Hybrids

MECH4301 2015 L 12 Hybrid Materials (2/2) 1/35

Lecture 12, 2015.

Design of Composites / Hybrid Materials, or

Filling Holes in Material Property Space (2/2)

Textbook Chapter 12, Tutorial 6

Papers:

Microtruss core 1

Microtruss core 2

Foam Topology


Hybrid Materials: four families of configurations

Composite

Sandwich

Lattice

Segment


Review: Fibre and particulate composites: the math

Rule of

mixtures

Reuss’

bound

Voigt’s

bound

Possible Mg-matrix fibre reinforced composites


Reuss'

bound

Voigt's

bound

E1/2/(criterion of excellence

for beams)



Composite

Sandwich

Lattice

Segment


Hybrid Materials of Type 2: Sandwich Panels

Strong/stiff faces

carry most of the load

(flexural stiffness)

Core is

lightweight,

Resists shear

Rule of mixtures for density

Fibre composites Sandwich panels

Rule of mixtures for stiffness

Fibre composites (tension) Sandwich panels (bending)

equivalentflexural modulus (P.320)

MECH4301 2015 L# 11 Hybrid Materials 7/35

A Sandwich Panel as a Monolithic Material: the Maths

f = 2t/d

E face

face

c = t – d, Ec ~0c = t – d, Ec ~0


The efficiency of Sandwich Structures: S/W Panels vs Monolithic Materials

E1/3/

face

core

Optimum

at f = 0.04

E



Composite

Sandwich

Lattice

Segment


Hybrid Materials of Type 3 and 4:

Cells, Foams and Lattices & Segmented structures

There are two main types of Lattices:

Bending dominated and Stretch dominated


Bending dominated structures

Cable Leaf

spring

We use Shaping to give the sections a LOWER flexural stiffness

per kg than the solid sections from which they are made.


Bending dominated structures: Foams

F

F

F

F

Very flexible structure = low effective E*

Prove this

Prove:

Proportionality

constant of

order 1


Compressive deformation behaviour of foams

MECH4301 2015 L 12 Hybrid Materials (2/2)14/35

metallic foam

(plastic hinges)

elastomeric

foam

(elastic

buckling)

ceramic foam

(hinges crack)

Collapse of foams


Stretch dominated structures

flexible over-constrainedrigid

bending-dominated

(mechanism)stretch-dominated structures

2D lattice

3D lattice

b for beams

j for joints


Stretch dominated structures:

A micro-truss structure



Micro-truss core designs for panels and towers

http://www.cellularmaterials.com/coredesigns.asp

Periodic cellular material cores are based on a regularly repeating

geometric unit, or cell, like a cube (square honeycomb) or pyramid.

This technology allows for consistently spaced open-cells, which

facilitate the addition of materials like magnets, cables, or ceramics,

for example and therefore increase functionality. The open cells also

permit fluid flow that can achieve more efficient thermal management.

Communications Tower

Guangzhou City


http://etd.gatech.edu/theses/available/etd-11222005-162952/unrestricted/wang_hongqing_v_200512_phd.pdf

http://www.srl.gatech.edu/publications/2005/DETC2005-85366.pdf

Bone = Foam (bending dominated) or

= Micro-truss (stretch dominated)?

A foam in a panel’s core behaves like a micro-truss structure:

shear stretches the diagonals of the cell walls, whereas the

panel’s faces are under “stretching” stresses. (See the bubble

charts in slides 28-29 later on)

http://etd.gatech.edu/theses/available/etd-11222005-162952/unrestricted/wang_hongqing_v_200512_phd.pdf

http://www.srl.gatech.edu/publications/2005/DETC2005-85366.pdf



(Zhang et al, 2015) Distribution of local strains. Stretched in tension by Mg-La (30% solid) (a) ~0.4% and (b) ~0.6% strain and (c) ~0.8% strain.

