Range of Applicability of the Method of Caustics around Holes

Badalouka, B.; Papadopoulos, George Α.

doi:10.1111/j.1475-1305.2006.00289.x

Cited by 5 publications

(3 citation statements)

References 11 publications

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“…The effort is mainly focused on the interaction of the shape of the caustics with that of the plastic zones developed around the crack tip [6, 7, 29, 33]. On the contrary, there are only limited references for the respective problem in case of perforated plates [34].…”

Section: Introductionmentioning

confidence: 99%

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

Pazis

Agioutantis

Kourkoulis

2011

Strain

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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%.KEY WORDS: caustics, finite element method, plate with a central hole, poly-methyl-meth-acrylate Ó

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Section: Introductionmentioning

confidence: 99%

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

Pazis

Agioutantis

Kourkoulis

2011

Strain

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“…al. [4] and Badalouka et al [5]. Recent work, Unger et al [6] and Hedans et al [7], has demonstrated that the method of caustics can be used to study the plasticity around the crack tip.…”

Section: Introductionmentioning

confidence: 99%

Experimental Evaluation of the Plastic Zone at Crack Tip by Caustics

Badalouka¹

2012

TOMEJ

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Abstract: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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“…Also, three-dimensional wedge problems, bimaterial wedges in antiplane shear deformation and rubber wedges in large strain analysis were studied [14][15][16]. The optical method of caustics has been applied to study of the singular stress fields near holes [17,18] and in the contact problems of anisotropic materialas [19].…”

Section: Introductionmentioning

confidence: 99%

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

Papadopoulos¹

2012

TOMEJ

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Abstract-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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Range of Applicability of the Method of Caustics around Holes

Cited by 5 publications

References 11 publications

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

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

Experimental Evaluation of the Plastic Zone at Crack Tip by Caustics

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

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