Volume 20 - Materials Selection and Design Part 5 ppsx

Table 1 Percentage of emissions generated during each stage of the vehicle life cycle for a steel unibody
and an average aluminum design
Emissions produced, % Emission type

Mining/refining

Production

Use Post-use

Steel unibody
CO
2

2.32 0.05 97.63

0
HC
0.10 0 99.90

0
NO
x

2.21 0.04 97.74

0
CO
0.05 0 99.95

0

Particulate
23.30 0.50 76.20

0
SO
x

97.78 1.97 0 0.25
Aluminum body
CO
2

8.65 0.09 91.26

0
HC
0.40 0 99.60

0
NO
x

8.27 0.08 91.64

0
CO
0.21 0 99.79

0
Particulate

84.10 0.05 15.85

0
SO
x

98.98 0.99 0 0.04

Results show that the aluminum designs perform better in the pollutant categories that dominate during the use phase
(CO
2
, hydrocarbons, NO
x
, and CO). However, for particulates and sulfur oxides, the steel design is more competitive.
Emissions associated with the aluminum design are greater for the mining and refining stage (sulfur oxides and
particulates). For the categories that arise predominantly during vehicle use (CO
2
, hydrocarbons, NO
x
, and CO), the
lightweighting achieved in the aluminum designs pays off.
Analysis of the inventory data does not lead to an unambiguous result. On a cost basis, even with a life cycle approach,
the steel unibody is most competitive. However, if the goal is to reduce greenhouse gases and smog precursors, one of the
aluminum designs may be preferred (Fig. 13).


Emission
Type
Change when
using aluminum, %

CO
2

-1.24
HC
-7.71
NO
x

-1.50
CO
-7.50
Particulate

+438
SO
x

+264


Fig. 13 Emissions throughout the entire product life cycle for steel and aluminum automobile bodies

Impact and Evaluation. Most efforts to develop the LCA technique have focused on constructing a complete set of
procedures for the collection and organization of the information that must be developed in the course of a LCA.
However, determining what to do with this information, once it is collected, has so far been only imperfectly addressed.
Although the reason for employing LCA is to develop activities that reduce environmental impact, establishing how this
mass of data informs specific problems has proven to be extremely difficult for all but the simplest of situations.
In particular, the most problematic aspect of LCA has been the final, "improvement analysis" component. Improvement

analysis implicitly assumes that it is possible to choose (and implement) a "best" action from the set of possible actions,
thus yielding improvement. Aside from simple cases where it is possible to find an action that leads to reductions in all
impacts on the environment, this choice depends upon the relative importance placed upon each of the possible
consequences that are indicated by the analysis. This relative rating of importance is a reflection of the strategic objectives
of the user objectives that are not necessarily shared by all interested stakeholders.
Example: Method for Estimating the "Environmental Load" of Materials.
To illustrate the potential and limitations of LCA method, the Swedish Environmental Priority Strategies (EPS), under
development by the Swedish Environmental Research Institute, Chalmers Institute of Technology, and the Federation of
Swedish Industries, are discussed (Ref 29). EPS translates emissions into a single monetary metric that allows the direct
costs of manufacturing, use, and recycling/disposal to be compared with the social costs generated by emissions.
EPS is specifically constructed to associate an "environmental load" with individual activities or processes on a per unit
of material consumed or processed basis. For example, EPS might associate X units of environmental load (ELUs) per
kilogram of steel produced and Y units of environmental load per kilogram of steel components stamped. Thus, the
environmental load of stamping a 5 kg automobile component, requiring 5.3 kg of steel, would be (5.3 X + 5 Y). This
load could then be compared to the load associated with a different process stream or with using a different material. The
interesting questions are: how are these environmental loads established and what do they mean.
Based on the environmental objectives of the Swedish Parliament, EPS relates all of the physical consequences of the
processes under consideration to their impact on five environmental "safeguard subjects": biodiversity, production (i.e.,
reproduction of biological organisms), human health, resources, and aesthetic values. Because the impacts on any one
safeguard subject by a process may take several forms, EPS allows for individual consideration of each of these
consequences, called "unit effects." Two criteria are applied when establishing which impacts will become unit effects:
the importance of the impact on the sustainability of the environment and the existence of an ability to establish a
quantitative value for that impact within traditional economic grounds. Examples of unit effects for human health include:
mortality due to increased frequency of cancer; mortality due to increased maximum temperatures; food production
decreases (and, hence, increased incidence of starvation) due to global warming.
Once the individual unit effects are established, their value must be determined. This valuation is accomplished by
expressing each unit effect in terms of its economic worth and associated risk factors. Formally, the value of each unit
effect is set equal to the product of five factors, F1 through F5. F1 is a monetary measure of the total cost of avoiding the
unit effect. The extent of affected area (F2), the frequency of unit effect in the affected area (F3), and the duration of the
unit effect (F4), represent "risk factors" similar to those employed in toxicological risk evaluations. F5 is a normalizing

factor, constructed so that the product F1 × F5 is equal to the cost of avoiding the unit effect that would arise through the
use or production of one kilogram of material. The product of all five factors yields the contribution of a particular unit
effect to environmental load. Summing the value of each unit effect yields the "environmental load index" (ELI) in units
of environmental load per unit of material consumed or processed (ELU/kg). Since these unit effects were specified
according to their relevance to the five safeguard subjects, the ELI represents the total environmental load (or impact) of
the process.
While this formulation of valuation raises important questions of scientific feasibility (insofar as the ability to characterize
fully the unit effects of every process or activity that might be developed is debatable), the crucial valuation questions
arise from two other aspects of this scheme: (a) the nature of the economic measures used in calculating the cost of
avoiding a unit effect, and (b) the assumption that the value of the total environmental impact of an action (the
"environmental load") is equal to the sum of each individual environmental load weighted by the size of each unit effect.
The first of these valuation questions relates to the distinction between "cost" and "worth." While the theory of
competitive markets argues that prices are the worth of an object, the theory rests upon assumptions that are difficult to
support in the case of environment. In the first place, perfect markets assume the availability of perfect information to all
participants, which clearly is not the case, or there would be no need to develop life cycle analysis in the first place.
Furthermore, the theory of markets routinely discusses "consumer surplus," which can roughly be defined as the
difference in the prevailing market price and the higher price that some consumers would have been willing to pay (recall
that demand curves slope downward). Finally, there is the critical question how to establish these costs/prices when
markets do not exist. While litigators are prepared to place a value on wrongful death or pain and suffering during a civil
suit, there are no markets for pain, clean air, or future well-being. Generally, most environmental attributes are "external"
to markets; many of the classical examples of market externalities are based on environmental issues.
Where markets exist, EPS uses market prices to establish the costs of avoidance. Where market prices do not exist, EPS
relies upon two alternatives. If there are governmental funds allocated to resolve specific problems (e.g., funds to protect
a particular species), these funds are normalized and extrapolated to obtain a cost figure (e.g., the value of maintaining
biodiversity is established by normalizing the annual budget of the Swedish government for species protection). If
relevant financial allocations do not exist, then the method of contingent valuation is employed. This method (or set of
methods) is based on direct inquiries of representative populations to determine their willingness to pay to avoid specific
effects. As might be expected, this last approach to establishing the appropriate costs of avoidance is somewhat
controversial, since it is hard (both conceptually and practically) to design questions that demonstrably extract the
"correct" measure of value.

