Experimental Method Of Caustics Research Articles

Double initial and caustic curves in diametrically compressed transparent discs - Application to the contact length

General formulae for double initial and caustic curves (reflected and transmitted) are obtained in the case of smooth contact of two cylindrical elastic bodies of arbitrary radii. Namely, based on the method of reflected and transmitted caustics, the conditions for the development of double initial and contact caustic curves are established as functions of six independent para­meters, while easy-to-use closed-form expressions are given for obtaining the contact length. An experimental protocol is then implemented in the case a thin cylindrical transparent disc is compressed between the jaws of the Inter­na­tional Society for Rock Mechanics suggested device for the execution of the Brazilian-disc test. The experimental method of caustics can provide the con­tact length quite accurately, even in the case of double curves which seem that are not always a consequence of a wide contact region.

Evaluation of stress intensity factors of rounded V and U notches under mixed mode loading, using the experimental method of caustics

The caustic method has proven to be a useful optical method to determine stress intensity factors. In this paper, the theory of caustics was developed for rounded V and U notches. The caustic curve was calculated by applying stress and optic formulas in terms of stress intensity factors and geometrical properties of V and U notches and the specimen. In this study, stress intensity factors were determined by measuring specific lengths in image plane. The models were subjected to bending and experiments were conducted as a function of applied load, notch length to notch width ratios, notch tip radiuses, and notch opening angles. The results compared well with the FEM method. The paper finally establishes the reliability of the reflected caustic for determination of stress intensity factors in rounded V and U notches under mixed mode loading.

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 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.

Experimental Study of a Structure Under Stress Pulse Simulating Vertical Ground Motion

This article is an attempt to study the effects of a stress pulse simulating strong vertical excitation, particularly at the first steps of the mode of propagation. The structural model represents a two-story single column, having two pairs of cantilever beams on either side. The study is carried out by means of the experimental method of caustics. The areas of maximum stress concentration, as well as the wave front direction within the horizontal elements of the structure, are determined. The influence of the wave and the reflected effects on the top of the column are also studied. The experimental results are compared with the corresponding results obtained by finite element analysis. The results could be used for the development of rules for the effects of the vertical component.

Experimental Study of the Reduction at Crack-Tip Stress Intensity Factor KI by Bonded Patches

Patch repair of cracked structures has become a rapidly grown technology. The major function of a repair is to reduce the stress intensity factor at the crack-tip. Calculation of stress intensity factor of a repaired crack has been performed by analytical and numerical methods. However, these methods are based on simplifying assumptions regarding material behavior and repair conditions. In the present paper an experimental and an numerical determination of mode-I stress intensity factor (SIF), KI at the tip of an edge crack reinforced with bonded patches is undertaken by using the optical method of caustics and the finite element analysis (FEA). The experimental method of caustics is simple in its application and has successfully been used for the solution of a host of crack problems of engineering importance. The experimental results are compared with the corresponding one obtained by FEA. The program ANSYS 11 was used for the FEA. The cracked used plates were made of Lexan (PCBA) and the patches were made of Plexiglas (PMMA).

Caustics and Buckling of Cracked Columns

The experimental method of caustics is applied to buckling behaviour of straight cracked columns. Two major parameters of the problem may be defined through the caustics method: the SIF and the high strain internal region. The knowledge of these parameters may be used to improve predictions of the buckling behaviour of cracked columns.

Technical Note: Experimental Estimation of the Load Distribution in Bearings by the Method of Caustics

The objective of this paper is the experimen- tal estimation of the load distribution in roller-bearing by the metrhod of caustics. Contact problems have many practical and important applications. ) For the solution of such prob- lems, besides mechanical analysis, the experimental method of caustics 2 can also be applied. The optical method of caus- tics is suitable for the experimental study of singularities in stress fields created either by discontinuities or by loading. Previously, caustics has been applied to the study of singular stress fields developed near concentrated or uniformly dis- tributed loads which are applied along straight boundaries. 3,4 In this work, it is applied to study the load distribution in roller- bearings.

