Strength and Modulus of Particulate Reinforced Composite Materials ME 7501 Reinforced Composite Materials Lecture 3 Part 2 Particulate Reinforcement Example idealized cubic array of spherical particles ID: 360965
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Slide1
Engineering Equations for Strength and Modulus of Particulate Reinforced Composite Materials
M.E. 7501 – Reinforced Composite Materials
Lecture 3 – Part 2Slide2
Particulate Reinforcement
Example: idealized cubic
array of spherical particlesSlide3
Flexural stress-strain curves for 30 µm glass bead-reinforced epoxy composites of various
bead volume fractions. (From Sahu, S., and Broutman, L. J. 1972.
Polymer Engineering
and Science
, 12(2), 91-100. With permission.)
Experiments show that, for
typical micron-sized particulate
reinforcement, as the particle
volume fraction increases, themodulus increases but strengthand elongation decrease
Experimental observations on effects of
particulate reinforcementSlide4
(6.65)
Yield strength of particulate composites
Nicolais-Narkis semi-empirical equation for case
with no bonding between particles and matrix
where
S
yc
is the yield strength of the composite
S
ym
is the yield strength of the matrix material
v
p
is the volume fraction of particles
the coefficient 1.21 and the exponent 2/3 are selected so as to insure
that
S
yc
decreases with increasing
v
p
, that
S
yc
= S
ym
when
v
p
=0
,
and
that
S
yc
=0 when
v
p
=0.74 , the particle volume fraction corresponding
to the maximum packing fraction for spherical particles of the same
size in a hexagonal close packed arrangementSlide5
Liang – Li equation includes particle – matrix
interfacial adhesion
(6.66)
where
θ
is the interfacial bonding angle,
θ
= 0
o
corresponds to good adhesion, and
θ
= 90
o
corresponds to poor adhesionSlide6
Finite element models for particulate composites
Finite element models for spherical particle reinforced composite.
(From Cho, J., Joshi, M. S., and Sun, C. T. 2006.
Composites Science and Technology
,
66, 1941-1952. With permission)
development of axisymmetric RVE
axisymmetric finite element models of RVESlide7
Modulus of particulate composites
Katz -Milewski and Nielsen-Landel generalizations of
the Halpin-Tsai equations
(6.67)
where Slide8
and where
is the Young’s modulus of the composite
is the Young’s modulus of the particle
is the Young’s modulus of the matrix is the Einstein coefficient is the particle volume fraction is the maximum particle packing fractionSlide9
Semi empirical Models
Use empirical equations which have a theoretical basis in mechanics
Halpin-Tsai Equations
(3.63)
Where
(3.64)Slide10
And curve-fitting parameter
2 for
E
2 of square array of circular fibers 1 for
G12As Rule of Mixtures
As Inverse Rule of Mixtures Slide11
Comparison of predicted and measured values of Young’s modulus for glass
microsphere-reinforced polyester composites of various particle volume fractions.Slide12
Improvement of mechanical properties of conventional unidirectional E-glass/epoxy composites
by using silica nanoparticle-enhanced epoxy matrix. (a) off-axis compressive strength. (b) transverse
tensile strength and transverse modulus. (From Uddin, M. F., and Sun, C. T. 2008.
Composites
Science and Technology
, 68(7-8), 1637-1643. With permission.)
Hybrid multiscale reinforcements