material selection notes 2

W. Warnes: Oregon State University Week One:

ME480/580: Materials Selection Lecture Notes for Week One

Winter 2012

MATERIALS SELECTION IN THE DESIGN PROCESS

Reading: Ashby Chapters 1, 2, and 3. Reference: Kenneth G. Budinski, Engineering Materials: Properties and Selection

Fifth edition, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1996.

HISTORICAL CONTEXT

Ashby does a nice job of setting the historical context of the development of materials over the years with the cover illustration for Chapter One.

Note: Change from NATURAL materials (on left) toward MANUFACTURED materials (on right) toward ENGINEERED materials (near future). We have an increasingly large number of materials to deal with, on the order of 160,000 at present!

Other books for general reading on the history and development of materials science and engineered materials are:

J. E. Gordon, The New Science of Strong Materials, or Why You Don't Fall Through the Floor, Princeton University Press, Princeton, NJ.

M. F. Ashby and D. R. H Jones, Engineering Materials Parts 1, 2, and 3, Pergamon Press, Oxford, UK.

F. A. A. Crane and J. A. Charles, Selection and Use of Engineering Materials, Butterworths, London, UK.

P. Ball, Made to Measure: New Materials for the 21st Century, Princeton University Press, 1997.

MATERIALS PROPERTIES

Before we can discuss the appropriate selection of materials in design, we have to have a foundation of what we mean by "materials properties". Both Budinski and Ashby provide lists of these in the texts. For example:


This is a pretty complete list. Budinski discusses these in his chapter 2, and Ashby has his own definitions and discussion in chapter 3 in which he breaks the materials down into six categories: METALS, POLYMERS, CERAMICS, ELASTOMERS (which Budinski groups with plastics), GLASSES (which Budinski groups with ceramics), and HYBRIDS (or composite materials). In all, about 120,000 different materials with property values ranging over 5 orders of magnitude!

The importance of these chapters is that unless you have a clear idea of how a property value is measured (see Homework One), you cannot properly use the property for calculations in mechanical design. To these properties, we will add two other important materials properties: PRICE, and EMBODIED ENERGY (and other environmental materials properties.)

MATERIALS IN THE DESIGN PROCESS

Different authors have different ideas about how the design process should work. Budinski's design strategy is found in figure 18-1.


BUDINSKI FIGURE 18.1 NOTES:

1. Calculations in the first block! Analysis is important! (NOTE: ALGEBRA is a critical skill for success in this class, as is UNIT ANALYSIS. You’ve been warned!)

2. Analysis appears multiple times throughout design process. 3. Materials selection is in the last step. 4. Iteration?


In my opinion, Ashby uses a better design strategy, especially in terms of materials selection. He breaks the design flow path into three stages, called CONCEPTUAL DESIGN, EMBODIMENT DESIGN, and DETAIL DESIGN (see figure 2.1).

CONCEPTUAL DESIGN:

All options are kept open. Consideration of alternate working principles. Assess the functional structure of your design.

EMBODIMENT DESIGN:

Use the functional structure to ANALYSE the operation. Sizing of components. Materials down-selection. Determination of operational conditions.

DETAIL DESIGN:

Specifications written for components. Detailed analysis of critical components. Production route and cost analysis performed.

How does materials selection enter into Ashby's process? (Figure 2.5)

Materials selection enters at EVERY STAGE, but with differing levels of CONSTRAINT and DETAILED INFORMATION.

CONCEPTUAL DESIGN:

Apply PRIMARY CONSTRAINTS (eg. working temperature, environment, etc.). (Budinski figure 18-2 has a good list of primary constraints to consider.) 100% of materials in, 10-20% candidates come out.

EMBODIMENT DESIGN:

Develop and apply optimization constraints. Need more detailed calculations and Need more detailed materials information. 10-20% of materials in, 5 candidate materials out.


DETAILED DESIGN:

High degree of information needed about only a few materials. May require contacting specific suppliers of materials. May require specialized testing for critical components if materials data does not already exist.

CLASS APPROACH

Two different philosophies have been presented here:

Budinski: get familiar with a set of basic materials from each category, about seventy-five in total, and these will probably handle 90% of your design needs (see Figure 18-8).

Ashby: look at all 160,000 materials initially, and narrow your list of candidate materials as the design progresses using some technique to narrow your choices.

Materials selection has to include not only properties, but also SHAPES (what standard shapes are available, what shapes are possible), and PROCESSING (what fabrication route can or should be used to produce the part or raw material, eg. casting, injection molding, extrusion, machining, etc.). It can also include ENVIRONMENTAL IMPACT.

The point is that the choice of materials interacts with everything in the engineering design and product manufacturing process (see Ashby Figure 2.6).

In the remainder of this course we will develop a systematic approach to dealing with all these interactions and with looking at the possibilities of all 160,000 of these materials based on the use of MATERIALS SELECTION CHARTS as developed by Ashby.

Flow of the course:

• Optimization of selection without considering shape effects. • Optimization under multiple constraints. • Optimization of selection considering shape effects. • Considerations of environmental impact. • Optimization of material process selection.

SELECTION CHARTS (Ashby chapter 4)

1. Materials don't exhibit single-valued properties, but show a range of properties, even within a single production run (see Ashby, Figure 4.1 for example.)

EXAMPLES: The elastic modulus of copper varies over a few percent depending on the purity, texture, grain size, etc.


The mechanical strength of alumina (Al2O3) varies by more than a factor of 100 depending on its porosity, grain size, etc.

Metal alloys show large changes in their mechanical and electrical properties depending on the heat treatments and mechanical working they have experienced.

NOTE: Because the properties of materials may vary over large ranges, it will be critical to be able to interpret property data using SEMI-LOG and LOG-LOG plots. If you aren’t comfortable with logarithmic math and making and reading log axes on plots REVIEW IT!

2. Performance is seldom limited by only ONE property.

EXAMPLE: in lightweight design, it is not just strength that is important, but both strength and density. We will need to be able to compare materials based on several properties at once.

Because of these facts, we can produce charts such as this selection chart from Ashby:

There is a tremendous amount of information and power in these charts. First of all, they provide the materials property data as "balloons" in an easy to compare form. Secondly, other physical information can be displayed on these charts.


EXAMPLE: the longitudinal wavespeed of sound in a material is given by the equation

V =E!

"#$

%&'

1/2

Rewrite this equation by taking the base-10 logarithm of both sides to get:

log V( ) = 12

log E( ) ! log "( )#$ %& or log E( ) = 2 log V( ) + log "( ).

This is an equation of the form Y = A + BX, where:

Y = log(E),

A = constant = 2log(V) = y-axis intercept at X = 0,

B = slope = 1, and

X = log(ρ).

This appears as a line of slope = 1 on a plot of log(E) versus log(ρ). Such a line connects materials that have the same speed of sound (constant V).

NOTE: X = 0 means what for the value of density?


EXAMPLE: The selection requirement for a particular minimum weight design (derived next time) is to maximize the ratio of

E1/2

!= C = constant, which leads to 1

2log E( ) = log C( ) + log !( ) , or

log E( ) = 2 log C( ) + 2 log !( ), Y = A + BX.

This is a straight line of slope = 2 on a plot of log(E) versus log(ρ).

Such a line connects materials that will perform the same in a minimum weight design, that is, all the materials on this line have the same value of the constant, C.

End of File.



Winter 2012

PERFORMANCE INDICES Reading: Ashby Chapters 4 and 5.

Materials Selection begins in conceptual design by using PRIMARY CONSTRAINTS - non-negotiable constraints on the material imposed by the design or environment. Examples might include "must be thermally insulating", or "must not corrode in seawater".

These take the form of "PROPERTY > PROPERTYcritical", and appear as horizontal or vertical lines on the selection charts.

NOTE: Don't go overboard on primary constraints. They are the easiest to apply and require the least thought and analysis, but they can often be engineered around, for example, by active cooling of a hot part, or adding corrosion resistant coatings.

After initial narrowing, you should develop PERFORMANCE INDICES.

DEFINITIONS:

PERFORMANCE:


OBJECTIVE FUNCTION:

CONSTRAINT:

PERFORMANCE INDEX:

In the following, we will assume that performance (P) is determined by three factors:

FUNCTIONAL REQUIREMENTS (carry a load, store energy, etc.) GEOMETRICAL REQUIREMENTS (space available, shape, size) MATERIALS PROPERTIES

What we want to do is OPTIMIZE our choice of materials to maximize the performance of the design subject to the constraints imposed on it, so that we will try to makeP! Pmax .

We will further assume that these three factors are SEPARABLE, so that the performance equation can be written as:

If this is true, then maximizing performance will be accomplished by independently maximizing the three functions fn1, fn2, and fn3.

fn1 is the place where creative design comes in.


fn2 is where geometry can make a difference.

fn3 is the part we're most interested in. When the factors are separable, the materials selection doesn't depend on the details of fn1 or fn2! This means we don't have to know that much about the design to make intelligent materials choices.

Our first step in this class will be to maximize performance by only considering fn3 (selection of materials without shape effects). Later on we'll look at adding in the effect of shape on performance by maximizing the product of fn2 x fn3.

EXAMPLE ONE: Design a light, strong tie rod.

The design requirements are:

• to be a solid cylindrical tie rod • length L • load F, which may include a safety factor • minimum mass

Let's start by doing this the "old" way:

OLD WAY: PART ONE

1) CALCULATIONAL MODEL to use in the analysis

(pretty simple for this example).

2) We know an equation for the failure strength of a tie rod:


We know F, and we can always look up σf, so we can find the right cross sectional area, A. In the past, this part has always been made in our company from STEEL, which we know if a good high strength material, so we can look up in a database somewhere the σf(steel). Now we know what the smallest area will be:

3) And now we can find the mass of the rod, the measure of performance:

From our analysis, we can see that by choosing a higher strength steel, we can use a smaller A and thereby reduce our mass. Our recommendation: use a high strength steel.

OLD WAY: PART TWO

A new engineer comes along and she says "Wait...the design constraint says minimum mass, and your analysis shows that we can ALSO lower the mass by going to a lower density material. Let's use a high strength Al alloy instead of steel."

From the materials properties I found that the MASS (Aluminum) / MASS (Steel) = 60% which means we can get an increase in performance of 1.67 times. Our recommendation: use a high strength aluminum.

What's wrong with these two approaches? Nothing really. They both rely on established tradition in the company, and the use of "comfortable" materials. They both also ASSUME a material essentially at the outset.


ASHBY APPROACH (LINEAR OPTIMIZATION THEORY)

Looking at this list of requirements, we start with


2) Determine the MEASURE OF PERFORMANCE (MOP), P.

In this case, we have been told that the goal is to get a part that has a minimum mass.

NOTE: P is defined so that the larger it is the better our performance; we want to maximize P. This is our OBJECTIVE FUNCTION. NOTE also that Ashby defines P to be either minimized or maximized, just so long as you keep track of which one it is. We could also write the MOP as

3) IDENTIFY the parameters in our analytical model and MOP:

L= A= F= ρ=

4) Write an equation for the CONSTRAINED variables: (we have to safely carry the load F)


5) Rewrite the constraint equation for the free variable and substitute this into the MOP:

6) Regroup into the three functional groups fn1, fn2, and fn3

To maximize P we want to choose a material that maximizes the ratio

! f

"#$%

&'(= M = MATERIALS PERFORMANCE INDEX.

NOTE: We don't need to know anything about F, or A, to choose the best material for the job!

EXAMPLE TWO: Design a light, stiff column.

The design requirements are:

• slender cylindrical column • length L fixed • compressive load F • minimum mass



2) MEASURE OF PERFORMANCE (MOP), P. Minimum mass again.

3) IDENTIFY the parameters in our analytical model and MOP:

L= A= F= ρ=

4) CONSTRAINT equation: (no Euler buckling of this column)

where n is a constant that depends on the end conditions, and E is the Young’s Modulus.

(NOTE: There are a number of convenient mechanics equations in the appendix in the back of Ashby, appendix B, which I will use almost exclusively. You may use any analytical equations you like as long as you understand them!)

5) Rewrite the constraint equation for the free variable and substitute this into the MOP:


6) Regroup into fn1, fn2, and fn3

7) PERFORMANCE INDEX = MMAX =

RECIPE FOR OPTIMIZATION

1) Clearly write down the design assignment/goal. 2) Identify a model to use for calculations. 3) Determine the measure(s) of performance with an equation (weight, cost, energy content, stiffness, etc.) 4) Identify the FREE, FIXED, PROPERTY, and CONSTRAINT parameters. 5) Develop an equation for the constraint(s). 6) Solve the CONSTRAINT equation for the FREE parameters and substitute into the MOP. 7) Reorganize into the fn1, fn2, fn3 functions to find M.

NOTES:

i) M is always defined to be maximized in order to maximize performance. ii) A full design solution is not needed to find M! You can do a lot of materials optimization BEFORE your design has settled into specifics.

End of File.



Winter 2012

MATERIALS OPTIMIZATION WITHOUT SHAPE Reading: Ashby Chapter 5, 6.

RECIPE FOR OPTIMIZATION

1) Clearly write down the design assignment/goal. 2) Identify a model to use for calculations. 3) Determine the measure(s) of performance with an equation (weight, cost, energy content, stiffness, etc.) 4) Identify the FREE, FIXED, PROPERTY, and CONSTRAINT params. 5) Develop an equation for the constraint(s). 6) Solve the CONSTRAINT equation for the FREE parameters in the MOP. 7) Reorganize into fn1, fn2, fn3 functions to find M.

NOTES:

i) M is always defined to be maximized in order to maximize performance. ii) A full design solution is not needed to find M! You can do a lot of materials optimization BEFORE your design has settled into specifics.

EXAMPLE THREE: Mirror support for a ground based telescope. Typically these have been made from glass with a reflective coating--the glass is used only as a stiff support for the thin layer of silver on the top surface. Most recent telescopes have diameters in the 8-10 m range, and are typically limited by the mirror being out of position by more than one wavelength of the light it is reflecting (λ). The design requirements are that the mirror be large, and that it not sag under it's own weight by more than 1-λ when simply supported. Since the mirror will need to be moved around to point it in the right direction, it needs to be very light weight.

DESIGN ASSIGNMENT:

• Circular disk shaped mirror support • Size = 2r • lightweight • deflects (δ) under own weight by less than λ.


MODEL:

MOP: minimize mass

PARAMETERS:

r = t = ρ = δ =

NOTE: For clearly explaining this design process to others, let’s start using a table to list the design requirements. This will become much more important to you in the design project at the end of the term, so start practicing it now.

Design Requirements for Telescope Mirror Supports Function Support reflective surface for ground-based optical telescope Constraints Radius, r, specified (and large!)

Stiff enough to not deform under own weight by more than λ Objective Minimize mass Free Parameters Thickness, t.


CONSTRAINT EQUATION: (use the helpful solutions in appendix B of Ashby or a mechanics textbook)

For a simply supported disk under its own weigh, the center deflection is:

(NOTE: The “less-than-or-equal” sign is a good way to identify a constraint parameter.)

APPLY TO MOP: Solve for the free parameter, t.

CAUTION: m (mass) appears in the constraint equation, so it’s now on both sides of the equation. We have to solve for m so we can plug it into the objective function, P.

Since the MOP is minimum mass,Pmax =1m

:


NOTE: This is equivalent to an M =E!3 , or M =

E1/3

!; maximizing any of these will

maximize our performance. For reasons that will become clear later, it is always best to use the performance index that comes directly from the optimization analysis, in this

case, M =E!3

"#$

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1/2

APPLYING PERFORMANCE INDICES TO SELECTION CHARTS

Use the telescope mirror support as an example. We use Ashby's CHART 1 (E versus ρ).

We could apply PRIMARY CONSTRAINTS and say that, in order for the design to work, the modulus must be E > 20 [GPa], and the density, ρ < 2 [Mg/m3].

Our selection region will be in the upper left, and we end up with expensive candidate materials such as CFRP.


OR: we can use the performance index from above:

which gives us a line of slope = 3 on a log(E) versus log(ρ) plot (Chart 1). How do we plot this on the chart? Start with an X-Y point, say

X = log(density) = log(ρ) = log(0.1 [Mg/m3]) = -1 Y = log(modulus) = log(E) = log(0.1 [GPa]) = -1

Now, for every decade unit in X we go up three decade units in Y (slope = 3).

one unit in X gives X = log(ρ) = 0, which gives ρ = 1.0 [Mg/m3], and three units in Y gives Y = log(E) = 2, which gives E = 100 [GPa].

This is a line of slope = 3. Ashby helps us out with some guide lines for common design criteria.

M =E!3

"#$

%&'

1/2

=E1/2

!3/2:


NOTES:

1) This line connects materials with the SAME PERFORMANCE INDEX for this design (same value of M).

What are the units of the performance index? It will be different for every design situation, but for the telescope example:

Let's just use . It will always be easiest to leave the units of the

performance index in the scale units of the plot of materials properties.

Look at our line-- it passes through the point E = 0.1 [GPa], ρ = 0.1 [Mg/m3].

It also passes through the point

E = 100 [GPa,] ρ = 1 [Mg/m3].

This means that all materials on this line will perform the same, and should be considered as equal candidates for the job.

M =GPa[ ]1/2Mg

m3!"#

$%&3/2


2) As we move the line (keeping the slope the same), we change the value of the performance index (M), and thus the PERFORMANCE of the material in this design. For example, if we move the line to the lower right to the point

E = 1000 [GPa], ρ = 5 [Mg/m3], then

These materials do not perform as well as the first set of materials with

M = 10 GPa1/2

Mgm3( )3/2

!

"

####

$

%

&&&&

.

3) As we move to larger E and smaller ρ, does M increase or decrease?

Remember, we have to keep the line slope equal to three, or we won't have an equi-index line.

We want high performance, so we keep shifting the line to the upper left until we only have a small set of materials above the line -- THESE are the CANDIDATE materials for this design.

We find a lot of materials that perform AS WELL AS OR BETTER THAN the composites!

4) As M changes, what does that mean?

so a material with an M = 4 weighs HALF that of a material with an M = 2, but TWICE an M = 8. By maximizing M, we minimize the mass... just what our design calls for.


5) We stated earlier that we can use any of these ratios for M:

M =E1/2

!3/2 or M =E!3 or M =

E1/3

!.

Let's check to see if that makes sense:

E1/3

!

CHART:

CHART:

CHART:

SLOPE:

SLOPE:

SLOPE:

UNITS OF M:

UNITS OF M:

UNITS OF M:

The VALUE of the M will be different in each case, the UNITS of M will be different, but because the SLOPE and the SELECTION CHARTS are the same, the MATERIALS SELECTED WILL BE THE SAME!

E1/2

!3/2E!3


6) Reality Check Number One:

This optimization procedure has given us the BEST PERFORMING MATERIALS given our stated objective (measure of performance) and constraint. But are the answers sensible? How do we know?

