B Konh T Sorensen A Trimble Z Song 1 of XXME 481 ndash Fall 2018

Material Selection

Senior Design ME481

Fall 2017Dr Bardia Konh

Fall 2018Dr A Trimble

B Konh T Sorensen A Trimble 2 of XXME 481 ndash Fall 2018

Materials Selection in Design

This Lecture

- Importance of material selection in design

- Exploring materials using materials property charts

- Materials selection process

- Selecting materials materials indices

- Case studies

Material selection is critical part of almost all engineering designs

So many factors to consider

strength stiffness durability corrosion cost formability etc

Design ishellip

ldquohellipthe process of translating a new idea or a market need into detailed

information from which a product can be manufacturedrdquo

M F Ashby ldquoMaterials Selection in Mechanical Designrdquo

B Konh T Sorensen A Trimble 3 of XXME 481 ndash Fall 2017

Materials Selection in Design

B Konh T Sorensen A Trimble 4 of XXME 481 ndash Fall 2017

Materials selection is a key step for a successful design

A large number of materials to select from

Recently there has been more emphasis on the role of materials

Discovery of new and advanced materials

The Role of Materials Selection in Design

Function

Mechanical

Properties Failure

ModeManufacturability

CostEnvironmental

Considerations

Advanced new materials can introduce

new products with more efficiencies

lower manufacturing costs

Exhibit desired behavior

An ability to select materials that best meet requirements of a design

Access to information and tools for comparison and selection

B Konh T Sorensen A Trimble 5 of XXME 481 ndash Fall 2017

Need for a new product and new materials

Development of a new materials

httphleelabhomewixsitecommysiteresearch2

httphleelabhomewixsitecommysite

bull Soft active materials

bull Biologically inspired design principles

Soft robotics

Dr Howon Lee

Rutgers University

Soft multi-material actuators

Dr Conor Walsh

Harvard University

httpsbiodesignseasharvardedusoft-robotics

bull Large bending motions

B Konh T Sorensen A Trimble 2 of XXME 481 ndash Fall 2018

Materials Selection in Design

This Lecture

- Importance of material selection in design

- Exploring materials using materials property charts

- Materials selection process

- Selecting materials materials indices

- Case studies

Material selection is critical part of almost all engineering designs

So many factors to consider

strength stiffness durability corrosion cost formability etc

Design ishellip

ldquohellipthe process of translating a new idea or a market need into detailed

information from which a product can be manufacturedrdquo

M F Ashby ldquoMaterials Selection in Mechanical Designrdquo

B Konh T Sorensen A Trimble 3 of XXME 481 ndash Fall 2017

Materials Selection in Design

B Konh T Sorensen A Trimble 4 of XXME 481 ndash Fall 2017

Materials selection is a key step for a successful design

A large number of materials to select from

Recently there has been more emphasis on the role of materials

Discovery of new and advanced materials

The Role of Materials Selection in Design

Function

Mechanical

Properties Failure

ModeManufacturability

CostEnvironmental

Considerations

Advanced new materials can introduce

new products with more efficiencies

lower manufacturing costs

Exhibit desired behavior

An ability to select materials that best meet requirements of a design

Access to information and tools for comparison and selection

B Konh T Sorensen A Trimble 5 of XXME 481 ndash Fall 2017

Need for a new product and new materials

Development of a new materials

httphleelabhomewixsitecommysiteresearch2

httphleelabhomewixsitecommysite

bull Soft active materials

bull Biologically inspired design principles

Soft robotics

Dr Howon Lee

Rutgers University

Soft multi-material actuators

Dr Conor Walsh

Harvard University

httpsbiodesignseasharvardedusoft-robotics

bull Large bending motions

B Konh T Sorensen A Trimble 3 of XXME 481 ndash Fall 2017

Materials Selection in Design