コースティックス法によるモードＩ，ＩＩおよびＩＩＩ荷重下における応力拡大係数の測定に関する実験的・数値解析的検討

The experimental method of caustics is a useful technique for the determination of the stress intensity factor K. In this paper, the stress intensity factors under mode I, II and III loadings are measured by the method of caustics, and the effect of those loading modes on the measurement accuracy is experimentally and numerically examined. Furthermore, a numerical method based on the 3-D finite element method (3D-FEM), which can directly simulate the caustic images, is proposed. As a result, it is found that the minimum initial curve radius rmin0 obtained in this study depends on the type of loading that is of mode I or mode II. In the case of mode III loading, however, the measured value of K agrees with the theoretical one regardless of the change of the initial curve radius r0. And the simulated results are in good agreement with the experimental images.

Application of the Method of Caustics to Rolling Contact Fatigue and Simulation of the Caustic Images.

As a series of studies to clarity the mechanism of crack initiation and propagation in rolling contact fatigue, the experimental method of caustics has been applied to disk-to-disk rolling contact fatigue tests. The cusp-like and round type caustic images were generated from the rolling contact point and the crack tip, respectively. Although the shape and size of the cusp-like image depending on the magnitude of applied load was constant, that of the round image was markedly changed with the relative position between the crack and the rolling contact point. The experimental caustic images have been simulated using a computer program developed by combining the theory of caustics with the theory of boundary element method. By comparing experimental caustic images with simulated ones, it is shown that the round type caustic image obtained in rolling contact is strongly affected by shear deformation of the crack.

Various theoretical applications of the maximum modulus principle to the experimental method of caustics

Various theoretical applications of the maximum modulus principle to the experimental method of caustics

Complex Stress Intensity Factors in Bent Plates With Cracks

The experimental method of caustics was applied to the study of asymmetric bending of isotropic cracked plates and to the determination of the complex stress intensity factors (S.I.F’s) at the crack tips. It was shown that the method of reflected caustics is convenient for detecting and evaluating both KI and KII stress intensity factors. Based on the singular approximation of the elastic solution around the crack tip, the theory of formation of the caustics was developed and related to the evaluation of both components of stress intensity factors. It was also shown that the generalized method of caustics, known as the method of pseudocaustics, is a potential and simple method for determining S.I.F’s in cracked plates submitted to bending. Experimental evidence with specimens made either of optically inert materials, such as plexiglass, or of any opaque material like steel, and elastically loaded, has corroborated the theoretical results.

An improved method for the determination of mode i stress intensity factors by the experimental method of caustics

A modification of the usual way of determining mode I stress intensity factors at crack tips by using the experimental method of caustics is proposed. In accordance with the proposed modification, both principal diameters of an experimentally obtained caustic should be taken into account so that the influence of the part of the stress field behaving like r1/2 near the crack tip is minimized ( r being the polar distance from the crack tip). This modification makes the method of caustics much superior to the photoelastic and interferometric methods for the evaluation of mode I stress intensity factors, not only from the experimental but also from the theoretical point of view. Some interesting geometrical properties of the caustics formed at crack tips are also deduced in this paper.

Caustic Image Simulation Based On BoundaryElement Method

The experimental method of caustics has been applied to rolling contact fatigue for determining the crack growth mechanism. Caustic images formed from stress fields under rolling contact with a crack are very complicated. Therefore, the theoretical background of the experimental caustic images formation has been studied through caustic image simulations. The simulation has been done by the scheme combining directly caustics method with boundary element method. The size and shape of simulated caustic images, which are formed from the contact region and crack tip in disk-on-disk rolling contact fatigue, was coincident with experimental caustic images. In the present paper, the computer program was extended to simulate not only caustic images but also their initial curves that are loci of points in the disk through where the light rays passed. This program is utilized to discuss the mechanism of damage formation in rolling contact fatigue and to examine experimental results.