Look back at the derivation. All but one of the parameters are known (FIXED) or are determined by the optimization process (MATERIAL PROPERTIES). To check the design, it is important to use the materials that have been suggested to determine the value of the free parameter, t in this case, to see if it is indeed sensible.

For a first check, let's compare the relative thicknesses needed for the different materials to function in the design:

From the derivation, we know:

Solve for t to get the free parameter as a function of the other parameters in the design:

The relative thickness of two competing materials is given by:

NOTE: The advantage of comparing the relative thickness is that a lot of the design parameters cancel out, so that we don’t need to know a lot about the details of the design to look at the relative values of the free parameter.


For several candidate materials, we have the following property data (obtained from the Ashby chart #1):

E [GPa] ρ [Mg/m3] (ρ / E) [Mg/m3GPa] (ρ / E)1/2 [Mg/m3GPa]1/2

Glass 100 2.2 0.022 0.148 Composites 30 1.5 0.05 0.224 Wood Products 4 0.8 0.2 0.447 Polymer Foams 0.1 0.2 2 1.4

Compare these materials against a "standard" material; for instance, glass has been commonly used in this application.

Material t / t(glass), or how much thicker than glass the mirror must be. Composites Wood Products Polymer Foam

NOTE that all four of these materials PERFORM the same—they have the same value of M and the same performance (MASS). But, because they have different properties, they have different values of the free parameter needed to make them work.

7) Reality Check Number Two:

So, we know the relative thicknesses, but what about the actual thicknesses? To find these, we need to have values for all of the FIXED and CONSTRAINT parameters—we need to know more about the design. Let's pick some reasonable values:

r =

g = 9.8 [m/s2]

λ =

From the analysis, we know t =

Material t = Mirror Thickness [m] Glass Composites Wood Products Polymer Foam


WOW! These are HUGE!!! What went wrong?

Two important points here. FIRST, the optimization process tells you the best materials for the job. It doesn't guarantee that your design will work. It is quite possible that the design cannot be built to work using existing materials. If this is the case, what are your options?

GIVE UP, or REDESIGN.

SECOND, the design requirements, calculational model, or constraint equations may be wrong or too simple to accurately describe the design. Your options are:

GIVE UP, CHECK YOUR ASSUMPTIONS, or REDESIGN.

In this case we know an 8 [m] mirror has been constructed from glass that is only about 1 [m] thick and that it works. How could we redesign to reduce the thickness needed for the mirror?

One option:

Now the model must change, perhaps to a simple beam like this, or something more complex.

(NOTE - for the simple beam model shown above, the performance index turns out to be the same, which yields the same materials for the selection process. Changing to a more realistic model or design changes the constants in the equations, but not the best choice of materials. Woooo...cool!)

End of File.

W. Warnes: Oregon State University Week Two: Page 1

ME480/580: Materials Selection Lecture Notes for Week Two

Winter 2012

MATERIALS SELECTION OPTIMIZATION WITHOUT SHAPE EFFECTS -- II

Reading: Ashby Chapters 5 and 6.

EXAMPLE: Materials for Flywheels

DESIGN ASSIGNMENT: Design a flywheel to store as much energy per unit weight as possible and not fail under centripetal loading.

MODEL: Solid disk of diameter 2R and thickness t rotating with angular velocity ω.

MOP: Maximize energy per unit mass

Kinetic energy of spinning disk:

Mass of flywheel:


PARAMETERS:

R = ω = t =

Design Requirements for Flywheels Function Store as much energy per unit mass as possible without failure Constraints Size? Possibly…

No failure when spinning with angular velocity of ω Objective Maximize energy/mass stored Free Parameters Radius, R

Thickness, t

To complete our list of constraint and materials property parameters, we'll need to look at the "no failure" constraint. Basically, we'll keep increasing the rotational velocity until the flywheel comes apart. What is the maximum stress in the flywheel?

Our constraint is that the maximum stress must be less than the yield strength, so

CONSTRAINT EQUATION: rewrite in terms of the free parameters as

APPLY TO MOP:


APPLY TO SELECTION CHART: Given our performance index, we probably want to use a selection chart like log(σ) versus log(ρ), and look at a line of slope = 1.

MATERIALS SELECTION: We want to consider materials above and to the left of our line, as these have larger values of σ / ρ. What materials do we get?

First, let's examine the units of M, and then make a table from data in the selection chart:

MATERIAL M[ MPa/(Mg/m3) ] CERAMICS CFRP GFRP Be alloys

Steels Ti alloys Mg alloys Al alloys Woods

Lead Cast Iron


WOW! Why did we not select lead and cast iron in favor of low density materials?

Our design requirement was maximum U/m, which led us to increase ω up to the failure constraint--a strength limited design.

For lead and cast iron flywheels, the design statement is different. If we just want to maximize U, then the

MOP =

(The message is: the design statement is critical to getting the right answer!)

Look at the list again: The best performer is CERAMICS-- BUT, we need to check on the measurement of σf for ceramics used in Ashby's chart. In the description of the selection chart it says that σf means:

• 0.2% offset tensile yield strength for METALS • non-linear stress point for POLYMERS • compressive crushing strength for CERAMICS

The flywheel is in tensile loading, so ceramics are not such good performers. The best performers are:

Materials for Flywheels Material M = ! f / "( ) MPa / Mg /m3( )#$ %&

Comment CFRP 200-500 Excellent choice, expensive GFRP 100-400 Cheaper alternative to carbon Be alloys 300 Manufacturing toxicity issues Other alloy systems 100-200 Many inexpensive and common

alternatives. Lead 3 Steam-punk option Cast Iron 8-10 Classic choice for energy storage

To down-select, we need another constraint criterion (COST?). This brings up an important issue about MULTIPLE CONSTRAINTS, which we'll postpone until a future time.

End of File.


Lecture Notes for Week Two Winter 2012

MATERIALS SELECTION OPTIMIZATION WITHOUT SHAPE EFFECTS -- III

Reading: Ashby Chapter 5 and 6.

A DIFFERENT EXAMPLE: Spring design

We use springs for storing elastic energy. We usually want to maximize the energy/volume, or the energy/mass. Stored elastic energy is found from the stress-strain curve for the material as the work done by the applied stress:

ENERGY/VOL=

Because we are in the elastic region.

This is the area under the stress-strain curve up to the yield stress, and gives us

[ENERGY/VOL]axial =

Leaf springs and torsion bars are less efficient in storing energy than axially loaded springs because not all the material is loaded to the yield point, so

[ENERGY/VOL]torsion =

[ENERGY/VOL]leaf =


In all of these cases, the performance index will be M1-MAX=

Look at the selection chart of modulus versus strength:

BUT!! This time better materials appear to the LOWER RIGHT (increasing σ and decreasing E).

We find lots of conventional materials for springs (elastomers, steels) but also many others:

• Ceramics- good in compression • Glass- often used in high precision instrumentation • Composites-look interesting

WHAT ABOUT ENERGY/MASS SPRINGS?


In this case, the performance index becomes M2-MAX =

What do we use for a selection chart? Since the mass is a key consideration in these spring designs, we want to have ρ represented in both the axes:

Now we can use selection chart 5:

The selection leads us to elastomers, ceramics and polymers, but the metals lose out because of their high density.


This raises the question of "how do I know which selection chart to use?"

Two ideas to keep in mind at this point:

1. As already stated, the mass is important, so keeping ρ in the axes is a good idea. 2. We don't have selection charts for the other ones.

But what if we did?

We can construct the other selection plots using the CES software, and the net result is that, while the selection plots are somewhat different, the materials that pass the selection are identical.

End of File.


ME480/580: Materials Selection Lecture Notes for Week Two

Winter 2012

CASE STUDY: NATURAL BIOMATERIALS Reading: Ashby chapter 12.9

BIOMIMETICS

Natural materials have continually been used by mankind in the development of new engineering applications. Many natural materials continue into the present day as useful materials, including wood, bamboo, and natural fibers, such as cotton, hemp, and silk. Especially recently, as materials engineers have become increasingly facile at building new materials from the ground up (composites, multilayers and heterostructures, functionally gradient materials, quantum well structures, etc.), natural materials have become a focus for developing materials for engineering applications. This field of research has become known as “biomimetics”—using natural materials as models for new engineered materials.

Recognizing why biomimetics is such an exciting research area starts by looking at the materials that nature has developed for its use. In almost all cases, natural materials are composite, or “hybrid”, materials, often displaying structural features over large range of dimensional scales. Ashby has collected the physical properties of many natural materials in his book and in the CES software (which we’ll look at next week). Chapter 12 has a set of Selection Charts hidden away that focus on natural materials.


LOW-MASS ELASTIC MATERIALS (Figure 12.13)

This selection chart is used for selecting materials for applications involving stiffness per unit mass. We’ve already analyzed a couple of different applications which require light-stiff materials under different loading conditions, leading to the three guidelines shown on the plot.

Let’s put STEEL and Al on the figure, just for reference:

Density [kg/m3] Young’s Modulus [GPa] Strength [MPa] Steel 7900 216 1000 Al alloy 2800 80 500

Cellulose is the winner for tensile stiffness: M =E!

, beating steel by a factor of 3 to 4,

and pushing flax, hemp and cotton up pretty high. Woods, palm, and bamboo perform

very well in bending and buckling M =E1/2

!"#$

%&'

.


LOW-MASS HIGH-STRENGTH MATERIALS (Figure 12.14)

Again, natural materials show up nicely on this chart, with silk having the best strength-to-weight ratio.


ELASTIC ENERGY STORAGE MATERIALS (Figure 12.15)

For this chart, the best materials are those with large values of σ and small values of E: in

the upper left corner. Spring materials are those with large values of M =! 2

E, while

elastic hinge materials are those with large values of M =!E

.

What’s the best natural material for springs?

What’s best for elastic hinge applications?

Interesting!


TOUGH NATURAL MATERIALS (Figure 12.16)

Materials with large values of toughness are at the top of the chart (antler, bamboo, and bone), good for impact loading.

The criterion for carrying a load safely when a crack is present is shown by the lines of constant fracture toughness (the dashed lines at 45 degrees.)


CASE STUDY: IMPLANTABLE BIOMATERIALS ("Biomaterials-An Introduction", J. B. Park, R. S. Lakes, Plenum Press, 1992, and “Biomedical

Engineering and Design Handbook”, Volumes 1&2, Myer Kutz, editor, McGraw-Hill Co. Inc., 2009 )

I. HISTORY

• 1860's: Aseptic surgical techniques developed by Lister. • 1890's: Bone repair using plaster of Paris. • early 1900's: Metallic plates used for bone fixation during skeletal repair.

Problems with corrosion and failure. • 1930's: Development of stainless and Co-Cr alloys. First successful joint

replacements. • 1940's: WWII pilots-PMMA shows low bioreactivity, and leads to development

of PMMA as an adhesive and skull bone replacement. • 1950's: Blood vessel replacements. • 1960's: Cerosium- an epoxy filled porous ceramic used as a direct bone

replacement. • 1970's: Bioglasses.

II. DESIGN CONCERNS

1. Material properties (strength, fatigue, toughness, corrosion). 2. Design (load distribution, stress concentrators). 3. Biocompatibility (immune system, toxicity, inflammation, cancer).

Other effects on success rate include surgical technique, patient health, and patient activity.

Relative importance of these issues changes with time:


III. A PARTIAL LIST OF BIOLOGICAL APPLICATIONS (from Park)


IV. BIOPOLYMERS

Five types and three reactivities:

1. WATER SOLUBLE (used in solution for lubrication, improving hydrophyllic interactions at surfaces, reduce thrombogenesis)

2. HYDROGELS (poly hydroxyethylmethacrylate [PHEMA] used in soft contact lenses, others used for drug delivery systems)

3. GELS (react in-situ to form soft structures; natural fibrin cross-links to form clots) 4. ELASTOMERS (principally silicones and polyurethanes, PUR)

a. Silicones more bio-inert than PUR and is oxygen permeable b. Silicones are thermosets, while PUR are thermoplastics c. PUR can be processed to larger range of properties d. Silicones: artificial finger joints, blood vessels, heart valves, catheters,

implants (breast, nose, chin, ear) e. PUR: pacemaker leads, angioplasty balloons, heart membranes

5. RIGID (main ones are Nylons [significant water absorbance issues], PET, PEEK, PMMA, PVC [external uses], PP. PE [especially UHMWPE in hip and knee prosthetics as a low friction and wear surface, tricky in a metal-PE wear couple though][LDPE can’t be autoclaved since Tm is too low so only outside body uses], and PTFE [bioinert])

The reactivities are described as BIOINERT, BIOERODABLE, and BIODEGRADABLE.


V. BIOLOGICAL CERAMICS

Four main types, or classes, determined by reaction rate in body:

1. INERT 2. POROUS INGROWTH 3. BIOACTIVE 4. RESORBABLE

Initial research on ceramic biomaterials was fueled by an interest in the chemical inertness of them as a class, but over the past 25-30 years there has been a definite shift toward the bioactive ceramics.

V.A. INERT BIOCERAMICS

Oxides (chemically stable), Carbon. In general these are characterized as: no change is found in tissue, or the degradation product is easily handled by the body's natural regulation process. In inert ceramics, the body tissue forms micron sized fibrous membranes around the insert, and it is locked into place by mechanical interlocking of the rough surfaces.


Typical inert ceramics are:

• Al2O3 for joint prosthetics, dental applications. Alumina has a very low abrasion rate, about 10X less than a PE/metal wear surface in joints replacements.

• ZrO2 is an alternative to alumina, with a higher fracture toughness and even better wear resistance.

• LTI (low temperature isotropic) carbon for heart valves and coatings on some prosthetics.

• DLC-(Diamond-like Carbon) films because of their stability.

V.B. POROUS INGROWTH BIOCERAMICS

Surface preparation of the ceramics is a critical part of the functionality of the implant. Made with a porous or roughened surface can allow essentially inert bioceramics to establish a strong mechanical “bond” with natural tissue by allowing tissue growth into pores and rough surfaces.

V.C. SURFACE REACTIVE BIOCERAMICS

Small amount of selective chemical reactivity with tissue leads to a CHEMICAL BOND between the tissue and the implant. Implant is protected from further degradation due to the reacted "passivation" layer.

• BIOGLASS: Na2O-CaO-CaF2 – P2O5 – SiO2 • APATITE: Ca10 (PO4) - 6OH2

Used for small bone replacements (low stress) and as coatings on other inserts to enhance bonding.

Surface coatings often experience failure due to fatigue of the substrate, and the coatings are not so good in tension.


V.D. RESORBABLE BIOCERAMICS

Materials that fill space and are taken up by the body with time, presumably to be replaced with new bone growth. The goal is to provide a “scaffold” on which new healthy tissue can grow and eventually replace the implanted ceramic.

Example:

VI. APPLICATION EXAMPLES

Corrosion Issues

Mixed Metals (Galvanic Corrosion)


Dental prosthetics: the most successful area of application of composite materials in the bio-applications is in the dental prosthetic area, particularly involving ceramic composites. (Dr. Kruzic: Research on mechanical failure in dental composites.)

Mechanical Design


Hip/Knee Prosthetics

Ti shaft in bone fixed by glue (PMMA) or cement. High density Al2O3 ball and socket joint. Better than Ti on HDPE because no release of metallic and polymeric wear particles (toxicity).

State of the art: replace the Ti with C fiber reinforced graphite, or with thermoplastic matrix/carbon fiber composite and protective coating.

VII. FDA REGULATIONS

Biomaterials is one of the engineering areas most involved in government regulation. The definitions are specific but not always obvious. For instance, an example given in the Kutz book (vol. 2, p. 22, emphasis added by me):

“How does this affect your morning toothbrushing? When you brush your teeth you are using a MEDICAL DEVICE—the brush. The brush works in a mechanical manner on your teeth to remove unwanted material. The toothpaste you use could be a COSMETIC in that it is applied to the teeth to cleanse. However, if you choose a fluoride toothpaste you are using a DRUG, since the fluoride is metabolized in the body in order to prevent tooth decay. If you choose to use an oral rinse to reduce adhesion of plaque to your teeth before you brush, you are using a MEDICAL DEVICE. The oral rinse loosens plaque that is then removed by your brushing.”

End of File.

W. Warnes: Oregon State University Week Three: Page 1

ME480/580: Materials Selection Lecture Notes for Week Three

Winter 2012

MULTIPLE CONSTRAINTS IN MATERIALS SELECTION: OVERCONSTRAINED DESIGN I

Reading: Ashby Chapter 7 and 8.

Most design problems are more complex than those examples we've discussed so far. Let's look at a more complex design:

EXAMPLE

DESIGN ASSIGNMENT:

• Cantilever beam of square cross section and fixed length L. • Support an end load, F, without failing. • End deflection must be less than δ. • Minimum mass.

MODEL:

MOP: minimum mass:

PARAMETERS:

L: F: t: ρ: δ:


Design Summary:

Design Requirements for Stiff, Strong Cantilever Function Support end load, F, without failure. Constraints Length, L, specified;

No plastic yielding in bending; Stiff enough to not deform under end load by more than δ.

Objective Minimize mass. Free Parameters Square cross section of t x t.

Okay…let’s tackle these two constraints as if they were each a separate constraint, using the optimization recipe.

FIRST CONSTRAINT: No failure under the end load, F.

SUBSTITUTE INTO THE MOP:

WHAT ABOUT THE OTHER CONSTRAINT (ON DEFLECTION)?

SUBSTITUTE INTO MOP:

Uh-oh... we've got two constraints, and now we have two materials performance indices (M) and they're DIFFERENT! What do we do?


This type of design is called an OVERCONSTRAINED design-- That is, we have more constraints than free parameters. Most materials selection problems are OVER-CONSTRAINED. There are several ways we can deal with multiple constraints in the selection process, by using DECISION MATRICES, MULTIPLE SELECTION STAGES, ACTIVE CONSTRAINTS, COUPLING EQUATIONS, and PENALTY FUNCTIONS.

I. DECISION MATRICES

Commonly used and presented in other design classes. One version comes from Crane and Charles (see syllabus for reference).

In simplest form, a matrix is developed with the DESIGN REQUIREMENTS along the columns and the CANDIDATE MATERIALS along the rows:

I.A.

Materials are rated in a GO-NO GO fashion as either acceptable (a), under-value (U), overvalue (O), or excessive (E).

PROBLEMS:

1. 2. 3.

Next best (but still not very good) approach is to inject some quantitative measure by replacing U, a, O, E with numbers 1-5 (increasing is better).


I.B.

This provides a quantifiable selection criterion, but

PROBLEMS:

1. 2.

To eliminate concern #2, we could add WEIGHTING FACTORS,

I.C.

but this just adds another level of subjectivity. How can you back-up the assertion that the rigidity is 2.5 times more important than cracking resistance?

