23
lecturers : Jean-Jacques Blandin : [email protected] Yves Bréchet : [email protected] Emilie Ferrié : [email protected] Luc Salvo : [email protected] Fabien Volpi : [email protected] David jauffrès : [email protected] Lectures in « english » Slides in english (you do not have all slides) Do not hesitate to ask questions in french if you want !!! Material and process selection You : SIM, McMaster, CNAM … Material and process selection Objectives : Understand Materials properties and Process attributes How to select materials ? How to select process ? How to find an application ? How to deal with environment ? Apply all these background on a real case study Lecture + practical work on CES + long project long project Real case study given by an industrial (confidential) 3-4 students per group 1 Lecturer A report (30-40 pages) An oral presentation Material and process selection ~15 projects / year since 1995 Rq : project are given or you can bring one (contact us !!) Various industrial very small to large companies Several kind of projects … Changing existing materials with conventional materials Changing existing materials with new materials Validate existing materials Exploring application of new materials Find methodology for selection Material and process selection Rq : Some projects ends up with a training period

Material and process selection lecturers : Objectiveschamilo2.grenet.fr/inp/courses/PHELMAA3SIM5PMMSEL0/document/slides/...Process: a method of shaping, joining or surface-treating

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lecturers :

Jean-Jacques Blandin : [email protected] Bréchet : [email protected] Ferrié : [email protected]

Luc Salvo : [email protected] Volpi : [email protected]

David jauffrès : [email protected]

Lectures in « english » Slides in english (you do not have all slides)

Do not hesitate to ask questions in french if you want !!!

Material and process selection

You :SIM, McMaster, CNAM …

Material and process selection

Objectives :

Understand Materials properties and Process attributes

How to select materials ? How to select process ?

How to find an application ?

How to deal with environment ?

Apply all these background on a real case study

Lecture + practical work on CES + long project

long projectReal case study given by an industrial (confidential)3-4 students per group1 Lecturer

A report (30-40 pages)An oral presentation

Material and process selection

~15 projects / year since 1995

Rq : project are given or you can bring one (contact us !!)

Various industrial

very small to large companies

Several kind of projects …

Changing existing materials with conventional materialsChanging existing materials with new materialsValidate existing materialsExploring application of new materialsFind methodology for selection

