Material selection is a step in the process of designing any physical object. In the context of product design, the main goal of material selection is to minimize cost while meeting product performance goals.[1] Systematic selection of the best material for a given application begins with properties and costs of candidate materials. Material selection is often benefited by the use of material index or performance index relevant to the desired material properties.[2] For example, a thermal blanket must have poor thermal conductivity in order to minimize heat transfer for a given temperature difference. It is essential that a designer should have a thorough knowledge of the properties of the materials and their behavior under working conditions. Some of the important characteristics of materials are : strength, durability, flexibility, weight, resistance to heat and corrosion, ability to cast, welded or hardened, machinability, electrical conductivity, etc.[3] In contemporary design, sustainability is a key consideration in material selection.[4] Growing environmental consciousness prompts professionals to prioritize factors such as ecological impact, recyclability, and life cycle analysis in their decision-making process.
Systematic selection for applications requiring multiple criteria is more complex. For example, when the material should be both stiff and light, for a rod a combination of high Young's modulus and low density indicates the best material, whereas for a plate the cube root of stiffness divided by density
\sqrt[3]{E}/\rho
E/\rho
\sqrt[2 ]{E}/\rho
Reality often presents limitations, and the utilitarian factor must be taken in consideration. The cost of the ideal material, depending on shape, size and composition, may be prohibitive, and the demand, the commonality of frequently utilized and known items, its characteristics and even the region of the market dictate its availability.
An Ashby plot, named for Michael Ashby of Cambridge University, is a scatter plot which displays two or more properties of many materials or classes of materials.[5] These plots are useful to compare the ratio between different properties. For the example of the stiff/light part discussed above would have Young's modulus on one axis and density on the other axis, with one data point on the graph for each candidate material. On such a plot, it is easy to find not only the material with the highest stiffness, or that with the lowest density, but that with the best ratio
E/\rho
\sqrt[3]{E}/\rho
The first plot on the right shows density and Young's modulus, in a linear scale. The second plot shows the same materials attributes in a log-log scale. Materials families (polymers, foams, metals, etc.) are identified by colors.
Cost of materials plays a very significant role in their selection. The most straightforward way to weight cost against properties is to develop a monetary metric for properties of parts. For example, life cycle assessment can show that the net present value of reducing the weight of a car by 1 kg averages around $5, so material substitution which reduces the weight of a car can cost up to $5 per kilogram of weight reduction more than the original material. However, the geography- and time-dependence of energy, maintenance and other operating costs, and variation in discount rates and usage patterns (distance driven per year in this example) between individuals, means that there is no single correct number for this. For commercial aircraft, this number is closer to $450/kg, and for spacecraft, launch costs around $20,000/kg dominate selection decisions.[6]
Thus as energy prices have increased and technology has improved, automobiles have substituted increasing amounts of lightweight magnesium and aluminium alloys for steel, aircraft are substituting carbon fiber reinforced plastic and titanium alloys for aluminium, and satellites have long been made out of exotic composite materials.
Of course, cost per kg is not the only important factor in material selection. An important concept is 'cost per unit of function'. For example, if the key design objective was the stiffness of a plate of the material, as described in the introductory paragraph above, then the designer would need a material with the optimal combination of density, Young's modulus, and price. Optimizing complex combinations of technical and price properties is a hard process to achieve manually, so rational material selection software is an important tool.
Utilizing an "Ashby chart" is a common method for choosing the appropriate material. First, three different sets of variables are identified:
Next, an equation for the performance index is derived. This equation numerically quantifies how desirable the material will be for a specific situation. By convention, a higher performance index denotes a better material. Lastly, the performance index is plotted on the Ashby chart. Visual inspection reveals the most desirable material.
In this example, the material will be subject to both tension and bending. Therefore, the optimal material will perform well under both circumstances.
In the first situation the beam experiences two forces: the weight of gravity
w
P
\rho
\sigma
L
P
A
w
\rho,\sigma
The stress in the beam is measured as
P/A
w=\rhoAL
A
A=P/\sigma
w=\rho(P/\sigma)L=\rhoLP/\sigma
w=(\rho/\sigma)LP
Since both
L
P
w
\rho/\sigma
Performanceindex=Pcr=\sigma/\rho
Next, suppose that the material is also subjected to bending forces. The max tensile stress equation of bending is
\sigma=(-My)/I
M
y
I
w=\sqrt{6MbL2}(\rho/\sqrt{\sigma})
L
b
b
L
M
PCR=\sqrt{\sigma}/\rho
At this point two performance indices that have been derived: for tension
\sigma/\rho
\sqrt{\sigma}/\rho
For the tension performance equation
PCR=\sigma/\rho
log(\sigma)=log(\rho)+log(PCR)
y=x+b
PCR
PCR
The bending performance equation
PCR=\sqrt{\sigma}/\rho
log(\sigma)=2 x (log(\rho)+log(PCR))
PCR
First, the best bending materials can be found by examining which regions are higher on the graph than the
\sqrt{\sigma}/\rho
Lastly, the
\sigma/\rho
The performance index can then be plotted on the Ashby chart by converting the equation to a log scale. This is done by taking the log of both sides, and plotting it similar to a line with
Pcr
As seen from figure 3 the two lines intercept near the top of the graph at Technical ceramics and Composites. This will give a performance index of 120 for tensile loading and 15 for bending. When taking into consideration the cost of the engineering ceramics, especially because the intercept is around the Boron carbide, this would not be the optimal case. A better case with lower performance index but more cost effective solutions is around the Engineering Composites near CFRP.
. M. F. Ashby. Materials Selection in Mechanical Design. 3rd. Butterworth-Heinemann. Burlington, Massachusetts. 1999. 0-7506-4357-9. registration.