Material property charts were introduced in Chapter 6. They are of two types: bar charts and bubble charts. A bar chart is simply a plot of one or a group of properties; Chapter 6 has several of them. Bubble charts plot two properties or groups of properties. Constraints and objectives can be plotted on them.
Screening: constraints on charts. As we have seen, design requirements impose nonnegotiable demands ("constraints") on the material of which a product is made. These limits can be plotted as horizontal or vertical lines on material property charts. Figures 8.5 and 8.6 show two examples. The first is a bar chart of embodied energy. A selection line has been placed to impose the limit embodied energy < 10MJ/kg; all the materials below the line meet the constraint. The second shows a schematic, the modulus-density chart. We suppose that the design imposes limits on these of modulus > 10 GPa and density < 2000kg/m3, shown on the figure. All materials in the window defined by the limits, labeled "Search region," meet both constraints.
Screening using a bar chart. Here we seek materials with embodied energies less than 10MJ/kg. The materials in the “Search region" below the selection line meet the constraint.
Density, P (kg/m3)
Screening using a bubble chart. Two constraints are plotted: modulus >10 GPa and density < 2000kg/m3. The materials in the “Search region" at the upper left meet both constraints.
Ranking: indices on charts. Material indices measure performance; they allow ranking of the materials that meet the constraints of the design. We use the design of light, stiff components as examples; the other material indices are used in a similar way.
Figure 8.7 shows a schematic of the E-p chart shown earlier. The logarithmic scales allow all three of the indices p/E, p/E1/3 and p/E1/2, listed in Table 8.3 of the last section, to be plotted onto it. Consider the condition
M = — = constant, C (8.1)
that is, a particular value of the specific stiffness. Taking logs
log(E) = log(p) – log(C (8.2)
For a fixed value of C this is the equation of a straight line of slope 1 on a plot of log(E) against log(p), as shown in the figure. Similarly, the condition
M = p = constant, C (8.3)
becomes, on taking logs,
log(E) = 3log(p) – 3log[C) (8.4)
This is another straight line, this time with a slope of 3, also shown. And by inspection, the third index p/Em will plot as a line of slope 2. We refer to these lines as selection guidelines. They give the slope of the family of parallel lines belonging to that index. Selection guidelines are marked on the charts presented later in this chapter.
It is now easy to read off the subset of materials that maximize performance for each loading geometry. For example, all the materials that lie on a line of constant M = p/Em perform equally well as a light, stiff panel; those above the line perform better, those below, less well. Figure 8.8 shows a grid of lines corresponding to values of M = p/Em fromM = 100 to M = 10,000 in units of (kg. m-3)/GPa1/3. A material with M = 100 in these units gives a panel that has one tenth the weight of one with M = 1000. The texts listed under Further Reading develop numerous case studies illustrating the use of the method.