Material and process selection

Rq : Some projects ends up with a training period

Associative projectLow cost budgetRealisation

Virginie BULLEAlexis LENAINAna-Clara PRADOMarie WOLFFHUGEL

Bruno RIBEIR, Daniel CASTRO , Othmane ARHMIR

Student projectDatabaseSmall excel selector

Thomas Dehaye,Tamirys Dos Santos,

Océane Lambert, Adrien Skora

Confidential projectApplication finding

Material and process selection

Project can start the 10 of octoberTime slot are scheduled for it

but you can meet your contact when possible

type week day hour duration location Prof

course s37 12 sept.-18 sept. 2016 Mardi 10h15 2h C012 (V) L.SALVO

course s38 19 sept.-25 sept. 2016 Mardi 10h15 2h C012 (V) L.SALVO

course s39 26 sept.-02 oct. 2016 Mardi 10h15 2h C012 (V) J.J. BLANDIN

TD s40 03 oct.-09 oct. 2016 Lundi 13h30 3h C-TP102-info (V) L.SALVO/D.JAUFRES

TD s41 10 oct.-16 oct. 2016 Lundi 13h30 3h C-TP106-info (V) L.SALVO/D.JAUFRES

project s41 10 oct.-16 oct. 2016 Mardi 10h15 2h C-TP009 Academic tutor

course s42 17 oct.-23 oct. 2016 Mardi 10h15 2h C012 (V) J.J. BLANDIN

course s43 24 oct.-30 oct. 2016 Mardi 10h15 2h C012 (V) J.J. BLANDIN

project s42 17 oct.-23 oct. 2016 Lundi 13h30 4h C-TP009 Academic tutor

project s43 24 oct.-30 oct. 2016 Lundi 13h30 4h C-TP009 Academic tutor

course s45 07 nov.-13 nov. 2016 Lundi 13h30 2h C-014(V) Y. BRECHET

project s45 07 nov.-13 nov. 2016 Lundi 15h45 2h C-TP009 Academic tutor

course s45 07 nov.-13 nov. 2016 Mardi 10h15 2h C012 (V) F.VOLPI

project s46 14 nov.-20 nov. 2016 Lundi 13h30 4h C-TP009 Academic tutor

course s46 14 nov.-20 nov. 2016 Mardi 10h15 2h C012 (V) E. FERRIE

course s47 21 nov.-27 nov. 2016 Lundi 13h30 2h C-014(V) Y. BRECHET

project s47 21 nov.-27 nov. 2016 Lundi 15h45 2h C-TP009 Academic tutor

project s47 21 nov.-27 nov. 2016 Mardi 10h15 2h C-TP009 Academic tutor

project s48 28 nov.-04 déc. 2016 Lundi 13h30 4h C-TP009 Academic tutor

project s49 05 déc.-11 déc. 2016 Lundi 13h30 4h C-TP009 Academic tutor

project s50 12 déc.-18 déc. 2016 Lundi 13h30 4h C-TP009 Academic tutor

project s2 09 janv.-15 janv. 2017 Lundi 13h30 4h C-TP009 Academic tutor

project s3 16 janv.-22 janv. 2017 Lundi 13h30 4h C-TP009 Academic tutor

defence s5 30 janv.-05 févr. 2017 mardi all day 45min C012 jury

Material and process selection

All documents are available on line on CHAMILO Platformhttp://chamilo2.grenet.fr/inp/courses/PHELMAA3SIM5PMMSEL0/index.php

Materials Selection In Mechanical DesignM.F. Ashby624 pages Butterworth-Heinemann Ltd; 3rd Revised edition (dec 2004)

Materials: Engineering, Science, Processing and DesignH. Schercliff, D. Cebon, M.F. Ashby528 pages Butterworth-Heinemann Ltd; 1st edition (feb 2007)

Materials and the Environment: Eco-Informed Material ChoiceM.F. Ashby400 pages Butterworth-Heinemann Ltd; 3rd Revised edition (nov 2009)

Sélection des matériaux et des procédés de mise en oeuvre (TM volume 20) Y. Bréchet, M.F. Ashby, L. Salvo495 pagesPPUR (2001)

Material and process selection : references

Slides : credits @ grantdesign

1 – Background / Introduction

DatabasesIntroduction Data on materialsMaterials propertiesData on processesProcesses AttributesShape

Selection strategyIntroduction TranslateScreenRankMaterial indexCase study

Relative importance changes with time : competition between materials !!

1 – Background / Introduction

Competition between aluminium / steel

Competition between wood / composites

1 – Background / Introduction

modificationChanging existing material

1 – Background / Introduction

scalingChange of scale

originalNew product

Metals, ceramics, glasses

MATERIALSpolymers

composites...

Flat and dished sheet

SHAPESprismatic,

3-D

Casting , moulding

PROCESSESpowder methods,

machining...

What is needed to produce something ??

Example : difficult to find wood tube

+

environment

1 – Background / Introduction 1 – Background / Introduction

See lecture on Eco Design and course on ACV

Concept

Embodiment

Detail

Tools for Design(Material needs)

Data for all materials and processes, Shape simplification,

low precision

Data for fewer materials or processes, more realistic shape,

higher precision

Data for one material or process, Real shape

highest precision

Market need

Des

ign

phas

e

Production

Use

Disposal

Tools forlife-cycle analysis

Redesign

Life

pha

se

1 – Background / Introduction

The goal of design:“To create products that perform their function effectively, safely, at acceptable cost”

What do we need to know about materials to do this? More than just test data.

Test Test data

Data capture

Statisticalanalysis

Design data

Mechanical Properties

Bulk Modulus 4.1 - 4.6 GPaCompressive Strength 55 - 60 MPaDuctility 0.06 - 0.07Elastic Limit 40 - 45 MPaEndurance Limit 24 - 27 MPaFracture Toughness 2.3 - 2.6 MPa.m1/2

Hardness 100 - 140 MPaLoss Coefficient 0.009- 0.026Modulus of Rupture 50 - 55 MPaPoisson's Ratio 0.38 - 0.42Shear Modulus 0.85 - 0.95 GPaTensile Strength 45 - 48 MPaYoung's Modulus 2.5 - 2.8 GPa

Successful applications

$

Economic analysisand business case

Selection ofmaterial and process

Potential applications

Characterisationwhat you know ….