One significant improvement we can add here is to use PERFORMANCE INDICES rather than materials properties. This essentially takes us beyond primary constraints into the realm of optimization. For each constraint or design goal, we develop an M value to use as one of the columns:


I.D.

Crane and Charles convert these to dimensionless numbers (relative values) by dividing by the largest property value, and then sum these to determine the overall rating of the material.

This is better (we're selecting based on performance indices) but now we're back to treating all of these with the same importance. The last act of Crane and Charles is to apply weighting factors to the performance indices:

I.E.

This is pretty good except that it is STILL SUBJECTIVE because there is no justification for the weighting factors that are used.

The difficulty with most of the decision matrix approaches is simply this subjectivity. There are some schemes for improving that, and Dr. Ullman's group at OSU has been studying the design methodology and has developed an approach that has resulted in a computer program called the Engineering Decision Support System (EDSS).

http://www.cs.orst.edu/~dambrosi/edss/info.html


II. MULTIPLE SELECTION STAGES

A second approach to the multiple constraints problem is the use of selection stages. Each of the constraints is used to develop a performance index as we did in the earlier example:

M1, M2, M3, ..., Mn.

These are rank ordered in order of importance (uh-oh...) from most important to least. We use the first performance index on the appropriate selection chart, and select a large enough (uh-oh...) group of materials to leave something for the other constraints to work with. Repeat with the other performance indices.

(Why the "uh-oh"s? How do we decide on the rank ordering? Subjective decision. How do we decide on the number of materials to leave in the pool at each stage? Subjective decision again.)

II.A. EXAMPLE: Multiple Stage Selection for a Precision Measurement System (micrometer).

There are several design goals we want to meet with this design:

1. minimize the measurement uncertainty due to vibrations of the stiff structure, 2. minimize the distortions of the structure due to temperature effects, 3. keep the hardness high for good wear properties, and 4. keep the cost low.

Design Requirements for Precision Measurement Tool Function Choose material for an inexpensive high precision hand-held

micrometer Constraints Handheld limits size and mass--not too limiting. Objective Minimize vibrational errors;

Minimize thermal distortions due to temperature gradients; High hardness for improved wear properties; Minimize the cost.

Free Parameters Choice of material

Let's tackle these one at a time--

II.A.1. VIBRATIONS

We want to drive the natural frequency of the main structure as high as possible. The useful approximations give us the natural frequency as:


II.A.2. THERMAL DISTORTION

The strain due to a change in the temperature of the structure is determined by

If we want to know how the thermal strain changes along the length of our structure due to a temperature gradient, we take the derivative to find

We also know (for a 1-D heat flow approximation) that the heat flux is given by

To minimize the thermal distortion d!Tdx

"#$

%&' for a given heat flow, we need to maximize

II.A.3. HIGH HARDNESS

We can treat the hardness, H, as a direct function of the yield strength:


II.A.4. COST

Finally to keep the cost low, we want to maximize

So, to summarize, we have FOUR design goals, each of which gives us a different performance index:

Minimize vibrations:

Minimize thermal distortion:

Maximize hardness:

Minimize cost:

With the multiple stage selection approach we will take each of these individually and make a series of selection charts.


II.B. First Selection Stage: We will use Ashby's chart 1, with a slope of 1, and the selection area above and left of the line:

We don't want to eliminate too many materials, otherwise, there'd be nothing left for the other criteria to do.

Rank ordered list of materials that "passed" this selection stage, from highest performers to lowest:

Ceramics Be CFRP Glasses/WC/GFRP Woods/Rock, Stone, Cement/Ti, W, Mo, steel, and Al alloys.


II.C. Second Selection Stage: We will use Ashby's chart 10, with a slope of 1, and the selection area below and right of the line:


Ceramics Invar SiC/W, Si, Mo, Ag, Au, Be (pure metals) Al alloys Steel

Notice that there is some overlap between materials that passed the first stage and those that passed the second. That’s good.


II.D. Third Selection Stage: We will use Ashby's chart 15, and apply the last two constraints as primary constraints. We want to search in a selection area in the upper left of the chart:


Glasses Steel/Stone Al alloys/Composites Mg, Zn, Ni, and Ti alloys/Ceramics

Compare these in a table:

First Selection Stage Second Selection Stage Third Selection Stage Ceramics Ceramics Glasses Be Invar Steel/Stone

CFRP SiC/(pure metals) W, Si, Mo, Ag, Au, Be Al alloys/Composites

Glasses/WC/GFRP Al alloys Mg, Zn, Ni, and Ti alloys/ Ceramics

Woods/Rock, Stone, Cement/Ti, W, Mo, steel, and Al alloys

Steel


The candidate materials that make it through all three stages are STEELS and Al ALLOYS.

We might want to relax the selection criteria a bit to take another look at ceramic materials, which appear in two of the lists.

The main advantage of this multiple stage selection process is that the assumptions are simple and clearly stated regarding the rank ordering of the performance indices. The disadvantage is that it is still subjective in determining the rank ordering and the position of the selection lines on each of the charts.

The quantitative approach to multiple constraints combines the decision matrices and selection stages with coupling equations and/or penalty functions. These are topics we’ll look at next.

End of File.


ME480/580: Materials Selection Tutorial Overview Notes on CES-Edupack

Winter 2012

INTRODUCTION TO CES (CAMBRIDGE ENGINEERING SELECTOR)-EDUPACK

SOFTWARE FOR WINDOWS

Nomenclature:

Throughout these notes references to buttons or icons that should be clicked will be given in BOLD and pull-down menu items will be given in ITALICS .

1) Log onto your Engineering account.

2) Once in Windows, open the MIME Apps and start the CES-EduPack 2010 program. (We still have the older version, CES Selector 3.1, on-line. Don’t use it by mistake!)

INSIDE CES:

You will see the WELCOME screen when you startup, and a “Choose Configuration” window.

There are three “levels” of material and process database information in this version of the software:

Level 1: about 70 materials and 70 processes, with a limited set of property data;

Level 2: about 100 materials and 110 processes, with an extended set of property data;

Level 3: about 3000 materials with a comprehensive data set for each.

1) For now, choose “English -- Level 1” until you are used to the program. Later on we’ll switch to Level 3 to use all the information for doing problems and the design project.

2) You should now be in the main program control window. At the top on the left, you should see the database you are using, along with a pull down menu for the TABLE


(MaterialUniverse), and SUBSET (Edu Level 1). You will also see a toolbar with several icons along the top of the main window. These are how you will interact with CES.

CES INFORMATION:

There is a large amount of on-line help and database information available in CES.

1) You should automatically be in the browsing tool, but if not click on the BROWSE tab to see the information in the materials database.

2) Double click on a folder to open it. Eventually you'll work your way through the hierarchy to an individual material record. Take a look at the materials record. This is the database information that has been developed for each material in the database.

3) You can change the database to browse by choosing a different TABLE or SUBSET from the pull-down menus. Try several different tables to see what they offer.

4) You may also change databases by clicking on the CHANGE button. If you change to Level 3, you will find SEVEN different TABLES, and a larger number of SUBSETS. Within the Level 3 MaterialsUniverse, for example, there are a number of SUBSETS, including All Bulk Materials, Ceramics, Foams, Magnetic Materials, Metals, Polymers, and Woods. You might use these to narrow down a selection process to a smaller class of materials.

5) You can also SEARCH the database using the SEARCH button. ‘Nuf said.

6) Reference material is also available on-line, as well as an on-line help function. Click on the HELP button or the menu item. The "CES InDepth" is an on-line reference book about CES and the selection process we have been using in class. In fact, all of the appendices form the textbook can be found in here (if you know where to look!)

7) There are also video tutorials and getting started guides that you can access if you want to learn more about the capabilities of the program.

8) For the last thing to do on this part, click on the TOOLS button and select OPTIONS. Click on the UNITS tab to set the preferred units of the data. Choose the currency you want to use for cost analysis here. This also allows you to set the units for the selection charts. Choose “SI (consistent)” for the unit system. (HINT: using USD [$] instead of Myanmar Kyat would probably be a good idea).

MAKING A SELECTION CHART (the cool stuff):


1) Click on the SELECT tab to start. (Alternatively, you can choose the NEW PROJECT menu item in the File Menu.) You will need to choose a database and subset to use in the selection project.

2) Now click on the NEW GRAPH STAGE icon on the toolbar or from the SELECT menu. (The toolbar buttons are, from left to right, NEW GRAPH STAGE, NEW LIMIT STAGE, NEW TREE STAGE.)

3) You should get a window with the "Graph Stage Wizard" title. Make sure that the X-AXIS tab is selected, and then use the ATTRIBUTES pull-down menu to choose the material property to plot on the x-axis. Choose YIELD STRENGTH (ELASTIC LIMIT) from the pull down list.

3) Click on the Y-AXIS tab to set the material property for the Y-axis.

4) Select YOUNG'S MODULUS from the ATTRIBUTES menu.

5) Click OK.

6) You should now have a new window labeled "Stage: 1" with a graph of your selection chart, showing on the right side of the screen, along with a new tool bar row with about 16 icons on it.

CHANGING AND USING A SELECTION CHART:

1) Click on the STAGE PROPERTIES icon (the first icon on the left of the new tool bar.)

2) You can now change the axes of the active stage. Change the SCALES to be LINEAR in both X and Y. Click OK. Now you know why the data is usually plotted on a log-log plot.

3) Click on any bubble on the chart to find out what the material is. Drag the pop-up label around, and it should leave a connecting line behind pointing to the bubble. Double-clicking on a bubble brings up the materials data sheet for that material.

4) Delete the label by selecting it with the mouse and pushing the DELETE key.

5) Change the axes back to log-log.

6) There are three types of selection tools you can use: point-line, gradient-line, and box. These are the icons that follow the CURSOR icon.

7) For simple or primary constraints, you should use the BOX selection tool. Click on the BOX button. Then click on a point in the selection chart and drag the mouse to enclose a


set of materials in the box. Note that the STATUS BAR (at the bottom left of the screen) gives you the X,Y location of your cursor in the plot units. Note also that any material bubble that is partly inside the selection box is colored, while the others are greyed-out. The colored bubbles have been selected by the selection process, and now show up as a list in the RESULTS section on the left side.

8) Now click on the GRADIENT-LINE selection tool button. Type in the slope of the selection criterion (line slope) you want (use 1 for now), and click OK.

9) Click on some X-Y position to position the line, and the line will be drawn for you at that location. Notice that the STATUS BAR shows you the value of the selection criterion for the line position you have chosen, along with the value of M for that line (be wary of the units, though!). The final step is to click either ABOVE or BELOW the line to tell the program which region is the selection region. Again, colored materials have passed this selection, and greyed materials have failed.

10) Moving the cursor onto the selection line allows you to reposition the selection line for higher or lower M values. If you want to change the slope, you can start over by clicking the GRADIENT-LINE selection tool button again.

11) Note that you may have only ONE selection criterion operating at a time on a single selection chart. If you want more than one criterion for a particular set of x-y axes, you need to make-up additional STAGES with the same axes and apply the other selection criteria to those.

12) The RESULTS section in the left of the window shows you the materials passing your selection criterion. You can modify the results section by using the pull-down menu to choose what results to view. This is especially helpful when using multiple stages.

13) Finally, you can save this set of selection criterion to disk and recall it later using the SAVE PROJECT menu item. In the FILE menu

A MULTIPLE STAGE EXAMPLE:

We want to do a materials selection for a high quality precision measuring system, essentially a top line micrometer (we did this one in class as our example of a multiple stage selection process). After extensive analysis, we have found that we need a material that will produce a LOW THERMAL DISTORTION (M1 = λ / α), LOW VIBRATION (M2 = (E / ρ)1/2), maximize the HARDNESS (M3 = H), and minimize the cost (M4 = 1/C ρ).

1) First you will need to start with a clean project. In the FILE menu click on the NEW PROJECT item. We will use the “EduLevel 1: Materials” database for this example. Make sure this is set up in the selection data section.


2) Stage 1 will deal with M1: Click NEW GRAPHICAL STAGE selection, and in the X-Axis properties choose the THERMAL CONDUCTIVITY property. For the Y-Axis properties choose THERMAL EXPANSION COEFFICIENT, and click on the OK button.

3) Now click on the GRADIENT-LINE selection tool button. Type in the slope of the selection criterion you want (use 1), and click OK. Locate the point for λ = 10 [W/m-°C], and α =1 X 10-6 [1/°C]. (Remember that you can use the Status Bar at the bottom of the window to tell you the X-Y position of the cursor.) Click BELOW the line (since we want large λ and small α).

4) Now that you have a selection criterion on the graph, click on the STAGE PROPERTIES icon. A new tab is available that lets you change the details of your selection- slope, side of the line, and exact location! Use this to place your selection line in exactly the same position that I have used (X = 10, Y = 1). If you’ve done everything the same as I have, you should see SEVEN candidate materials in results list.

5) Stage 2 will deal with M2: Click NEW GRAPHICAL STAGE, and in the X-Axis properties choose the DENSITY. In the Y-Axis properties choose YOUNG'S MODULUS, and click on the OK button.

6) Now click on the GRADIENT-LINE selection tool button. Type in the slope of the selection criterion you want (use 1), and click OK. Locate the point for E = 2 x 109 [Pa], and ρ = 100 [kg/m3]. Click ABOVE the line (since we want large E and small ρ).

7) If you click on the STAGE PROPERTIES button while in Stage 2 you can choose to turn off or on the display to show the RESULT INTERSECTION, those materials that have passed all the stages so far. If you only want to see the materials that pass, choose to HIDE FAILED RECORDS. (I don't recommend this at the beginning!). Your results list should show SIX materials now that pass both selection criterion.

8) Stage 3 will deal with M3 and M4: Click NEW GRAPHICAL STAGE, and for the X-Axis properties we have to do something fancy. There is not a property listed for COST, but there are properties PRICE [USD/kg] and ρ [kg/m3]. First, for the x-axis, click on the ADVANCED button. You should see a hierarchical list of all the materials properties available. Click on the GENERAL PROPERTIES in the pull-down menu and you will see a list of the general properties. By choosing properties from the list and using the math function buttons, you can set up quite complicated materials selection axes. Wow! Isn't this cool? Select PRICE and multiply it by DENSITY to get the X-axis to be the [USD/volume] you need for minimum cost design. Click OK. We should also change the name of the axis to at least include the UNITS!!!! (something like MATERIAL COST [$/m^3]) so we know what we are looking at in the selection chart.

9) In the Y-Axis properties choose HARDNESS-VICKERS, and click on the OK button.


10) Now click on the BOX selection tool button. Use the box to select the materials with a MATERIAL COST less than 10,000 [USD/m3], and a HARDNESS greater than 1 x 109 [Pa].

11) Go to the RESULTS window and check your results. You can view the selection criteria you have used here, as well as the materials that have passed each stage. If you have done this problem the same way I have, you will end up with three materials passing: Al Alloys, Silicon, and Silicon Carbide.

NOTES:

You may only search one database at a time. To change databases:

1) Click the CHANGE button in the “Selection Data” section and select the database you want to search.

2) Then choose the subset of materials you want to “Select From…” You can fiddle with this, for instance, by choosing to look only at ceramics or metals.

Once you have developed a selection stage, changing databases does not change your selection stage(s) or selection criteria. CES will automatically run through the selection process using the new database whenever you change databases. It's easy to search the other databases this way. My advice is to always start off with the ALL BULK MATERIALS subset in the LEVEL 3 database, and use the others as your design develops.

(If you do this now, you should have 14 candidate materials from the three stage selection, using the Level 3 database.)

End of File.


ME480/580: Materials Selection Lecture Notes for Case Study

Winter 2012

CASE STUDIES IN MATERIALS SELECTION: POLYMER FOAMS

("Polymeric Foams", Klempner and Frisch, 1991; "Plastic Foams" Frisch and Saunders, 1973)

Why look at foams? EXAMPLE: Simply supported beam in bending- minimum mass (or cost). Assume b, L, are fixed, h is free, and the center deflection under load, F, is limited.

Use Rule of Mixtures to determine foam properties, e.g. 90% air foam:

SO…this means the foam material, which is 90% nothing with no properties, has a performance nearly FIVE TIMES the solid polymer beam ( or, looked at another way, for hf = 2hs you can get the same deflection with 80% less mass!).

One can also laminate the surface of foams with a high strength layer to drive strength/weight ratio even farther up.


Foams also have energy absorption properties due to the compressibility of the gas in the cells.

New materials class—Foamed metals (Al and steel) behave exactly the same way! Foams are nifty!

TYPES OF POLYMER FOAMS:

• Gas-dispersed foams, using "blowing agents" • Syntactic foams, using hollow spheres of glass or plastic. • • Open-cell vs. closed-cell.

POLYURETHANE FOAMS:

Most widely used. Depending on chemistry can vary their properties from flexible cushions to rigid foams for structural applications, with density ranging from 0.0096-0.96 Mg/m3.

Can be made in a continuous process as a "bun" 2-8 feet wide X 1-5 feet thick X 10-60 feet long.

Can be processed as "integral skin" foams.

POLYSTYRENE FOAMS: Also very widely used in the form of extruded blocks. Formed by:

1. Force volatile liquid (neopentane) into crystalline spheres of PS (ρ ~ 0.96 Mg/m3) 2. Pre-expansion done with steam, spheres expand to 0.016-0.16 Mg/m3. 3. Final-expansion in a mold with steam heat, spheres fuse together.

ABS FOAMS: Used in pallets, and as structural material in furniture.


SYNTACTIC FOAMS: Use hollow microspheres (30 micron diameter) of glass, ceramic, or plastic for difficult to foam materials, such as epoxies.

ARCHITECTURAL USES OF FOAMS:

Besides insulating properties (PUR foams among the lowest thermal conduction materials), can also be used as a primary structural material, as in this University of Michigan study from the late 60's.

Major controlling factor: keeping within small elastic and creep deformation limits. Looked at double-curved shells. Several different approaches:

POLYSTYRENE SPIRAL GENERATION

POLYURETHANE SPRAY APPLICATION


FOLDED PLATE STRUCTURES WITH POLYURETHANE/PAPER BOARDS

FILAMENT WINDING ON PUR BOARD

End of File.

W. Warnes: Oregon State University Week Four: Page 1

ME480/580: Materials Selection Lecture Notes for Week Four

Winter 2012

OVERCONSTRAINED DESIGN PART II:

ACTIVE CONSTRAINT METHOD

Let's look at an example with a single design objective (MOP), but several constraints, an OVERCONSTRAINED problem. One way to approach it is to use a multiple selection stage process, as we did for the precision micrometer example in the last lecture. A difficulty with the approach is the ordering of the constraints and selection stages, and the subjective placement of the selection line in the multiple stages. A more systematic approach uses the "active constraint" approach. An example:

EXAMPLE: The support rod for an infrared-electronics cooling cryogenic fluid container in a spacecraft is to be designed. The most important characteristic of this tie rod is that it should carry a minimum amount of conductive heat into the cryogenic container. The conductive heat flow equation tells us that the conductive heat flow along this support rod is:

where C is a constant (the temperature gradient), λ is the thermal conductivity of the rod, and A is the cross sectional area of the rod.

