Masahisa Takashi

Dynamic photometric imaging polarizer-sample-analyzer polarimeter: instrument for mapping birefringence and optical rotation

An imaging dynamic photopolarimeter in an optical configuration P(α)SA(n) (polarizer-sample-analyzer) having harmonically rotating polarizer (P) and analyzer (A), is presented for studies of inhomogeneous birefringent media. The method is capable of simple and precise measuring of birefringence and optical rotation across a two-dimensional field. Although the basic principle upon which the method operates has been proposed earlier, the focus here is on its extension, applicable to a whole field, and immediate measurement of three optical parameters, which have direct physical meaning. Earlier versions of the instrument either operate with a single beam or measure components of Jones or Mueller matrices. The operation of the given method is consistent with a general idea of dynamic photopolarimetry by discrete Fourier analysis and entails digital procession of intensity images, obtained at nine equispaced positions of the polarizer and the analyzer during synchronous rotation of them. A technique of data acquisition is described, and a detailed error analysis is provided. Theoretical considerations are supplemented with testing measurements of a quartz phase plate.

Photoelastic Analysis with a Single Tricolor Image

A new approach to simultaneous measurement of isochromatics and isoclinics from a single image using a tricolor light, called as the tricolor photoelastic technique, is proposed in order to enable and facilitate the analysis of time varying phenomena. Not only an apparatus of experiment but the whole analysis system and procedure are developed. Using a color digital camera and a tricolor light source under linear polarization, fringe order and the principal direction of birefringence are obtained from a piece of color image data by a single shot using the method proposed. It is emphasized that this method can be applicable to time varying phenomena in which good repeatability and reproducibility of experiments are not expected, since multiple exposures are not necessary for sufficient data acquisition in the completion of stress analysis.

A new method for photoelastic fringe analysis from a single image using elliptically polarized white light

Abstract A new two-dimensional photoelastic method for the analysis of fringe order and the principal direction of birefringence from a single image combining an elliptically polarized white light and color image processing is demonstrated. To determine fringe order, a database-search approach based on the primary color analysis is employed. After determining fringe order, the principal direction of birefringence is obtained by solving a non-linear equation. The equation of emerging light intensity is derived and the theory of the proposed method is described. Then, the successful application of the method to photoelastic analysis is shown. It is emphasized that the proposed method can be applicable to time-varying phenomena since multiple exposures are not necessary for sufficient data acquisition for the completion of stress analysis.

Instantaneous phase-stepping photoelasticity for the study of crack growth behaviour in a quenched thin glass plate

A new approach to simultaneous acquisition of phase-stepped photoelastic fringes using a CCD camera equipped with a pixelated micro-retarder array is described for the investigation of time-variant problems. This method is applied to the study of quasi-static crack growth in a quenched thin glass plate. The distributions of the principal direction as well as the principal stress difference around a growing crack tip are obtained by the proposed method. Then, not only the mixed-mode stress intensity factors but also the T-stress are evaluated from the distribution of the principal stress difference, and they are validated using the reconstructed phase maps. The results show that the proposed instantaneous phase-stepping technique is effective for the study of the crack growth behaviour in a thin glass plate.

Experimental Analysis of Rolling Contact Stresses in a Viscoelastic Strip

An experimental approach to two-dimensional, viscoelastic, steadily moving rolling contact is described. The photoviscoelastic technique is employed for the analysis of rolling contact stresses between a viscoelastic plate and a rigid rolling cylinder in which the principal axes of stress, strain and birefringence are not coincident with each other. Using an elliptically polarized white light, the distribution of isochromatic fringe order and the principal axes of birefringence at an instant are determined from a single photoviscoelastic image. The time variations of the differences of the principal stresses and strains, as well as their directions, are obtained by use of the optical constitutive equations of photoviscoelasticity. The experimental results involving the time variation of the stresses around the contact surface and their distributions are analyzed.

