material and process selection lecturers :...
TRANSCRIPT
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
=
yσ
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
Mρ
E1/2=
23
Mρ
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