Performance Indices

A merit index is a combination of certain properties not a material that may be used during the materials selection process to compare different materials under a particular criterion.

An application may require several unconnected attributes such as resistance to corrosion, strength, stiffness, etc. Only consider one at a time.

Ex. Bars are required to withstand a load, P, and are of length ,L with lowest weight (or mass). What attribute is being sought?

The attribute you seek is 1/(mass), therefore, r.

(1) mass = density x volume

m = r x A L

(2) eliminate from right hand side anything that is either a property (e.g., r) nor a prescribed quantity (e.g., L), in this case A.

A depends on strength, s.

s = P / A (only in tension case)

A = P / s.

(3.) Substitute P / s for A in (1).

1/ m = s / (r P L)

1/m = 1/ (P L) ( s/r)

1/ m µ s / r

s / r is the merit index for the criterion (largest value of s / r)

Summary:

General method for deriving a merit index:

1. Write down any true expression for the attribute sought.

2. Eliminate any parameter that is not a property or fixed quantity.

3. The merit index is the combination of properties on the right hand side of the equation.