The method of caustics in conjunction with the method of birefringent coatings for the solution of fracture mechanics problems

Abstract

Optical methods of stress analysis including photoelasticity, moirr, holographic and moire interferometry and caustics have extensively been used in fracture mechanics problems. Among them, the optical method of caustics is gaining ground in the determination of stress intensity factors in crack problems under static and dynamic loading. In this method [ 1,2], the area in the vicinity of the crack tip is illuminated by a collimated light and the reflected or transmitted rays from an envelope in space. When this envelope is cut by a reference plane, a highly illuminated curve, the caustic, is formed. By measuring a diameter of the caustic the stress intensity factor is determined. The caustic is the image of the circumference of a circle on the specimen centered at the crack tip, which is called the initial curve. In the application of the method care should be taken to ensure that the initial curve lies in the plane-stress region, so that the plane-stress assumption made in developing the evaluation equations of caustic is valid. The implication of this assumption regarding the selection of material, load level, specimen size and optical arrangement has been discussed by Konsta-Gdoutos and Gdoutos [3-5]. In the beginning, the method of caustics was applied to transparent specimens and later on its use was extended to metals by Theorcaris and Gdoutos [6,7]. The optical quality of the specimens used in the method of caustics should meet high standards. Specimens used in transmission arrangements must have constant thickness and density. On the other hand, specimens used in reflection arrangements must have an optically planar surface of high reflectivity at least in the neighborhood of the crack tip where the caustic is generated. In metal specimens mirrored surfaces are prepared by grinding, lapping and polishing their front surface. Preparation of mirror-like surfaces of specimens used in the method of caustics constitutes not only an elaborate task but difficulties arise in a number of cases. A characteristic example is bone, which due to its spongy nature cannot be adequately polished to the point that Snell's reflection law applies. Analogous problems are encountered in fiber or particulate composite materials. Another class of problems in which the method of caustics cannot be