The second of these valuation questions is a reflection of the fact that the mathematical structure of the value function is a
consequence of critical assumptions about the nature of the subject's preferences. The valuation employed in the EPS
system is an example of a linear, additive preference structure. Each unit effect is reduced to a monetary value,
normalized for risk/exposure and for material quantity. Thereafter, the net impact of each increment in unit effect is the
same, regardless of how large the effect is, and regardless of the size of any other unit effect. While such value functions
are simple to represent and employ (linear combinations of linear functions), it is difficult to argue that they are an
accurate, general purpose formulation of value functions for environmental impact. Although the appropriate form of the
value function may be linear, EPS does not explicitly make this assumption. Rather, the linearity of EPS valuation is
based on the assumption that, because monetization reduces all effects to a common metric, the resulting metrics should
be additive. In fact, most individuals do not even exhibit linear preferences for money, much less for more subjective
attributes. (For example, most individuals would consider paying $0.50 to play a game offering a 50:50 chance of
winning $1.00, while rejecting out of hand paying $5,000 to get a 50:50 chance of winning $10,000). In practice,
preferences usually reflect nonlinearities in both individual effects and in substitution between effects.
The first two issues (money as a measure of value and linear additive preferences) are not necessarily crippling
assumptions when considering the development of value functions for the environment. While difficult, it may be
possible for someone to establish the dollar value that exactly offsets a particular unit effect. Similarly, linear additive
preferences may be able to model the behavior of an individual over a restricted range. However, it is impossible to state
that the same dollar value, or the same linearization of preferences, will be agreeable to every individual in the affected
population in the case of environmental considerations. And, if individuals cannot agree on the value or the structure of
their preferences, then no single value function can be constructed to represent their wants.
A recent methodology developed at MIT (Ref 30) is similar to EPS, but provides a set of broad ranges of value, in dollars
per kilogram of each emission, based on estimates of willingness to pay to avoid the environmental impacts of each
pollutant. These ranges reflect scientific uncertainty, variation in context or location, and large variations of possible
values for parameters that have a subjective component. The dollars per kilogram ranges can be applied to the life cycle
inventories of products to compare material or process alternatives.
The methodology was used to analyze the life cycle costs of three material alternatives for automotive fenders produced
at low volumes (60,000/year). The three materials under consideration were steel, aluminum, and Noryl (Noryl is a
trademark of General Electric Company for a polyphenylene oxide blend thermoplastic). The results of the base case,
employing "best guess" for scientific data and economic valuation, are shown in Fig. 14.

Fig. 14 Estimated life cycle costs by life phase for competing materials for an automobile fender application

In this scenario, the private costs of manufacturing and use (with German gasoline prices) are significantly greater than
the social costs from emissions to the environment. Figure 15 shows the implications of allowing the scientific and
economic assumptions to take on the highest and lowest values possible, based on a review of published estimates.

Fig. 15 Total costs relative to steel of competing materials for an automobile fender application

The externalities are the environmental costs of emissions from the extraction to the manufacturing and use stages. The
private costs include manufacturing, use, and disposal. The specific assumptions employed in this case study lead to a
lower total cost for Noryl, although no clear winner arises under this set of assumptions. Even when no clear choice
emerges, the environmental cost drivers can be identified. For instance, the fender case study shows that only 4 or 5
emissions categories account for more than 95% of the total environmental cost for each material.
The EPS system is a commendable attempt at simplifying the enormous detail of inventory data to a representative
environmental load. The developers of EPS have pointed out that this system is based on their subjective value
judgments, which are not necessarily supportable in all situations worldwide. The ultimate goals for improvement
analysis based on life cycle inventories are laudable, but can only be realized by some kind of consensus on the values for
avoiding environmental degradation. This suggests that achieving the ultimate stage of LCA will require the development
of a basis for devising (and revising) this consensus. In the absence of a common strategic objective, it will be impossible
to use LCA to designate ways to achieve environmental improvement beyond straightforward pollution
prevention/precautionary principle strategies, because a strategic consensus is required to trade off competing
environmental, economic, and engineering goals.
Uses of LCA. In summary, life cycle analysis is a technique that has already shown great promise for improving our
understanding of the wider implications and relationships that must be taken into consideration when incorporating
environmental concerns into technical decision making. As these concepts diffuse into industrial and technical decision
making, LCA will enable industry and government to find ways to be both more efficient and less harmful to the
environment.
However, practitioners and proponents must guard against using LCA to determine "best" modes of action when the
consequences of the alternatives expose conflicting objectives and values within the group of decision makers. In these
cases, no amount of analysis will directly resolve the conflict. Rather, the role of LCA should be to articulate clearly the

consequences of each alternative and to provide a framework for the necessary negotiations.
Additional information about LCA is provided in the articles "Life-Cycle Engineering and Design" and "Environmental
Aspects of Design" in this Volume.

References cited in this section
28.

F.R. Field, J.A. Isaacs, and J.P. Clark, Life Cycle Analysis and Its Role in Product and Process
Development, J. Environmentally Conscious Manufacturing, 1996
29.

B. Steen and S O. Ryding, The EPS Enviro-Accoun
ting Method: An Application of Environmental
Accounting Principles for Evaluation and Valuation of Environmental Impact in Production Design,

Swedish Environmental Institute, Dec 1992
30.

