Create charts of multiple index lines

About charts of multiple index lines

Creating multiple index lines on a chart allows you to illustrate how the choice of material is affected by the design application.

The chart below shows index lines with different slopes, corresponding to the performance indices for different components. Each component (tie in tension, beam in bending, and panel in bending) has a different geometry and load condition and therefore has a different performance index to optimize.

The objective and limiting constraint is the same for each component: the objective is to minimize mass for a stiffness-limited component.

Loading geometry		Material index to maximize	Material choice
Tie in tension		E / ρ	Steels, Al alloys, Ti alloys, PEKK-40% CF
Beam in bending		E1/2 / ρ	Al alloys, composites
Panel in bending		E1/3 / ρ	Al alloys, PP-10% CF

The different performance indices contain the same material attributes (Young’s modulus (E) and density (ρ)) but in different relations. This means that one chart of Young’s modulus vs. density can be used to simultaneously compare the different loading conditions and geometries.

The position of a material relative to the index line tells you how well a material will perform for that application. Materials that are on the line will all perform equally well in a given design. Materials above the line have a higher performance index and will therefore perform better; those below the line have a lower index value.

Looking at the chart above, different material choices are needed in order to optimize the performance of each component. For a tie in tension, the index line passes through several alloy classes, including steels and aluminum alloys, and so all of these materials would perform equally well. The final material choice may then be a steel, as they are cheaper than aluminum alloys.

However, for a panel in bending, steel is below the index line and so would not perform well in this application. Instead, a polymer such as PP-10% CF would be a more suitable material.

Calculate slope of line from performance index

To calculate the slope of the line from the performance index:

1. Identify the performance index to maximize. (By convention, performance indices are written so that maximizing the index optimizes the performance.)
   • For a panel in bending, the index to maximize is:
     Performance index: M = E^1/3/ρ
2. Rearrange this equation in terms of the numerator:
   E = ρ³ * M³
3. Take the logarithm of each side:
   log(E) = 3log(ρ) + 3log(M)

This is now in the form of an equation for a straight line (y=mx+c), where m is the gradient (or slope) and c is the y-intercept. This means that on a logarithmic chart of Young’s modulus vs. density, an index line of slope 3 will allow you to compare and select materials for a panel in bending.

Create multiple index lines

To create multiple lines on a chart:

1. Plot a chart with the material attributes from the performance index on the chart axes.
   • For example, plot Young's modulus on y-axis and density on x-axis.
2. In the chart stage toolbar, click  Index and Display Lines.
3. Enter a Slope value for the gradient of the line.
4. Specify what you want the line to do:
   • Select Maximize the index to select only the materials that maximize the index.
   • Select Minimize the index to select only the materials that minimize the index.
   • To add a display line that does not perform any selection, select Show line for display only.
5. Click OK.
6. Click on the chart where you want to place the line.
7. Repeat steps 2 through 6 for the other material indices, this time selecting Show line for display only.