Digital image processing and isoclinics

Isoclinics contain very important information about the direction of principal stresses. Unfortunately, it is frequently found that the isoclinics are vague or vanish altogether in certain regions of a plate. The isoclinic lines representing stress direction and the isochromatic lines representing stress magnitude are superimposed on each other. It is extremely difficult to separate them and to get isoclinics.In 1985, Zhang and Su introduced the TX-1 digital-image-processing system and sought new ideas to track isoclinics. In 1986, Yao developed a new image-division method (IDV) which is easy to apply in the digital image processing techniques to track isoclinics. This paper introduces other new methods: an image-differentiation method (IDF) and an image-division and differentiation method (IDD), and discusses some image-processing techniques. Experiments with a disk in diametral compression and with a slice from a three-dimensional frozen model are used to demonstrate such methods.     

Determining isoclinics from fringe patterns

A procedure has been developed which imparts new flexibility and increased usefulness to the bonded-polariscope technique. It also may help to increase the precision of the shear-difference method of principal-stress separation by providing greater precision to the determination of principal-stress directions. The procedure involves bonding a uniaxially stress-frozen plate of model material into a model between Polaroid sheets to function as a bonded polariscope. The fringe data obtained under load provide information for determining the principal-stress directions throughout the model by solution of a simple algebraic relation which lends itself readily to accurate plotting for graphical analysis. The inherent precision should exceed that of isoclinic analysis, particularly in regions where indistinct isoclinics might be expected, since accuracy increases with loading. Accurate fringe-order data also can be obtained by plotting fringe order as a function of position. The basis for the procedure is the modification of the applied-stress field by the presence of the residual (frozen)-stress field. Furthermore, the frozen-fringe order combines with the fringes applied at room temperature as though both stress fields were applied at room temperature. Theory and experimental confirmation are presented, together with a sample principal-stress map which is compared with that obtained from theory, and also from isoclinics. In addition, the chart for rapid graphical solution is included.     

Limitation of fourier transform photoelasticity: Influence of isoclinics

The application of the Fourier transform to photoelasticity was used in the evaluation of the retardation using a carrier system of fringes. In photoelasticity, the light intensity from the analyzer in a circular polariscope depends on both the retardation (isochromatics) and the isoclinic parameter. The theoretical analysis shows that the angle between the principal stresses in the model and in the carrier system of fringes influences the evaluation of the retardation (isochromatics), as occurs when misaligned compensators (namely, Babinet) are used. As a consequence, this method may not be applied as a full-field technique, although the error is small if the angle between the principal stresses in the model and in the carrier is less than 25 deg. Numerical simulations and experimental tests were conducted to corroborate this prediction.     

Real-time analysis of isochromatics and isoclinics using the phase-shifting method

This paper studies a new real-time phase-shifting method for the analysis of isochromatic and isoclinic parameters in photoelasticity. By rotating an analyzer at a constant rate and an output quarter-wave plate at a double rate of the analyzer and recording images by a CCD camera continuously, sequential images which brightness is integrated by sensors in a CCD camera during phase-shifting are obtained. Then, the distributions of the isochromatic and isoclinic parameters are obtained immediately and quantitatively using the proposed phase-shifting algorithm. The proposed method can be applied to high-speed inspection of optical elements or glass products. Also, it is expected that slowly varying time-dependent problems can be analyzed by the proposed method.     

Computerized image processing for whole-field determination of isoclinics and isochromatics

A new computerized method for the whole-field determination of isoclinic and isochromatic parameters in a stressed photoelastic model is presented. The intensity data obtained from the fringe pattern at three analyzer positions (0, 45, and 90 degrees) in a plane polariscope, are used for the computations. The relationships between the intensity values and the photoelastic parameters are derived using Stokes representation of polarized light. The experiments were carried out using a computer-based image-processing system. The accuracy achieved is assessed by comparing the theoretical and measured values. Accuracies of within ±3 degrees for isoclinics and ±0.05 fringe for isochromatics are shown to be possible.     

Plotting isoclinics for hybrid photoelasticity and finite element analysis

Displacement-based finite element method formulations are coupled with stress-based photoelasticity analysis. As the stress field is discontinuous at the interelement boundaries, the introduced smoothing procedure enables the generation of high-quality digital images acceptable for hybird experimental-numerical techniques. The proposed methods are applicable for the analysis of static and dynamic results of experimental photoelasticity.     

Computer-aided photoelastic analysis of orthogonal 3D textile composites: Part 1. Whole-field determination of isochromatics and isoclinics

Two correlative methods are developed for the computer-aided photoelastic analysis of orthogonal 3D textile composites comprising 6 mm×6 mm highly heterogeneous unit cells in-plane. The first method, presented in Part 1, is used for the whole-field determination of isochromatics and isoclinics; the second method, presented in Part 2, is applied for subsequent photoelastic stress analysis. Part 1 delineates precisely how one circular polariscope and two plane polariscope photoelastic images are implemented to extract the isochromatic parameterR and isoclinic parameter α using the digital image processing technique. The photoelastic experiments were performed with orthogonal 3D textile composite as well as aluminum plates containing a hole under the uniaxial tension loading. The obtained values ofR and α, for the case of the aluminum plate, are smoothly distributed over the field and show consistent agreement with those computed from finite element analysis (FEM). In the case of the composite plate, the global distribution ofR and α also agree well with FEM results employing the homogenized composite properties. However, bothR and α exhibit local variations according to the 3D fabric structure, and the varying amplitude of α is relatively larger than that ofR.     

