introduction to property (ashby)...

Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed

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Introduction to property (Ashby) charts

Each property of an engineering material has a characteristic range of

values. The span can be large: many properties have values that range over

five or more decades. One way of displaying this is as a bar chart like that of

Figure 1 for Young’s modulus. Each bar describes one material; its length

shows the range of modulus exhibited by that material in its various forms.

The materials are segregated by class. Each class shows a characteristic

range: Metals and ceramics have high moduli; polymers have low; hybrids

have a wide range, from low to high. The total range is large—it spans a

factor of about 106—so logarithmic scales are used to display it.

Fig.1 A bar chart showing modulus for families of solids. Each bar shows the range

of modulus offered by a material, some of which are labeled.

More information is displayed by an alternative plot “Material property

charts” or what called “Ashby chart” which are a good way of summarizing


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a wide range of material properties. Two properties are plotted; one on

each axis of the graph. Common combinations are:

• Modulus – Density, Modulus – Strength, Strength – Cost, Fracture

Toughness - Strength

Bubbles are drawn for individual materials, whole classes of materials

or subsets to show the range of properties available. Any type of material

can be drawn on these charts including porous materials, such as foams,

and composites of two or more bulk materials. Notice that scales are

logarithmic making it possible to show a wide range of materials on just

one chart. Notice that materials cluster together within their classes.

Fig.2 A schematic E − ρ chart showing a lower limit for E and an upper limit for ρ

E/ρ


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Performance (Merit Index): is a grouping of properties which, when

maximized, give some maximum performance of a material. When

designing something, we often have particular objectives such as minimum

weight or maximum stiffness. A merit index helps us to compare the

performance of different materials in achieving the objective.

For example, E/ρ is a typical merit index for minimum weight, deflection

limited design. On a property chart this ratio forms a set of straight lines of

slope 1. Materials which are lighter and stiffer in comparison to other

materials lie above and to the left of this line (Fig.2).

Table 1 below shows the performance indices for different components.


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The modulus–density chart

To select materials which have at least a tensile modulus of, say 10

GPa a line is drawn across the chart at that value and all the material

above that line form the selected subset. If we also have the

requirement of density less than 3gm/cm3 then we draw a line on the

chart at this value and all the material to the left of that line follow this

criteria. So the subsets of materials with both criteria are those in the

upper left quadrant (fig.2).

If we want a cantilever with maximum stiffness and minimum mass,

then the performance index will be C=E1/2/ρ, not that the log-log scale

will be plotted, then:

lgC= 1/2 lgE –lg ρ lg E= 2 lg ρ +2 lg C Slope=2

So, family of straight lines will be available for this case.

But in some cases further limitation will be done like (E/ ρ =1000).

Doing log to both side give lg E -lg ρ=lg 1000

lg E=lg ρ+3

This will be a line on the chart with a constant slope of 1 and intercept

of 3 with lg E axis (red line in figure 3) will indicate to the optimum

criteria. Also in some cases we need the material subsets with fitted

criteria (intercept). Figure 4 show more details help with the selection

of proper material subsets.


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Fig. 3 Young’s modulus E plotted against density ρ

E/ρ=1


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Fig. 4 Young’s modulus E plotted against density ρ. The heavy envelopes enclose data for a

given class of material. The diagonal contours show the longitudinal wave velocity. The guide

lines of constant E/ρ, E1/2/ρ, and E1/3/ρ allow selection of materials for minimum weight,

deflection-limited, design.

EXAMPLE: the longitudinal wave speed of sound in a material is given

by the equation

V = (𝐸

𝜌)1/2

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

get:


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log (V) = 1

2 [log(E)-log(ρ)] or log (E) =2log(V) +log(ρ).

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?

The strength–density chart

The word “strength “mean:

For metals and polymers, it is the yield strength, but since the range

of materials includes those that have been worked or hardened in

some other way as well as those that have been softened by

annealing, the range is large.

For brittle ceramics, the strength plotted here is the modulus of

rupture (The flexural strength). It is slightly greater than the tensile

strength, but much less than the compression strength, which for

ceramics is 10 to 15 times greater than the strength in tension.

For elastomers, strength means the tensile tear strength.


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For composites, it is the tensile failure strength (the compressive

strength can be less by up to 30% because of fiber buckling).

We will use the symbol σf for all of these.

The range of strength for engineering materials, like the range for

the modulus, spans many decades: from less than 0.01 MPa (foams,

used in packaging and energy-absorbing systems) to 104 MPa (the

strength of diamond, exploited in the diamond-anvil press).

Figure 5 Strength σf plotted against density ρ (yield strength for metals and polymers, Flexural

strength for ceramics, tear strength for elastomers, and tensile strength for composites). The

guide lines of constants σf /ρ, σf 2/3 /ρ, and σf

1/2 /ρ are used in minimum weight, yield-limited,

design.

introduction to property (ashby)...

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