There are three constraints on the rod:

First, that the loading due to the mass of the cryogenic fluid and container should not exceed the failure strength of the tie rod (ignore the mass of the rod).

Second, the deflection, δ, should be less than a critical value, δmax.

Third, the vertical frequency of vibration must be high enough to not affect the measure-ments being made. In other words, f should be larger than a critical frequency, fmin.


MODEL:

Assume a SOLID CYLIDER for the rod, A = !r2 .

MOP: minimum heat flow into the cryogen:

PARAMETERS

L = λ = A (or r) = δmax = fmin = F = q =

DESIGN SUMMARY:

Design Requirements for Space Cryogenic Support Rod Function Support end load, F, without conducting heat into cryogenic fluid. Constraints Length, L, specified;

No plastic yielding in bending; Stiff enough to not deform under end load by more than δ; Fundamental vibration frequency larger than fmin.

Objective Minimize conductive heat flow. Free Parameters Cross section of solid cylinder, A.


PERFORMANCE EQUATION ONE : Start with the load constraint:

PERFORMANCE EQUATION TWO : Now use the deflection constraint:

PERFORMANCE EQUATION THREE : And finally the vibration constraint: For a vibrating rod with a mass at the end, the fundamental (lowest) frequency is

where K is the elastic stiffness, given by


and m is the mass of the cryogenic container, mc. Then

To perform the multiple selection stage process, we would set up two stages, one for M1 and one for M2, M3.

For the active constraint approach, we have to know more about the design, especially the details of the values of the fixed and constraint parameters. First, write out the equations for the MOP using each of the constraints:

PMAX(M1)=

PMAX (M2)=

PMAX (M3)=


If we know, or can estimate, the values of the fixed and constraint parameters, we can calculate numerical values of the measures of performance for each material. Let's put some numbers down for this design:

F (= mc*a) = 196 [N]

mc = 20 [kg]

δmax = 0.01 [m]

fmin = 5 [Hz] = 5 [1/s]

L = 0.1 [m]

C = temperature gradient = (300 [K])/(0.1 [m]) = 3000 [K/m]

Now we can set up a spreadsheet table of values for the material properties of the materials we're interested in and calculate the measures of performance. My spreadsheet in EXCEL looks something like this, and I pulled the rough values from the Ashby selection charts:

For each individual material, we look at the SMALLEST value of P. WHY?

In order to satisfy all the constraints, we must satisfy the one that most limits our performance. If we can satisfy that one (by choosing a particular value of r, the free parameter), we will satisfy all of them,

In this example, the minimum performance for all of the materials is different for each material -- the ACTIVE CONSTRAINT varies for the materials we have examined. If we don't satisfy it, the design will fail.

VARIABLES:L [m] = 0.1

mc [kg] = 20F [N] = 196

Delta Max [m] = 1.00E-02f min [Hz] = 5

C [K/m] = 3000

SIGMA E LAMBDA Load Deflection Vibration MinimumMaterial [MPa] [GPa] [W/m-K] P1 [1/W] P2 [1/W] P3 [1/W] P [1/W]

CFRP 1500 200 0.6 2.71E+01 2.74E+01 2.73E+01 2.71E+01GFRP 1200 90 0.6 2.34E+01 1.84E+01 1.83E+01 1.83E+01Ti alloys 700 100 12 8.16E-01 9.69E-01 9.66E-01 8.16E-01Al alloys 300 70 200 2.78E-02 4.87E-02 4.85E-02 2.78E-02Steel 1000 220 30 4.14E-01 5.75E-01 5.73E-01 4.14E-01Polymer Foam 6 0.3 0.04 1.03E+01 1.59E+01 1.59E+01 1.03E+01


Now, we can pick the material with the LARGEST value of the active constraint performance (from the last column in this example) to be the optimal performer for the design, in this case CFRP.

What have we learned by going through this active constraint analysis that we didn't know before?

1) To become more objective and quantitative in the selection process for OVERCONSTRAINED designs, we need to know more detailed information about the design.

2) It's a lot more work and time to do all of the quantitative calculations, but...

3) We now know what the limiting constraints on the materials are. With the spreadsheet, we can play some "what if" games with the fixed parameters-- how do the P's change if you decrease the cutoff frequency, or increase the mass, or allow less deflection? These trade-offs can be used to tune up the design and go back to your boss/client with a quantitative reason to consider changing one of the fixed parameters. As the values of these parameters change, at some point one of the other constraints will become the active constraint for a given material.

The Last Step: REALITY CHECK: Let's plug back into the constraint equations to find the value of the cylinder radius in each case:

End of File.

SIGMA E LAMBDA Load Deflection Vibration MaximumMaterial [MPa] [GPa] [W/m-K] r1 [m] r2 [m] r3 [m] r [m]

CFRP 1500 200 0.6 2.55E-03 2.54E-03 2.54E-03 2.55E-03GFRP 1200 90 0.6 2.75E-03 3.10E-03 3.11E-03 3.11E-03Ti alloys 700 100 12 3.29E-03 3.02E-03 3.03E-03 3.29E-03Al alloys 300 70 200 4.37E-03 3.30E-03 3.31E-03 4.37E-03Steel 1000 220 30 2.92E-03 2.48E-03 2.48E-03 2.92E-03Polymer Foam 6 0.3 0.04 1.61E-02 1.29E-02 1.29E-02 1.61E-02


ME480/580: Materials Selection Lecture Notes for Week Four

Winter 2012

OVERCONSTRAINED DESIGN PART III: COUPLING EQUATIONS

Consider a design situation in which we have one design goal (MOP), two constraints, and one free parameter. We are over-constrained in this situation.

By calculating a performance index analysis using the first constraint, we end up with:

With the second constraint, we have:

Now, the MOP is the same, so we can equate these two (we only have one design, which will perform at a given level, P):

The relative weighting of the two performance indices is DETERMINED BY THE DESIGN and not by our subjective judgments!

III.A. EXAMPLE: A Light Tie Rod


III.A.1. DESIGN ASSIGNMENT:

• cylindrical tie rod of length L • minimum weight • support a load F • extension less than δX

III.A.2. MODEL: Same as before

III.A.3. MOP: minimum mass:

III.A.4. PARAMETERS

L = F = δX = A = ρ =

DESIGN SUMMARY:

Design Requirements for Light Tie Rod Function Support end load, F, without conducting heat into cryogenic fluid. Constraints Length, L, specified;

No plastic yielding in tension; Stiff enough to not deform under end load by more than δx;

Objective Minimize the mass of the rod. Free Parameters Cross section of solid cylinder, A.


III.A.5. PERFORMANCE EQUATION ONE (derived previously in the example from Week One)

III.A.6. PERFORMANCE EQUATION TWO

III.A.7. DEVELOP THE COUPLING EQUATION:


Result

The best performing material will be one in which E/ρ is maximized, σ/ρ is maximized, and their ratio is held at L/δX.

How do we apply this to a selection chart? We want to use a chart for this example like chart 5.

We want both of our performance indices to be maximized, so we'll be looking at materials in the upper right hand corner of the chart. For our particular design, we'll have a given value of L/δX that is determined by the constraints of the design. Lets say it is 100.

We will look at a straight line of slope 1 on the plot, and we want the line for which the ratio of the performance indices is 100


By moving along this line of constant L/δX, we improve our performance by increasing the values of the performance index, and we simultaneously maintain the weighting factor determined by the design.

Our best choice of material is...

We probably want to open up the search region a bit, to allow some materials other than diamond in the mix, so for this case we can use a rectangular search region centered on the line of L/δX = 100.

By moving away from the line, we shift toward STIFFNESS DOMINATED designs (to the upper left) or toward STRENGTH DOMINATED design (to the lower right).

NOTE: If you use coupling equations, you don't need to use multiple stage selection processes, but you may have to generate your own Ashby Selection Charts!

MULTIPLE CONSTRAINT DESIGN: FULLY

DETERMINED DESIGNS

Look back at previous lectures -- we had an example of OVERCONSTRAINED design with the cantilever beam. We had two constraints (no failure under an end load, F, and deflection less than δ), and only one free parameter (square cross section of t X t). We ended up with two materials performance indices, M1 and M2, which we could use in a two-stage selection process.

Alternatively, we could use a coupling equation to couple the two M values together and do a one stage process, as just described (check out HW3...).

A last possibility is to revise the design statement to increase the number of free parameters. This will give us two free parameters and two constraints--fitting the definition of a FULLY DETERMINED design.

EXAMPLE: Light cantilever beam

DESIGN ASSIGNMENT: Let's change it slightly, from a square beam of t X t to a rectangular beam of b X h.


• Cantilever beam of rectangular cross section and length L. • Support an end load, F, without failing. • End deflection must be less than δ. • Minimum mass.

MODEL:

MOP: minimum mass:

PARAMETERS:

L: F: b: h: ρ: δ:

DESIGN SUMMARY:

Design Requirements for Light Cantilever Beam Function Support end load, F, without failure. Constraints Length, L, specified;

No plastic yielding in bending; Stiff enough to not deform under end load by more than δ.

Objective Minimize mass of beam. Free Parameters Cross section of solid rectangle, b x h.


We've got two free parameters (b and h) and two constraints!

CONSTRAINT ONE:

CONSTRAINT TWO:

SOLVE FOR b AND h:


SUBSTITUTE INTO MOP:

This type of design is called FULLY DETERMINED design. We can get a complete solution (with one M value), because we have the same number of free parameters as constraints.

MULTIPLE CONSTRAINT OPTIMIZATION

(A GENERAL DESCRIPTION)

The first part of the optimization process is writing out the following:

1. Measure(s) of Performance: quantitative functions to maximize the relative success of different designs. (P)

2. Constraining Equation(s): functions that set acceptable limits on the behavior of the design in use. (C)

3. Design-fixed Parameters: parameters that appear in the P and/or C equations that are not changeable under the conditions of the design. (D)

4. Free Parameters: the additional parameters from P and/or C that are not fixed. (F)

There are several possible scenarios:


I.A. SINGLE MOP DESIGNS

For designs with a single measure of performance, we can imagine several possibilities:

I.A.1. Zero Free Parameters

This is a pretty unusual situation, but it is conceivable when an existing design is to be used and only requires a change in material. Not a lot of opportunity here for optimization.

I.A.2. One Free Parameter

I.A.2.a. One Constraint Equation (1C1F)

With one C and one F we are FULLY DETERMINED, and the constraint, C, is applied to the measure of performance, P, through the free parameter, F, to develop a single performance index, M.

I.A.2.b. Two Constraints (2C1F)

Now the design is OVERCONSTRAINED. We treat each constraint separately as in the 1C1F case. In so doing, we end up with two performance indices:

Since we still have only one P, these two functions can be equated to find a coupling equation (or a relative weighting factor) of M1 / M2:


I.A.2.c. Three (and more) Constraints

The design is definitely overconstrained. We start the same way we did for the 2C1F design:

Using the pairs of performance index functions, we can determine the relative weightings of these M's.


I.A.3. Two Free Parameters

I.A.3.a. One Constraint (1C2F)

In this case the design in UNDERCONSTRAINED. We need to find a way of either fixing one of the parameters, or come up with another constraint. In some cases we may be able to change variables to reduce to 1F.

EXAMPLE: A minimum mass connecting rod of rectangular cross section with heat flow larger than some value qo.

Convert from 2F to 1F using A = bh, since both constraint and MOP depend only on the area A.

I.A.3.b. 2C2F

Fully determined design. Solve the two constraining equations for the two unknowns (F1, F2) and plug into the P.

We end up with ONE performance index, M.

I.A.3.c. 3C2F

Overconstrained, and can be treated as three independent 2C2F problems:


Since we are still talking about 1P designs, we can generate coupling equations here as well:

I.A.4. General Results for 1P Designs

C < F Underconstrained; need to add a constraint. C = F Fully determined; one performance index, M. C > F Overconstrained; multiple M's, coupling equation(s).

I.B. MULTIPLE MOP DESIGNS

The first step will be to rank order the P's. Remember how to determine whether you are dealing with a P or a C:

• If the feature is to be MINIMIZED or MAXIMIZED, then it is a P. • If the feature must be GREATER THAN or LESS THAN a

reference value, then it is a C.

With a rank ordered list of the P's, we can treat each one separately as a single MOP problem:


NOTES:

1. The DESIGN will generally have a single set of constraints that can be applied to all of the P's, but the free parameters may be different in different P equations. In this example, P1 depends only on F1 and F2, while P2 depends on F1 and F3.

2. If a constraint equation doesn't involve any of the F's in a particular P, then the constraint can't be used to optimize this measure of performance. In this example, C3 does not apply to P1.

3. You can't get coupling equations between M's determined from different P's. In this example:

We can form coupling equations by coupling the three P2 equations, but we can't find a coupling equation relating M(2)

12 and M(1)12 because P1 is

not equal to P2.


WHAT NEXT?

What do you do with all of these performance indices and coupling equations? Two choices:

Rank order the performance indices by order of importance and perform a multiple stage selection process, or;

Get more information about the design and determine the active constraint for each material in a tabular matrix, or:

Set up a decision matrix based on the performance index values for each material. the decision matrix can be rank ordered, or can be set up with weighting factors as determined from the coupling equations.

End of File.

W. Warnes: Oregon State University Week Five: Page 1

ME480/580: Materials Selection Lecture Notes for Week Five

Winter 2012

CALCULATING MASSIVELY OVER-CONSTRAINED DESIGNS

It is often a good idea at the beginning of a design project to figure out how intense the analysis is going to be by calculating the total number of performance indices and coupling equations you are likely to end up with. Just a quick word about how to do this as a combinatorial problem.

EXAMPLE: You have a design with

• ONE measure of performance, • THREE free parameters, and • EIGHT constraints.

To find a materials performance index, we need to have a FULLY DETERMINED design, so we'll want to take three of the eight constraints at a time to solve for the three free parameters. How many combinations of the eight constraints do we have in sets of three?

Now, the problem with this counting is that it counts the combination of constraint 1+2+3 as different from the combination of 1+3+2 and 3+2+1. We need to divide the total by the number of combinations of three constraints (in any order) that we can have. This overcounting factor is found by:


So, the total number of UNIQUE combinations of the eight constraints in sets of three is 56! WOW...that's 56 M-values in this problem!

BUT WAIT...THAT'S NOT ALL! How many combinations of the M-values can we have in groups of two to create unique coupling equations do we have? Using the same process, we get:

That's a LOT of coupling plots to make up...even with CES.

Here is a plot showing the rapid increase in the number of M-values and coupling equations with the number of constraints for a single MOP, four free parameter design. Ouch!

What can we do to make this better? One choice is to do what I told you not to do...change one of the constraints into a measure of performance (for example, instead of having a maximum allowable cost, set up a minimum cost measure of performance).


This changes the problem. We now have a design with

• TWO measures of performance, • THREE free parameters, and • SEVEN constraints.

Using the combinatorial calculations above, we would have (for each of two MOPs)

This is still pretty ugly, but is a lot more tractable than the original problem. Of course, we've replaced the original problem with needing to (subjectively) determine which MOP is the most important.

The main message is that, when you are massively OVER-CONSTRAINED it is best to try to reduce the number of constraints you have to being only one or two larger than the number of free parameters you have, and the way to do this is to turn some of the constraints into MOPs.

REMEMBER: If you have the same number of free parameters as constraints, you will have only ONE M-value, no matter how many free parameters you have!


CES AND COUPLING CHARTS

You may have wondered by now how to do the coupling charts in CES and have CES tell you the best materials in the RESULTS section. The answer is that you have to trick it, and here's how.

FIRST: Make up a coupling chart the way that you usually do, with M1 on the Y-axis and M2 on the X-axis. This will be STAGE ONE of a multiple stage selection process. Find the correct location of the coupling equation line (slope of one and at the correct location for the design parameters) and set the line on the chart at the correct location. This is shown schematically in the figure to the right with the correct value of the coupling constant shown as the dotted line. The solid line is slightly offset above the correct position for clarity in the last couple of plots.

Now, click BELOW this line so that CES selects all the materials that touch the line or are below it.

(NOTE: The position of the coupling line can be EXACTLY placed on the selection chart in CES by looking (in the "Project" Menu) for "Stage Properties". The dialog box has a tab for "Selection" that allows you to enter exact values for where you want the line placed.)

SECOND: Make a COPY of the first selection stage by clicking on it in the PROJECT window, choosing COPY, and PASTE. This will make an identical version of your first stage as STAGE TWO. In stage two, choose the selection region to be the area ABOVE the line.


By setting the conditions of Stage Two to show only the subset of materials that have passed BOTH stage one and two, you will see only those materials that touch the selection line (shown schematically to the right). The RESULTS window will also list only these materials.

To select the BEST MATERIALS, make one more copy of the original stage, setting it as STAGE THREE. For this stage, use a selection line that is approximately at right angles to the coupling equation line and select the region ABOVE the line to be the active region. By moving this selection line up and down you can pick off the materials that give you the MAXIMUM values of M1 and M2, AND are on the coupling line. The RESULTS window now lists the materials passing all three stages. You can move the third stage selection back and forth to determine the rank order of the materials as well.

If you have a design that has more than one coupling equation, you will have to make a number of selection stage sets, three stages for each coupling equation. If you use the copy and paste functions, though, this is not too tough to do, and you only have to fiddle with the selection line in the third stage of each coupling equation set.

End of File.


ME480/580: Materials Selection Lecture Notes for Week Five

Winter 2012

DEALING WITH CONLFICTING OBJECTIVES Reading: Ashby Chapters 7 and 8.

So far we have talked about the myriad techniques for dealing with overconstrained designs, using the active constraint method, or the coupling equation approach. In all of these designs, we have been very careful to define only one measure of performance. But, there are some design situations in which you find yourself with two or more design objectives; multiple measures of performance. In many cases, these multiple objectives are conflicting; you can’t satisfy them both with the same material. This requires a different approach taken from optimization theory called TRADE-OFF PLOTS, and PENALTY FUNCTIONS.

NOTE: The biggest difference in our process and thinking from what we have done so far is that the objective function must be defined such that we want to MINIMIZE it in order to get the best performance. I have been careful to require everything to be defined in terms of MAXIMIZING PERFORMANCE, but for this type of optimization analysis, we need to define a minimizing function that will maximize performance. Ashby calls these objective equations P, as before, so we just need to be careful that we know whether the P requires maximizing or minimizing to bring success.