J. Clark, S. Newell, and F. Field, Life Cycle Analysis Methodology
Incorporating Private and Social Costs,
in Life Cycle Engineering of Passenger Cars, VDI Verlag GmbH, 1996, p 1-19
Techno-Economic Issues in Materials Selection
Joel P. Clark, Richard Roth, and Frank R. Field III, Massachusetts Institute of Technology

Conclusions
There is an ever growing need for consistent methodologies for analyzing the use of new materials, designs, and
technologies in many applications. Advances in materials science and in the development of new processing technologies
have presented product designers with a wide array of choices previously unavailable to them. This has made the
selection of a material for a given application a far more challenging task.
The difficulty confronting designers is compounded by the increasing number of objectives that product designers must

satisfy. In the past, the designer simply had to meet a set of performance criteria, at or below a specified cost, from a very
limited set of design alternatives. The current situation is much more complicated. In addition to the increasing number of
design choices, there are potentially conflicting performance, cost, and environmental characteristics.
Central to all product evaluations is a consideration of the economic consequences of design and materials choice. Cost is
one of the key strategic elements of product competitiveness, and an early appreciation of the relationship between major
design choices and the cost of the resulting product is a vital element of effective product development. However, cost
remains an elusive element of design evaluation. The tools are largely outside the control of the design engineers. The
results suggest only a limited number of ways in which cost can be changed, and the costs tend to focus only upon the
cost consequences to the firm itself. Unfortunately, designers require a far more comprehensive appreciation of cost,
particularly as the number and complexity of design objectives have increased.
The combined technical cost modeling and life cycle analysis methodology offers the product designer a much needed
systematic approach for analyzing the trade-offs associated with various choices of materials and technologies. Technical
cost modeling enables designers to estimate the manufacturing costs of alternative designs. Its main advantages lie in the
fact that it is predictive and allows one to investigate the sensitivity of the outcome to changes in the input parameters.
Because it is predictive, it can be used with new processes for which there is no past experience upon which to base cost
estimates. The ability to do sensitivity analysis enables the product designer to look at the effects of unknown or uncertain
model parameters, capturing the scope and consequences of important processing and market assumptions.
The advantages of the life cycle approach are also two-fold. First, life cycle analysis enables one to look at cost over the
entire life of the product, not just the manufacturing phase. For many products, cost can be quite substantial during other
parts of the product life, especially the use phase. Second, life cycle analysis is useful for looking at issues relevant to
environmental concerns, such as tracking selected emissions throughout the product life. While valuation techniques are
rather imperfect, they provide a means for translating these diverse parameters into a common metric, as well as a context
for analyzing the implications of distinctions in the strategic objectives of all parties affected by the product and design
choice.
The integrated approach provided by technical cost modeling and life cycle analysis is particularly important in industries
such as the automotive sector, where both consumer and regulatory pressures are causing the producers to continuously
innovate. The combined life cycle cost and emissions methodology offers a systematic and predictive method for
addressing some of the fundamental considerations involved in selecting materials and designs for specific products.
Techno-Economic Issues in Materials Selection
Joel P. Clark, Richard Roth, and Frank R. Field III, Massachusetts Institute of Technology

References
1. R. Roth, F. Field, and J. Clark, Materials Selection and Multi-Attribute Utility Analysis, J. Computer-
Aided Mater. Des., Vol 1 (No. 3), ESCOM Science Publishers, Oct 1994
2. J.V. Busch and F.R. Field III, Technical Cost Modeling, Blow Molding Handbook,
Donald Rosato and
Dominick Rosato, Ed., Hanser Publishers, 1988, Ch 24
3. M.F. Ashby, Materials Selection in Mechanical Design, Pergamon Press, 1992
4. R. Cooper and P. Kaplan, Measure Costs Right: Make the Right Decisions, Harvard Business Review,

Sept-Oct 1988
5.
"Implementing ABC in the Automobile Industry: Learning from Information Technology Experiences,"
MIT International Motor Vehicle Program working paper
6. J.F. Elliot, J.J. T
ribendis, and J.P. Clark, "Mathematical Modeling of Raw Material and Energy Needs of
the Iron and Steel Industry in the USA.," Final Report to the U.S. Bureau of Mines, NTIS PB 295-
207
(AS), 1978
7. F.E. Katrak, T.B. King, and J.P. Clark, Analysis of the
Supply of and Demand for Stainless Steel in the
United States, Mater. Soc., Vol 4, 1980
8. P.T. Foley and J.P. Clark, U.S. Copper Supply An Engineering/Economic Analysis of Cost-
Supply
Relationships, Resour. Policy, Vol 7 (No. 3), 1981
9. J.P. Clark and
G.B. Kenney, The Dynamics of International Competition in the Automotive Industry,
Mater. Soc., Vol 5 (No. 2), 1981
10. J.P. Clark and M.C. Flemings, Advanced Materials and the Economy, Sci. American, Oct 1986
11. Lee Hong Ng and Frank R. Field III, Mat

erials for Printed Circuit Boards: Past Usage and Future
Prospects, Mater. Soc., Vol 13 (No. 3), 1989
12.
S. Arnold, N. Hendrichs, F.R. Field III, and J.P. Clark, Competition between Polymeric Materials and
Steel in Car Body Applications, Mater. Soc., Vol 13 (No. 3), 1989
13.
V. Nallicheri, J.P. Clark, and F.R. Field, A Technical & Economic Analysis of Alternative Manufacturing
Processes for the Connecting Rod, Proceedings, International Conference on Powder Metallurgy

(Pittsburgh, PA), Metal Powder Industries Federation, May 1990
14. C. Mangin, J. Neely, and J. Clark, The Potential for Advanced Ceramics in Automotive Engines, J. Met.,

Vol 45 (No. 6), 1993
15. F.R. Field and J.P. Clark, Automotive Body Materials, Encyclopedia of Advanced Materials, R.W.
Cahn et
al., Ed., Pergamon Press, 1994
16. H. Han and J. Clark, Life Cycle Costing of the Body-in-White: Steel vs. Aluminum, J. Met., May 1995
17. G. Potsch and W. Michaeli, Injection Molding: An Introduction, Hanser Publishers, 1995
18. P. Kennedy, Flow Analysis Reference Manual, Moldflow Pty. Ltd., Australia, 1993
19. J.V. Busch, "Technical Cost Modeling of Plastics Fabrication Processes," MIT Ph.D. thesis, June 1987
20. G.H. Geiger and D.R. Poirier, Transport Phenomena in Metallurgy, Addison-Wesley
Publishing
Company, 1973
21.
D. Politis, "An Economic and Environmental Evaluation of Aluminum Designs for Automotive
Structures," MIT S.M. thesis, May 1995
22. M.A. DeLuchi, "Emissions of Greenhouse Gases from the Use of Transportation Fuels and Electri
city,"
Vol 2, U.S. Department of Energy, 1993
23. OECD, Automobile Fuel Consumption in Actual Traffic Conditions, Organization for Economic Co-

