm + EmV f
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5
Rule of Mixtures
(iso-strain)
Upper bound
** **
*
*
Ec = EmVm + E fV f
*
Lower bound
conc. of fibers
E - fiber
E- matrix
(iso-stress)
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EmE f
Ec =
E fVm + EmV f
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Tensile Strength
o In longitudinal
direction, the
tensile strength is
given by the
equation below if
we assume the
fibers will fail
before the matrix:
σ∗c = σ’mVm + σ’fVf
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6
Example
o Calculate the composite modulus for
polyester reinforced with 60 vol% E-glass
under iso-strain conditions.
• Epolyester = 6.9 x 103 MPa
• EE-glass = 72.4 x 10 3 MPa
Ec = (0.4)(6.9x103 MPa) + (0.6)(72.4x103 MPa)
= 46.2 x 103 MPa
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Week 14-1
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Influence of Fiber Length
o Mechanical properties depend on:
• mechanical properties of the fiber
• how much load the matrix can transmit to the fiber
• depends on the interfacial bond between the fiber and the
matrix
o Critical fiber length - depends on
• fiber diameter, fiber tensile strength
• fiber/matrix bond strength
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Influence of Fiber Length
o Critical fiber length • “Continuous” fibers
L >> 15 Lc
• “Short” fibers are
anything shorter 15 Lc
Lc
Lc = σfd/2τc
No
Reinforcement
where
d = fiber diameter
τc = fiber-matrix bond
strength
σf = fiber yield strength
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Week 14-1
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Interfacial Bond Strength
• In polymer matrix and metal matrix composites (PMCs
and MMCs), it is important that interfacial bond strength
be high, because fibers are the stronger phase
• In ceramic matrix composites (CMCs), the matrix is
strong but brittle, so desirable for interfacial bond strength
to be low (“fiber pullout” is desired to increase toughness
or resistance to fracture.)
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8
Large Aggregate Composites
• Particles reinforce the matrix phase
• Most common example is concrete
– rock (coarse) and sand (fine) aggregates
» usually chosen from locally available deposits)
– aluminosilicate (cement) matrix
» Portland cement (Ca-aluminosilicates)
• Weight of concrete used each year exceeds that of
all metals combined
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Week 14-1
Aggregate” Composites Performance
Tungsten particles
350
in copper matrix
300
Upper Bound
Ec=EmVm+EpVp
250
200
150
0
20
40
60
80
100
Modules of Elasticity (GPa)
“Large
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Tungsten Concentration (vol%)
Lower Bound
Ec=EmEp / { E/mVm+EpVp }
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Sandwich Panel
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Week 14-1
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Composites Summary
• Reinforced composite materials include fiber
(both natural and synthetic) and particulate
(aggregate) reinforced composites
• Property averaging schemes depend on the
quantities, shape and orientation of
reinforcement phase
* Reading: relevant sections of Ch. 14
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