A SIMPLE EXAMPLE: We’ll go back to a previous problem–the simple cantilever. The design statement has been:

• MINIMUM MASS (our measure of performance), • Fixed length, L, • Square cross section, b X b, • Not fail plastically under end load F.

This is a FULLY DETERMINED design, and the only change we need to make from previous analysis is that the measure of performance, Pmin, will be a minimizing function:


Going through the usual routine with the constraint gives us the following expression for the measure of performance:

In the normal analysis, we’d want to pull out the materials selection index, in this case,

and then use it to make a selection plot. (NOTE: Do we want to find materials that have large or small values of M?)

For our design, we are also told that we must MINIMIZE THE COST. This is clearly a second design objective, and the chance that the material that minimizes mass will also minimize cost is pretty slight. Here we have a case of multiple and conflicting objectives.

We will go ahead and analyze the design using the second constraint, which we write as

where C is the material property of “Price”, having units of [USD/kg]. Pushing through with the analysis (using the load constraint) gives us the following result for P:

Two objectives, two M-values, can we couple them? NO! The P’s are different, so we can’t set them equal to find a coupling equation.

To proceed, we need to know more about the design. As in other complex designs, we need to know the values of the fixed parameters to carry on. Let’s assume

F = L =

Then the constant factor in the first measure of performance is


Plugging this into the measure of performance to be minimized, we get:

In this case, the constant factor in the second measure of performance is the same, so our second measure of performance to be minimized is:

We can use CES to make a plot for us of the two MOP’s, mass and cost. Using the ADVANCED axis option, we can write out the equation

m =113 !" f2/3 = 113 * [Density] / [Yield Strength (Elastic Limit)] ^ 0.6667

Now the Y-axis will be the MASS of the beam, in [kg]. Similarly, we can set up the X-axis to be the COST of the beam in [USD]. Schematically, the plot looks like this:

Okay…time for some optimization theory terminology. Each of the bubbles on this plot is called a SOLUTION, because it represents, for a particular material, the cost and mass of a beam that will satisfy the constraint.


Look at the bubble labeled “A”—we can see that there are many other solutions that have either a smaller value of mass or a smaller cost, represented by the vertical and horizontal lines on the plot. The materials between the lines have BOTH a smaller mass and lower cost. A is said to be a DOMINATED solution, because there is at least one other solution that outperforms it on BOTH performance metrics.

The B bubble, on the other hand, is a NON-DOMINATED solution, because there are no other solutions that have both a smaller mass and a lower cost. But is B the OPTIMUM solution?

Looking at the plot shows that there are, in fact a whole variety of solutions that are non-dominated. We can draw a line through them all and we arrive at a boundary, which is called the TRADE-OFF SURFACE, along which all the non-dominated solutions lie.

We can, at this point, use our expertise or intuition to choose the best materials from all of the candidate, non-dominated, solutions, but there must be some quantitative way of dealing with this. The answer is to develop PENALTY FUNCTIONS.


ME480/580: Materials Selection Lecture Notes for Case Study

Winter 2012

CASE STUDIES IN MATERIALS SELECTION:

SHIPBUILDING (REFERENCE: "Brittle Behavior of Engineering Structures", E. R. Parker, John Wiley

and Sons, NY, 1957.)

There are two basic parts to a ship- the hollow HULL, and the SUPERSTRUCTURE.

The hull is subjected to two forces:

1) gravity due to the mass of the ship and the cargo, and 2) buoyancy of the hull.

While these forces balance, they are not always uniformly distributed, and can be strongly affected by cargo loading.

For shorter cargo ships, "HOGGING" is common, as the buoyancy in the center is larger per unit length than it is at the ends.

Longer ships tend to "SAG", even in still water, but the worst case comes from riding the waves.

The hull is subjected to a large bending moment, and so tends to fail in panel buckling. The superstructure is used as a panel stiffener to prevent hull buckling.


We can analyze this using simple beam bending:

The first performance measure will be to minimize the mass of the ship:

subject to the constraint of no failure:

The second performance measure is to minimize the deflection subject to the failure constraint:


Since these are two DIFFERENT MOP's, we can't generate a coupling equation. Look at potential materials using a multi-stage selection.

SELECTION STAGE 1) σ versus ρ = CHART 2, slope = 1, upper left

CANDIDATE MATERIALS:

• CFRP • GFRP • Steels • Ti alloys • Al alloys • Wood


SELECTION STAGE 2) E versus σ = CHART 4, slope = 1, upper left

CANDIDATE MATERIALS:

• Al alloys • Steels • Ti alloys • CFRP, GFRP, Wood

PERFORMANCE:

CANDIDATE MATL σ [MPa] ρ [Mg/m3] E [GPa] M1 M2

CFRP 700 1.6 30 440 0.043 GFRP 400 1.6 20 250 0.050 Steels 1800 7.8 220 230 0.122 Ti Alloys 1000 4.2 100 240 0.100 Al Alloys 430 2.6 60 165 0.140 Woods 110 0.6 1 185 0.009

For M1 the best performers are polymer composites, but they lose out to steel in M2 for which they show deflections three times larger than the steels. Ti and Al look pretty good, but they lose out when we throw cost into the equation. HIGH TENSILE STRENGTH STEEL is the commonly used material, except in high performance weight-driven designs (racing yachts with CFRP).


STEEL SHIP PLATES AND FRACTURE

In the early 1900's, ship plates were completely riveted together. At the end of WWI a push for faster construction times drove shipbuilders toward using substantially welded ship plates, but as the war stopped, the money for development dried up. In 1921 a small merchant ship (the FULLAGAR, 150 ft. long) was the first fully welded ship to hit the water, and worked in England for many years.

At the start of WWII, the push came on to rapidly produce ships for the merchant marine fleet to supply the war effort, and welding technology was again pushed. The approach was a "cookie cutter" one, with a small number of ship plans, and many shipyards producing the same design. The construction was begun in 1941, and in total,

2500 Liberty Ships 500 T-2 tankers 400 Victory ships

were constructed. Shortly after these ships entered service, they began breaking apart, sometimes spectacularly! The rapid and massive scale-up required by the war meant that unskilled laborers and inadequate welding practice were used, and blamed for what happened.


Two major causes of the failures were found:

1) STRESS RAISERS: access holes through the decking plates and structural plates were cut for ladderways and cargo loading. These were initially cut as rectangular holes. Many cracks initiated at the corners of these holes. By changing the design to rounded holes, many fewer failures were reported.

2) UNKNOWN EFFECTS: (at the time)

No correlation was found between failure and the tensile strength of the steel samples taken from various parts of the failed ship plates. Loading at failure was typically around 700 [MPa], well within the design load.

Extensive study of the brittle fracture energy (toughness) using the Charpy impact test found the following:


Ductile to Brittle Transition Temperature (DBTT) is arbitrarily set as about 15 [ft-lbs] of fracture energy. ANSWER: the DBTT was too high (the steel was brittle at the temperatures of the North Sea).

(NOTE: This is not the story of what happened to the Titanic, a fully riveted ship built and sunk in 1912. Substandard wrought-iron rivets used in the hull, as opposed to the good quality steel rivets used elsewhere in the ship, failed prematurely in the cold water iceberg-collision. The riveted hull plates separated, bringing her down.)

End of File.

W. Warnes: Oregon State University Week Six: Page 1

ME480/580: Materials Selection Lecture Notes for Week Six

Winter 2012

CONFLICTING OBJECTIVES: PENALTY FUNCTIONS

The penalty function is basically a way of combining the different measures of performance into a single-valued figure of merit that quantitatively describes the performance. This is done by defining a figure of merit, Z, such that

where the α’s are called EXCHANGE CONSTANTS. The exchange constants are defined mathematically as the change in Z associated with an independent change in the performance metric, P:

We often find that cost is one of the performance metrics, and it has been a standard process in optimization theory to use money as the overriding figure of merit by letting the units of the figure of merit be in dollars:

Let’s look at how this shows up on our trade-off plot. For the cantilever beam example, there are two performance metrics, minimum mass and minimum cost. The penalty function is then written as:

and we want to find the one solution, or material, that minimizes the value of Z.

For a given value of Z, the penalty function is a linear equation relating the mass and the cost as


For each constant value of Z, this equation plots as a line of slope = ! 1" , so that the

trade-off plot looks schematically like this:

Each of the lines is a line of constant Z, with the same slope (or exchange constant, α), and the material that is the best choice minimizes Z, as shown in the left figure. Since we usually need to plot the materials data on log-log plots, the log-log version is shown on the right, with the only real difference being the shape of the constant Z lines—the linear equations now become curves in the log-log plot.

The main difficulty in performing the penalty function analysis comes down to finding the exchange constants, α. How does one decide how many dollars the designer is willing to trade for a kg change in mass? Looking at the trade-off plot, we can see that the exact value of the exchange constant is not really needed. Examine the figure on the next page: we have the same solution (material) for any value of α between α1 and α2.


Only when the exchange constant is outside that range do we end up with a different solution being the best choice. That means we may be able to be a little sloppy in our determination of α without affecting our choice of material.

Let’s go back to the example and see what, if anything, we gain by working through the trade-off plots. The design involved a simple cantilever to support an end load, and we required both minimum mass and minimum cost.

MULTI-STAGE SELECTION OF THE CANTILEVER (from Week Five Lectures)

We can use a two-stage selection process with one stage for each performance metric. We have that

Which gives two M values,

-1/α1

-1/α2


FIRST STAGE: MINIMUM MASS; M1 MIN( ) = !" f2/3 :

Use ! f versus " (Y vs. X) with a slope of 3/2:

OKAY…we draw the line no problem…now, which side of the line do we want to look at? In this case, we have defined the M based on minimizing the performance metric, P, so that we want a small value of M. This pushes us towards the materials in the upper left.

Looking at our candidate materials, we have (I used CES 2011 to get my list):

With the best material being


SECOND STAGE: MINIMUM COST; M2 MIN( ) = C!" f2/3 :

Use ! f versus C" (Y vs. X) with a slope of 3/2 (we must use CES for this one…)

Candidate materials include:

The overlap of materials is

(NOTE that I used a first stage to eliminate ceramic and natural materials from the final answer.)


PENALTY FUNCTION SELECTION OF THE CANTILEVER

We can use CES to generate a trade-off plot using the analysis we have already done. The X-axis will be set up as COST using

$( ) = 113 Nim( )2/3m!"#

$%&C'( f2/3 , and the Y-axis as the

MASS using

m = 113 Nim( )2/3m!"#

$%&

'( f2/3 . The plot in CES looks like this:

(Note that I used a first stage to eliminate the ceramic and natural materials again, which are greyed out. Be sure to CHECK YOUR UNITS!)

Based on the selection line I drew, the top four materials are:


(NOTE: Here’s what the CES Trade-off plot looks like with LINEAR axes.)

What is the difference between the two procedures (multi-stage versus trade-off plot)?

1) We ended up with pretty nearly the same materials in both cases—that’s good. 2) We needed one less selection plot in using the trade-off plot, since it captured

everything on one plot—that’s better. 3) We also have a quantitative reason for our materials when we use the trade-off

plot and the penalty function because we can justify each material choice based on the range of exchange constants over which it is the best choice. This is definitely a good thing, and makes the penalty function approach the better choice.


ME480/580: Materials Selection Lecture Notes for Week Six

Winter 2012

OVERCONSTRAINED DESIGN: PART IV A FINAL EXAMPLE

Let's try an example of a more complicated design. A microbrewery in Oregon wants to redesign their shipping and storage containers for their fine malt products. Being responsible members of society, they have a strong interest in "green" design; that is, having their storage containers be as environmentally benign as possible. They have put together the following list of requirements for us:

• As environmentally benign as possible; • hold about 10 gallons of liquid; • reusable; • be able to be stacked three high while in storage; • capable of being refrigerated; • hold their refrigerated temperature over a long time period.

After conversation with our customers, we find that they really are committed to the green design, even if it costs them more to build. This gives us our

MEASURE OF PERFORMANCE: (Use Ashby's approach of minimum embodied energy, and make sure that the container can be reused, to get at the “green” design.)

MODEL: Initially, let's start off with a basic cylinder design. Also, let's assume we're going to get a thin walled container.


Since it has to hold 10 gallons, this fixes our L and R, though we could get a little fancy and set:

PARAMETERS:

CONSTRAINTS: Given the list of requirements we have, the constraints might be broken out as

1: Not fail under a crushing load, F, equal to the weight of two full containers; 2: Keep the time to warm up the contents greater than some critical value; and 3: Not fail due to refrigeration.

Constraint 3 seems pretty trivial--not many materials that wouldn't pass that at the temperatures of interest here (though if we were to go below freezing point, it might be a different story due to thermal stresses between container and contents).

CONSTRAINT ONE: No fail under end load, F.


CONSTRAINT TWO: Time to warm up should be long. Let's look at this a bit. The main problem is with the liquid refreshment warming up by some amount (call it Θ in ˚C) over a time period of t seconds. Heat will have to flow through the walls of the container by conduction. How much heat energy do we need to heat up the fluid by Θ?

Now, how long does it take to get that much heat energy in through the sides of the container? Use 1-D heat flow equation:

Plug the total energy needed into the heat flow equation, and solve for the free parameter, w.


SUB INTO THE PERFORMANCE EQUATION:

OKAY! We have an overconstrained problem (2C1F), so we end up with two materials performance indices, M1 and M2. What do we do now?


MULTI-STAGE SELECTION

FIRST STAGE: Use M1 = σ/q*ρ (NOTE: This is now Figure 15.10 in edition 4)

Slope =

Selection Region =


SECOND STAGE: Use M2 = 1 / (q*ρ λ)

Chart =

Slope =

AN ASIDE: MAKING YOUR OWN FIRST ORDER SELECTION CHARTS

λ versus q*ρ is a combination of chart 9 (λ versus a) and chart 18 (σ versus q*ρ). We can generate the selection chart we want by making a transparency overlay, tracking the range of values we are interested in for each material, and transferring it to the new selection chart:

With much grunting and sweating, we come up with a pretty fair selection chart for λ versus q*ρ by hand (using only the charts in the book!):


(Or, spend the money to use Ashby's program, CES, and have the computer do it for you in about 5 minutes).

OKAY- back to the design. With our new selection chart of λ versus q*ρ, we need to know:

SELECTION REGION =

Now we can do the two stage selection process to get our materials choices (left as an exercise for the reader...)

What about the active constraint? We want to look, for each material, at the MINIMUM value of P as determined by the two performance equations we have:

PMAX-1 = PMAX-2 =


Comparing these shows that we need to know the following design parameters to determine the value of the measure of performance of each of the materials:

Wow! Basically, we need to know everything about the design! We might as well go ahead and do the coupling equation approach, since the information that we need about the design is the same. (We'll do this next time.)

What about a reality check? We need to calculate w (wall thickness) for each material:

w (strength) = w(thermal) =

Again, we need to know a fair amount about the details of the design to finish the reality check. We'll do this in the next section.


COUPLING EQUATION FOR THE BEER KEG

According to our understanding of 2C1F designs, we should be able to put together a coupling equation. Set the two performances equal to each other to get:

This tells us we want a plot of

How do we get this? EITHER: use CES, OR make a table of all the materials you are interested in, possibly by first looking at the two stage selection process.

How do we use the coupling equation? At this point, we need to put in some values for the parameters in the coupling equation. Early in the design, we can make approximations:

HEAT CAPACITY:

LOAD F: Customers tell us they want to stack three high. The bottom container needs to support a weight equal to two full containers.


CONTAINER FIXED DIMENSIONS R AND L:

TEMPERATURE RISE, Θ:

TIME TO HEAT UP, t:

TEMPERATURE GRADIENT, ΔT: (between the temperature of the beverage and the outside temperature)

Plug these values into the coupling equation, and this tells us that

M1 / M2 =

What does this look like on the coupling plot?


How do we find the place to put the line? It’s all about UNITS!

NOTE: Use the STAGE PROPERTIES option in CES to set the line exactly where you want it.

Plot the M-values on the two axes (M1 versus M2) and set the line at the value of 9.2 x 10-3 [MPa-W / m-K]. Choosing only materials that lie along this line, we want the ones with the highest values of M1 and M2 (on the line and to the upper right). This selection gives us:


Best materials (in rank order) come out to be: (there are only SIX)

Ultra Low Density Wood (Transverse), Low Density Rigid Polymer Foam Very Low Density Rigid Polymer Foam Medium Density Flexible Polymer Foam Carbon Foam (Reticulated, Vitreous) Low Density Flexible Polymer Foam

What about the active constraint? We want to look, for each material, at the MINIMUM value of P as determined by the two performance equations we have. Since there are only six, let's compare all the candidate materials:

This time, we see that, for some materials, the thermal constraint is limiting the performance and for others it is the strength constraint. Selecting our minimum performance for each material gives us the final column. The materials with the largest value of minimum performance is ULD Wood, with VLD Rigid Poly Foam coming in second. The order is a little different from the rank order found from the coupling

SIGMA RHO q LAMBDA Strength Thermal Minimum Material [MPa] [Mg/m^3] [MJ/kg] [W/m-K] P1 [1/kJ] P2 [1/kJ] P [1/kJ]

ULD Wood (Trans) 0.65 0.15 5.15 0.037 1.95E-03 7.48E-04 7.48E-04 LD Rigid Poly Foam 1 0.0655 160 0.0315 2.21E-04 6.48E-05 6.48E-05 VLD Rigid Poly Foam 0.17 0.028 150 0.0305 9.37E-05 1.67E-04 9.37E-05 MD Flex Poly Foam 0.374 0.0865 140 0.0595 7.15E-05 2.97E-05 2.97E-05 Carbon Foam 0.255 0.05 167.5 0.075 7.05E-05 3.41E-05 3.41E-05 LD Flex Poly Foam 0.16 0.055 140 0.0495 4.81E-05 5.61E-05 4.81E-05


equation, but that is due to the (single) values of the material properties I used in doing the active constraint. Both processes give us the same answers.

What about a reality check? We need to calculate w (wall thickness) for each material:

Strength Thermal Maximum Material W1 [m] W2 [m] W [m]

ULD Wood (Trans) 1.31E-03 3.40E-03 3.40E-03 LD Rigid Poly Foam 8.49E-04 2.89E-03 2.89E-03 VLD Rigid Poly Foam 4.99E-03 2.80E-03 4.99E-03 MD Flex Poly Foam 2.27E-03 5.47E-03 5.47E-03 Carbon Foam 3.33E-03 6.89E-03 6.89E-03 LD Flex Poly Foam 5.31E-03 4.55E-03 5.31E-03

Again, we can see that the "active" constraint is different for different materials (it is the one that requires the largest wall thickness to be satisfied). Do the thicknesses seem reasonable?

End of File.

W. Warnes: Oregon State University Week Seven: Page 1

ME480/580: Materials Selection Lecture Notes for Week Seven

Winter 2012

MATERIALS SELECTION WITH SHAPE:

PART ONE Reading: Ashby Chapters 9 and 10.