Operation and Development, Dec 1981
24. SRI International, Potential for Improved Fuel Economy in Passenger Car
s and Light Trucks, Prepared for
the Motor Vehicle Manufacturers Association, Menlo Park, CA, 1991
25.
F.R. Field and J.P. Clark, Recycling Dilemma for Advanced Materials Use: Automotive Materials
Substitution, Mater. Soc., Vol 15 (No. 2), 1991
26. A.C.
Chen, "A Product Lifecycle Framework for Environmental Management and Policy Analysis: Case
Study of Automobile Recycling," MIT Ph.D. thesis, June 1995
27.
A.C. Chen, H.N. Han, J.P. Clark, and F.R. Field, A Strategic Framework for Analyzing the Cost
Effectiveness of Automobile Recycling, Proceedings, International Body Engineering Conference

(Detroit), M.N. Uddin, Ed., Society of Automotive Engineers, 1993, p 13-19
28. F.R. Field, J.A. Isaacs, and J.P. Clark, Life Cycle Analysis and Its Role in Product an
d Process
Development, J. Environmentally Conscious Manufacturing, 1996
29. B. Steen and S O. Ryding, The EPS Enviro-
Accounting Method: An Application of Environmental
Accounting Principles for Evaluation and Valuation of Environmental Impact in Production Design,

Swedish Environmental Institute, Dec 1992
30.
J. Clark, S. Newell, and F. Field, Life Cycle Analysis Methodology Incorporating Private and Social
Costs, in Life Cycle Engineering of Passenger Cars, VDI Verlag GmbH, 1996, p 1-19


Material Property Charts
M.F. Ashby, Engineering Design Centre, Cambridge University

Introduction
MATERIAL PROPERTIES limit performance. However, it is seldom that the performance of a component depends on
just one property. Almost always it is a combination (or several combinations) of properties that matter: one thinks, for
instance, of the strength-to-weight ratio,
f
/ , or the stiffness-to-weight ratio, E/ , which are important in design of
lightweight products. This suggests the idea of plotting one property against another, mapping out the fields in property-
space occupied by each material class, and the subfields occupied by individual materials.
The resulting charts are helpful in several ways. They condense a large body of information into a compact but accessible
form, they reveal correlations between material properties that aid in checking and estimating data, and they lend
themselves to a performance-optimizing technique (developed in the article "Performance Indices" following in this
Section of the Handbook), which becomes the basis of the selection procedure.
The idea of a materials-selection chart is developed below. Further information about the charts and their uses can be
found in Ref 1, 2, 3 and in the article "Performance Indices."
Acknowledgements
The charts reproduced as Fig. 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13 first appeared in Ref 1, where more details about
their use can be found.
The author wishes to thank Dr. David Cebon for helpful discussions. The support of the Royal Society, the EPSRC
through the Engineering Design Centre at Cambridge, and the Advance Research Project Agency through the University
Research Initiative under Office of Naval Research Contract No. N-00014092-J-1808 are gratefully acknowledged.

References
1.

M.F. Ashby, Material Selection in Mechanical Design, Pergamon Press, 1992
2.

M.F. Ashby and D. Cebon, Case Studies in Material Selection, Granta Design, 1996

3.

CMS Software and Handbooks, Granta Design, 1995
Material Property Charts
M.F. Ashby, Engineering Design Centre, Cambridge University

Displaying Material Properties
Each property of an engineering material has a characteristic range of values. The values are conveniently displayed on
materials selection charts, illustrated by Fig. 1. One property (the modulus, E, in this case) is plotted against another (the
density, ) on logarithmic scales. The range of the axes is chosen to include all materials, from the lightest foams to the
heaviest metals. It is then found that data for a given class of materials (polymers for example) cluster together on the
chart; the subrange associated with one material class is, in all cases, much smaller than the full range of that property.
Data for one class can be enclosed in a property-envelope, as shown in Fig. 1. The envelope encloses all members of the
class.

Fig. 1 The idea of a Materials Property Chart: Young's modulus, E, is plotted against the density,
, on log
scales. Each class of material occupies a characteristic part of the chart. The log scales allow the longitudinal
elastic wave velocity v = (E/ )
1/2
to be plotted as a set of parallel contours.
All this is simple enough just a helpful way of plotting data. However, by choosing the axes and scales appropriately,
more can be added. The speed of sound in a solid depends on the modulus, E, and the density, ; the longitudinal wave
speed v, for instance, is


or (taking logs)
log E = log + 2 log v

For a fixed value of v, this equation plots as a straight line of slope 1 on Fig. 1. This allows the addition of contours of
constant wave velocity to the chart: They are the family of parallel diagonal lines linking materials in which longitudinal
waves travel with the same speed. All the charts allow additional fundamental relationships of this sort to be displayed.
A number of mechanical and thermal properties characterize a material and determine its use in engineering design; they
include density, modulus, strength, toughness, damping coefficient, thermal conductivity, diffusivity, and expansion. The
charts display data for these properties for the nine classes of materials listed in Table 1. Within each class, data are
plotted for a representative set of materials, chosen both to span the full range of behavior for the class and to include the
most common and most widely used members of it. In this way the envelope for a class encloses data not only for the
materials listed in Table 1, but for virtually all other members of the class as well.



Table 1 Engineered material classes included in the material property charts (Fig. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
,
11, 12, 13)

Engineering alloys

Aluminum (Al) alloys

Copper (Cu) alloys

Lead (Pb) alloys

Magnesium (Mg) alloys

Molybdenum (Mo) alloys

Nickel (Ni) alloys

Steels (MS, mild steels and SS, stainless steels)

Cast irons

Tin (Sn) alloys

Titanium (Ti) alloys

Tungsten (W) alloys

Zinc (Zn) alloys

Beryllium (Be)

Boron (B)

Germanium (Ge)

Silicon (Si)

Engineering plastics (thermoplastics and thermosets)

Epoxies (EP)

Melamines (MEL)

Polycarbonate (PC)

Polyesters (PEST)

High-density polyethylene (HDPE)

Low-density polyethylene (LDPE)

Polyformaldehyde (PF)

Polymethyl methacrylate (PMMA)

Polypropylene (PP)

Polytetrafluoroethylene (PTFE)

Polyvinyl chloride (PVC)

