KEYWORDS: Interfaces, Finite element methods, Digital image correlation, Aluminum, Copper, Mechanics, Electronic components, Temperature metrology, Numerical integration, Data modeling
In this study, a method for evaluating a fracture parameter, J-integral, for an interface crack from the displacement fields under thermal deformation is developed for studying the fracture behavior of an interface crack in an actual electronic component. First, the displacement fields around an interface crack tip are measured using digital image correlation (DIC). Second, the displacement gradient and strain are determined from the displacement fields using a finite element smoothing technique on the domain of integration. Then, the stress components are determined from the strains using the elastic-plastic relations with the incremental strain theory and the each material property. Finally, the J-integral value is determined by the numerical integration on the domain of integration. The effectiveness of this evaluation method is demonstrated by applying this method to the displacement fields obtained from the elastic-plastic finite element analysis.
In this study, a method for identifying the elastic material characteristics of a heterogeneous material from measured displacements is proposed. The virtual fields method is employed for determining the elastic material characteristics. The solid propellant is considered as heterogeneous materials for the test subject. An equation representing the distribution of the material properties of the solid propellant is obtained by Fick’s law, and the distribution is applied to the virtual fields method. The effectiveness of the proposed method is demonstrated by applying to displacement fields obtained using finite element analysis. Results show that the heterogeneous material properties can be obtained by the proposed method.
In this study, the effect of the plastic deformation on the microscopic structure and the anisotropy of the elastic modulus in the cold-rolled steel sheet (SPCC) is investigated. Various uniaxial plastic strains (0%, 2.5%, 5%, 7.5%, and 10%) are applied to the annealed SPCC plates, then, the specimens for the tensile tests are cut out from them. The elastic moduli in the longitudinal direction and the transverse direction to the direction that are pre-strained are measured by the tensile tests. Cyclic tests are performed to investigate the effects of the internal friction caused by the movable dislocations in the elastic deformation. Also, the movable dislocations are quantified by the boundary tracking for TEM micrographs. In addition, the behaviors of the change of the elastic modulus in the solutionized and thermal aged aluminum alloy (A5052) are measured to investigate the effect on the movable dislocations with the amount of the depositions. As a result in SPCC, the elastic moduli of the 0° and 90° directions decrease more than 10% as 10% prestrain applied. On the other hand, the elastic modulus shows the recovery behavior after the strain aging and the annealing. The movable dislocation and the internal friction show a tendency to increase as the plastic strain increases. The marked anisotropy is not observed in the elastic modulus and the internal friction. The elastic modulus in A5052 with many and few depositions decreases similarly by the plastic deformation. From the above, the movable dislocations affect the elastic modulus strongly without depending on the deposition amount. Moreover, the elastic modulus recovers after the plastic deformation by reducing the effects of them with the strain aging and the heat treatment.
We describe a phase-stepping and subsequent phase-unwrapping technique with tricolor images for the analysis of isochromatics and isoclinics using arbitrary retarded retarders. A retarder used in the proposed method is not necessarily a quarter-wave plate specified for the wavelength of the light used. Not only the isochromatic and isoclinic parameters but also the retardation of the input and output retarders are determined simultaneously by the proposed phase-stepping method. Thus, any wavelength of visible light can be used in a single polariscope requiring matching the wavelength of the quarter-wave plate. Utilizing the characteristics of the proposed method, phase-unwrapping and ambiguity correction can be performed with phase maps obtained for three different wavelengths.
An instantaneous phase stepping and subsequent phase analysis method, using a charge-coupled device (CCD) camera with a pixelated form-birefringent microretarder array, is proposed for 2-D birefringence distribution measurement. A birefringent sample placed behind a polarizer and a quarter-wave plate is analyzed by the proposed method. Light emerging from the sample is recorded using a CCD camera that has a pixelated microretarder array on the CCD plane. This microretarder array has four different principal directions. That is, an image obtained by the CCD camera contains four data corresponding to four different optical axes of the retarder. The four images separated from the image recorded by the CCD camera are reconstructed using gray-level interpolation. Then, the distributions of the Stokes parameters that represent the state of polarization are calculated from the four images. The birefringence parameters, that is, the angle of the principal axis and the phase retardation, are then obtained from these Stokes parameters. This method is applicable to real-time inspection of optical elements as well as the study of the mechanics of time-dependent materials, because multiple exposures are unnecessary for sufficient data acquisition in the completion of data analysis.
A method of lens distortion correction is proposed in order to improve the measurement accuracy of digital image correlation for two-dimensional displacement measurement. The amounts of lens distortion are evaluated from displacement distributions obtained in a rigid body in-plane translation or rotation test. After detecting the lens distortion, its coefficient is determined using the method of least squares. Then, the corrected displacement distributions are obtained. The effectiveness of the proposed method is demonstrated by applying the correction method to an in-plane translation test and tension tests. The experimental results show that the proposed distortion correction method eliminates the effect of lens distortion from measured displacements.
An instantaneous phase-stepping and subsequent phase analysis method, using a CCD camera with a form-birefringent micro-retarder array, is proposed for two-dimensional birefringence distribution measurement. A birefringent sample placed behind a polarizer and a quarter-wave plate is analyzed by the proposed method. Light emerging from the sample is recorded using a CCD camera that has micro-retarder array on the CCD plane. This micro-retarder array has four different principal directions. That is, an image obtained by the CCD camera contains four data corresponding to four different optical axes of the retarder. The four images separated from the image recorded by the CCD camera are reconstructed using gray level interpolation. Then, the distributions of the Stokes parameters that represent the state of polarization are calculated from the four images. The birefringence parameters, that is, the principal direction and the phase retardation are then obtained from these Stokes parameters. This method is applicable to real-time inspection of optical elements as well as the study of mechanics of time-dependent phenomena because multiple exposures are unnecessary for sufficient data acquisition in the completion of data analysis.