Selection and implementationwhat we will see !!

1 – Background / Introduction

1 – Background / Introduction

DatabasesIntroduction Data on materialsMaterials propertiesData on processesProcesses AttributesShape

Selection strategyIntroduction TranslateScreenRankMaterial indexCase study

PE, PP, PCPA (Nylon)

Polymers,elastomers

Butyl rubberNeoprene

Polymer foamsMetal foams

FoamsCeramic foams

Glass foams

Woods

Naturalmaterials

Natural fibres:Hemp, Flax,

Cotton

GFRPCFRP

CompositesKFRP

Plywood

AluminaSi-Carbide

Ceramics,glasses

Soda-glassPyrex

SteelsCast ironsAl-alloys

MetalsCu-alloysNi-alloysTi-alloys

Focus on materials

1 – Background / Data on materials

� Handbooks, compilations

� Suppliers’ data sheets (web site)

� The Worldwide Web

�www.matweb.com

�www.techniques-ingenieur.fr

�www.designinsite.dk

� Scientific community

1 – Background / Materials properties 1 – Background / Materials properties / Handbook

Example: Typical properties of wrought Al-alloys (extract)

1 – Background / Materials properties / Handbook

http://sicd1.ujf-grenoble.fr/

1 – Background / Materials properties / supplier

http://www.specialmetals.com/

1 – Background / Materials properties / Mat web 1 – Background / Materials properties

A type of wood

export

Limited list ofproperties

1 – Background / Materials properties

Not the sameProperties …

A type of aluminium

No possible comparisonbetween materialsNo link with processes

1 – Background / Materials properties / Techniques ingénieur

Do not download too many papers !!!

1 – Background / Data on materials

1995 : CMS (materials, little process)

2000 : CES (materials, Process, Shape)

2009 : new CES

2012 : introduction of architectured materials

Software

Cambridge Engineering Selector

1 – Background / Introduction

DatabasesIntroduction Data on materialsMaterials propertiesData on processesProcesses AttributesShape

Selection strategyIntroduction TranslateScreenRankMaterial indexCase study

Kingdom Family Class AttributesMember

• Ceramics

• Polymers

• Metals

• Natural

• Foams

• Composites

Steels

Cu-alloys

Al-alloys

Ti-alloys

Ni-alloys

Zn-alloys

10002000300040005000600070008000

Materials

A material record

Density

Mechanical props.

Thermal props.

Electrical props.

Optical props.

Corrosion props.

Supporting information

-- specific

-- general

Structuredinformation

Unstructuredinformation

1 – Background / Data on materials

Implementation in CES

1 – Background / Data on materials

1 – Background / Data on materials

Various kind of propertiesLow precision data

Numeric Data : range [min max]Ranking data : A, B, C, D, E, F

Non structured dataBut maybe useful !!!

1 – Background / Data on materials

High precision data

1 – Background / Data on materials

Materials properties should be understoodlook in references or CES help if needed

2- material charts

Full maps in chamilo

2- material charts

Full maps in chamilo

2- material charts

Full maps in chamilo

2- material charts

Full maps in chamilo

2- material charts

Full maps in chamilo

2- material charts

Full maps in chamilo

2- material charts

Full maps in chamilo

1 – Background / Introduction

DatabasesIntroduction Data on materialsMaterials propertiesData on processesProcesses AttributesShape

Selection strategyIntroduction TranslateScreenRankMaterial indexCase study

Process: a method of shaping, joining or surface-treating a material

Fusion welding

Sand casting

Thermal-spray coating

Unit 3, Frame 3.2

Blow moulding

Sha

ping

Sha

ping

Join

ing

Sur

face

trea

t

1 – Background / Data on processes

� Handbooks, compilations

� Suppliers’ data sheets (web site)

� The Worldwide Web

�www.techniques-ingenieur.fr

�www.designinsite.dk

� Scientific community

1 – Background / Data on processes 1 – Background / Data on processes / Handbook

DescriptionGraphsNo informationon cost

1 – Background / Data on processes / website

No quantitative data

1 – Background / Introduction

DatabasesIntroduction Data on materialsMaterials propertiesData on processesProcesses AttributesShape