Polyimides

Elastomers

Natural rubber

Hard butyl rubber

Polyurethanes (PU)

Silicone rubber

Soft butyl rubber

Polymer foams

Cork

Polyester

Polystyrene (PS)

Polyurethane (PU)

Engineering composites (polymer-matrix composites)
(a)


Carbon-fiber-reinforced polymer (CFRP)

Glass-fiber-reinforced polymer (GFRP)

Kevlar-fiber-reinforced polymer (KFRP)

Engineering ceramics

Alumina (Al
2
O
3
)

Diamond

Sialons

Silicon carbide (SiC)

Silicon nitride (Si
3
N
4
)

Zirconia (ZrO
2
)

Beryllia (BeO)

Mullite

Magnesia (MgO)

Porous ceramics (traditional ceramics)

Brick

Cement

Common rocks

Concrete

Porcelain

Pottery

Glasses

Borosilicate glass

Soda glass

Silica (SiO
2
)

Cermets

Tungsten carbide/cobalt (WC-Co)

Woods
(b)


Ash

Balsa

Fir

Oak

Pine

Wood products (laminates)



(a)
A distinction is drawn in the charts between the properties of uniply and laminated
(laminates) composites.
(b)
Separate property envelopes describe properties of wood parallel, , and
perpendicular, , to the grain.

The charts show a range of values for each property of each material. Sometimes the range is narrow; the modulus of
copper, for instance, varies by only a few percent about its mean value, influenced by purity, texture, and the like.
Sometimes the range is wide; the strength of alumina-ceramic can vary by a factor of 100 or more, influenced by porosity,
grain size, and so on. Heat treatment and mechanical working have a profound effect on yield strength, damping, and the
toughness of metals. Crystallinity and degree of cross-linking greatly influence the modulus of polymers, and so on.
These structure-sensitive properties appear as elongated bubbles within the envelopes on the charts. A bubble encloses a
typical range for the value of the property for a single material (see Fig. 2). Envelopes (heavier lines) enclose the bubbles
for a class.

Fig. 2 Young's modulus, E, plotted against density, , for various engineered materials. The heavy enve
lopes
enclose data for a given class of material. The diagonal contours show the longitudinal wave velocity. The guide
lines of constant E/ , E
1/2
/ , and E
1/3
/ allow selection of materials for minimum weight, deflection-
limited,
design.

The data plotted on the charts have been assembled from a variety of sources, the most accessible of which are listed as
Ref 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,
37, 38, 39, and 40.

References cited in this section
4. American Institute of Physics Handbook, 3rd ed., McGraw-Hill, 1972
5. Metals Handbook, 9th ed., and ASM Handbook, ASM International
6. Handbook of Chemistry and Physics, 52nd ed., The Chemical Rubber Co., Cleveland, OH, 1971
7. Landolt-Bornstein Tables, Springer, 1966
8. Materials Selector, Materials Engineering, Penton Publishing, 1996
9. C.J. Smithells, Metals Reference Book, 7th ed., Butterworths, 1992
10.

C.A. Harper, Ed., Handbook of Plastics and Elastomers, McGraw-Hill, 1975
11.

A.K. Bhowmick and H.L. Stephens, Handbook of Elastomers, Marcel Dekker, 1986
12.

S.P. Clarke, Jr., Ed., Handbook of Physical Constants, Memoir 97,
The Geological Society of America,
New York, 1966
13.

N.A. Waterman and M.F. Ashby, Ed., The Elsevier Materials Selector, Elsevier and CRC Press, 1991
14.

R. Morrell, Handbook of Properties of Technical and Engineering Ceramics, Parts I and II
, National
Physical Laboratory, London, U.K., 1985 and 1987

15.

J.M. Dinwoodie, Timber, Its Nature and Behaviour, Van Nostrand-Reinhold, 1981
16.

L.J. Gibson and M.F. Ashby, Cellular Solids, Structure and Properties,
2nd ed., Cambridge University
Press, 1996
17.

M.L. Bauccio, Ed., ASM Engineered Materials Reference Book, 2nd ed., ASM International, 1994
18.

Materials Selector and Design Guide, Design Engineering, Morgan-Grampian Ltd, London, 1974
19.

Handbook of Industrial Materials (1992), 2nd ed., Elsevier, 1992
20.

G.S. Grady and H.R. Clauser, Ed., Materials Handbook, 12th ed., McGraw-Hill, 1986
21.

A. Goldsmith, T.E. Waterman, and J.J.Hirschhorn, Ed.,
Handbook of Thermophysical Properties of Solid
Materials, Macmillan, 1961
22.

Colin Robb, Ed., Metals Databook, The Institute of Metals, 1990
23.

J.E. Bringas, Ed., The Metals Black Book, Vol 1, Steels, Casti Publishing, 1992
24.

J.E. Bringas, Ed., The Metals Red Book, Vol 2, Nonferrous Metals, Casti Publishing, 1993
25.

H. Saechtling, Ed., International Plastics Handbook, Macmillan Publishing (English edition), 1983
26.

R.B. Seymour, Polymers for Engineering Applications, ASM International, 1987
27.

International Plastics Selector, Plastics, 9th ed., Int. Plastics Selector, San Diego, CA, 1987
28.

H. Domininghaus, Ed., Die Kunststoffe and Ihre Eigenschaften, VDI Verlag, Dusseldorf, Germany, 1992
29.

D.W. van Krevelen, Ed., Properties of Polymers, 3rd ed., Elsevier, 1990
30.

M.M. Schwartz, Ed., Handbook of Structural Ceramics, McGraw-Hill, 1992
31.

R.J. Brook, Ed., Concise Encyclopedia of Advanced Ceramic Materials, Pergamon Press, 1991
32.

N.P. Cheremisinoff, Ed., Handbook of Ceramics and Composites, Vol 3, Marcel Dekker, 1990
33.

D.W. Richerson, Modern Ceramic Engineering, 2nd ed., Marcel Dekker, 1992
34.

R. Morrell, Handbook of Properties of Technical and Engineering Ceramics,
Parts 1 and 2, National
Physical Laboratory, Teddington, U.K., 1985
35.

W.E.C. Creyke, I.E.J. Sainsbury, and R. Morrell, Design with Non Ductile Materials, Applied
Science,
London, 1982
36.

N.P. Bansal and R.H. Doremus, Ed., Handbook of Glass Properties, Academic Press, 1966
37.

D.S. Oliver, Engineering Design Guide 05: The Use of Glass in Engineering,
Oxford University Press,
1975
38.

