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National Advisory Committee for Aeronautics, Technical Notes - A Special Investigation to Develop a General Method for Three Dimensional Photoelastic Stress Analysis

It is known that purely photoelastic procedures cannot solve the
general three-dimensional stress problem. The photoelastic method fur-
nishes five independent equations, whereas the complete specification
of the state of stress at a point requires six relations to determine
six unknown stress components.

In order to obtain a sixth relation it has been suggested that the
frozen slices removed from the model be annealed and strain measurements
be made'after annealing. This suggestion has recently received a rather
extensive treatment from Prigorovsky and Preiss in Russia (reference 1).
A careful analysis of this suggested method shows that its successful
application requires model materials having relatively low values of
Poisson's ratio at the elevated temperatures used in the freezing proc—
ess.. Such materials are not available in this country. Fosterite and
Bakelite, which are the best available materials, have Poisson’s ratios
approximately equal to 1/2. It is further shown that the method of strain
measurement after annealing breaks down when this ratio approaches 1/2.

In this report a new method is described.which does not depend on
Poisson‘s ratio and therefore can be used with models made of Fosterite
and Bakelite. This method employs frozen stress patterns from normal
and oblique incidence. The separation of the principal stresses is
obtained by the numerical integration of one of the differential
equations of equilibrium in Cartesian coordinates rather than by strain
measurement after annealing which involves Poisson's ratio. It will be
shown that this permits the determination of-all Six stress components
at each point of a body.

The report consists of three parts. The first part comprises a
survey and analysis of the method in.three-dimensional photoelasticity
which rests on.the freezing and slicing processes and strain measure-
ment after'annealing. The second part presents the_theory ofmthe new
method. The third part contains the application of the new method to
the determination of stresses in a diametrically compressed sphere.

The investigation was conducted in the Photoelastic Laboratory of
the Mechanics Department—at the Illinois Institute of Technology under
the sponsorship and with the.financial assistance of the National Advisory
Committee for Aeronautics.