B Konh T Sorensen A Trimble 4 of XXME 481 ndash Fall 2017

Materials selection is a key step for a successful design

A large number of materials to select from

Recently there has been more emphasis on the role of materials

Discovery of new and advanced materials

The Role of Materials Selection in Design

Function

Mechanical

Properties Failure

ModeManufacturability

CostEnvironmental

Considerations

Advanced new materials can introduce

new products with more efficiencies

lower manufacturing costs

Exhibit desired behavior

An ability to select materials that best meet requirements of a design

Access to information and tools for comparison and selection

B Konh T Sorensen A Trimble 5 of XXME 481 ndash Fall 2017

Need for a new product and new materials

Development of a new materials

httphleelabhomewixsitecommysiteresearch2

httphleelabhomewixsitecommysite

bull Soft active materials

bull Biologically inspired design principles

Soft robotics

Dr Howon Lee

Rutgers University

Soft multi-material actuators

Dr Conor Walsh

Harvard University

httpsbiodesignseasharvardedusoft-robotics

bull Large bending motions

B Konh T Sorensen A Trimble 4 of XXME 481 ndash Fall 2017

Materials selection is a key step for a successful design

A large number of materials to select from

Recently there has been more emphasis on the role of materials

Discovery of new and advanced materials

The Role of Materials Selection in Design

Function

Mechanical

Properties Failure

ModeManufacturability

CostEnvironmental

Considerations

Advanced new materials can introduce

new products with more efficiencies

lower manufacturing costs

Exhibit desired behavior

An ability to select materials that best meet requirements of a design

Access to information and tools for comparison and selection

B Konh T Sorensen A Trimble 5 of XXME 481 ndash Fall 2017

Need for a new product and new materials

Development of a new materials

httphleelabhomewixsitecommysiteresearch2

httphleelabhomewixsitecommysite

bull Soft active materials

bull Biologically inspired design principles

Soft robotics

Dr Howon Lee

Rutgers University

Soft multi-material actuators

Dr Conor Walsh

Harvard University

httpsbiodesignseasharvardedusoft-robotics

bull Large bending motions

B Konh T Sorensen A Trimble 5 of XXME 481 ndash Fall 2017

Need for a new product and new materials

Development of a new materials

httphleelabhomewixsitecommysiteresearch2

httphleelabhomewixsitecommysite

bull Soft active materials

bull Biologically inspired design principles

Soft robotics

Dr Howon Lee

Rutgers University

Soft multi-material actuators

Dr Conor Walsh

Harvard University

httpsbiodesignseasharvardedusoft-robotics

bull Large bending motions

B Konh T Sorensen A Trimble 6 of XXME 481 ndash Fall 2017

Evolution of materials

[ASHBY99] - Materials Selection In Mechanical Design

httpwwwutcfr~hagegebeUVMQ12CORRECTIONS_TD5BASHBY995D20-

20Materials20Selection20In20Mechanical20Design202Edpdf

B Konh T Sorensen A Trimble 7 of XXME 481 ndash Fall 2017

Material Properties

Physical

ndash Density

ndash Melting point

ndash Vapor pressure

ndash Viscosity

ndash Porosity

ndash Permeability

ndash Reflectivity

ndash Transparency

ndash Optical properties

ndash Dimensional stability

Chemical

ndash Corrosion

ndash Oxidation

ndash Thermal stability

ndash Biological stability

ndash Stress Corrosion

ndash hellip

Electrical

ndash Conductivity

ndash Dielectric constant

ndash Coersive force

ndash Hysteresis

Thermal

ndash Conductivity

ndash Specific Heat

ndash Thermal expansion

ndash Emissivity

Mechanical

ndash Hardness

ndash Elastic constants

ndash Yield strength

ndash Ultimate strength

ndash Fatigue

ndash Fracture Toughness

ndash Creep

ndash Damping

ndash Wear resistance

ndash Spalling

ndash Ballistic performance

ndash helliphellip

B Konh T Sorensen A Trimble 8 of XXME 481 ndash Fall 2017

httpwwwmatwebcom

What do we expect from a design

The products should perform their functions effectively safely at acceptable costrdquo