S. Musikant, What Every Engineer Should Know about Ceramics, Marcel Dekker, 1991
39.

J.W. Weeton, D.M. Peters, and K.L. Thomas, Ed., Engineers Guide to Composite Materials,
ASM
International, 1987
40.

M.M. Schwartz, Ed., Composite Materials Handbook, 2nd ed., McGraw-Hill, 1992

Material Property Charts
M.F. Ashby, Engineering Design Centre, Cambridge University

Types of Material Property Charts
The Modulus-Density Chart (Fig. 2). Modulus and density are familiar properties. Steel is stiff, rubber is
compliant: these are effects of modulus. Lead is heavy; cork is buoyant: these are effects of density. Figure 2 shows the
full range of Young's modulus, E, and density, , for engineering materials. Data for members of a particular class of
material cluster together and can be enclosed by an envelope (heavy line). The same class-envelopes appear on all the
diagrams, corresponding to the main headings in Table 1.
The density of a solid depends on three factors: the atomic weight of its atoms or ions, their size, and the way they are
packed. Metals are dense because they are made of heavy atoms, packed densely; polymers have low densities because
they are largely made of carbon (atomic weight: 12) and hydrogen in a linear, 2-, or 3-dimensional network. Ceramics, for
the most part, have lower densities than metals because they contain light oxygen, nitrogen, or carbon atoms. Even the
lightest atoms, packed in the most open way, give solids with a density of around 1 Mg/m
3
(60 lb/ft
3
). Materials with
lower densities than this are foams materials made up of cells containing a large fraction of pore space.
The moduli of most materials depend on two factors: bond stiffness, and the density of bonds per unit area. An
interatomic bond is like a spring: it has a spring constant, S (units: N/m). Young's modulus, E, is roughly


(Eq 1)
where r
o
is the "atom size" ( is the mean atomic or ionic volume). The wide range of moduli is largely caused by the
range of values of S. The covalent bond is stiff (S = 20 to 200 N/m, or 0.1 to 1 lb/in.); the metallic and the ionic a little

less so (S = 15 to 100 N/m, or 0.075 to 0.5 lb/in.). Diamond has a very high modulus because the carbon atom is small
(giving a high bond density), and its atoms are linked by very strong springs (S = 200 N/m, or 1 lb/in.). Metals have high
moduli because close packing gives a high bond density and the bonds are strong, though not as strong as those of
diamond. Polymers contain both strong diamondlike covalent bonds and weak hydrogen or Van der Waals bonds (S = 0.5
to 2 N/m, or 0.0025 to 0.01 lb/in.); it is the weak bonds that stretch when the polymer is deformed, giving low moduli.
But even large atoms (r
o
= 3 × 10
-10
m, or 1.2 × 10
-8
in.) bonded with weak bonds (S = 0.5 N/m, 0.0025 lb/in.) have a
modulus of roughly


(Eq 2)
This is the lower limit for true solids. The chart shows that many materials have moduli that are lower than this, but these
are not true solids; they are either elastomers or foams. Elastomers have a low E because the weak secondary bonds have
melted (their glass transition temperature, T
g
, is below room temperature), leaving only the very weak "entropic" restoring
force associated with tangled, long-chain molecules. Foams have low moduli because the cell walls bend (allowing large
displacements) when the material is loaded.
The chart shows that the modulus of engineering materials spans five decades, from 0.01 GPa (0.5 ksi) (low-density
foams) to 1000 GPa (1.5 × 10
5
ksi) (diamond); the density spans a factor of 2000, from less than 0.1 to 20 Mg/m
3
(6 to
1200 lb/ft

3
). At the level of precision of interest here (that required to reveal the relationship between the properties of
materials classes) the shear modulus, G, by 3E/8 and the bulk modulus, K, by E, for all materials except for elastomers
(for which G = E/3 and K E), may be approximated so the G- chart and the K- chart both look almost identical to
Fig. 2.
The log scales allow more information to be displayed. The velocity of elastic waves in a material, and the natural
vibration frequencies of a component made of it, are proportional to (E/ )
1/2
; the quantity (E/ )
1/2
itself is the velocity of
longitudinal waves in a thin rod of the material. Contours of constant (E/ )
1/2
are plotted on the chart, labeled with the
longitudinal wave speed, which varies from less than 50 m/s (160 ft/s) (soft elastomers) to a little more than 10
4
m/s
(33,000 ft/s) (fine ceramics). Note that aluminum and glass, because of their low densities, transmit waves quickly despite
their low moduli. One might have expected the sound velocity in foams to be low because of the low modulus; however,
the low density almost compensates. The sound velocity in wood is low across the grain, but along the grain, it is high
roughly the same as steel a fact made use of in the design of musical instruments.
The modulus-density chart helps in the common problem of material selection for applications in which weight must be
minimized. Guide lines corresponding to three common geometries of loading are drawn on the diagram; they correspond
to the three indices for stiffness-limited minimum-weight design listed in Table 5(a) in the article "Performance Indices"
in this Volume, in which their use in selecting materials is explained.
The Strength-Density Chart (Fig. 3). The modulus of a solid is a well-defined quantity with a sharp value. The
strength is not. The word "strength" needs definition. For metals and polymers, it is the yield strength, but because the
range of materials includes those that have been worked, the range extends from initial yield to ultimate strength; for most
practical purposes it is the same in tension and compression. For brittle ceramics, it is the crushing strength in
compression, not that in tension which is about 15 times smaller; the envelopes for brittle materials are shown as broken

lines as a reminder of this. For elastomers, strength means the tear strength. For composites, it is the tensile failure
strength (the compressive strength can be less, because of fiber buckling).