Up until now, all our materials optimization has considered all materials on a same shape basis. But, for many mechanical designs, the shape of the material plays a large role in its performance. For example, I-beams have a better stiffness/weight ratio for bending loads than solid square beams of the same cross sectional area.

Let's look at an example of how the shape of the material might affect the design. An important example is for the case of torsion.

EXAMPLE:

Minimum mass torsion bar with square cross section, A = b X b, and limited torsional deflection.

MODEL:

MOP:


CONSTRAINT:

For a beam of solid square cross section, the torsional moment of area, K is (reference Tabel 9.2, or Appendix B.2)

PLUG INTO THE MOP:

Okay, we get a reasonable materials performance index, not that different from what we've used before. BUT, if we allowed the beam to be a hollow cylindrical one, we could put more material further away from the neutral axis of the torque, and improve the stiffness and strength of the torsion bar.


Look at the torsional moment of area of a hollow cylinder, Khc:

If we write it as a factor multiplied by the K of a solid square, we can DEFINE the factor (call it φ) as the shape factor for twisting:

φ depends on the inside and outside diameter. If I make a plot of the variation of φ with the inside diameter of a hollow cylinder for a fixed cross sectional area, I see something like this:

As the inside diameter increases, holding the area constant, the shape factor increases. What does this mean for the torsion bar? Let’s find out…


We now can write our constraint equation as:

Plug into the MOP to get:

Our materials performance index now includes the shape factor, φ, and in such a way that, in order to maximize performance, we also want to increase the φ value: a hollow cylinder is a better performer in this application than a solid square cross section, even if we use the same volume of material.

This is no surprise, but why should it affect our choice of materials? The reason is that different materials have different limits on the shapes they can be formed into (processing) and different mechanical limits on how thin they can be made and used without buckling failure. In other words, the mechanical properties and available processing (both properties of the material) set limits on the possible shapes, and therefore the maximum value of φ for a given material can be thought of as a material property as well. The ultimate limit of the value of φ is determined by the mechanical properties responsible for Euler buckling of the thin wall; as φ increases, the wall gets thinner and thinner until it will elastically buckle under the required load.

Empirical measurements of the shape factors for particular materials have been carried out and are described in Ashby's book, similar to Figures 9.6 and 9.8, reproduced below:


SHAPE FACTORS

Ashby approaches this with the idea of a shape factor which is defined as a dimensionless number that characterizes the efficiency of a shape, regardless of size, for a given mode of loading, referenced to a solid square section of the same cross sectional area. (Note: any shape may be used as the “reference” shape.)

There are four shape factors:


For STIFFNESS (deflection limited design) !Be (bending) !T

e (twisting) For STRENGTH (failure limited design other than

buckling) !Bf (bending) !T

f (twisting)

Derivation: TENSILE LOADING

The deflection in tensile loading is given by

Since δ depends only on the cross sectional area, A, it doesn't matter what the shape of the cross section is, so no shape factor will be needed in tensile loading design (φ = 1 always).

Derivation: BENDING STIFFNESS

For a cantilever beam, the deflection is

where I is the second moment of the area. Now a change in shape does affect the deflection because I depends on the shape.

The second moment for a solid square section is:

We write the moment for the shape we are interested in as a multiple of that for the square:

The shape factor, φ, is a dimensionless number that describes how much the shape affects the deflection relative to the square cross section:


Derivation: BENDING STRENGTH

The maximum stress in a cantilever beam is at the point farthest away from the neutral axis:

Where Z is the section modulus =Iym

!"#

$%&

, so again the failure will depend not only on the

cross sectional area, but also on the SHAPE of that area. In a similar way to what we did with bending stiffness, let's look at Z = I/ym for a solid square cross section:

Now we can define our shape factor:

So we end up with the following four shape factors (shown in detail in Ashby's Table 9.3):


EXAMPLE: Lightweight beam in bending with a deflection limit.

MODEL:

MOP:

CONSTRAINT:

SHAPE: (elastic design in bending)

plug into the constraint equation:

plug into the MOP:


pull out the performance index:

If we don't consider the shape (or all the materials shapes are the same) then we can remove the φ's from the performance index and we get the same performance index as before:

What does the shape analysis tell us? We can increase the performance of our material by forming it into a shape with a large value of φ. Since the possible range of φ depends on the ability of the shape to resist failure by local elastic or plastic deformation (which is determined by the buckling equations), we can consider φ-MAX to be a material property. Approximate values for these material limits can be found in Table 9.4 (or in the CES datbase.)

Ashby lists two “rules of thumb” in determining the maximum shape factor for a material, based on mechanics assumptions about local elastic buckling:

Useful for initial estimates of what’s possible!



Winter 2012

MATERIALS SELECTION WITH SHAPE:

PART TWO Reading: Ashby Chapters 9 and 10.

Perhaps another shape factor example will help clarify the idea behind the use of shape factors. Let's look at an entirely new design:

A SIMPLY LOADED BEAM IN BENDING!

We want this beam to be centrally loaded, not fail under load, and have a limited center deflection. The beam will be made of an I-beam of an as yet unspecified material. We want to use the least expensive material to do the job. Start with the regular, plain-vanilla, no-shape-factor approach:

THE MODEL is simple and straightforward:

The cross section is a little more complicated than usual, being an I-beam. We have a breadth of b, height of h, webbing thickness of t, and length of L, which is fixed. The others are free to vary:


Our measure of performance is:

where A is given by the cross sectional area of an I-beam: A = 2t b + h ! 2t( ) .

We have two constraints: limited deflection, and no failure under load:

DEFLECTION CONSTRAINT:

NO FAILURE UNDER LOAD CONSTRAINT:

Okay, where does that leave us? We have two constraint equations and three unknowns...UNDERCONSTRAINED. We can either

• Add a reasonable constraint (hmmm... maybe limited mass? vibration frequency? heat flow?)

• Fix one of the dimensions (which one?)

In any case, we are going to be stuck with an awful looking algebra problem to do to solve these equations for the three unknowns b, h, and t. We might get some help by making a thin wall approximation somewhere, but even so, the algebra is unpleasant (unless you're that kind of engineer...).


SHAPE FACTOR TO THE RESCUE?

Let's look at the problem using a shape factor. The big advantage of a shape factor is that it massively simplifies the algebra by replacing the complicated formula for second moments and section moduli with easy-to-use equations. The hard algebra is put off until later.

DEFLECTION CONSTRAINT WITH SHAPE FACTOR

The second moment of the area for an I-beam is now written as:

This gets us to a materials selection index right away!

NO FAILURE UNDER LOAD CONSTRAINT WITH SHAPE FACTOR:

where the section modulus is now written as:


which leads us to a second selection index:

Now, we can couple these constraints together to give us a coupling equation:

We have a very different situation from the first approach, because we have traded off the THREE free parameters of b, h, and t for ONE free parameter of A. And the algebra is nice (even if you're NOT one of those kinds of engineers...).

CHOOSING THE RIGHT I-BEAM

So, how do we find the dimensions of the I-beam so we can order parts and finish up on schedule? The MATERIAL CHOICE (determined above from the coupling equation) gives us values for all the materials properties:

• Elastic Limit • Young's Modulus • Price • Density • Shape Factor for Elastic Bending • Shape Factor for Bending Strength


Once we have the material properties, we can do a REALITY CHECK calculation to find the necessary cross sectional area:

We know we want an I-beam shape, so we also know the following information:

Shape Factor for Elastic Bending:

Shape Factor for Bending Strength:

Cross Sectional Area:

It looks like we're in good shape; three equations, and three unknowns will provide us with the necessary b, h, and t. The algebra is pretty ugly now, but we can either suffer through it, use one of the symbolic manipulators (in math packages such as Mathematica or Maple), or make friends with one of those kinds of engineers.

In addition, by using the shape factor approach, we don't even have to decide about the shape until the end. This can be a particular advantage if one is incorporating aestheic design into the problem as well.

End of File.



Winter 2012

MATERIALS SELECTION WITH SHAPE: PART THREE

EXAMPLE: MATERIALS FOR BICYCLE FORKS

DESIGN: Minimize mass while supporting a load in bending without failure.

MODEL: Cantilever beam in bending.

CONSTRAINT: No failure under an end load F.

Use the definition of the shape factor for failure in bending:

This produces the constraint equation as:

Solve for A:

Substitute into the MOP = P =1m

:


On a chart of σ versus ρ (chart 2), we start by ignoring the shape effects (let φ = 1) ); this let’s us generate a set of viable candidate materials easily (and besides, we don’t have any charts that include the shape factor…):

Top candidate materials are (ignoring ceramics): CFRP, G&K-FRP, Woods, and Al, Mg, Ti alloys.

How do these perform without shape?

Calculate the performance index based on the properties:


MATERIALS σ [MPa] ρ [Mg/m3] M [(MPa) 2/3/(Mg/m3)] CFRP 500 1.5 42 G&K FRP 300 1.5 30 Woods 50 0.4 34 Al alloy 500 2.8 23 Mg alloy 250 1.9 21 Ti alloy 1000 4.3 23

Now, how does shape affect these?

MATERIALS M [(MPa) 2/3/(Mg/m3)] φφΒ∗ M x φ2/3

CFRP 42 9 182 G&K FRP 30 9 130 Woods 34 3 71 Al alloy 23 10 107 Mg alloy 21 5.6 66 Ti alloy 23 4.9 66 Steel 16 13 88

(*All data for φ taken from Ashby's Table 9.4 except Mg and Ti, which came from the “rule-of-thumb” rules from last lecture.)

Steel, which was out of the running before, shows up pretty well when we consider shape.

SUMMARY- Selection With Shape

1. Analyze using Ashby's method to determine shape dependent performance index. 2. Apply to selection chart as if φ = 1 (no shape effects). 3. Generate a list of the top performing candidate materials (and near misses). 4. Apply the shape factor to the performance index for each material and compare.

OR

5. Analyze using CES to include maximum shape factors in the selection chart.

REMINDER: The shape factors are only useful in bending or torsion (not tension) loading where shape can make a difference.


SHAPE FACTORS: REALITY CHECKS

Look again at designing a low weight bicycle fork. We had one constraint, on strength, modeled as a cantilever beam and analyzed with the shape factor appearing in our definition of Z. The final selection criterion was

What does the selection table tell us? First Column: M is tied to the MOP 1m

!"#

$%& , so that

the CFRP fork will weigh about 2.6 times less than the steel fork (Msteel =16, versus MCFRP= 42), and about 1.8 times less than aluminum. Since the φ doesn't appear in column 1, this is the comparison on an EQUAL SHAPE basis.

Reality check time: Look back at our derivation for the performance index. We developed an equation for the free parameter A as

If we make some assumptions about the loading, F = 100 [lbs.] = 445 [N], and L = 0.3 [m], then

Plug these into the equation for the free parameter to find the cross sectional area:

MATERIALS σ f [N/m2] A (φ=1) [m2] CFRP 1.5 x 109 6.59 x 10-5 Al alloy 6.0 x 108 1.21 x 10-4 Steel 2.0 x 109 5.44 x 10-5

The column of areas assumes a solid square cross sectional area (because we have assumed φ = 1).


Now, let's think about shape. Look at our equation for the cross sectional area (free parameter). It depends on the shape factor! If we use a shaped material, we can accomplish the same job with less cross sectional area, and therefore lower mass, and therefore higher performance!

What do we gain by using a shaped steel material at its limit of shape factor (about 13 according to Ashby)?

First, we know that using a shape factor of 13 for steel makes it perform almost twice as well as a solid square of CFRP (φ = 1).

Second, we know that the shape factor for the steel will allow us to lower the amount of material by lowering the cross sectional area needed to do the job:

This is a drop in mass by a factor of six! Shapes are good! Shapes are our friends!

What does a shape factor of 13 look like for the steel? (Using the shape factor table on page 252-3 is really helpful here...)

OVAL CROSS SECTION:


RECTANGULAR CROSS SECTION:

HOLLOW CYLINDRICAL CROSS SECTION:


So, there are two points from this:

1) φ values will affect the value of the free parameter (shaping the material means we can use less to do the job).

2) With a given φ and a given AREA, the choice of the shape to use is still up to us.

End of File.

W. Warnes: Oregon State University Week Eight: Page 1

ME480/580: Materials Selection Lecture Notes for Case Study, Week Eight

Winter 2012

MATERIALS SELECTION CASE STUDY:

GOLF CLUBHEADS ("Advanced Materials to the Fore", S. K. Liu, MRS Bulletin, Nov 1993, p.93; "Advanced Materials in Golf

Clubs: The Titanium Phenomenon", C. S. Shira, F. H. Froes, Journal of Metals, May 1997, p.35.)

There is a lot of mystique and controversy over the use of "high-tech" materials in sports equipment. There is also a lot of hype, to the point that there are now rules in place to protect consumers from unscrupulous manufacturers searching for the "tech-appeal" buck.

With a little thought, we can decide if the hype is valid or not, from an engineering point of view. One example is the material used in golf clubheads.

There are three types of clubs--woods, irons and putters. These have different use conditions, purposes and therefore, design requirements.

One thing that all the clubheads have in common, in recent design, is the goal to increase the moment of inertia as the head rotates around the shaft. The idea is that, if the rotational moment of inertia is large, the head will twist less during contact with the ball, and give you a straighter shot.


PUTTERING AROUND

The result of the increase in rotational moment for a putter ends up something like this:

High density W addition on the ends of a lightweight Ti clubface. Why Ti?

Why not look at Al or Mg?

Other constraints on the putter are pretty limited.


IRONING OUT THE PROBLEMS

For the irons, a similar modification to existing clubs can be made, and manufacturers are doing so. With irons, we have a second concern: supplying repeatable backspin to the ball. In this case the designers have gone to increasing the surface roughness in the face plate in order to increase the coefficient of friction with the ball (there is a maximum allowable roughness).

With many materials (steel, or brass for instance) the surface roughness decreases with use, as the surface asperities get worn down or plastically flattened due to the contact stresses.

Basically what one needs is a very high hardness material in the asperities so that they do not plastically deform. Look at chart 2 again:


By far, the winners are the engineering ceramics, followed by cermets, steels, composites and Ti.

One approach is to embed diamond particles in a strong matrix, such as steel. No one has looked at cermets (to my knowledge).

Step back, and remember that we also want to increase the moment of inertia, which means using a low density matrix and adding high density materials to the periphery: (Ti + diamond) + W.

WHAT WOOD WE DO NEXT?

The thinking here has been along similar lines: increase the moment of inertia around the shaft to avoid off-center shots. This has led to hollow head castings, to push the mass out as far as possible. We also have a couple of concerns having to do with distance.

The first MOP is minimum deflection (DELTA). The argument goes that you want a small deflection so that you're not storing a lot of energy in the clubhead; you'd rather have it in the ball.

We can model the clubhead as a flexible circular plate clamped around the edge:

We could chicken out and decide to maximize E, but we can come up with some constraints, which makes this into an optimization problem:

• no failure under bending load • mass less than a fixed value (about 200 [g]) • no brittle failure • no yielding under impact with the ball

How many free parameters do we have here?


Lets pick two constraints to make this a fully determined design:

Plug into the MOP:


What if we pick another pair of constraints?


For M1, we can use chart 5, with a slope of 2, upper left selection region:

Candidates are:

• Lead, tin alloys • Al, Mg, Cu alloys, concrete • Steels, Zn, polymer foams • W • Ti

For M2, we need to prepare a table (or use CES software), since we don't have an appropriate Ashby chart in the book.

The big winners for M2 are the ones with large KIc: steels, Ni-alloys, Ti, Cu.


A second MOP is the damping capacity, which is a measure of the ANELASTICITY of the material. If the anelastic deformation takes energy away from the ball, that's bad.

The energy loss is:

The candidate materials are:

• Steels, Cu, Ti, Al, Mg all look good • Zn, concrete, composites, woods and foams all look bad.

End of File.


ME480/580: Materials Selection Lecture Notes for Week Eight

Winter 2012

USING COUPLING CHARTS — AN EXAMPLE

Assume we have an overconstrained design that gives us two materials selection criteria, M1, and M2:

The performance equation for this design is

so we want to make a coupling equation that looks like this:

Our coupling chart will have axes of M1 versus M2, and we know that we want to select materials with a constant value of M2/M1 = A/B. Assume A/B = 0.004 [dimensionless for this example]. We find the position of the coupling line as follows.


The slope for the coupling line is 1 (as it ALWAYS is for all coupling charts). This gives us the following position of the line on the coupling chart (I made the chart with CES):

The materials that are selected from this coupling chart (in rank order) are:

Rank Material 1 High Carbon Steel 2 Low Alloy Steel 3 Medium Carbon Steel 4 Wood (parallel grain) 5 Cast Iron 6 Al Alloys

Alrighty...let's say we notice that the ratio of M2/M1 could be simplified by canceling out the C*ρ from both axes.


Our design still gives us M2/M1 = A/B = 0.004, but we have a different set of axes for the coupling chart. The position of the line on the new coupling chart is

First, let's look at the plots. Are they the same? NO! What about the materials that they produce? The second chart gives the following set of rank ordered materials:

Rank Material 1 Low Alloy Steel 2 High Carbon Steel 3 Ni Alloys 4 Medium Carbon Steel 5 Stainless Steel 6 Ti Alloys

For SELECTION charts (using a single M) we can simplify the equations and axes and get the same materials, but for COUPLING charts we CAN'T simplify the axes. The best rule of thumb is to NEVER SIMPLIFY THE AXES.


ME480/580: Materials Selection Lecture Notes for Week Eight

Winter 2012

DESIGN WITHIN LIMITS

There are some types of designs in which a constraint parameter must operate within a range of values, rather than as either a maximum or minimum value, as we've talked about so far. How does this change the optimization process? Let's do an

EXAMPLE: Minimum mass cantilever beam (yawn).

MODEL: Rectangular cross section (h x b), fixed L, b, free h, load F.

MOP:

CONSTRAINT:

(Oooooooh.... is this two constraints or just one?)

Let's start off assuming it's two constraints and analyze them separately:


MAXIMUM DEFLECTION:

MINIMUM DEFLECTION:

Uh-oh... they're the SAME? How can we tell them apart? Do we really want to have the same materials performance index for a maximum deflection limit and a minimum deflection limit?

REALITY CHECK:


So... the design optimization is the same, max or min, but the value of the free parameter will be different. The difference between a maximum and a minimum limit comes in the reality check.

NOTE: Optimal design gives you the best material for the job, and tells you the free parameter values you need for that material to work based on EXACTLY MATCHING your constraint; there's no overdesign and no underdesign--it's OPTIMAL. If you're faint of heart, you can shift the free parameter away from the optimal choice (thereby increasing your safety factor and moving away from optimal design). If you include a safety factor in to begin with, then you have already covered yourself and can go with the optimal choice.

