mech4301 2008 l 12 hybrid materials (2/2) 1/25 lecture 12, 2008. design of composites / hybrid...

MECH4301 2008 L 12 Hybrid

Materials (2/2) 1/25

Lecture 12, 2008. Design of Composites / Hybrid Materials, or Filling Holes in Material Property Space (2/2)

Textbook Chapter 13, Tutorial 6

Papers (light reading):

Microtruss core 1

Microtruss core 2



Hybrid Materials: four families of configurations

Composite

Sandwich

Lattice

Segment



Review: Fibre and particulate composites: the math

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.




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



A Sandwich Panel as a Single Material: the math Rule of mixtures for density Fibre composites

Sandwich panels

Rule of mixtures for stiffness Fibre composites (tension) Sandwich

panels (bending)

equivalent

flexural

modulus

E face




Composite

Sandwich

Lattice

Segment



Lattices: Bending dominated vs. Stretch dominated structures

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



Collapse of foams

metallic foam (plastic hinges)

elastomeric foam (elastic buckling)

ceramic foam (hinges crack)



Stretch dominated structuresflexible

over-constrained

rigid

bending-dominated

(mechanism)

stretch-dominated structures



Stretch dominated structures:

A micro-truss structure



Micro-truss core designs for panels

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.



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, only with slightly less efficiency



micro-truss hybrids: ultraligth, high flexural stiffness

Foams: ultraligth solids

Micro-truss: linear relationships Flexural loading

Foams: power law relationships (involve the second moment I) Loaded in compression

Bending dominated vs. Stretch dominated structures

Panels with foamed cores: linear relationship as well

E(flex) =(/ s)Eface=3f Ef (the foam as panel core

behaves like a micro-truss structure)

1/3 of the bars are loaded in

tension



Stiffness vs density for foams and micro-truss structures

Foams

Ef =(/s)2 Es

Slope 2

Micro-trussSlope 1

Micro-truss structures fill up another hole in property space

E

panels also

belong in here

(slope 1)

Eflexural =3f

Eface



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



Damage tolerance of segmented structures: Weibull statistics

Metals m = 25

Ceramics m = 5

Max slope = Weibull modulus m

Vt = volume of whole body

Vs = volume of one element

n = Vt/Vs number of elements

P* = critical failure probability

D, D* = fraction /critical fraction/ of elements that failed

t* s* = design stress, damage

and of solid body and segmented body

Vo, o, m = Weibull parameters

Kc stress concentration factor

P

Design for single large elementsegmented body

fails at *, D*

Effect of segmentation on available stress



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

coarse cells

fine cells

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)



Schematic illustrations of microtruss lattice structures with tetrahedral, pyramidal, Kagome and woven textile truss topologies

doi:10.1016/j.actamat.2004.09.024 Acta MaterialiaCellular metal lattices with hollow trusses Douglas T. Queheillalt and Haydn N.G. Wadley

mech4301 2008 l 12 hybrid materials (2/2) 1/25 lecture 12, 2008. design of composites / hybrid...

Documents

hybrid materials of

addition of materials

resists shear slide

microtruss structure

foams f f f f

panels http

math rule of mixtures

microtruss core