Test Test data

Data

capture

Statistical

analysis

Allowables

Mechanical Properties

Bulk Modulus 41 - 46 GPa

Compressive Strength 55 - 60 MPa

Ductility 006 - 007

Elastic Limit 40 - 45 MPa

Endurance Limit 24 - 27 MPa

Fracture Toughness 23 - 26 MPam12

Hardness 100 - 140 MPa

Loss Coefficient 0009- 0026

Modulus of Rupture 50 - 55 MPa

Poissons Ratio 038 - 042

Shear Modulus 085 - 095 GPa

Tensile Strength 45 - 48 MPa

Youngs Modulus 25 - 28 GPa

Successful

applications

$

Economic analysis

and business caseSelection of

material and process

Potential

applications

Characterization Selection and implementation

DATA INFORMATION KNOWLEDGE

B Konh T Sorensen A Trimble 8 of XXME 481 ndash Fall 2017

httpwwwmatwebcom

What do we expect from a design

The products should perform their functions effectively safely at acceptable costrdquo

Test Test data

Data

capture

Statistical

analysis

Allowables

Mechanical Properties

Bulk Modulus 41 - 46 GPa

Compressive Strength 55 - 60 MPa

Ductility 006 - 007

Elastic Limit 40 - 45 MPa

Endurance Limit 24 - 27 MPa

Fracture Toughness 23 - 26 MPam12

Hardness 100 - 140 MPa

Loss Coefficient 0009- 0026

Modulus of Rupture 50 - 55 MPa

Poissons Ratio 038 - 042

Shear Modulus 085 - 095 GPa

Tensile Strength 45 - 48 MPa

Youngs Modulus 25 - 28 GPa

Successful

applications

$

Economic analysis

and business caseSelection of

material and process

Potential

applications

Characterization Selection and implementation

DATA INFORMATION KNOWLEDGE

B Konh T Sorensen A Trimble 9 of XXME 481 ndash Fall 2017

Materials Data - Organization

bull Properties for a particular material is called the ldquomaterial attributesrdquo

bull Includes both structured and non-structured information

bull We need to find the best match between the design requirements and the

materials attributes

B Konh T Sorensen A Trimble 10 of XXME 481 ndash Fall 2017

Material stiffness

httpwwwgrantadesigncomdownloadpdfteaching_resource_books2-Materials-Charts-2010pdf

B Konh T Sorensen A Trimble 11 of XXME 481 ndash Fall 2017

Metals

Metal Examples of application

Ferrous Metals Carbon Steels Utensils construction automotive transmission

towers hellip

Stainless Steels Off shore drilling rigs naval construction

chemical transport food preparation medical

instruments

Cast Irons Cylinders pistons motor blocks construction

wear resistant materials

Light Alloys Aluminum Alloys Aerospace construction transport packaging

electrical conductors

Magnesium Alloys Aerospace automotive sporting equipment

Titanium Alloys Aerospace chemical industry

Copper Alloys Copper Electrical conductors

Bronze Heat exchangers chemical industry maritime

industry

Brass Pressure vessels fittings

Nickel Alloys Aerospace currency

B Konh T Sorensen A Trimble 12 of XXME 481 ndash Fall 2017

Interactions

Material

ProcessShape

Functionality

Materials Selection Methodology

Ashby Methodology

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 13 of XXME 481 ndash Fall 2017

Material selection

[ASHBY99] - Materials Selection In Mechanical Design

B Konh T Sorensen A Trimble 14 of XXME 481 ndash Fall 2017

First Step Translation

ldquoExpress design requirements as constraints and objectivesrdquo

Using design requirements analyze four items

1 Function What does the component do

2 Objective What essential conditions must be met

3 Constraints What is to be maximized or minimized

4 Free variables Which design variables are free

ndash Which can be modified

ndash Which are desirable

B Konh T Sorensen A Trimble 15 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Function

Support a tension load

Objective

Minimize mass

Constraints

Length specified

Carry load F wo failure

Free variables

Cross-section area

Material

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 10 of XXME 481 ndash Fall 2017

Material stiffness

httpwwwgrantadesigncomdownloadpdfteaching_resource_books2-Materials-Charts-2010pdf

