Digital Curves

Digital Curves for Digital Prototypes?

Prior to the advent of computers, curve fitting equations to data
was a labor intensive and time consuming effort. The basic reason for
fitting the data was to find an equation to relate the variables in
subsequent calculations, and to be able to transmit the curve from person
to person easily, without re-fitting the data. In handbooks such as
Peterson's Stress Concentration Factors a second form of information
transmittal was used, simply visual plots of x vs y, which saved the
user from performing repeatative solutions to the often complex
equations needed for data fitting.

In the computer age there is still a great need to be able to
transmit the fitted curve. Computers need a definition of how the
variables are related, and thus at present, engineers still request
the six constants that fit the Strain-Life curve, for example, to plug
into their computers. The computer programs themselves are used to
transform strain to life values. As such there is no inherent reason to
be concerned about the constants themselves. In order to facilitate
computational efficiency, the constants and equations are often expressed
in terms of look-up tables of points along the "curve" of interest.
As in many fields of science, there are "boundary" data sets that do
not really conform to the equations. Steels that transform material
phases when subjected to plastic strain do not fit the Coffin-Manson
strain life equations, for example. The new periodic overstrained life
curves also do not conform to Coffin-Manson fits, and there are other
problems introduced by fitting interdependant curves such as the
plastic strain vs life, elastic strain vs. life, and stress vs strain
curves.

The question to ask ourselves is "Why do we need to fit this type of
data to a set of equations?" The computers do not care what the
equation is. All they want is the relationship between x and y,
preferrably in digital form. Rather than add various kluges(sp?) to
the application of the equations to fit the special cases, we should
simply abandon the use of equations and their fits altogether, for
purposes of computing, and find methods to "fit" a digital set of x and
y points that express the relationship between the two variables of
strain vs. life, for example. In many data sets where the fitted
equation deviates from the raw data, the human eye can provide a better
fit than the mathematics. We need to duplicate this visual type of
fitting in computer software. With this simplification we can fit any
shape of experimental points, save the best fit co-ordinates, and
transfer the fitted co-ordinate sets for further application.

Research Plan: (done)

Find some data sets that are poor fits (An Example) For graph click on the "Send for Processing" button.
In the graph one can see that the "fitted" line, using the standard least squares fits on

plastic and elastic strains, does a poor job of representing the data. In such a case
a manual fit of the three variables total strain, stress and life becomes necessary for
good predictions of initiation fatigue life.
A comparison can be made of original and digitally fitted files here.