Some critical points related to the applicability of the optical method of reflected caustics in the case of a plate with a central hole are explored in the present paper. The study is carried out in a combined experimental and numerical procedure: poly-methyl-meth-acrylate plates with a central hole are subjected to uniaxial tension and the diameter of the caustics developed is measured for various load steps from a series of successive photographs with the aid of suitable software. The remote stress is then calculated according to the method of caustics and the results are compared with those of the load cell. In addition, the finite element method is employed for the determination of the stress field and the shape and magnitude of the plastic zones around the hole. Conclusions are drawn concerning the range of the external load for which the results of the method of caustics are valid as a function of the relative dimension of the width of the plate versus the diameter of the hole. In addition, the factors influencing the results of the method are considered and the sensitivity of the results to the even the slightest misalignments of the experimental set-up, to the kind of the optical setup preferred and to the slightest deviation from flatness of the lateral faces of the plate is pointed out. This sensitivity of the method was proved to be responsible for discrepancies between theory and experiment, which sometimes exceed 100%.

The Optical Method of Reflected Caustics Applied for a Plate With a Central Hole: Critical Points and Limitations

Caustics, pseudocaustics and the related illuminated and dark regions with the computational method of quantifier elimination

The study of this paper was to determine the plastic zone dimension at the crack tip by the experimental method of caustics. The caustics shape at the crack tip depends on plastic zone which is small for brittle materials and large for ductile ones. The plastic zone dimensions depends on the crack length, the plates thickness and the loading level. The experimental method of caustics is an excellent tool for the plasticity and stress intensity factors evaluation of loaded cracked structures.

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Experimental Evaluation of the Plastic Zone at Crack Tip by Caustics

The experimental method of caustics was used for the evaluation of the stress-singularities created by concentrated oblique load applied at the apex of a wedge or on the horizontal straight boundary of a half-plane. The wedge was considered to be elastic, isotropic and under generalized plane stress conditions. According to the method of caustics, the light rays impinging normally at the thin plate are partly reflected from either the front or the rear faces of the plate. The reflected rays are deviated because of the important constraint of the plate at the vicinity of the applied concentrated load and the significant variation of the refractive index there. The deviated light rays, when projected on a reference screen, are concentrated along a singular curve which is strongly illuminated and forms a caustic. It was proved that the shape and size of the caustic depend on the stress singularity at the point of application of the load. The parametric equations of caustics created by such a singularity were studied in relation with the loading mode of the wedge. Thus, by measuring the dimensions of the caustic, one can evaluate the state of stress at the singularity. The experimental evidence, based on the above method on Plexiglas (PMMA) wedges, corroborated existing elastic theories concerning the order of singularities for concentrated loads. The relations for the calculation of the load, the components of stress and the concentration factor based on the geometrical characteristic of caustics, which were reflected from the front face of the wedge, were given.

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Evaluation of Concentrated Oblique Load at the Apex of a Wedge by the Method of Caustics

The experimental method of caustics was used for the evaluation of the stresssingularities created by concentrated load applied at the apex of a wedge or on the horizontal straight boundary of a half-plane. It was proved that the shape and size of the caustic depend on the stress singularity at the point of application of the load. The parametric equations of caustics created by such a singularity were studied in relation with the loading mode of the wedge. Also, the stress singularity created by a concentrated load applied at the apex of the wedge or on the horizontal straight boundary of a half-plane was studied by isochromatic fringes of photoelasticity. Thus, by measuring the dimensions of the caustic, one can evaluate the state of stress at the singularity. The relations for the calculation of the load, the components of stress and the concentration factor based on the geometrical characteristic of caustics and on isochromatic fringes were given.

Study of concentrated vertical load at the apex of a wedge by the experimental methods of caustics and photoelasticity

The range of applicability of the optical method of caustics, which is based on plane stress conditions, around cylindrical holes in plane specimens is investigated. The position of the generatrix curve of the caustic and the conditions, which influence its size, are defined. The dimensions of the specimen, the ratio of the thickness to the diameter of the hole, the applied stress and the dimensions of the optical set-up influence the position of the generatrix curve of the caustic. At a critical distance from the boundary of the hole the state of stress degenerates from three-dimensional to plane stress. In this paper, the extent of this region was defined by finite element analysis, in case of uniaxial tension. The defined critical distance was correlated with the condition, which influence the caustic, thus the range of applicability of the method of caustic around hole was defined. The validity of this range was experimentally checked.

B. G. Badalouka

Papers

Range of Applicability of the Method of Caustics around Holes