mech4301 2008 l# 11 hybrid materials 1/28 mech 430-1 2008 lecture 11 design of hybrid materials or...
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MECH4301 2008 L# 11 Hybrid
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Mech 430-1 2008 Lecture 11 Design of Hybrid Materials
or Filling Holes in Material Property Space (1/2)
Textbook Chapter 13
Reading Materials: Technical Papers Folder
Penalty Functions (P. Sirisalee, M. F. Ashby, G. T. Parks and P. J. Clarkson, "Multi-Criteria Material Selection of Monolithic and Multi-Materials in Engineering Design", Adv. Engng. Mater., 2006, 8, 48-56.) (simple, quite readable)
Hybrids (M. F. Ashby and Y. J. M. Brechet, "Designing hybrid materials", Acta Materialia, 2003, 51, 5801-5821.) (advanced reading)
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Holes in Material Property Space
big empty area
E
Is it possible to create a
material to fill this empty
space?(A compliant- high thermal conductivity material ??)
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Making Hybrid Materials
Hybrid materials combine the properties of two or more monolithic materials, (CFRP, GFRP)
or of one material and space (foams),
or of a single material in two different forms, (dual phase steels, eutectic alloys, PSZ, ABS)
Shape and scale add two more dimensions.
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What might we hope to achieve?
Best of both
Rule of mixtures
Weakest link
Least of both
Zn-coated steel
Unidirectional (fibre) composites (stiffer, stronger) CFRP; GFRP
Particulate (filler) composites (harder, cheaper)
Wax-metal sprinklers
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Hybrid Materials defined
A hybrid material is a combination of two or more materials in a predetermined configuration, relative proportion and scale (size and shape), optimised for a specific engineering purpose.
A + B + Configuration + Scale
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Lneed strong electrically conductive material for
power line
Example of a Hybrid material filing a hole in the Material Property Space
Trade-off surface
Best point empty
Resistivity
1/TS
A + B + conf + scale Cu => min
elect. resist. Fe => max TS
interleaving fine strands
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Hybrid Materials: four families of Configurations
4 hybrid configurations:
Composite
Sandwich
Lattice
Segment
See list of properties in Fig. 13.4, p. 344
Keyword to
understand
hybrids
Lecture 11
Lecture 12
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Hybrid Materials of Type 1: Fibre and Particulate Composites
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Properties of Hybrids
It is difficult to calculate/predict the actual behaviour of the composite.
Easier to find general bounds and limits that bracket the expectations/possibilities.
Criteria of Excellence: Material Indices. Used to decide whether (or not) the hybrid outperforms existing materials.
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Fibre and particulate composites: the maths Rule of mixtures for density (exact value)
Rule of mixtures for stiffness Along the fibres (upper bound, Voigt)
Across the fibres (lower bound, Reuss)
Same sort of equations for strength, heat capacity, thermal and electrical conductivity, etc. pp. 351-353
Exercise 9.2
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Composites for a stiff beam of minimum mass Bounds for the elastic moduli of hybrids
Beryllium fibres
Aluminium alloys
Alumina fibres
E
E1/2/ (beams)
Beryllium fibres have a stronger effect due to their low density; Alumina gives almost no gain.
Criterion of excellence
better
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(Exercise 9.1) creating ligth/stiff composites
Compare composites made of Ti matrix, reinforced with ZrC,
Alumina, SiC fibres
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Solution to Exercise 9.1
Ti matrix
E
UD composites, Eq. 13-2 for upper bound and Eq. 13-3 for lower bound, Eq. 13-1 for
Selection lines for tie rods, beams and
panelsUse parametric plotting find upper/lower
bounds
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Exercise 9.1: Parametric plotting of E and (f : free parameter)
f
E// (GPa
)
E+ (GPa
)
(Mgr/m3)
0 111.00 111.00 4.60
0.05 114.51 119.80 4.54
0.1 118.25 128.60 4.48
0.2 126.52 146.20 4.36
0.3 136.02 163.80 4.24
0.4 147.08 181.40 4.12
0.5 160.09 199.00 4.00
0.6 175.62 216.60 3.88
0.7 194.49 234.20 3.76
0.8 217.90 251.80 3.64
0.9 247.72 269.40 3.52
1 287.00 287.00 3.40
ETi = 111 GPa
Ti = 4.6 Mgr/m3
EAlumina= 287 GPa
Alumina = 3.4 Mgr/m3
1 10density (M gr/m 3)
10
100
1000
elas
tic m
od
ulu
s (G
Pa
)
Repeat procedure for ZrC and SiC fibres
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Solution to Exercise 9.1
Ti matrix
E
Selection lines for tie rods, beams and
panelsAlumina fibers shift the
properties in the best direction
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Hybrid Materials: four families of configurations
Composite
Sandwich
Lattice
Segment
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Beams and Panels: Shaping increases efficiency (more GPa/kg)
E1/2/E1/3/
Low density materials are paramount for efficient panels => foamed cores
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Hybrids of Type II. Sandwich Structure: properties defined
Face: Ef Thickness tIncreases I, takes load
Core: Ec
Thickness c
Prevents shear !