B Konh T Sorensen A Trimble 11 of XXME 481 ndash Fall 2017

Metals

Metal Examples of application

Ferrous Metals Carbon Steels Utensils construction automotive transmission

towers hellip

Stainless Steels Off shore drilling rigs naval construction

chemical transport food preparation medical

instruments

Cast Irons Cylinders pistons motor blocks construction

wear resistant materials

Light Alloys Aluminum Alloys Aerospace construction transport packaging

electrical conductors

Magnesium Alloys Aerospace automotive sporting equipment

Titanium Alloys Aerospace chemical industry

Copper Alloys Copper Electrical conductors

Bronze Heat exchangers chemical industry maritime

industry

Brass Pressure vessels fittings

Nickel Alloys Aerospace currency

B Konh T Sorensen A Trimble 12 of XXME 481 ndash Fall 2017

Interactions

Material

ProcessShape

Functionality

Materials Selection Methodology

Ashby Methodology

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 13 of XXME 481 ndash Fall 2017

Material selection

[ASHBY99] - Materials Selection In Mechanical Design

B Konh T Sorensen A Trimble 14 of XXME 481 ndash Fall 2017

First Step Translation

ldquoExpress design requirements as constraints and objectivesrdquo

Using design requirements analyze four items

1 Function What does the component do

2 Objective What essential conditions must be met

3 Constraints What is to be maximized or minimized

4 Free variables Which design variables are free

ndash Which can be modified

ndash Which are desirable

B Konh T Sorensen A Trimble 15 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Function

Support a tension load

Objective

Minimize mass

Constraints

Length specified

Carry load F wo failure

Free variables

Cross-section area

Material

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 11 of XXME 481 ndash Fall 2017

Metals

Metal Examples of application

Ferrous Metals Carbon Steels Utensils construction automotive transmission

towers hellip

Stainless Steels Off shore drilling rigs naval construction

chemical transport food preparation medical

instruments

Cast Irons Cylinders pistons motor blocks construction

wear resistant materials

Light Alloys Aluminum Alloys Aerospace construction transport packaging

electrical conductors

Magnesium Alloys Aerospace automotive sporting equipment

Titanium Alloys Aerospace chemical industry

Copper Alloys Copper Electrical conductors

Bronze Heat exchangers chemical industry maritime

industry

Brass Pressure vessels fittings

Nickel Alloys Aerospace currency

B Konh T Sorensen A Trimble 12 of XXME 481 ndash Fall 2017

Interactions

Material

ProcessShape

Functionality

Materials Selection Methodology

Ashby Methodology

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 13 of XXME 481 ndash Fall 2017

Material selection

[ASHBY99] - Materials Selection In Mechanical Design

B Konh T Sorensen A Trimble 14 of XXME 481 ndash Fall 2017

First Step Translation

ldquoExpress design requirements as constraints and objectivesrdquo

Using design requirements analyze four items

1 Function What does the component do

2 Objective What essential conditions must be met

3 Constraints What is to be maximized or minimized

4 Free variables Which design variables are free

ndash Which can be modified

ndash Which are desirable

B Konh T Sorensen A Trimble 15 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Function

Support a tension load

Objective

Minimize mass

Constraints

Length specified

Carry load F wo failure

Free variables

Cross-section area

Material

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 12 of XXME 481 ndash Fall 2017

Interactions

Material

ProcessShape

Functionality

Materials Selection Methodology

Ashby Methodology

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 13 of XXME 481 ndash Fall 2017

Material selection

[ASHBY99] - Materials Selection In Mechanical Design

B Konh T Sorensen A Trimble 14 of XXME 481 ndash Fall 2017

First Step Translation

ldquoExpress design requirements as constraints and objectivesrdquo

Using design requirements analyze four items

1 Function What does the component do

2 Objective What essential conditions must be met

3 Constraints What is to be maximized or minimized

4 Free variables Which design variables are free

ndash Which can be modified

ndash Which are desirable

B Konh T Sorensen A Trimble 15 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Function

Support a tension load

Objective

Minimize mass

Constraints

Length specified

Carry load F wo failure

Free variables

Cross-section area

Material

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 13 of XXME 481 ndash Fall 2017

Material selection

[ASHBY99] - Materials Selection In Mechanical Design

B Konh T Sorensen A Trimble 14 of XXME 481 ndash Fall 2017

First Step Translation

ldquoExpress design requirements as constraints and objectivesrdquo

Using design requirements analyze four items

1 Function What does the component do

2 Objective What essential conditions must be met

3 Constraints What is to be maximized or minimized

4 Free variables Which design variables are free

ndash Which can be modified

ndash Which are desirable

B Konh T Sorensen A Trimble 15 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Function