Fig. 3 Strength,
f
, plotted against density,
, for various engineered materials. Strength is yield strength for
metals and polymers, compressive strength for ceramics, tear strength f
or elastomers, and tensile strength for
composites. The guide lines of constant
f
/ , / , and / are used in minimum weight, yield-
limited,
design.
Figure 3 shows these strengths, using the symbol
f
despite the different failure mechanisms involved, plotted against
density, . The considerable vertical extension of the strength bubble for an individual material reflects its wide range,
caused by degree of alloying, work hardening, grain size, porosity, and so forth. As before, members of a class cluster
together and can be enclosed in an envelope (heavy line). Each envelope occupies a characteristic area of the chart.
The range of strengths for engineering materials, like that of their moduli, spans about five decades: from less than 0.1
MPa (15 psi) (foams, used in packaging and energy-absorbing systems) to 104 MPa (1500 ksi) (the strength of diamond,
exploited in the diamond-anvil press). The single most important concept in understanding this wide range is that of the
lattice resistance or Peierls stress, which is the intrinsic resistance of the structure to plastic shear. Plastic shear in a crystal
involves the motion of dislocations. Metals are soft because the nonlocalized metallic bond does little to prevent
dislocation motion, whereas ceramics are hard because their more localized covalent and ionic bonds, which must be
broken and reformed when the structure is sheared, lock the dislocations in place. In noncrystalline solids, on the other
hand, the energy is associated with the unit step of the flow process: the relative slippage of two segments of a polymer
chain, or the shear of a small molecular cluster in a glass network. Their strength has the same origin as that underlying
the lattice resistance: if the unit step involves breaking strong bonds (as in an inorganic glass), the materials will be

strong; if it only involves the rupture of weak bonds (the Van der Waals bonds in polymers for example), it will be weak.
Materials that fail by fracture do so because the lattice resistance or its amorphous equivalent is so large that fracture
happens first.
When the lattice resistance is low, the material can be strengthened by introducing obstacles to slip: in metals, by adding
alloying elements, particles, grain boundaries, and even other dislocations ("work hardening"); and in polymers by cross-
linking or by orienting the chains so that strong covalent as well as weak Van der Waals bonds are broken. When, on the
other hand, the lattice resistance is high, further hardening is superfluous the problem becomes that of suppressing
fracture (see the Section "The Fracture Toughness-Density Chart" in this article).
An important use of the strength-density chart is in materials selection in lightweight plastic design. The guide lines
performance indices (Table 5b in the article "Performance Indices," which follows in this Section of the Handbook) for
materials selection in the minimum-weight design of ties, columns, beams, and plates, and for yield-limited design of
moving components in which inertial forces are important.
Aspects of fatigue the endurance limit, for example can be displayed in a similar way. Charts relating to fatigue can be
found in Ref 41.
The Fracture Toughness-Density Chart (Fig. 4). Increasing the plastic strength of a material is useful only as
long as it remains plastic and does not fail by fast fracture. The resistance to the propagation of a crack is measured by the
fracture toughness, K
Ic
. It is plotted against density in Fig. 4. The range is large: from 0.01 to over 100 MPa (0.01 to
100 ksi ). At the lower end of this range are brittle materials that, when loaded, remain elastic until they fracture.
For these, linear elastic fracture mechanics works well, and the fracture toughness itself is a well-defined property. At the
upper end lie the supertough materials, all of which show substantial plasticity before they break. For these the values of
K
Ic
are approximate, derived from critical J-integral (J
c
) and critical crack-opening displacement (
c
) measurements (by
writing K

Ic
= (EJ
c
)
1/2
, for instance). They are helpful in providing a ranking of materials, but must be used as an indicator
only. Guide lines for minimum weight design are based on the indices listed in Table 5(e) in the article "Performance
Indices," which follows in this Section of the Handbook. The figure shows one reason for the dominance of metals in
engineering; they almost all have values of K
Ic
above 20 MPa (20 ksi ), a value often quoted as a minimum for
conventional design.

Fig. 4 Fracture toughness, K
Ic
, plotted against density, . The guide lines of constant K
Ic
, / , and
/ , and so forth, help in minimum weight, fracture-limited design. Data for K
Ic
are valid below 10 MPa
;
data above 10 MPa are for ranking only.
The Modulus-Strength Chart (Fig. 5). High tensile steel makes good springs. But so does rubber. How is it that
two such different materials are both suited for the same task? This and other questions are answered by Fig. 5, the most
useful of all the charts.

Fig. 5 Young's modulus, E, plotted against strength,
f
, for various engineered materials. Strength is yield

strength for metals and polymers, compressive strength fo
r ceramics, tear strength for elastomers, and tensile
strength for composites. The design guide lines help with the selection of materials for springs, pivots, knife
edges, diaphragms, and hinges.
It shows Young's modulus, E, plotted against strength,
f
. The qualifications on "strength" are the same as before: yield
strength for metals and polymers, compressive crushing strength for ceramics, tear strength for elastomers, and tensile
strength for composites and woods; the symbol
f
is used for them all. The ranges of the variables, too, are the same.
Contours of normalized strength,
f
/E, appear as a family of straight parallel lines.
Examine these first. Engineering polymers have normalized strengths between 0.01 and 0.1. In this sense they are
remarkably strong; the values for metals are at least a factor of 10 smaller. Even ceramics, in compression, are not as
strong, and in tension they are far weaker (by a further factor of 15 of so). Composites and woods lie on the 0.01 contour,
as good as the best metals. Elastomers, because of their exceptionally low moduli, have values of
f
/E larger than any
other class of material: 0.1 to 10.
The distance over which interatomic forces act is small a bond is broken if it is stretched to more than about 10% of its
original length. So the force needed to break a bond is roughly


(Eq 3)
where S, as before, is the bond stiffness. If shear breaks bonds, the strength of a solid should be roughly


(Eq 4)

The chart shows that for some polymers it is. Most solids are weaker, for two reasons.
First, nonlocalized bonds (those in which the cohesive energy derives from the interaction of one atom with large number
of others, not just with its nearest neighbors) are not broken when the structure is sheared. The metallic bond, and the
ionic bond for certain directions of shear, are like this; very pure metals, for example, yield at stresses as low as E/10,000,
and strengthening mechanisms are needed to make them useful in engineering. The covalent bond is localized, and for
this reason covalent solids have yield strengths which, at low temperatures, are as high as E/10. It is hard to measure them
(though it can sometimes be done by indentation) because of the second reason for weakness: They generally contain
defects concentrators of stress from which shear or fracture can propagate, often at stresses well below the "ideal" E/10.
Elastomers are anomalous (they have strengths of about E) because the modulus does not derive from bond stretching, but
from the change in entropy of the tangled molecular chains when the material is deformed.
The performance index for selecting materials for springs (Table 5c in the article "Performance Indices," which follows in
this Section of the Handbook) is


A guide line for this index is shown on the chart. Using it in the way explained in the article "Performance Indices"
reveals that elastomers, high-strength steels, and glass-fiber-reinforced polymer (GFRP) all make good springs.
Equivalent charts for the endurance limit can be found in Ref 41.
The Specific Stiffness-Specific Strength Chart (Fig. 6). Many designs particularly those for things that move
call for stiffness and strength at minimum weight. To help with this, the data of the modulus-strength chart (Fig. 5) are
replotted in Fig. 6 after dividing, for each material, by the density; it shows E/ plotted against
f
/ .

