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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
Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed
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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
Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed
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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.
Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed
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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.
Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed
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Fig. 3 Young’s modulus E plotted against density ρ
E/ρ=1
Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed
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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:
Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed
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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.
Lec.7 Performance Indices and property (Ashby charts) by Dr. Ahmed Ameed
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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.