Selection strategyIntroduction TranslateScreenRankMaterial indexCase study

Kingdom Family Class AttributesMember

Joining

Shaping

Surfacing

Casting

Deformation

Moulding

Composite

Powder

Rapid prototyping

Compression

Rotation

Injection

RTM

Blow

ProcessesStructuredinformation

A processrecord

Size Range

Min. section

Tolerance

Roughness

Economic batch

Material

Shape

Supporting information

-- specific

-- general

Unstructuredinformation

1 – Background / Process Attributes

See practical CES Process

1 – Background / Process Attributes

Attribute of forming process

Low precision data

1 – Background / Process Attributes

Casting Composite forming Deformation Machining processes Molding Powder methods Rapid prototyping

Mass

range (

kg)

0.001

0.01

0.1

1

10

100

1000

10000

Sand casting

Evaporative pattern sand casting

Lay-up methods

BMC (DMC) molding

Forging

Sheet stamping, drawing and blanking

Polymer extrusion

Blow moldingPowder injection molding

Laminated object manufacture

Larger ranges than for materials properties

1 – Background / Process Attributes

Full maps in chamilo

Batch SizeComponent Mass=1kg, Material Cost=7.26EUR/kg, Overhead Rate=84.1EUR/hr, Capital Write-off Time=5yrs,

Load Factor=0.5

1 10 100 1000 10000 100000 1e6 1e7 1e8 1e9

Rela

tive

cost

index

(per

unit)

10

100

1000

10000

higher precision data

Cost model

1 – Background / Process Attributes 1 – Background / Introduction

DatabasesIntroduction Data on materialsMaterials propertiesData on processesProcesses AttributesShape

Selection strategyIntroduction TranslateScreenRankMaterial indexCase study

Metals, ceramics, glasses

MATERIALSpolymers

composites...

Flat and dished sheet

SHAPESprismatic,

3-D

Casting , moulding

PROCESSESpowder methods,

machining...

What is needed to produce something ??

+

environment

1 – Background / Data on processes

Some processes can make only simple shapes, others, complex shapes.

� Wire drawing, extrusion, rolling, shape rolling: prismatic shapes� Stamping, folding, spinning, deep drawing: sheet shapes� Casting, molding, powder methods: 3-D shapes

All shapes

Prismatic Sheet 3-D

Circular Non-circular Flat Dished Solid Hollow

Unit 3, Frame 3.4

1 – Background / Data on shape

1 – Background / Introduction

DatabasesIntroduction Data on materialsMaterials propertiesData on processesProcesses AttributesShape

Selection strategyIntroduction TranslateScreenRankMaterial indexCase study

Credit to Granta Design

3 – Selection strategy / introduction

Product specification

Concept

Embodiment

Detail

Material & process needs

Data for material family(metals, ceramics, polymers..)

Data for material class(Steel, Al-alloy, Ni-alloy…..)

Data for single material(Al-2040, Al-6061, Al-7075…..)

Problem statement

Market need

3 – Selection strategy / introduction

ConceptsNeed

Embodiments

Direct pull Levered pull Spring assisted pullGeared pull

3 – Selection strategy / introduction

Detail Embodiment

Design requirements: expressed as

Constraints and

Objectives

Data:Material attributesProcess attributes

Documentation

Final selection

Comparison engine

� Screening

� Ranking

� Documentation

Density

Price

Modulus

Strength

Durability

Process compatibility

More…….

Able to be molded

Water and UV resistant

Stiff enough

Strong enough

As light as possible

As cheap as possible

3 – Selection strategy / introduction 3 – Selection strategy / introduction

The selection strategy:

Translate

Screen

(Rank)

Documentation

Translation: “express design requirements as constraints and objectives”

ObjectivesWhat measure of performance is to be maximized or minimized ?

� Be strong enough� Conduct electricity� Tolerate 250 C� Be able to be cast

� Cost � Weight� Volume� Eco-impact

Constraints What essential conditions must it meet ?

Design requirements

3 – Selection strategy / translate

Translation: a heat sink for power electronics

Power micro-chips get hot. They have to be cooled to prevent damage.

Translation

Constraints

� Maximum service temp > 200 C

� Good electrical insulator

� Good thermal conductor

(or T-conduction > 25 W/m.K)

Keep chips below 200 C without any electrical coupling.

Design requirements

3 – Selection strategy / screen

What properties are required ? Which maps ?