Back to the design: Since we are thinking of these as two separate constraints, we should be able to couple the performance indices together. What happens if we do?

Okay... not such a good idea. Why not? They're not really two different constraints! It's one constraint with two limiting values.

SO for this design, with 1 free parameter and 1 constraint, we still have only one M index, and the job of meeting the two limiting values falls on the reality check and final choice of the free parameter.


Let's complicate it a little (oh goody!). Let's introduce a second constraint to get a 2C1F over-constrained design.

FAILURE CONSTRAINT:

So, we have two performance indices:

Let's couple these together. We'll get two coupling equations:


How does this show up on the selection charts? We need to make a coupling equation chart:

The search region is still the upper right of the plot, since this region maximizes both M indices. We should look for materials that fall between the two coupling lines. We'll still need to do a reality check against both limits of the deflection constraint.

AND SPEAKING OF COUPLING EQUATIONS...

What happens if you have a design that gives you coupling between similar indices even though the constraints they come from are different?

EXAMPLE: A lightweight cylindrical column, unknown A, fixed length.

CONSTRAINT ONE: No buckling


CONSTRAINT TWO: Natural frequency high

COUPLING EQUATION:

Since both M’s are essentially the same, all materials lie on a common line on the selection chart. The big question then is “where does your coupling constant line lie?” In this case, the materials lie along a line of slope = 2. What happens if your coupling constant doesn’t intersect the materials line at all?

If the performance indices are IDENTICAL, what happens then? Let’s say we have a design situation in which we have two selection indices such as


The coupling equation gives us:

The values of A and B are found from the known (or assumed) fixed parameters for the design. If the ratio of A/B does not equal 1 then the coupling equation cannot be satisfied by any material. The coupling equation tells you whether the design is possible or not. Nifty!

Not only that, but you now have a clear explanation of WHY the design will not work. Writing out the equation A/B = 1 will show you what variables need to be changed (and by how much) in order to make the design work. It may also require a change in operational approach that will require a whole new analysis.

USING COUPLING EQUATIONS WITH LIMITS

Consider a design that gives you coupling a coupling chart, and the constraint parameter is a limiting value, for instance ! <= !O .

After analysis and preparation of the coupling chart, you find your coupling chart as schematically shown to the right.

Now, the coupling line gives you the optimized materials, for which ! = !O , but, the RED region gives you the materials that have a SMALLER value of the constraint parameter, and therefore satisfy ! < !O .

A handy way of thinking about the selection process, contributed by one of the design groups in the W06 class in their final report.

End of File.

W. Warnes: Oregon State University Week Nine: Page 1

ME480/580: Materials Selection Lecture Notes for Week Nine

Winter 2012

OPTIMAL DESIGN WITH COMPOSITES Reading: Ashby Chapter 11 and 12

As you have probably noticed by now, there are often times when the design statement requires two conflicting constraints or objectives and no single material can do a good job of fulfilling the job. In many cases, the job can be better done using a combination of two or more materials together, essentially requiring a composite approach to the materials selection. Ashby calls these materials “hybrids.”

The goal in composites is to get a beneficial set of behaviors out of the components without taking a hit on some other front. Ashby suggests that the behavior of composites follows one of the models shown in the figure below:

A: Best of Both

B: Rule of Mixtures (based on volume fractions, f)

P1C = f1P11 + 1! f1( )P12

C: Weak link behavior

D: Worst of both

It doesn’t happen very often that we can take advantage of the type A behavior, but we can usually count on something between the rule of mixtures (ROM) and the weak link behaviors. Just how the composite material behaves depends a lot on the geometry of the composite structure as well as the properties in question.

Ashby organizes the broad world of composites into four geometrical types, as shown in the figure below. These are the conventional composite material, the sandwich structure, the lattice structure, and the segmented structure.


In addition to developing a taxonomy of composite materials types, Ashby presents (in an earlier edition) a nice summary table of the potential for functional improvement allowable by each composite type:

The rest of chapter 11 is more focused on developing new composite materials than in finding composites to fit a particular design situation. I’ll take a slightly different tack for this issue.


In designing using composite materials, there are three approaches, which I'll break into two different categories: MONOLITHIC COMPOSITES, and COMPOSITE STRUCTURES.

Ashby describes these as the “simple solution” and the “hybrid solution.”

First, let's look at MONOLITHIC COMPOSITES, or the SIMPLE SOLUTION.

What do I mean by monolithic composites? These are composites for which we treat the material as a homogeneous piece of material with properties of the bulk composite.

One way of designing with monolithic composites (and by far the easiest) is to have a comprehensive database of composite materials properties. With such a database, all the materials are treated just as we'd treat a metal alloy or a polymer. Their properties would be plotted on the materials selection charts and everything proceeds as we have been doing. We have a (small) database of composite properties already in the Ashby selection charts, covering the polymer matrix composites, a couple of cermet materials (WC-Co, for example), and concrete (a rock, sand, cement composite).

BUT, what if we want to invent our own composite materials, or try to extrapolate the behavior of a composite that is not listed on the selection charts?


Start with the Rule of Mixtures:

We can look up the properties of the individual components from the selection charts and using the rule of mixtures, determine the properties of the monolithic composite. But what do we use for Vr? The advantage of the composite is that we have adjustable properties, so it would be nice to leave Vr as something adjustable for our application. How to do this?

Using the rule of mixtures, we can work out the change in the composite properties as a function of Vr, given the properties of the individual components:

MATRIX MATERIAL Strength [MPa] 1 Density [Mg/m3] 1,000 REINFORCEMENT MATERIAL Strength [MPa] 100 Density [Mg/m3] 10 VOL% REINFORCEMENT

Composite Strength [MPa]

Composite Density [Mg/m3]

0 1 1000 0.001 1.099 999.01 … … … 0.9 90.1 109 1 100 10

Now we can plot these on the selection charts. How do these sets of materials appear on the selection charts? Well, they are nicely behaved LINEAR functions of Vr, but we want to look at them on LOG-LOG plots. Tricky, because of the conversion from a linear plot to a log-log plot. Look at some examples for a guide: For each example below the change in the first property (X-axis) is two decades (from 1 to 100). The second property changes by a fixed amount either increasing (red line) or decreasing (blue line) with volume fraction of reinforcement. On the left is the linear-linear plot, and on the right is the matching log-log plot.


NOTICE that even though the change in the properties is linear with volume fraction of reinforcement material, the data does not plot that way on a (log-log) selection chart. There is a significant difference in the selection chart appearance depending on whether or not the property1-property2 behavior has a positive slope or a negative slope. In addition, the positive slope case changes its curvature depending on whether there is a bigger change in the X-axis property or in the Y-axis property. Let's sketch this for a couple of new cutting-edge composites on a selection chart.

2X-1Y

2X-2Y

2X-3Y


The next point is that, by doing the optimization process for materials selection, you develop a selection line. DEPENDING ON THE SLOPE OF THE SELECTION LINE, AND THE SELECTION REGION you will find out whether or not a particular composite material will be a better performer for you. With the selection line, you can determine the Vr that would be needed to optimize the performance of the composite.

1) PP matrix-Al reinforcement composite (1/2 x 1 positive)

2) Epoxy matrix-Fir reinforcement composite (1/2 x 0 zero)

3) Pb matrix-SiC reinforcement composite (1/2 x 2 negative)

4) Pb matrix-Mo reinforcement composite (0 x 1 inf)

5) LDPE matrix-SiC reinforcement (1/2 x 3 positive)


NOTES:

1. The underlying assumption is that the composite will obey the ROM for the properties of interest. This is not always true, especially near the limits of large and small Vr, but is a good start for the initial design stage.

2. If the composite line on the selection chart is a straight line, this almost always means that the composite doesn't help you at all: one of the components will almost certainly be a better performer. However, when one looks at a different set of properties, the value of the composite might come into play. (EXAMPLE: SiC reinforced- Al matrix composites. Compare composite properties on chart 2 against chart 7.)

COMPOSITE STRUCTURES

This is the term I use for the second category of optimal design with composites. Often times what you find as you start the optimization process is that no single (monolithic) material can actually give you the performance you want. This is discovered either from doing a "reality check" with the materials selection indices you have developed, or from the coupling equations. Your only choices at this point are to either

• change the fixed parameter and constraint levels of the design to make it fit the materials available,

• give up, or • use more than one material to do the job.

To pursue the third option, there are a variety of approaches, which range from fairly straightforward to infinitely complex. Let's start with a straightforward one, and use an example we've already been working with--the container design for the microbrewery from week five. In this design we had a basic model of a cylindrical thin walled shape in which only the wall thickness was a free parameter. We applied two constraints (no failure under a compressive load due to stacking, and long time with small change in the temperature), found a 2C1F overconstrained design, developed two performance indices, M1 and M2, and coupled these together to get the best choice of a MONOLITHIC material to do both jobs. Let's revisit this with a COMPOSITE STRUCTURE approach.

First, draw the new model:


then write the MOP: Minimum energy content:

Since this now depends on two materials we have a more complicated design. For the straightforward approach, let's assume that the two materials we will use are independent- that is, material 1 will ONLY help us with constraint 1, and material 2 will only help us with constraint 2. If this is the case, then the MOP will be maximized if we can independently minimize the energy content of each layer:

In essence, we are changing from a one MOP design to a two MOP design. What we end up with is a materials selection criterion for the strength layer given by

and a materials selection criterion for the thermal insulation layer given by


Applying these to the appropriate selection charts (chart 18, strength versus energy content; and the self-generated chart from the week five lecture, thermal conductivity versus energy content), we can find the materials that best satisfy these needs of this design.

(The answer, which you may convince yourself of outside of class, is to use wood, pottery ceramics, or steel for the strength layer, and polymer foam or wood for the thermal layer. It is interesting that historically these containers were made out of pottery and wood long before stainless steel and aluminum came along!)

The third, and more complicated, approach is to allow each material to provide some benefit to each constraint. The strength constraint becomes:

The thermal constraint can be simplified if the thermal conductivity of one of the layers is much larger than the other, to give:

With two constraint equations and two free parameters, we can solve for the free parameters:

And plug into the MOP:


UGLY! Why? We have crossed the line for an initial assumption (made in the first week) on which the optimization process we've been using is predicated: the measure of performance can be separated into the three INDEPENDENT functions of f1, f2, and f3. By doing the composite structure analysis, we have coupled together the geometrical properties and the material properties so that these are no longer separable!

Does that invalidate what we've got for our MOP above? NO WAY! It now means the optimal choice of materials will require a different selection approach, which gets us into the realm of non-linear, non-separable optimization theory, and a need for another course.

(NOTE: Rule of Mixtures modeling of composites is very rudimentary and not nearly the while story on composite properties. To learn more about the real composite models, consider taking the Composite Manufacturing course (ME499, Fall term), or Polymer Composites (WSE530, spring term of odd numbered years.))

End of File.


ME480/580: Materials Selection Lecture Notes for Week Nine

Winter 2012

ENVIRONMENTAL MATERIALS SELECTION Reading: Ashby Chapter 15.

In the course this term we have looked briefly at environmental concerns in materials selection using the idea of ENERGY CONTENT as a way of measuring the impact of the processing of materials on the environment. In Ashby’s new edition book, he has further developed the ideas involved in environmental design. In fact, he is also now offering an add-on to the CES software called the CES Eco-selector, which provides additional information for ecological concerns in materials selection for design.

One of the difficulties in considering environmental aspects of materials use in design is that there is not universal agreement about how to account for “green” design, or even what constitutes “green” design. As well, the interaction between materials and the environment is a complex one, and really requires a broad, systems-level approach.

One view of the complex interactions surrounding materials and energy consumption is shown in this schematic. Often seemingly straightforward changes (such as new technology) result in complex changes in materials use and energy consumption.


Design for the environment focuses on a time scale of 10 years, while design for sustainability looks at the longer time scale of 10-100’s of years. The later requires a different set of tools than what we can deal with here (legislative, global, political, social), so we’ll look at the shorter term problems.

THE MATERIALS LIFE-CYCLE

The first step in thinking about materials and the environment involves understanding the life-cycle of a material in an application. Ashby breaks the life-cycle of materials or products into four phases; Material production, product manufacture, product use, and product disposal.

The following figure schematically illustrates that, at each of these phases, there is a potential for the consumption of energy and materials as inputs, and for the production of waste (as either heat or physical waste).

Based on these four phases, we can develop some measures for the environmental impact of various products and materials in each of these phases. To begin, let’s think about the energy input required to produce a raw material in the first phase.

MATERIAL PRODUCTION: PHASE ONE

Most energy consumed in this life-cycle picture comes at present from fossil fuels, and we can come up with a figure for the number of MJ of energy consumed per kg of material produced. This is called the production energy of the material, and can vary widely, for instance between aluminum and copper.


Some of the production energy is stored in the material and can be recovered in some way later on (perhaps in burning the material at disposal). Other materials also contain another type of stored energy. For instance, polymers are primarily made from oil feedstock which contains chemical energy, while timber contains solar energy stored in the wood during its growth. This energy is called intrinsic energy. The Ashby approach is to include this intrinsic energy in the production energy when it comes from non-renewable sources (like polymers), but not from renewable sources (like timber). Production energy values range typically from 10-100 [MJ/kg].

Producing materials also produces unwanted waste materials (pollution), including (but not limited to) CO2, NOx, SOx, and CH4. Sometimes these wastes can be significant (for instance, producing 1 [kg] of aluminum from fossil fuel energy produces 12 [kg] of CO2, 40 [g] of NOx, and 90 [g] of SOx. Other materials don’t have as large an impact on the environment from waste (timber has essentially a negative output of CO2).

In any case, the idea here is to track the energy input and pollution output associated with the production of each material—a significant and ongoing database effort.

PRODUCT MANUFACTURE: PHASE TWO

Processing materials into usable shapes also involves an energy input, and these energy costs can be measured and/or modeled. For example, we can estimate the energy needed to melt materials (as needed in a casting process) from basic properties.

Assuming a 30% efficiency of turning fossil fuels into electrical energy for the melting, we find

And for most metals and alloys, the melting energy is in the range of 0.4-4 [MJ/kg].

Similar estimates can be made for the energy of vaporization (used in physical vapor deposition processes) or deformation work (such as rolling or extruding). For metals and alloys, these numbers are in the range of 3-30 [MJ/kg] (vaporization) and 0.01-1 [MJ/kg] (deformation).


PRODUCT USE: PHASE THREE

The amount of environmental impact that occurs during product use clearly depends significantly on the particular product. For instance, a highway bridge consumes a lot of energy and material during the manufacturing phase, but requires very little energy in the use phase. Automobiles consume energy while they are being used as well as while they are being made. Ashby breaks down products into a set of product classes based on their energy and materials input, and the loads that they must sustain in use.

Again, we can track the flow of energy, materials, and waste production through the product use phase and we’ll see some pretty big differences in the performance of different products, designs and materials.

PRODUCT DISPOSAL: PHASE FOUR

Quantifying recycling is, apparently, quite a difficult operation. There are always energy costs associated with recycling, and these also contribute to the waste stream. However, generally recycling a material saves considerably on energy compared to the materials production energy.

Just because a recycling process is energy efficient, doesn’t mean that it is cost efficient. This often depends on how widely distributed the materials are. For scrap that is locally generated, during the manufacturing process for instance, the process of recycling is easy and generally already being done at high efficiency. Widely distributed materials, from junked products, are harder to collect and recycle, which costs more money to perform the recycling effort.

Many materials are not capable of being recycled at all. Metal matrix composites are an example. The intimate mixture of a ceramic reinforcement (for instance a metal carbide powder) within a metal matrix (such as aluminum) cannot readily be separated into the component metal and ceramic again. As design pushes toward more miniaturization, the economical separation of the component materials becomes even more difficult.


Generally, the information about recycling materials comes down to a non-quantitative indication of whether the material can or cannot be recycled, down-cycled, biodegraded, incinerated, or landfilled.

ENERGY CONSUMPTION BY PHASE

Generally, it is found in pratice that one of the four phases of the product life-cycle dominates in terms of the impact on the environment. If we simplify the data to consider just the energy consumption, we can produce a plot of the energy used by a product during the different phases of its life.

What the charts above show is that, quite often, one of the phases is the dominate phase, accounting for as much as 80% of the energy consumption during the entire product life cycle. Which phase is the dominant one clearly depends on the product, but the implication is that, in order to achieve significant benefits from redesign or informed materials selection, we will need to target the correct phase. Making a 20% reduction in the energy use in the manufacturing of a bicycle doesn’t really affect the environmental impact of the bicycle. A change in materials to one that has a smaller production energy cost will be more likely to produce results.

The other thing to notice about the figure above is that, when the differences between the phases are so large, precision in the data isn’t important. An uncertainty of a factor of two in the energy costs won’t really change the results, so quibbling about the details isn’t important (yet).


The process of environmental design, then, starts by figuring out which of the four phases of product life is the dominant one. What technique we use to attack environmental problems will depend on the dominant phase.

In thinking about the things we’ve discussed this term, the techniques for efficient design and working towards maximum performance are all focused on the PRODUCT USE phase. Improvements in performance by providing better strength to weight ratio materials, or optimizing the shape to produce the smallest mass possible for a given application, or providing the largest thermal insulation for the weight of material used, are all examples of positive ways to impact the environment through intelligent design.

The other phases require other techniques to make an impact, and some of these are listed in the figure below.

To impact the material production phase, we need to examine materials that will accomplish our design goal with a minimum of production energy content. We already looked at this a bit with the example of the “green” beverage container, which used the Ashby material property of energy content to produce materials selection indices such as:

The following plots show the large range of production energy content per kg and per m3 for materials.


With the CES software we can make selection charts that incorporate the production energy, as we have already seen, and in the newest version of the CES software, this can be done with properties such as the amount of CO2 produced per kg of material. Cool!


CASE STUDY: DRINK CONTAINERS

You probably suspect by now that I am inordinately concerned about containers for beverages, but I’ll go ahead with this case study from Ashby anyway. At least its not a cantilever beam!

Thinking about the energy consumption characteristics of beverage containers, we can see that the main energy consumption happens in the materials production and the product manufacturing phases.

To get the best material, we want to select the material that minimizes the production energy per unit of capacity of the container. We can start by looking at the production energies for the different materials. What materials look reasonable?

Okay, so we have a candidate materials list, with production energies for each. Just for giggles, let’s use as candidate materials the set of materials that are commonly found in drink containers at present and see how they stack up.

Now we can look up the product manufacturing energies (assuming we have a comprehensive database), and we get the following data:

Candiate Material

Production Energy MJ/kg

Forming Method

Forming Energy MJ/kg

PET 84 Molding 3.1 HDPE 80 Molding 3.1

Soda glass 15.5 Molding 4.9 5000 series Al alloy 210 Deep drawing 0.13 Plain carbon steel 32 Deep drawing 0.15

Interesting to note that the forming energy is a small fraction of the production energy for all these materials (with the exception of the soda glass).