Tricolor photoviscoelastic technique and its application to moving contact

A new technique for simultaneous determination of both fringe order and principal direction of birefringence in practical photoviscoelastic analysis using white incident light with a set of the primary colors, called tricolor photoviscoelasticity, is described. This method can determine both the fringe order and principal direction of birefringence from a single-color photoviscoelastic image under plane polarization. Then, the authors evaluate time dependent stresses and strains around a contact region in a viscoelastic strip plate under nonproportional loading condition. The variations of the principal stresses and strains are easily obtained over a wide time range by use of the optical constitutive equations of photoviscoelasticity and the characteristic material property functions.

Full-field automated photoelasticity by Fourier polarimetry with three wavelengths

The search for fast, precise, and robust testing techniques remains an important problem in automated full-field photoelasticity. The polarizer-sample-analyzer (PSA)-based three-wavelength polarimetric method presented here employs discrete Fourier analysis and a spectral content unwrapping algorithm to provide completely automatic, simple, fast, and accurate determination of both photoelastic parameters. Fourier analysis of experimental data and a three-wavelength approach reduce the effect of noise and efficiently cope with poor accuracy in regions of both isochromatic and isoclinic maps. Because any polarimetric technique yields the phase value in the principal range of the corresponding trigonometric function, the final step in data processing is phase unwrapping. Because of the good quality of the wrapped phase map and because each point is processed independently, our suggested three-wavelength unwrapping algorithm exhibits a high level of robustness. Unlike some other PSA three-wavelength techniques, the given algorithm here solves the problem of phase unwrapping completely. Specifically, it converts experimentally obtained arccosine-type phase maps directly into full phase value distributions, skipping the step of generating an arctangent-type ramped phase map and resorting to other unwrapping routines for final data processing. The accuracy of the new technique has been estimated with a Babinet-Soleil compensator. Test experiments with the disk in diametric compression and a quartz plate have proved that the technique can be used for precise determination of the isoclinic angle and relative retardation, even for large values of the latter.

A New Computer-Aided System for Photoelastic Stress Analysis with Structure-Driven Type Image Processing

Two major difficulties in the currfent computer-aided photoelastic analysis, namely automatic determination of principal stress direction and of fringe order over the whole area of specimen, were successfully overcome with single-valued representative functions for principal stress direction with the diagonal summation theorem and for fringe order with the concept of trans-versality of intersection in Catastrophe Theory. Utilizing a structure-driven type image processing, not only the stress trajectories but also the stress distribution on an arbitrarily designated axis are successfully calculated on the basis of theories of differential geometry and ordinary differential equations, respectively. A new system developed in this study is useful for two dimensional analysis as well as for the stress-frozen technique in three dimensional analysis, in which the isochromatics and the isoclinics are inevitably superimposed.

Modified intelligent hybrid technique reducing experimental error over the entire target area

The intelligent hybrid technique proposed by Nishioka et al. can be used to analyze stress intensity factors from displacement data obtained by experiments with high accuracy and reliability. However, the hybrid technique suffers from inevitable error and noise involved in extracting displacement fields from the boundary experimentally the boundary obtained experimentally. In this paper, a modified intelligent hybrid technique is developed to improve the shortcomings of the current technique. The proposed hybrid technique reduces the influence of experimental errors not only on/along the boundary but also inside the target area. Taking the SaintVenant principle and the results of test simulations into account, the effectiveness of the proposed hybrid technique is discussed. Then, applying the proposed hybrid technique to the plate with a hole under tensile loading, the distribution of strain, stress, and displacement over the entire target area is calculated with high accuracy and reliability.

Elliptically polarized white light photoviscoelastic technique and its application to viscoelastic fracture

The present paper demonstrates the successful application of the photoviscoelastic technique using elliptically polarized white light to the stress field evaluation of the crack growth in a viscoelastic strip. Using the proposed technique, which can determine both isochromatic and isoclinic parameters simultaneously from a single color image, the time-dependent stress state around a slowly propagating crack tip in a viscoelastic strip plate is successfully analyzed. Then, the time-dependent stress intensity factor extended for linearly viscoelastic materials is evaluated from the experimental results using a method based on the least squares. The results show that the proposed critical stress intensity factor for fast crack growth may be considered as a characteristic property of the material under monotonically increasing load.