Abstract

The reflected method of caustics, which is based on geometric optics, was used to define the principal stress difference and the principal directions at the interior of any generalized plane stress field by defining the stress distribution around small perforations drilled in the plate. A monochromatic coherent light beam, reflected on or transmitted through the plate at the neighborhood of the perforation, deviated by different amounts because of the refractive index variation and the thickness variation due to loading. The deviated light rays, received on a reference plane parallel to the plate, were concentrated along a singular curve, which enveloped a large part of the reflected or traversing rays and created a caustic. The properties of this singular curve were studied and found to depend on the biaxial stress field existing at the place of the perforation, as well as on the mechanical and optical properties of the material and the geometry of the optical setup. The double-kidney shape of the caustic presented a maximum diameter D_max, which coincided with one of the axes of symmetry of the caustic. The other axis of symmetry, which passed through the cusps of the caustic, coincided with the axis of maximum principal stress, while the size of D_max yielded the principal stress difference. Thus, the caustic constitutes a sensitive stress rosette, which defines the orientation and the size of the stress field.

© 1973 Optical Society of America

Some further properties of caustics useful in mechanical applications

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