Digital image correlation is used for the deflection measurement of a simple beam model in this study. The deflection distributions are obtained from images that are recorded using a digital camera with a shift lens. The experimental results show that the use of a shift lens is effective for the case of situations where direct view of the object is obscured. In addition, it is found that the deflection distribution of the relatively large structures can be measured using digital image correlation even if the random pattern is not painted on the object surface. The deflection measurement of bridges using digital image correlation for safety inspection is expected in the near future.
It is important to know mechanical properties of micro structures fabricated as a micro machine component by micro-stereolithgraphy(mSL). We developed new measurement equipment and measured Young's modules of micro cantilevers fabricated by mSL. Sample micro cantilevers were formed by changing irradiation laser power of mSL system and postcure processing time. We put load on the sample cantilever, then measured the relation between load and deflection of the cantilever. The young's modules of samples were calculated from the gradient of measured Load-Defection relation and the formula of strength of material. As the result, the young's module of cantilever made by mSL is depended on irradiation laser power. And the value increases by postcure which makes progress of un-cured part polymerization in the cantilever. Although the increased values are also depended on irradiate laser power.
KEYWORDS: Digital holography, Phase shifts, Holographic interferometry, Semiconductor lasers, Holograms, Holography, Near field diffraction, Denoising, Charge-coupled devices, 3D image reconstruction
Deformation measurement of a cantilever based on digital holographic interferometry is presented. The digital holograms of the cantilever before and after deformation are obtained by use of phase-shifting technique. By using the phase-shifting digital holography, the object wave information without zeroth order diffraction wave can be extracted. The phase difference of the reconstructed cantilever before and after deformation is obtained numerically using discrete Fresnel diffraction integral. Owing to the numerical analysis, the deformation of the cantilever can be obtained with high resolution of nanometer dimensions. The optical experimental results are shown to confirm our proposed method. Furthermore, we propose a mechanical movement free double-exposure method in phase-shifting digital holography using a laser diode.
To analyze fringe patterns, frequency and phase analysis of fringes becomes popular. It provides accurate results and automated processing. In this paper, the theories of the frequency and phase analysis methods using Fourier transform, Gabor transform, wavelet transform are introduced for shape analysis using gratin projection method, strain analysis using gratin method or iso chromatics and iso clinics analysis using photooelasticity. The applications of these methods are also described.
It is possible to measure the 3D shape of an object using grid projection methods. Moire topography which is a kind of grid projection methods can obtain the contour lines of the measured object in real-time. The authors developed a real-time shape measurement system based on the Moire topography. In order to perform quantitative and real-time shape measurement, we developed the integrated phase shifting method. However, the obtained distribution is wrapped in the range of -(pi) to (pi) . Therefore, a real-time phase unwrapping process is required. The present paper proposes a new unwrapping method using a composite rectangular grid which si composed of two rectangular waves of different pitches. The composite rectangular grid is projected onto an object. Each phase distribution of the two waves can be separated and calculated using the integrated phase-shifting method. The unwrapped phase distribution is produced from the two different phase distributions.
The present paper demonstrates the successful application of the photo viscoelastic 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 iso chromatic and iso clinic parameters simultaneously from a single color image, the time-dependent stress intensity factor extended for linearly viscoelastic materials is evaluated from the experimental results using a method based on least-squares. The result show that the value of the prosed critical stress intensity factor for fast crack growth may be considered as a characteristic property of the material under monotonically increasing load.
An optical system for lensless Fourier transformed holographic interferometry is constructed to enable the measurement of minute displacement from nm to micrometers scale and corresponding strain distribution using a CCD camera. In this technique, Fourier spectrum of the object beam is recorded on a hologram then the hologram image is easily reconstructed by a single pass of 2D FFT. In this paper, phase difference distribution is wrapped from -(pi) to (pi) , unwrapping process is required. The maximum spanning tree method is adopted here, which seeks a spanning tree that maximizes overall edge weights given by the cross amplitude. Displacement is calculated from the phase difference distribution. Even if there is no problem in the precision of loading device, displacement distribution of the object can be measured easily with high precision.
In this study, the authors propose a method for determining not only the secondary principal stress difference, but also its direction, using 3 image data obtained in various of polarization angles of incident light. As an example, a sphere under diametrical compressive load is analyzed to determine both the secondary principal stress difference and their directions, with or without rotation of the principal birefringent axis along the light path. The results show good agreement with theoretical/computed analyses.
In the current photoviscoelastic techniques, a set of multiple data, at least two images under plane polarization at a single instant, are necessary to determine not only fringe order but also principal birefringence direction simultaneously over the whole field of specimen. Therefore, the current techniques cannot be applied to such problems in which the good repetition and reproducibility of experiments are not expected. In order to overcome this type of difficulties in the analysis of time dependent phenomena, the authors proposed a photoelastic method using a white incident light with a set of the three primary colors. When using this method, not only fringe order but principal birefringence direction are successfully and easily determined from a single colored image. Utilizing this method together with photoviscoelastic constitutive equations, time dependent principal stress and strain difference, also their directions are successfully obtained. In this paper, the fundamentals of the white light photoviscoelasticity are described briefly, then a successful application of the method to the analysis of an example of viscoelastic problem is shown. An example problem of a viscoelastic strip having a hole under tension at several temperatures, at which the material shows remarkable viscoelastic behavior, is successfully analyzed.
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