Download Hybrid composites

Hybrid composites
John Summerscales
Hybrid: definition
• incorporation of two or more fibres
within a single matrix
• the resulting material is a
hybrid composite,
often abbreviated to just "hybrid".
• or it may be two resin systems
e.g. an interpenetrating network (IPN)
Hybrids: configuration
a. fibre-by-fibre mixtures
also known as "intimate" hybrids
b. tow-by-tow mixtures
a.k.a. "discrete" or "zebra" hybrids
c. layer-by-layer mixtures
d. skin-core-skin structures
i.e. sandwich structures
e. internal ribs
f. external ribs
Hybrids: configuration
a
d
b
c
e
f
Hybrids: rule-of-mixtures
For elastic modulus:
Ec = ηlA ηoA VA EA + ηlB ηoB VB EB + Vm Em
where subscripts A and B
represent each of the fibre reinforcements
Hybrids: strength
(lower bound)
• For unidirectional composites, assume
that the critical situation is fibre fracture and
that contribution of resin matrix is negligible,
then lower bound strength will be either:
σ´c = either VA EA ε´A or VB EB ε´B
Hybrids: strength
- constant strain (middle bound)
• previous slide assumes that only one
dominant fibre is carrying the load.
• the low elongation fibre can be assumed to
be the critical failure case and if the high
elongation fibre is also carrying load at the
same strain, then:
σ´c = VA EA ε´A + VB EB ε´A
• Do NOT use this equation
with different values of ε’
Hybrids: strength
constant strain graphical method
• matrix contribution
assumed negligible
• plot strength
(on y - axis)
from
σ´c = VA EA ε´A
σ´c = VB EB ε´B
vs percent of each
fibre composite
(on x-axis)
100% A
100% B
Hybrids: strength
constant strain graphical method
• as proportion of A
decreases so does
its contribution to
hybrid strength
100%A
100%B
Hybrids: strength
constant strain graphical method
• as proportion of B
decreases so does
its contribution to
hybrid strength
100%A
100%B
Hybrids: strength
constant strain graphical method
• read off the
lower bound
strength
from the graph
(yellow dashed line)
100%A
100%B
Hybrids: strength
constant strain graphical method
• A is low strain-tofailure fibre so carries
no significant load
when B fails
• B is high strain-tofailure fibre so can
carry load when A
fails (up to ε’A)
• assume ε’B = 3 ε’A
100%A
100%B
Hybrids: strength
constant strain graphical method
• A is low strain-tofailure fibre so carries
no significant load
when B fails
• B is high strain-tofailure fibre so can
carry load when A
fails (up to ε’A)
• assume ε’B = 3 ε’A
100%A
100%B
Hybrids: strength
constant strain graphical method
• by similar triangles,
the orange line can
be joined to S (σ’A)
• i.e. the triangles PQR
and SQR have the
same vertical height
P
S
R
100%A
100%B
Q
Hybrids: strength
constant strain graphical method
• hence, the composite
middle-bound
strength can
now be read from a
higher line
100%A
100%B
The hybrid effect !
(upper bound)
hybrid strength exceeds the rule of mixtures ?
… often referred to as
“synergistic strengthening “
The hybrid effect !
• for fibres with closely matched strains to
failure, where the high-modulus fibre has the
low strain to failure and vice versa
• failure strain of the low elongation fibre might
be increased to that for high elongation fibre
by isolating the individual critical fibre failures
such that broken fibres are uniformly
distributed through the composite.
• we might then predict a strength that
exceeds the rule-of-mixtures prediction.
The hybrid effect
1200
1000
Strength (MPa)
• experimental data
from Mark Gruber’s
MMAE thesis,
Delaware, 1981:
Kevlar 49/E-glass.
• theoretical model
from JS’ PhD thesis,
1983 using the
assumptions on the
previous slide.
800
600
400
200
0
0
20
40
60
Vol% Kevlar composites
80
100
However ....
There is an alternative explanation:
carbon fibre contracts on heating
o glass fibre expands on heating
o
if fibre-matrix bond
forms at cure temperature
then, on cooling to ambient,
carbon tries to expand
o glass tries to contract
o
• but they are constrained by the matrix ...
Thermal explanation of
the hybrid effect
• carbon fibre has residual compressive strain
• glass fibre has residual tensile strain
• when carbon is loaded in tension:
σ
constrained
unconstrained
ε
Summary
• six generic ways to combine the fibres
• additional term in rule-of-mixtures
• strength
lower bound (just the weaker fibre)
o middle bound (all fibres at ε’LEC)
o upper bound (hybrid effect)
do NOT use this model for design purposes?
o
• thermal effects with constraints