Mg-Nd (7.5% solid) (a) 0.4% (b) 0.8%

22

Stretch-dominated vs bending-dominated behaviour

23

Mg-La

Mg-La

Stretch-dominated

30% vol. fraction of solid

Mg-Nd Bending-dominated

7.7% vol. fraction of solid

Mg-Nd

MECH4301 2015 L 12 Hybrid Materials

(2/2)24/35

.

Stretch dominated

Bending

dominatedIsotropic

foams

Transition between

S-D to B-D at 20%

http://www.asminternational.org/news/industry/-/journal_content/56/10180/25845663/NEWS

25


Micro-truss hybrids: ultraligth, high flexural stiffness

Micro-truss (Stretch dominated)

linear relationships Design assumes

flexural macroscopic loading

Stretch Dominated vs. Bending Dominated hybrids

Panels with foamed cores: linear relationship as well

E(flex)/Ef ~ (/s) (panel stretch dominated structure)

(prove it!)

1/3 of the bars are

loaded in tension

Foams: ultralight, very flexible

Foams: power law relationships

(involve the second moment I)

Design assumes compressive loading

Linear at

low f=t/d


Open Cell Foam

properties

“sound”

polymer

Textbook pp. 333-334


Open Cell Foam

properties

Stretch

dominated

lattice

Stretch dominated:

doubles the stiffness Stretch dominated:

trebles the strength

Bending-dominated vs Stretch dominated


Foams: form a line of

Slope 2 (E = (ρ/ρs)2Es)

Micro-truss: line of

Slope 1 (E = (ρ/ρs)Es)


Foams

Ef =(/s)2 Es

Slope 2

Micro-truss

Slope 1

Micro-truss structures fill up another hole in property space

E (tension or

flexural)

Sandwich panels also

belong in here (slope 1)

Eflex /Eface~ /o


http://www.cellularmaterials.com/advantages.asp

http://www.cellularmaterials.com/advantages.asp



Composite

Sandwich

Lattice

Segment


bricks take compression but not tension or shear

carry out-of-plane forces and bending

carry in-plane loads

require a continuous clamping edge

Examples of topological interlocking

Unbonded structures

that carry load


Ashby & Brechet, 2003

Scale effects on the

strength of micro-

truss structures

metals ceramics

Gain in

strength

Loss of

strength

*s / *t = 1

Finer

this way

Weibull

modulus m

The strength of low Weibull

modulus (ceramics) micro-

truss structures increases

with segmentation

The strength of high Weibull modulus

(metals) micro-truss structures does not

increase with segmentation


The strength of ceramic foams of different cell sizes

5x

Colombo and Bernardo, Composites Sci. Tech., 2003, 63, 2353-2359.

For given density, foams

with fine cells are some 5

times stronger than

foams with coarse cells

Compressive

strength

density


Hybrids: The main points

Combining properties may help filling holes and

empty areas in material property-space maps.

Appropriate Hybrid materials can be created by

combining material properties and shape, the latter at

either micro or macro scale.

Properties of hybrid materials can be easily

bracketed by simple mathematical relationships

which allow straight forward description of behavior .

These functional relationships allow exploring new

possibilities.


The End

Lecture 12 (Hybrids, 2/2)

Tutorial 6 due on Sat Oct. 31st

at midnight.

See Paper “Foam topology” in BB


Lneed strong electrically

conductive material for power line


Example of a segmented structure filling 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

Pareto Plot


Example of a segmented structure filling a hole in the Material Property Space

Natural materials


Natural fibre composites: Comprehensive Ashby-type materials selection charts

Darshil U. Shah ⇑Oxford Silk Group, Department of Zoology, University of Oxford, Oxford OX1 3PS, UK

high-strength foam concrete

Microstructure of high-strength foam concrete

A. Just, B. Middendorf

M A T E R I A L S C H A R A C T E R I Z A T I O N 6 0 ( 2 0 0 9 ) 7 4 1 – 7 4 8


Date post:	04-Jan-2016
Category:	Documents
Upload:	lawrence
View:	213 times
Download:	0 times

Hybrids

Documents