Support a tension load

Objective

Minimize mass

Constraints

Length specified

Carry load F wo failure

Free variables

Cross-section area

Material

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 14 of XXME 481 ndash Fall 2017

First Step Translation

ldquoExpress design requirements as constraints and objectivesrdquo

Using design requirements analyze four items

1 Function What does the component do

2 Objective What essential conditions must be met

3 Constraints What is to be maximized or minimized

4 Free variables Which design variables are free

ndash Which can be modified

ndash Which are desirable

B Konh T Sorensen A Trimble 15 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Function

Support a tension load

Objective

Minimize mass

Constraints

Length specified

Carry load F wo failure

Free variables

Cross-section area

Material

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 15 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Function

Support a tension load

Objective

Minimize mass

Constraints

Length specified

Carry load F wo failure

Free variables

Cross-section area

Material

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 16 of XXME 481 ndash Fall 2017

Example Materials for a Light Strong Tie

Objective

Constraints

Rearrange to eliminate free variable

Minimizing weight by minimizing

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 17 of XXME 481 ndash Fall 2017

Second Step Screening

Eliminate materials that cannot do the job

Need effective way of evaluating large range of material classes and

properties

Metals Steels Cast irons Al-alloys Cu-

alloys Ti-alloys

Ceramics Alumina Si-carbide Si-nitride

Ziconia

Hybrids Composites Sandwiches Lattices

Segmented

Polymers PE PP PC PS PET PVC

PA (Nylon) Polyester Epoxy

Glasses Soda glass Borosilicate Silica

glass Glass ceramic

Elastomers Isoprene Butyl rubber

Natural rubber Silicones EVA

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 18 of XXME 481 ndash Fall 2017

Comparing Material Properties

Material Bar Charts

Good for elementary selection

(eg find materials with large modulus)

Material Property Charts

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 19 of XXME 481 ndash Fall 2017

Screening Example

Function

Heat Sink

Constraints

1 Max service temp gt 200 C

2 Electrical insulator

R gt 1020 μohm cm

3 Thermal conductor

T-conduct λ gt 100 Wm K

4 Not heavy

Density lt 3 Mgm3

Free Variables

Materials and Processes

Heat Sink for Power Electronics

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 20 of XXME 481 ndash Fall 2017

Heat Sink Screening Bar Chart

200 ordmC

λ gt 100 WmK

R gt 1020 micro ohm cm

temp gt 200 C

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 21 of XXME 481 ndash Fall 2017

Third Step Ranking

ldquoFind the materials that do the job bestrdquo

- What if multiple materials are selected after screening

- Which one is best

- What if there are multiple material parameters for evaluation

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 22 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Function

Transmit electricity

Objective

Minimize electrical Resistance

Constraints

Length L and section A are specified

Must not fail under wind or ice-load

Required tensile strength gt 80 MPa

Free variables

Material choice

gtgt Screen on strength rank on resistivity

Electrical resistivity

Overhead Transmission Cable

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 23 of XXME 481 ndash Fall 2017

Single Property Ranking Example

Screening on strength eliminates polymers some ceramics

Ranking on resistivity selects Al and Cu alloys

Overhead Transmission Cable

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 24 of XXME 481 ndash Fall 2017

Advanced Ranking The Material Index

Use this method

1 Identify function constraints objective and free variables

List simple constraints for screening

2 Write down equation for objective -- the ldquoperformance equationrdquo

If objective involves a free variable (other than the material)

Identify the constraint that limits it

Use this to eliminate the free variable in performance equation

3 Read off the combination of material properties that maximizes

performance -- the material index

4 Use this for ranking

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 25 of XXME 481 ndash Fall 2017

Optimized Selection

Example

Tension Load

strength limited

- Maximize M = σρ

- In log space

log σ = log ρ + log M

- This is a set of lines

with slope=1

- Materials above line are candidates

Using Material Indices amp Property Charts Strength

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 26 of XXME 481 ndash Fall 2017

