Page 802 - Carrahers_Polymer_Chemistry,_Eighth_Edition

Appendix N

Material Selection Charts

In the selection of a material for a specific application many considerations are involved. Today,
for the most part charts and other relationships are computerized. Here we will look at their use
but only by employing a graphical chart for illustration. Let us consider making a shaft for a blade
that mixes salt water with nonsalt water for controlled saline irrigation. The shaft material must be
strong and light weight and must be able to absorb twisting shear. While strength and weight are
only two important considerations, we will focus on only these two. A mathematical relationship
between weigh or mass and strength for a cylindrical shaft can be made such that
2/3
mass is proportional to [density/(shear stress) ] times some safety factors.
This tells us that the best light-weight material to make our shaft out is a material with a low
2/3
density/(shear stress) ratio.
Often, the inverse of this ratio is employed and given the name performance index P. (There are
performance indexes for many different relationships between various physical behaviors.) Here
then

2/3
P = (shear stress) /density
Taking the log of both sides gives

log P = 2/3log shear stress − density

Rearrangement gives

log shear strength = 3/2 log + 3/2 log P

This expression tells us that a plot of the log of the shear strength versus log density will give a
family of straight and parallel lines each with a slop of 3/2 with each straight light corresponding
to a different performance index, P. These lines are called design guidelines. Figure N.1 contains a
general plot of log shear strength versus density for a number of materials grouped together under

common headings. For instance, polytetrafluoroethylene exists in the midrange, extreme right on
the “Polymers” circle and so has a relatively high density and strength while polypropylene exists
in the upper left corner of the “Polymers” circle and has a relatively low density and relatively
good strength. Such charts allow the quick focusing in on the general type of material that exhibits
needed characteristics. Today, most of this is done by computer.

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