A neoteric interferometer for use in holographic photoelasticity

A shortcoming of the conventional holographic interferometer used in photoelasticity is that, for the double-exposure cases, the resulting fringe patterns are a complex combination of conventional isochromatic and isopachic fringes. This paper describes a holographic interferometer that may be used to obtain separate but simultaneous isochromatic- and isopachic-fringe patterns for photoelastic models in states of plane stress. The method requires a model with a partially reflecting front surface. Isopachics, which are proportional to the thickness change, are recorded using holographic interferometry from the transmitted light. The isochromatics are obtained from the transmitted light by conventional means. General equations relating the surface displacement of the specimen to the observed fringe patterns are developed, and examples of static and dynamic loadings are shown.     

A study of the dynamic nolophotoelasticity light rotation method

A method which allows simultaneously separating the isochromatia and isopachic fringes for transient plane-stress problems is presented. A set of double pulsed ruby laser and a terbium glass Faraday rotator are used. The double-order timing methods applied in the synchronous system of the impact load and trigger cine jit. Separated fringe patterns of a structure component are recorded a nine different instants after impact loading, and the dynamic material-fringe values of isochromatics and isopachics are obtained by experiment. Finally, dynamic stresses distributed along a section at different instants are resolved.     

全息动光弹性旋光法研究

本文提出了一个在全息动光弹性瞬态平面应力问题中同时获得分离的等差线及等和线条纹并分解平面瞬态应力的方法。文中给出了框架在冲击荷载作用下不同时刻等差线及等和线的分离条纹图和某个截面不同时刻的动态应力分布。     

A new method of resolving transient stresses in dynamic holophotoelasticity

A method which allows the simultaneous separation of the isochromatic and isopachic fringes for transient plane-stress problems is presented. A double pulsed ruby laser and a terbium glass Faraday rotator is employed to resolve the transient isochromatic and isopachic patterns. Separated fringe patterns for a structural component are recorded at nine different instants after impact loading. The dynamic material-fringe values of isochromatics and isopachics are obtained within the experiment. Finally, dynamic stresses distributed along a section at different time intervals are resolved.     

Interpretation of fringes in stress-holo-interferometry

Previous studies had concluded that stressholo-interferometry patterns consist of the independent superposition of the isopachic family (with half-order fringe shifts) and the isochromatic family. It is shown here that this interpretation is not always valid and can result in serious errors in some cases. In particular, it is demonstrated that the position, and even the existence of the fringes, are affected by the interaction of the isopachics and isochromatics. This effect is most pronounced when the two families of fringes are nearly parallel and of approximately the same spatial frequency. The independent superposition interpretation is most accurate when the two families of fringes are orthogonal, whatever the ratio of spatial frequencies might be. These properties are illustrated using computer-generated holographic interference patterns.     

Differential stress-holo-interferometry

In displacement analysis of opaque bodies using holographic interferometry, it is a common practice to record one hologram of the body at some arbitrary load and then to increase the load and record a second hologram on the same photographic plate. The fringes in the reconstructed image correspond to the change in the displacement occurring between the two exposures. A new technique for photoelastic analysis based on this same idea will be presented. This technique, to be referred to as differential stress-holo-interferometry, has several advantages over existing techniques. Using vector-algebra methods, the general intensity equations for a double-exposure hologram of a photoelastic model in which neither of the holograms is of the unstressed model is developed. In general the resulting interferogram is difficult to interpret; however, for selected types and levels of loading, a pattern which is easily interpreted results. It is shown that the isochromatic fringes in these patterns are more precisely defined than those in a conventional double-exposed hologram of a photoelastic model. In addition, the new technique offers the advantages of increased fringe visibility, isochromatic-fringe multiplication, and an aid for the determination of the isochromatic-fringe order. Finally, for certain types of models, a technique for producing an interferogram in which the isochromatics and isopachics are completely independent and the isopachics do not undergo a half-order-fringe shift is demonstrated.     

