mech4301 2008 l# 11 hybrid materials 1/28 mech 430-1 2008 lecture 11 design of hybrid materials or...

MECH4301 2008 L# 11 Hybrid

Materials 1/28

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)


Materials 2/28

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 ??)


Materials 3/28

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.


Materials 4/28

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


Materials 5/28

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


Materials 6/28

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


Materials 7/28

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


Materials 8/28

Hybrid Materials of Type 1: Fibre and Particulate Composites


Materials 9/28

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.


Materials 10/28

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


Materials 11/28

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


Materials 12/28

(Exercise 9.1) creating ligth/stiff composites

Compare composites made of Ti matrix, reinforced with ZrC,

Alumina, SiC fibres


Materials 13/28

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


Materials 14/28

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


Materials 15/28

Solution to Exercise 9.1

Ti matrix

E

Selection lines for tie rods, beams and

panelsAlumina fibers shift the

properties in the best direction


Materials 16/28

Hybrid Materials: four families of configurations

Composite

Sandwich

Lattice

Segment


Materials 17/28

Beams and Panels: Shaping increases efficiency (more GPa/kg)

E1/2/E1/3/

Low density materials are paramount for efficient panels => foamed cores


Materials 18/28

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


Materials 19/28

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


Materials 20/28

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


Materials 21/28

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 ?


Materials 22/28

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)


Materials 23/28

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


Materials 24/28

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


Materials 25/28

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


Materials 26/28

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


Materials 27/28

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)


Materials 28/28

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)


Materials 29/28

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)


Materials 30/28

The End Lecture 11


Materials 31/28

E- chart: Creating composites

High performance fibers

Metal matrix

compositesPoly-

matrix composit

es

Polymers

Metals

Hybrids fill previously empty

areas


Materials 32/28

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

mech4301 2008 l# 11 hybrid materials 1/28 mech 430-1 2008 lecture 11 design of hybrid materials or...

Documents

design of hybrid materials

hybrid materials of

conductive material

single material

monolithic materials

material indices

reading materials

existing materials