2- material charts

Mainly metalsAnd ceramics

2- material charts

� How rank those that remain?

� Screening removes candidates that cannot do the job.

� Material index do the job

3- Selection strategy / screen

� a material property group, eg modulus / density, E / ρ

What is a “material index”?Component performance is limited by:

The material indexfor the design

� a single material property eg thermal conductivity , λ

3- Selection strategy / rank

Heat exchanger:maximize heat flux for given ∆TChoose material with largest T- conductivity, λ

t, ∆T

Conduction

tT

J∆λ=Heat flux W/m2

Thermal conductivity

Thermal management

Good conductors:metals and ceramics

Good insulators:polymer foams, cork, wood, cardboard….

3- Selection strategy / rank

Minimum weight design

ρ

1/2E

Compressionstrut

σρ

3/2y

Undercarriage-compression

Tensile ties

σρ

y

Main spar- beam

ρ

1/2E

E = Young’s modulusρ = Density

yσ = Yield strength

3- Selection strategy / material index

Minimum cost designStructural

beam

σρCm

3/2yStructural

panels

σρCm

2/1y

Tensile ties

σρCm

y

Compressionstrut (column)

σρCm

y

Cm = Material cost / kg

ρ = Density

yσ = Yield strength

3- Selection strategy / material index

How can we obtainedthese performanceIndex ??

Index for a strong, light tie-rod, free area

Minimize mass m:m = A L ρ

Objective

• Length L is specified• Must not fail under load F• Free Area A

Constraints

Equation for constraint on A:

F/A < σy

Strong tie of length L and minimum mass

L

FF

Area A

Tie-rodFunction

m = massA = areaL = lengthρ = density

= yield strengthyσ

=

ρLFmPerformance

metric m Chose materials with largest

ρσ y

Free variable A:

A = F/ σy

3- Selection strategy / material index

Index for a stiff, light beam, free area

BeamFunction

Minimize mass m:Objective

• Length L is specified• Must have bending stiffness > S*• Free Area A

Constraints

Equation for constraint on A: m = massA = areaL = lengthρ = densityE = Young’s modulusI = second moment of area(I = b4/12 = A2/12)C = constant (here, 48)

Stiff beam of length L and minimum mass

L

Squaresection, area A = b2

b

3- Selection strategy / material index

= E

© Granta Design, January 2010 5

3. Elastic bending of beams

When a beam is loaded by a force F or moments M, the initially straight axis isdeformed into a curve. If the beam is uniform in section and properties, long inrelation to its depth and nowhere stressed beyond the elastic limit, the deflection,and the angle of rotation, , can be calculated using elastic beam theory (seeFurther reading in Section 16). The basic differential equation describing thecurvature of the beam at a point x along its length is

E Id 2 y

dx2= M

where y is the lateral deflection, and M is the bending moment at the point x onthe beam. E is Young's modulus and I is the second moment of area (SectionA.2). When M is constant this becomes

1

Ro

1

RMI

where Ro is the radius of curvature before applying the moment and R the radiusafter it is applied. Deflections and rotations are found by integrating theseequations along the beam. The stiffness of the beam is defined by

C1 E I

L3=S =

F

It depends on Young's modulus, E, for the material of the beam, on its length, L,and on the second moment of its section, I. The end-slope of the beam, , is givenby

F L2

C2EI =

Equations for the deflection,, and end slope, , of beams, for various commonmodes of loading are shown on the facing page together with values of C1 and

C2.

3- Selection strategy / material index

Useful documents in chamilo

IEC

FL3

=δC : depends on load andboundary constraintsI : inertia moment

Index for a stiff, light beam, free area

BeamFunction

Minimize mass m:Objective

• Length L is specified• Must have bending stiffness > S*• Free Area A

Constraints

Equation for constraint on A: m = massA = areaL = lengthρ = densityE = Young’s modulusI = second moment of area(I = b4/12 = A2/12)C = constant (here, 48)

Stiff beam of length L and minimum mass

L

Squaresection, area A = b2

b

3- Selection strategy / material index

© Granta Design, January 2010 4

2. Moments of sectionsA beam of uniform section, loaded in simple tension by a force F, carries a stress

⌠ = F / A

where A is the area of the section. Its response is calculated from the appropriateconstitutive equation. Here the important characteristic of the section is its area, A.For other modes of loading, higher moments of the area are involved. Those forvarious common sections are given on the facing page. They are defined asfollows.