Volume fraction of face
material :--- f = 2t/d
Core fraction : 1-f = 1-2t/d=(d-2t)/d=(c+2t-2t)/d = c/d
Correct typos in txtbk p. 359
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A Sandwich Panel as a Monolithic Material: the Maths Rule of mixtures for density Fibre composites
Sandwich panels
Rule of mixtures for stiffness Fibre composites (tension) Sandwich
panels (bending)
equivalent
flexural
modulus (Eq. 13-17b)
f = 2t/d
E face
face
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Unidirectional composites compared with sandwich structures
E1/3/
face
core
Sandwich Panel: 3 times more efficient (GPa/kg, in bending) than the Unidirectional Composite (in tension)
sandwich
U-D Composites
in tension, “in plane” value.
E
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Figure 13-16 from textbook revisited
Polymer Foam reinforced with Ti
wires, Eqs. 13-2 and 13-3
Criterion of excellence for panels (slope 3)
E
Sandwich structure: 3 times more efficient (GPa/kg, in bending) than the U-D Composite (in tension)
Panel with Ti faces
and Foamed
core Eq. 13-17a
K=1
Parametric plotting ?
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Parametric plotting of E and , f disposable parameter Polymer Foam reinforced with Ti wires, Eqs. 13-2 and 13-3
f E// (GPa)
E+ (GPa)
(kg/m3)
E panel
0 0.25 0.25 250 0
0.05 5.8 0.26 467.5 15.8
0.1 11.3 0.28 685 30.1
0.2 22.4 0.31 1120 54.2
0.3 33.5 0.36 1555 72.9
0.4 44.6 0.42 1990 87.0
0.5 55.6 0.5 2425 97.1
0.6 66.7 0.62 2860 103.9
0.7 77.8 0.83 3295 108.0
0.8 88.9 1.24 3730 110.1
0.9 99.9 2.45 4165 110.9
1 111 111 4600 111
E panel => Eq.13.17a, K =1, p. 360
E Ti 111 GPa;
Ti = 4600 kg/m3
E foam= 0.25
GPa, foam = 250 kg/m3
Sandwich structure: 3 times more efficient (GPa/kg, in bending) than the U-D Composite (in tension)
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Overloading of a sandwich panel leads to failure
Failure of panels
Face yieldsFace bucklesCore fails (shear)Face/core
debondingPiercing of face by
localised force
These mechanisms compete with each other
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Young's Modulus (GPa)1e-5 1e-4 1e-3 0.01 0.1 1 10 100 1000
Re
sist
ivity
(µ
oh
m.c
m)
1
100
10000
1e6
1e8
1e10
1e12
1e14
1e16
1e18
1e20
1e22
1e24
1e26
Butyl Rubber (BR) - 50% HAF black
PS (Heat Resistant) Silica
Very Low Density Flexible Polymer Foam (0.016-0.036)
Leather
Cork
Graphite Foam (0.12)
Ultra Low Density Aluminium Foam (0.064-0.14)
Plaster of Paris
Can we create a flexible electrically conductive material? => Percolation
Percolation: properties that switch on and off
E
Resistivity
Rubber filled with graphite
big empty
area
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Percolation
•A bottle full of marbles is only 66% full (75% full if the marbles are in an FCC of HCP arrangement).
•Between 25 and 34% of the volume is empty, interconnected space. Percolation may happen along the interconnected interstices.
•You need at least about 25-30% volume fraction of “liquid” to have interconnection (continuity) from top to bottom, hence percolation of properties.
•Percolation: important design tool for hybrids
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Switching percolation on and off V =
0.05 Isolated particles
V = 0.10 Small Isolated clusters
V = 0.15 Long Isolated clusters
V = 0.2 Long interconnected clusters:
percolation switches on
Minimum volume fraction for percolation: about 20%
Particles dispersed
in a continuum
matrix
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Percolation relates to the existence of a continuous path trough the structure.
Dispersed particles touch at Vf>0.2 Mixing metallic powders with
polymers result in electrically conducting polymers.
The property disappears (switches-off) at Vf<0.2.
Percolation: properties that switch on and off
Elastomer-metal hybrids fill the gap
Resistivity
E
Percolation affects other properties as well:
Thermal conductivityDuctility and fracture toughness of
compositesPercolation is affected by the shape of
the particles (fibres tend to touch each other more often than round particles)
Examples: fridge magnets, electrically conductive polymers, pressure sensitive pads ( electronic drums)
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Flexible ferromagnets: not just Fridge Magnets
Magnetostriction ( or Joule effect) is a property of ferromagnetic materials that causes them to change their shape when subjected to a magnetic field . The reciprocal effect, the change of the susceptibility of a material when subjected to a mechanical stress, is called the Villari effect. (Wikipedia)
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Answer to Exercise 9.2. Minimise thermal distortion Solved with Eq. 13-7 through 13.10. (p. 352, full equations, parametric plots)
Mg alloys
Better this way
/
Criterion of excellence (gradient 1)
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The End Lecture 11
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E- chart: Creating composites
High performance fibers
Metal matrix
compositesPoly-
matrix composit
es
Polymers
Metals
Hybrids fill previously empty
areas
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Bounds for the expansion coefficient/conductivity of hybrids E 9.2
Aluminium alloys
SiC
BN
/
Better this way
Adding SiC to Al enhances performance. BN reduces performance
Criterion of excellence