Limitations in mixed-mode stress intensity factor evaluation by the method of caustics

Abstract

Evaluation of stress intensity factors in crack problems by the method of caustics is complicated due to the changing state of stress in the neighborhood of the crack tip. Near the tip the state of stress is plane straina while at a critical distance from the tip it can be approximated as plane stress. Between the two regions the stress field is three-dimensional. The type of the state of stress has a tremendous effect on the values of stress-optical constants which enter into the evaluation equations of stress intensity factors. In almost all cases the assumption of plane stress is involved, which infers that the initial curve of the caustic should lie in the region where plane stress conditions dominate. This imposes limitations on the values of the applied loads, specimen dimensions and characteristic lengths of the optical arrangements for the correct application of the method. In the present work a thorough investigation of the limits of applicability of the method of caustics for the evaluation of mixed-mode stress intensity factors is undertaken. The case of an inclined crack in a uniaxial tensile stress field is studied in detail. Results are given for the selection of material, load level, specimen size and optical arrangement when the specimen is illuminated by a parallel, divergent or convergent light beam. It is shown that mixed-mode loading conditions impose more severe limitations on these quantities as compared to opening-mode loading.