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.

- 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.