Fig. 6 Specific modulus, E/ , plotted against specific strength
f
/
for various engineered materials. Strength
is yield strength for metal
s and polymers, compressive strength for ceramics, tear strength for elastomers, and
tensile strength for composites. The design guide lines help with the selection of materials for lightweight

springs and energy-storage systems.
Ceramics lie at the top right: they have exceptionally high stiffness and strength per unit weight. The same restrictions on
strength apply as before. The data shown here are for compression strengths; the tensile strengths are about 15 times
smaller. Composites then emerge as the material class with the most attractive specific properties, one of the reasons for
their increasing use in aerospace. Metals are penalized because of their relatively high densities. Polymers, because their
densities are low, are favored.
The chart has application in selecting materials for light springs and energy-storage devices (Table 5c in the article
"Performance Indices," which follows in this Section of the Handbook). Equivalent charts for the endurance limit are
contained in Ref 41.
The Fracture Toughness-Modulus Chart (Fig. 7). As a general rule, the fracture toughness of polymers is less
than that of ceramics. Yet polymers are widely used in engineering structures; ceramics, because they are "brittle," are
treated with much more caution. Figure 7 helps resolve this apparent contradiction. It shows the fracture toughness, K
Ic
,
plotted against Young's modulus, E. The restrictions described earlier apply to the values of K
Ic
: When small, they are
well defined; when large, they are useful only as a ranking for material selection.

Fig. 7 Fracture toughness, K
Ic
, plotted against Young's modulus, E. The family of lines are of constant /E

(approximately G
ic
, the fracture energy). These, and the guide line of constant K
Ic
/E, help
in design against
fracture. The shaded band shows the "necessary condition" for fracture. Fracture can, in fact, occur below this

limit under conditions of corrosion, or cyclic loading.
Consider first the question of the necessary condition for fracture. It is that sufficient external work be done, or elastic
energy released, to supply the surface energy (2 per unit area) of the two new surfaces that are created. This is written
as:
G 2


(Eq 5)
where G is the elastic energy release rate. Using the standard relation K (EG)
1/2
between G and stress intensity K, then
K (2 E )
1/2


(Eq 6)
Now the surface energies, , of solid materials scale as their moduli; to an adequate approximation = Er
o
/20, where r
o

is the atom size, giving


(Eq 7)
The right-hand side of this equation is identified with a lower-limiting value of K
Ic
, when, taking r
o
as 2 × 10

-10
m (8 × 10
-
9
in.),


(Eq 8)
This criterion is plotted on the chart as a shaded, diagonal band near the lower right corner (the width of the band reflects
a realistic range of r
o
and of the constant C in = r
o
/C). It defines a lower limit on values of K
Ic
: It cannot be less than this
unless some other source of energy (such as a chemical reaction, or the release of elastic energy stored in the special
dislocation structures caused by fatigue loading) is available, when it is given a new symbol such as (K
Ic
)
scc
. Note that the
most brittle ceramics lie close to the threshold; when they fracture, the energy absorbed is only slightly more than the
surface energy. When metals, polymers, and composites fracture, the energy absorbed is vastly greater, usually because of
plasticity associated with crack propagation. This is discussed in the following Section of this article.
Plotted on Fig. 7 are contours of toughness, G
Ic
, a measure of the apparent fracture surface energy (G
Ic
/E). The

true surface energies, , of solids lie in the range 10
-4
to 10
-3
kJ/m
2
(10
-2
to 10
-1
ft · lbf/ft
2
). The diagram shows that the
values of the toughness start at 10
-3
kJ/m
2
(10
-1
ft · lbf/ft
2
) and range through almost six decades to 10
3
kJ/m
2
(10
5
ft ·
lbf/ft
2

). On this scale, ceramics (10
-3
to 10
-1
kJ/m
2
, or 10
-2
to 10 ft · lbf/ft
2
) are much lower than polymers (10
-1
to 10
kJ/m
2
, or 10 to 1000 ft · lbf/ft
2
); this is part of the reason polymers are more widely used in engineering than ceramics.
The Fracture Toughness-Strength Chart (Fig. 8). The stress concentration at the tip of a crack generates a
process zone: a plastic zone in ductile solids, a zone of microcracking in ceramics, a zone of delamination, debonding,
and fiber pullout in composites. Within the process zone, work is done against plastic and frictional forces; it is this that
accounts for the difference between the measured fracture energy G
Ic
and the true surface energy 2 . The amount of
energy dissipated must scale roughly with the strength of the material, with the process zone, and with its size, d
y
. This
size is found by equating the stress field of the crack ( = K/ ) at r = d
y
/2 to the strength of the material,

f
, giving


(Eq 9)
Figure 8 (fracture toughness versus strength) shows that the size of the zone, d
y
(broken lines) varies enormously, from
atomic dimensions for very brittle ceramics and glasses to almost 1 meter for the most ductile of metals. At a constant
zone size, fracture toughness tends to increase with strength (as expected); it is this that causes the data plotted in Fig. 8 to
be clustered around the diagonal of the chart.

Fig. 8 Fracture toughness, K
Ic
, plotted against strength,
f
, for various engineered materials. Strength is yield
strength for metals and polymers, compressive strength for ceramics and glasses, and tensile strength for
composites. The contours show the value of /
f
roughly, the diameter of the process-
zone at a crack
tip. The design guide lines are used in selecting materials for damage-tolerant design.
The fracture toughness-strength diagram has application in selecting materials for the safe design of load-bearing
structures using the indices described in Table 5(e) in the article "Performance Indices," which follows in this Section of
the Handbook.
The Loss Coefficient-Modulus Chart (Fig. 9). Bells are traditionally made of bronze. They can be (and sometimes
are) made of glass; and they could (if one could afford it) be made of silicon carbide. Metals, glasses, and ceramics all,
under the right circumstances, have low intrinsic damping or "internal friction," an important material property when
structures vibrate. Intrinsic damping is measured by the loss coefficient, , which is plotted in Fig. 9.

Fig. 9 The loss coefficient, , plotted against Young's modulus, E, for various engineered materials.
The guide
line corresponds to the condition = C/E.
The loss coefficient, a dimensionless number, measures the degree to which a material dissipates vibrational energy. If a
material is loaded elastically to a stress
max
, it stores an elastic energy


per unit volume. If it is loaded and then unloaded, it dissipates an energy
U = d


The loss coefficient is