An interpretation of inelastic birefringence

The relationship between plastic thickness change and plastic isochromatics occurring beyond the plostic tensile instability point of a uniaxial tensile specimen is investigated. Mechanical thickness-change measurements and a hologram of thickness change are shown to be in close qualitative agreement with isochromatics in a region of gross plastic yielding. Analytical observations are discussed to aid the interpretation of the experimental results obtained. Finally, possible extensions and applications are discussed.     

Continuum interpretation of virial stress in molecular simulations

The equivalence of the virial stress and Cauchy stress is reviewed using both theoretical arguments and numerical simulations. Using thermoelasticity problems as examples, we numerically demonstrate that virial stress is equivalent to the continuum Cauchy stress. Neglecting the velocity terms in the definition of virial stress as many authors have recently suggested, can cause significant errors in interpreting MD simulation results at elevated temperatures (T > 0 K).     

The stress relaxation of molten PMMA at large deformations and its theoretical interpretation

Summary The stress relaxation behaviour of molten PMMA under large tensile deformations has been studied. Maximum values of the extension ratio were larger than 3.5. Similarly with previous results, the time dependence of the relaxing stress was found to be approximatively the same at all deformations. The deformation dependence was compared with the predictions of a theory byDoi andEdwards as well as with a modification of that theory which proves to agree better with the experimental results.

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Zusammenfassung Es wurde das Spannungsrelaxations-Verhalten von PMMA-Schmelzen unter großer Dehnbeanspruchung untersucht. Die maximalen Dehnungen waren dabei größer als 3,5. Ähnlich wie bei früheren Untersuchungen ergab sich die Zeitabhängigkeit der relaxierenden Spannung bei allen Deformationen als nahezu gleich. Der Deformationsverlauf wird mit den Voraussagen der Theorie vonDoi undEdwards, sowie denjenigen einer modifizierten Theorie verglichen. Es erweist sich, daß letztere die experimentellen Ergebnisse noch besser zu beschreiben vermag.

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With 5 figures     

Rapid interpretation of moiré photographs

The paper describes the possibilities of rapidly and conveniently obtaining results by means of the reflection moiré method. The moiré photographs are produced with the aid of a screen provided with a finely ruled grid. The contrast of the photographs is increased by optical means. By displacement of two equal moiré photographs, moiré fringes of second order for the curvature or the twist are obtained. It is shown how charts can be produced which indicate:

1. The distribution of the bending moments
2. The distribution of the bending moments for which the reinforcement should be designed
3. The distribution of the shear forces and the magnitude of the bearing reactions.

     

Molecular interpretation of the behaviour of polyisobutylene in different solvents

The effects of solvent environment on the behaviour of a high molecular weight polyisobutylene dissolved in kerosene and various grades of poly-1-butene solvent mixtures are investigated. The dependence of various molecular parameters such as zero-shear viscosity, intrinsic viscosity, specific viscosity, relaxation time and molecular expansion factor, on the polymer concentration, type of solvent and solvent viscosity is studied in the vicinity of dilute and semidilute regions (near the critical concentrationc ^*). The dependence of these parameters on solvent environment follows qualitatively Zimm's molecular model. The dependence on the polymer concentration deviates from this dilute solution theory. The effects of temperature on the zero-shear viscosity and the Maxwell relaxation time are also presented for two PIB solutions.     

A dynamical interpretation of flutter instability in a continuous medium

Flutter instability in an infinite medium is a form of material instability corresponding to the occurrence of complex conjugate squares of the acceleration wave velocities. Although its occurrence is known to be possible in elastoplastic materials with nonassociative flow law and to correspond to some dynamically growing disturbance, its mechanical meaning has to date still eluded a precise interpretation. This is provided here by constructing the infinite-body, time-harmonic Green's function for the loading branch of an elastoplastic material in flutter conditions. Used as a perturbation, it reveals that flutter corresponds to a spatially blowing-up disturbance, exhibiting well-defined directional properties, determined by the wave directions for which the eigenvalues become complex conjugate. Flutter is shown to be connected to the formation of localized deformations, a dynamical phenomenon sharing geometrical similarities with the well-known mechanism of shear banding occurring under quasi-static loading. Flutter may occur much earlier than shear banding in a process of continued plastic deformation.     

An interpretation of photoviscoelastic/plastic data

The birefringent effect of viscoelastic and viscoplastic polymeric materials is considered and shown to have separate contributions from the stress, recoverable strain and the permanent deformations. Experimental data for a number of materials are discussed and the procedure for analyzing these data described.     

On the physical interpretation of fractional diffusion

Even if the diffusion equation has been widely used in physics and engineering, and its physical content is well understood, some variants of it escape fully physical understanding. In particular, anormal diffusion appears in the so-called fractional diffusion equation, whose main particularity is its non-local behavior, whose physical interpretation represents the main part of the present work.