The second moment I measures the resistance of the section to bending about ahorizontal axis (shown as a broken line). It is

I = +section y2 b(y)dy

where y is measured vertically and b(y) is the width of the section at y. Themoment K measures the resistance of the section to twisting. It is equal to thepolar moment J for circular sections, where

J = +section2r3 dr

where r is measured radially from the centre of the circular section. For non-circular sections K is less than J.

The section modulus Z = I/ym (where ym is the normal distance from the neutralaxis of bending to the outer surface of the beam) measures the surface stressgenerated by a given bending moment, M:

MZ

M ymI

=⌠ =

Finally, the moment H, defined by

H = +section yb(y)dy

measures the resistance of the beam to fully-plastic bending. The fully plasticmoment for a beam in bending is

M p = H⌠ y

121212

243 AbbhI ===

bh = 2bA =

3- Selection strategy / material index

Useful documents in chamilo

Index for a stiff, light beam, free area

BeamFunction

Minimize mass m:Objective

• Length L is specified• Must have bending stiffness > S*• Free Area A

Constraints

Equation for constraint on A: m = massA = areaL = lengthρ = densityE = Young’s modulusI = second moment of area(I = b4/12 = A2/12)C = constant (here, 48)

Stiff beam of length L and minimum mass

L

Squaresection, area A = b2

b

Performance metric m

Chose materials with largest

3- Selection strategy / material index

Index for a strong, light beam, free area

BeamFunction

Minimize mass m:Objective

• Length L is specified• Must support F > F*• Free Area A

Constraints

Equation for constraint on A: m = massA = areaL = lengthρ = densityE = Young’s modulusI = second moment of area(I = b4/12 = A2/12)C = constant (here, 48)

Stiff beam of length L and minimum mass

L

Squaresection, area A = b2

b

3- Selection strategy / material index

E

© Granta Design, January 2010 6

4 Failure of beams and panels

The longitudinal (or "fiber") stress⌠ at a point y from the neutral axis of auniform beam loaded elastically in bending by a moment M is

=

1

Ro

1

R

MI

⌠y

where I is the second moment of area (Section A.2), E is Young's modulus, Rois the radius of curvature before applying the moment and R is the radius after it isapplied. The tensile stress in the outer fiber of such a beam is

MZ

M ymI

=⌠ =

where ym is the perpendicular distance from the neutral axis to the outer surface

of the beam and Z = I / ym is the section modulus. If this stress reaches the yield

strength⌠y of the material of the beam, small zones of plasticity appear at thesurface (top diagram, facing page). The beam is no longer elastic, and, in thissense, has failed. If, instead, the maximum fiber stress reaches the brittle fracture

strength,⌠f (the "modulus of rupture", often shortened to MOR) of the material ofthe beam, a crack nucleates at the surface and propagates inwards (seconddiagram); in this case, the beam has certainly failed. A third criterion for failure isoften important: that the plastic zones penetrate through the section of the beam,linking to form a plastic hinge (third diagram).

The failure moments and failure loads, for each of these three types of failure,and for each of several geometries of loading, are given on the diagram. Theformulae labelled "onset" refer to the first two failure modes; those labelled "fullplasticity" refer to the third. Two new functions of section shape are involved.Onset of failure involves the section modulus Z; full plasticity involves the fully-plastic modulus H. Both are listed in the table of Section 2, and defined in the textthat accompanies it.

Useful documents in chamilo

L

ZCF

σ=* Z or H : the section modulusmy

IZ =

ym distance to the neutral axis © Granta Design, January 2010 4

2. Moments of sectionsA beam of uniform section, loaded in simple tension by a force F, carries a stress

⌠ = F / A

where A is the area of the section. Its response is calculated from the appropriateconstitutive equation. Here the important characteristic of the section is its area, A.For other modes of loading, higher moments of the area are involved. Those forvarious common sections are given on the facing page. They are defined asfollows.

The second moment I measures the resistance of the section to bending about ahorizontal axis (shown as a broken line). It is

I = +section y2 b(y)dy

where y is measured vertically and b(y) is the width of the section at y. Themoment K measures the resistance of the section to twisting. It is equal to thepolar moment J for circular sections, where

J = +section2r3 dr

where r is measured radially from the centre of the circular section. For non-circular sections K is less than J.

