On the determination of the sum of the principal stresses in two-dimensional problems

Abstract

The well-known principle of the determination of the sum of principal stresses in plates by measuring thickness changes is applied in this paper to “frozen” plates and to models made with low-modulus materials, such as rubbers, deformed inside portable frames. It is shown that a sufficiently precise measurement of thickness changes is possible with a machine-shop comparator, rather than with the more delicate laboratory-type instruments. The necessary corrections to be introduced to the comparator readings when rubber models are used are described in the Appendix.

Two other methods based on moiré fringes, using the same two kinds of models, are also presented. The use of moiré on “frozen” specimens yields patterns of large response. Gratings on rubber models also yield precise moiré patterns that can be combined with isochromatics to separate the principal stresses. Two ways of conducting the moiré analyses are presented. The advantages and limitations of the several alternative methods are pointed out, and applications are given.