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

The method of strain measurement after annealing is reviewed
and found to be unsatisfactory for the materials available in
this country. A new, general method is described for the photo—
elastic determination of the principal stresses at any point of a
general body subjected to arbitrary loads. The method has
been applied to a sphere subjected to diametral compressive
loads. The results show possibilities of high accuracy.

It is known that purely photoelastic procedures cannot
solve the general three—dimensional stress problem. The
photoelastic method furnishes 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 treat-
ment 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 process. 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 differ—
ential 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.