Adding the energies, and dividing by the volume of the container, we can make a list of the performance of each of these materials in this application. Before we look at the answer, what is your bet about most environmentally sound material for this application? Notice that all of these materials can be fully recycled.


The answers are:

Material Container Mass g

Mass/liter g

Energy/liter MJ/liter

PET 400 ml bottle 25 62 HDPE 1 liter milk bottle 38 38

Soda glass 750 ml bottle 325 433 5000 series Al 440 ml can 20 45

Plain steel 440 ml can 45 102

Surprised at the results? Me too!

CASE STUDY: CRASH BARRIERS

I’m thinking here about two different types of crash barriers to protect people in automobiles. First, there are the static barriers that line the roads, particularly around sharp corners or steep drops. The second are the mobile kind, such as the fender and crash protection on the car itself.

In the static barriers, the dominant phases of energy consumption are the production and manufacturing phases, as in the drink containers. Once they’ve been put in place they don’t use any energy or create any pollution. We will want to maximize the energy the barrier can absorb per unit of production energy. The energy absorbed in a crash is given by the area under the stress-strain curve:

And the materials selection index will be:

The automobile fender is different. Since it is part of the car, it adds to the weight, and thus to the energy consumed in using the vehicle. The principle phase of energy consumption is that of product use. Here, we are more concerned with the weight that the fender adds to the car, so we’ll want to maximize energy absorption per unit weight, giving us:


The top chart is the one to use for static crash barriers. We want large values of energy per unit production energy, and we find that the steels are at the top. It also looks like PE and PP would be good choices. Anyone know what they use for those big plastic containers around construction sites?

The bottom chart is for moving crash barriers. Here Ti alloys and stainless look okay, but we see that the polymer materials really look much better.

The point is, different designs call for different measures of performance (where have I heard that before…?), and looking at the energy flow during product life is one way to help determine the best M-O-P for the J-O-B.


CASE STUDY: WALL PANELS

One last example and there ain’t no more. Here we look at the design of environmentally sound panels, and again, the application affects how we approach the choice of materials for the design. Let’s look at panels that emphasize each step in the product life phases.

MATERIAL PRODUCTION PHASE PREDOMINANT

We want a flat panel to provide a given strength, and be stiff enough to not buckle or deflect (or vibrate?). The application involves a stationary panel (like the wall of a storage container) and there are no energy concerns in its use (not a refrigerated container, I guess). From numerous examples over the course of the last nine and a half weeks, we know that the performance indices for these panels will be:

where we have used the minimum production energy as our MOP. The selection charts shown here are the inverse of the M-values given above; we want materials with LOW values on the plots.

Plywoods and particleboards look pretty good in these plots (bully for K-mart!), while steel comes out pretty good for the metals. Polymers all show higher energy contents.

PRODUCT MANUFACTURE PHASE DOMINANT

We saw when we looked at the drink containers that the manufacturing energy inputs are generally much smaller than the production energy content. Choice of material will dictate the choice of processing, but this has little impact on the overall energy content of the product. Probably more important is the impact of the manufacturing process on the LOCAL environment in terms of effluent release in the community. Probably clean manufacturing practices are the only solution to manufacturing phase dominant products.


PRODUCT USE PHASE DOMINANT

Now, our panel is in an energy intensive application (a panel for a storage refrigerator for fine beverages, or a beverage delivery truck side panel, or even a refrigerated beverage delivery truck side panel!), so we will want a different optimization.

Let’s assume a delivery truck side panel, so that stiffness and strength per unit mass become the important selection criteria. The selection plots are ones we’ve seen before (again, plotted as 1/M), and we see that the winners are CFRP, plywood and Be, with Al and Ti a lot better off than steel.


In strength based design, CFRP wins handily, and even polymers do better than steels.

PRODUCT DISPOSAL PHASE DOMINANT

This is an area that only recently has seen much interest from manufacturers. Recycling is difficult because of the contamination materials collect as they are used. This whole area is an ongoing research focus, and will be for the foreseeable future.

End of File.

W. Warnes: Oregon State University Week Ten: Page 1

ME480/580: Materials Selection Lecture Notes for Week Ten

Winter 2012

PROCESS SELECTION: PART ONE Reading: Ashby Chapters 13 and 14.

Why should we worry about process selection at all? There are several good, practical reasons to go through the effort of process selection:

• Different processes may produce the same component from the same material, but with different properties. (For example: spray forming (thermal-spray) vs. casting.) The SIZE OF THE BUBBLE on the selection charts gives a good idea of how much processing can vary the properties of a given material.

• Early consideration of processing can save a lot of money later on. • The [$/kg] material costs are usually only a small part of the total cost of making

something, especially compared to the [$/part] costs of manufacturing processes.

Ashby has pulled together a process database, both as part of the book, and as part of CES. This is another great tool to have in your design toolbox, as you‘ll see. I want to talk about the topic of process selection in four parts: Process Types, Process Attributes, Process Selection Using the Book, and Process Selection Using CES.

PROCESS TYPES

Ashby has done a survey of all the standard (and not-so-standard) processes for materials manufacturing, and has come up with a pretty useful way of categorizing them. As seen in Figure 13.2, he breaks them into four categories:

PRIMARY SHAPING PROCESSES: These are the big guns—processes like casting, deformation (which includes forging and rolling), powder processing (for ceramics, and increasingly, nano-structured materials), and special methods like electro-forming and rapid prototyping.

SECONDARY PROCESSES: There are only two of these, but they are important: machining and heat treatment. They are secondary because they are used on something that’s already been through some primary process.

JOINING: which includes welding, adhesive bonding, and fasteners. And finally…


FINISHING or SURFACE TREATMENT: Many of these are cosmetic, but there are important processes for performance here as well (polishing to get needed flatness or surface roughness, or coatings to provide environmental protection, for example.)

To become familiar with the different processing types, reading through section 13.3 is definitely a good idea.

PROCESS ATTRIBUTES

In putting together the process database, Ashby has followed the same philosophy as in the materials database. Each process is defined by a set of attributes, and, just as with the materials database, each attribute is filled in for each process. (Note that processes have a different sets of attributes based on which type of process they are.)

The process attributes is probably the most important part of the process database. A quick perusal of the database information will make you look like a total expert on processing—$$Ka-ching$$!

The attributes for each type of process are shown in figures 13.3 and 13.4, and the values of each attribute appear over a range, just as materials properties do. Ultimately, the process selection will involve matching the attributes of the candidate processes with the attributes of your design and material. SO…how do we do it?

PROCESS SELECTION BY THE BOOK

Process selection is similar to materials selection in that we want to initially consider ALL processes as candidates at the start of the design, and winnow down the options as we learn more about the design requirements. It is an iterative process and should ideally be considered at each stage of the design, in increasing detail as the design refines.

There are two types of process selection you may want to do. The first is to use an existing process as a way of eliminating materials, and the second is to use the materials/design to select a process. These two approaches differ in philosophy, requirements, and outcomes.

In the first case, your company may have an existing process or a specialization in a given process route. It would be useful to be able to choose materials for the component you are designing that will take advantage of the processing expertise that you already have, and the resources that are available.

In the second case, you may not have such processing capabilities, and plan to either develop them or contract them out. It is important to select the best, most economical process for the materials you plan to use, chosen from all of the processes out there. Essentially the measure


of performance for the process selection is going to be minimum cost, though it might alternatively be minimum time or maximum quality.

The first case is easy, as it fits into our existing system of materials selection, using an additional selection stage or two to help us choose an appropriate material.

CASE ONE: PROCESS SELECTION AS A MATERIALS CONSTRAINT

There is only one of the process selection charts from chapter 13 that we need to use in this case, figure 13.22. We may possibly want to look at the others, but we'll save them for later.

Figure 13.22 shows a generic overview of what materials may be fabricated with what processes. This can be used as a selection stage to eliminate materials not suitable for use with "your" process. Since it is a generic overview, it should be used with some caution.

EXAMPLE: You are designing a component, and your company specializes in RESIN TRANSFER MOLDING, which is essentially polymer molding operation. How do you use this process as a filter to eliminate materials in the selection process?

FIRST: Look at figure 13.22. It shows the set of materials that are compatible with resin transfer molding to be all in the polymers area, and specifically,

Now we can go to the materials selection part. For example, perhaps the design analysis tells us to choose materials with an


Use chart 2, and drop our line down to hit the materials left after the process selection.

CASE ONE: PROCESS SELECTION AS A MATERIALS CONSTRAINT USING CES

Of course, this is much easier to do with the help of CES, and more accurate, since the computer can track more detailed information about the processes and the materials than we can present on a graph.

With CES, the first stage in selecting a material can be a process selection stage, which will strongly limit your materials choices.

Let’s assume that our company is in the business of EXTRUSION (which is a deformation process.) Start by making a new GRAPHICAL SELECTION [NOTE: make sure that you are selecting from the materials database for your project. I used “all bulk materials” for this example.]

For the axis of your choice (the X-axis in my example), click the ADVANCED button, and then click on the TREES tab. From the pull-down menu, select the “ProcessUniverse” option. Now open the “Shaping” folder, and then the “Deformation” folder. Double-click on the


EXTRUSION select PROCESS from the list on the left, and choose the process, or processes you want to use from the list on the right. [NOTE: you can choose multiple processes by selecting more than one process from the list.] This will only select materials that can be EXTRUDED for the selection plot.

For the other axis, choose any material property that you want to--it doesn't have to be important for your design, but it could be. I chose PRICE. In my selection stage, a lot of materials passed. I didn't use any additional selection at this point; the plot only shows the materials that are capable of being extruded.

Now we can go ahead with the rest of the selection process as we are familiar with it. Perhaps our next selection stage uses chart 2 with a materials selection index of:


WOW! We end up throwing out a lot of materials, some with better performance in this application than the chosen materials, but we find out which materials are the best to use, given the limitations of the process that we will be using to fabricate them.

CASE TWO: SELECTION OF OPTIMUM PROCESS

To perform OPTIMAL process selection, we again let the design requirements drive the decision process. If we have done the materials selection analysis, we may already have a set of candidate materials with which to work. The selection process devolves to the task of matching PROCESS ATTRIBUTES, to the COMPONENT ATTRIBUTES. Each process has a set of attributes, as we’ve already seen.

The design requirements will generate a similar list of attributes that the component will need (for instance, a free parameter determined by the materials selection process), and we look for a match. As in the first approach, we can either do this by hand or by CES.

There are seven charts that Ashby has put together for process selection. These are:

Figure 13.22: The materials/process matrix, which we have already seen.


Figure 13.23: The shape/process matrix, which indicates which shapes are possible with which processes.

Figure 13.24: The mass range chart tells the limits on the size of the part, in kg, that can be made with any given process.

Figure 13.25: Section Thickness sets out the range of thicknesses that different processes can achieve.

Figure 13.30: Tolerance: Very useful for knowing how close to net final shape we can expect the process to get us. Will we need a final finishing stage?

Figure 13.31: The RMS Surface Roughness chart. How good a finish does the process leave?

Last of all is Figure 13.34, the economic batch size chart. How many parts can we expect to make economically using a given process approach?

The component attributes can be plotted on these charts as either boxes (if the attribute is within a range of values), or as a horizontal line (if the attribute has a maximum or minimum allowable value).

Some of these charts will be limiting in terms of processes available, and others will not. Let's do an example from Ashby involving a cantilever beam...

EXAMPLE: CERAMIC VALVES FOR FAUCETS

We are looking to replace the rubber washers and brass valve seats in standard water faucets with something that won't wear out (causing leaking) and won't corrode (causing leaking). The plan is to go with a pair of matched ceramic disks, with finely polished surfaces in contact. The ceramics have a high hardness and a high resistance to corrosion in water. Some far-sighted engineers (probably someone who took this course last year) has already developed Al2O3 faucet valves. The problem is that, when the water temperature changes rapidly, the Al2O3 cracks due to thermal stresses, either within the ceramic itself, or between it and the metal making up the faucet. Can we do better?

MODEL: Disk of ceramic.


MOP: Maximize temperature variation that leads to thermal shock cracking.

CONSTRAINT: Thermal strain in surface of the disk on a rapid temperature change is:

Check out chart 12: σ/E versus α.

The materials of choice are:

NOW, how do we make it? Stay tuned to this same station until next time...


ME480/580: Materials Selection Lecture Notes for Week Ten

Winter 2012

OPTIMAL PROCESS SELECTION: PART TWO Reading: Ashby Chapters 13 and 14.

Process Selection for the Ceramic Valve for the Faucet

In order to select the process, we need to determine the attributes of the design against which we will attempt to match the attributes of the process. To do this, we need to know some of the fixed parameters of the design, and the materials that have been selected from last lecture.

The design statement tells us some of the geometrical parameters of the valves:

• Diameter = • Thickness = • Mating surfaces flat and smooth:

Using this information, we can begin to fill out the attributes that are important for process selection.

VOLUME: easy...

SIZE (measured in units of weight):

NOTE: For many calculations, we can get by with a generic "average" density of 5000 [kg/m3] (or 1000 [kg/m3] for polymers). We don't have to be too precise with these calculations.


MINIMUM SECTION THICKNESS:

OKAY…Now we put all this together to help us plot the correct stuff on the process selection charts. I made the following table to help keep track of it all:

Design Attribute Value Volume [m3] 1.60 x 10-6

Section Thickness [mm] 5 Tolerance [mm] 0.02 Roughness [mm] 0.1 µm

Material Density (min) [kg/m3]

Density (max) [kg/m3]

Size (min) [kg]

Size (max) [kg]

SiAlON 3200 3300 5.12 x 10-3 5.28 x 10-3 SiN 2370 3250 3.79 x 10-3 5.20 x 10-3 SiC 3000 3200 4.80 x 10-3 5.12 x 10-3

Zr2O3 5000 6150 8.00 x 10-3 9.84 x 10-3 RANGE -- -- 3.79 x 10-3 9.84 x 10-3

Now we apply these to the Process Selection Charts using a multiple selection stage approach. Since the candidate materials in this case are all of the same class (ceramics), we can lump them together and use the range of values from all four materials to do our search.


Process Selection Stage 1: Materials Compatibility Chart (Figure 13.22): Already down to eight processes, only three of which are primary shaping processes.

Process Selection Stage 2: Process-Shape Chart (Figure 13.23):

This shape is slightly more complicated than a simple prismatic circular shape, but not too much more, so we'll say it’s a non-circular prismatic shape.

None of the primary processes are eliminated based on shape.


Process Selection Stage 3: Process-Mass Range Chart (Figure 13.24): We plot our mass range on here:

Powder methods are just on the edge. Do we eliminate them? Since they are so close, and we are still early in the design process, we better keep them in.

Process Selection Stage 4: Process-Section Thickness Chart (Figure 13.25):

Nothing eliminated here either.

Process Selection Stage 5: Process-Tolerance Chart (Figure 13.24):

Well, there goes powder processing—it’s way out of the needed range. Down to two…


Process Selection Stage 6: Process-Surface Roughness Chart (Figure 13.31):

Whoops! Now there’s nothing left in the primary processes! What do we do now?

Fortunately, all of the finishing processes can get us into the right surface roughness range, so we just need to check them against the materials compatibility chart to make sure we are alright there, and it looks as if grinding, lapping, and polishing are compatible with ceramics.

Because we have to introduce a secondary finishing process to meet the roughness spec, maybe we can reconsider powder methods. We can use the same finishing step to provide the powder methods with the needed tolerance, as well as getting the surface roughness correct. This leaves us with three potential approaches: powder methods, electro-machining, or conventional machining, each followed by a secondary finishing step.

Last of all is Figure 13.34, the economic batch size chart. A quick check of the batch size for the three primary shaping processes tells us what we have to do. If we are only making a 100 to a few 1000 parts, we can use one of the two machining processes, but for any number of parts larger than that we’ll want to go with powder processing.


PROCESS SELECTION USING CES

This is a case study out of the on-line literature that comes with CES. The design goal is to build a handle for opening and closing the windows in a house or building.

The materials selection analysis has already been done, and the cheapest material for the job turns out to be a zinc-based alloy. We want to determine the process. Putting together our design and materials attributes gives us a list of:

• Material Class: Non-ferrous Metal (Zn-based Alloy) • Process Class: Primary, discrete • Shape Class: 3D-solid • Mass: 0.1 [kg] • Minimum Section: 3 [mm] • Tolerance: 0.2 [mm] • Surface Roughness: 2 [um] • Batch Size: 1,000,000

Because we are looking to economically make a lot of these handles (on the order of 1,000,000), we want to try to get everything out of a primary process, without resorting to a secondary operation. The handles must have a good surface finish in order to operate well.

To start the process selection in CES, we need to start with a NEW PROJECT. First thing, we need to change the "Select From" to use "PROCESS UNIVERSE: Shaping Processes" rather than "MATERIALS". Now we will be using the process database to plot the selection charts. It would be a good idea to take a moment to look at a typical process data record. There is a lot of information here about a lot of different processes--very impressive database!

We want to build a selection chart, which happens in just the same way as with the materials selection charts, except that the axes are going to be different. For this example, there are five selection stages.


STAGE ONE: Mass Range (Size) versus Primary Process = TRUE

The process property of "PRIMARY" indicates whether or not the process can be used as a primary (or stand alone) processing route. It is of a Boolean-type, and when you initially plot this property, it will show two boxes on the X-axis, labeled "TRUE" and "FALSE". You can choose to display only one of these values (as I have done) by using the magnifying glass icon, and clicking on the value you want to display. In the selection plot, a box selection has been used to grab all the processes that are capable of producing a part in the size range of interest (around 0.1 kg).


STAGE TWO: Tolerance versus Shape Class = 3D-solid

The box selection chooses the processes capable of a tolerance of 0.2mm or better.

STAGE THREE: Roughness versus Process Class Discrete = TRUE

The Process Class of DISCRETE describes whether or not the process makes discrete (individual) parts, or many at a time.


STAGE FOUR: Minimum Section versus Materials Class = Non-Ferrous Metals

STAGE FIVE: Economic Batch Size versus Process Class Discrete = TRUE

Here we are looking for the cheapest way of producing the 1,000,000 parts we want. Only a few processes are economically viable at that batch size.


The final list of candidate processes that come through all the selection stages are:

• Automated machining • Die pressing of powder • Powder metallurgy forging • Powder injection molding • Pressure die casting

According to this analysis, the important attributes that really narrowed the selection were tolerance, roughness, and batch size. To determine more, we need to look more fully in detail at the costs of the candidate processes. The CES software has a complete set of ECONOMIC ATTRIBUTES for each process as well. This information can be used for more detailed cost analysis, a subject that we won't get into here.

End of File.

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