Material Indices amp Property Charts

Example

Stiff beam

- Maximize M = Ε12ρ

- In log space

log E = 2 (log ρ + log M)

- This is a set of lines

with slope=2

- Candidates change with objective

Stiffness

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 27 of XXME 481 ndash Fall 2017

Considering Multiple ObjectivesConstraints

With multiple constraints

Solve each individually

Select candidates based on each

Evaluate performance of each

Select performance based on most limiting

May be different for each candidate

With multiple objectives

Requires utility function to map multiple metrics to common performance

measures

Design performance is determined by the combination of

Shape Materials Process

Underlying principles of selection are unchanged

- BUT do not underestimate impact of shape or the limitation of process

Method for Early Technology Screening

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 28 of XXME 481 ndash Fall 2017

Ashby Method for Early Material Selection

Four basic steps

1 Translation express design requirements as constraints amp objectives

2 Screening eliminate materials that cannot do the job

3 Ranking find the materials that do the job best

4 Supporting information explore pedigrees of top-ranked candidates

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 29 of XXME 481 ndash Fall 2017

Other Materials Selection Charts

bull Modulus-Relative Cost bull Facture Toughness-Density

bull Strength-Relative Cost bull Conductivity-Diffusivity

Modulus-Strength bull Expansion-Conductivity

bull Specific Modulus-Specific

Strength

bull Fracture Toughness-

Modulus

bull Fracture Toughness-

Strength

bull Expansion-Modulus

bull Strength-Expansion

bull Strength Temperature

bull Wear Rate-Hardness

bull Environmental Attack Chart

bull Loss Coefficient-Modulus

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 30 of XXME 481 ndash Fall 2017

Summary

bull Material affects design based on

- Geometric specifics

- Loading requirements

- Design constraints

- Performance objective

bull Effects can be assessed analytically

bull Keep candidate set large as long as is feasible

bull Materials charts give quick overview software can be used to more

accurately find options

bull Remember strategic considerations can alter best choice

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 31 of XXME 481 ndash Fall 2017

Function Objective Constraint

What does

component do

What is to be maximized

or minimized

What specific requirements

must be met

Any engineering

component has

one or more

functions (to

support a load to

contain a pressure

to transmit heat

etc)

The designer has an

objective (to make it

as cheap as possible

or as light as possible

or as safe as possible

or some combination

of these)

The objective must be

achieved subject to

constraints (eg the

dimensions are fixed the

component must carry the

given load without failure it

should function in a certain

temperature range etc

Free variables What is the designer free to change

Defining the Design requirements

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 32 of XXME 481 ndash Fall 2017

1 List the constraints (eg no buckling high stiffness) of the

problem and develop an equation for them if possible

2 Develop an equation of the design objective in terms of functional

requirements geometry and materials properties (objective function)

3 Define the unconstrained (free) variables

4 Substitute the free variable from the constraint equation into the

objective function

5 Group the variables into three groups functional requirements (F)

geometry (G) and materials functions (M) to develop the performance

metric (P)

6 Read off the materials index M in order to maximize the

performance metric (P)

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 33 of XXME 481 ndash Fall 2017

Materials Selection Charts

bullThe performance metric of a design is limited by the materials

bullPerformance metric is a function of multiple properties f(multiple

properties)

bullCharts Property 1 versus Property 2 (P1 vs P2)

bullIt can be plotted for classes and subclasses of materials (Classes metals

ceramics polymers composites) (Sub-Classes engineering ceramics

porous ceramics etc)

bullCombinations of properties are important in evaluating usefulness of

materials

bullStrength to Weight Ratio f

bullStiffness to Weight Ratio E

bullThe properties have ranges

bullE(Cu) = few (purity texture etc)

bullStrength of Al2O3 can vary by a factor of 100 due to (porosity grain

size heat treatment etc)

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos

B Konh T Sorensen A Trimble 34 of XXME 481 ndash Fall 2017

Materials Indices

Materials indices are specific functions derived from design

equations that involve only materials properties that can be used in

conjunction with materials selection charts

bulleg strong light tie rod in tensionndashminimize ρσy

bulleg stiff light beam in bending ndashminimize ρE12

bulleg stiff light panel in bending -minimize ρE13

Derivation of MIrsquos