The section modulus Z = I/ym (where ym is the normal distance from the neutralaxis of bending to the outer surface of the beam) measures the surface stressgenerated by a given bending moment, M:

MZ

M ymI

=⌠ =

Finally, the moment H, defined by

H = +section yb(y)dy

measures the resistance of the beam to fully-plastic bending. The fully plasticmoment for a beam in bending is

M p = H⌠ y

666

2/332 AbbhZ

y

I

m

====

bh = 2bA =

3- Selection strategy / material index

Useful documents in chamilo

BeamFunction

Minimize mass m:Objective

• Length L is specified• Must support F > F*• Free Area A

Constraints

Equation for constraint on A:

L

ZCF

σ=*

m = massA = areaL = lengthρ = densityE = Young’s modulusI = second moment of area(I = b4/12 = A2/12)C = constant (here, 48)

Stiff beam of length L and minimum mass

L

Squaresection, area A = b2

b

3- Selection strategy / material index

666

2/332 AbbhZ

y

I

m

====

Index for a strong, light beam, free area

BeamFunction

Minimize mass m:

m = A L ρObjective

• Length L is specified• Must have bending stiffness > S*• Free Area A

Constraints

Equation for constraint on A: m = massA = areaL = lengthρ = densityE = Young’s modulusI = second moment of area(I = b4/12 = A2/12)C = constant (here, 48)

Stiff beam of length L and minimum mass

L

Squaresection, area A = b2

b

Performance metric m

Chose materials with largest

3- Selection strategy / material index

σσL

AC

L

ZCF

6*

2/3

==

Index for a strong, light beam, free area

� Material index = combination of material properties in the equation for performance

� Sometimes a single property

� Sometimes a combinationEither is a material index

Tension (tie)

Bending (beam)

Bending (panel)

E/ρ /ρσy

/ρE1/2 /ρσ2/3y

Stiffness StrengthConstraints

/ρE1/3 /ρσ1/2y

Objectiveminimise mass

Free variable

Area

Area

Thickness

3- Selection strategy / material index

What is important !!

Material indices = F (function, objectives, constra ints, free variable)

If you change one of the parameter of F Material Index will change !!!

There is no sense to always use σ / ρ or E / ρ !!!!

In some design the free variable is not totally free

this will give constraint on the properties

3- Selection strategy / material index

Log E = 2 log ρ + 2 log M

Take logs:

0.1

10

1

100

Metals

Polymers

Elastomers

Woods

Composites

Foams0.01

1000

100,000100 1000 10,000Density (kg/m3)

Youn

g’s

mod

ulus

E, (

GP

a)

Ceramics

Ranking, using charts

Indexρ

EM1/2

=

Light stiff beam:

2 2 MρE =

Rearrange:Increasing M

2

Function Index Slope

Tie 1

Beam 2

Panel 3

E/ρ

/ρE1/2

/ρE1/3

3- Selection strategy / material index

E1/2=

23

E1/3=

Results22 pass

Material 1 2230Material 2 2100Material 3 1950etc...

Rankedby Index /ρE1/2

1

MρE =

3- Selection strategy / material index

So what?

The four steps of selection

� Translation identifies constraints and objectives

� Screening removes the losers

� Ranking orders those that remain

� Documentation checks out the top-ranked candidates

Implementing the strategy

3- Selection strategy / material index

� Granta’s Web Portal (http://matdata.net) gives indexed access to information providers’ web sites.

Documentation: “now that the number of candidates is small, explore their character in depth”

Suppliers’ data sheets

Handbooksand texts

Material portals

Tradeassociations

Documentation:the “pedigree” of surviving candidates

3- Selection strategy / material index

3- Selection strategy / material index

What you should remenber from today

Where you can find data on materials and processes

What is a the selection strategy

What is a performance index

How it is possible to calculate them

And know all the materials properties ….

D

manche spatule

FUNCTION Light, stiff beam

OBJECTIVE Minimize mass

FREE VARIABLE Radius R free

CONSTRAINTS (a) Length L specified

(b) Bending stiffness S specified

(c) Toughness, Gc > 1 kJ/m2

(d) Cost, Cm < 100 USD/kg

Case study : a oar

Derive the performance index that minimize mass with R f ree