Application of holography to anisotropic composite plates

The application of holography to stress analysis of opaque, anisotropic composite plates subjected to static or dynamic transverse and in-plane loads is presented. The equations of motion show that, for flexed, anisotropic, laminated composite plates, the complete state of stress at a generic point in any lamina, plus the moments and shear forces, are related to the temporal and spatial partial derivatives of the transverse displacement of the middle surface. Interferometric holography is shown to be well suited for obtaining the transverse displacement. Methods of determining the required spatial and temporal partial derivatives are discussed, an example being demonstrated. The holographic determination of anisotropic-material properties, stress and strain concentrations and the nondestructive evaluation of critical buckling loads for composite structures, plus the use of holographically obtained isopachics to supplement photoelastic analyses of composites, are also discussed. Experimental results for statically and dynamically loaded composite plates and beams with and without geometric discontinuities are presented to illustrate the concepts and techniques.     

Dynamic stress-intensity-factor determination from isopachics

The governing equations for determination of dynamic stress-intensity factor at the tip of a running crack are developed from a dynamic analysis of dynamic isopachicfringe patterns. The equations are applied to investigate dynamic crack propagation in Homalite 100 by means of dynamic holographic interferometry. A simple method based on simultaneous measurement of the widths of two isopachics allows determination of Irwin's additional stress field, and a dynamic correction function for the stress-intensity factor is derived. It was found that dynamicK-values obtained from dynamic isopachic-fringe-pattern analysis are lower than their corresponding static values. This implies a modification of the crack velocity vs. stress-intensity-factor relationship towards lower values ofK for dynamic crack propagation.     

A new holographic interferometer for stress analysis

In holographic interferometry with a photoelastic model, two families of fringes are generated simultaneously when the model is stressed. One family represents the isochromatic-fringe pattern normally associated with photoelasticity which yields the difference between the principal stresses. The other family represents the isopachic-fringe pattern associated with interferometry which yields the sum of the principal stresses. From these complementary patterns, the magnitudes of the principal stresses can readily be determined throughout the field of observation. Unfortunately, these fringe patterns are not completely independent but interact in such a way as to make interpretation difficult in critical regions of the model. A new system has been developed which readily permits simultaneous acquisition of these fringe patterns without their undesirable mutual interaction, as well as providing increased sensitivity. This new interferometer uses a double-pass object beam and an optical rotator to eliminate the isochromatic-fringe pattern and its effect from the isopachic interferogram. Such a system has considerable value in experimental mechanics for applications to both static and dynamic model studies and to materials investigation.     

The generic nature of the absolute-retardation method of photoelasticity

The method of absolute-retardation measurements does not depend upon the use of any specific interferometer. Any one of the many extended field interferometers can be employed, including the Series, Michelson, Mach-Zehnder and Fizeau types. Where adequate monochromatic purity of light source is available, reflections from the two surfaces of the model can form the interferogram, thus dispensing with the necessity of any separate optical interferometer. The two-dimensional stress-optical relationships are derived in their most general form. The relationships are identical for all instruments or interference systems—only the calibration constants change with different systems. Interferograms from four distinctly different systems are shown. Interference-fringe sharpening is introduced and demonstrated. A laser-light source was used with two systems to provide high monochromatic purity. The interferometric method of Nisida and Saito is correlated with the absolute-retardation method. The opportunity to obtain information for a complete stress solution from one photograph makes the method attractive for both static and dynamic problems.     

Dynamic fracture toughness of Homalite-100

Dynamic fracture toughness of Homalite-100 determined by T. Kobayashi and Dally are compared with those previously obtained by the authors where similarities in the two results for single-edged-notch specimens of various configurations are noted. Dynamic fracture toughness of Araldite B obtained by Kalthoff, Beinert and Winkler and those of Homalite-100 obtained by the authors are then compared and, again, similarities in the two results and, in particular, the scatters in experimental data for wedge-loaded DCB specimens of different sizes are found. All three teams of investigators used static near-field solution to compute the dynamic stress-intensity factors from recored dynamic isochromatics or dynamic caustics. Errors generated through this use of static near-field solutions, as well as through the use of larger isochromatic lobes, are thus discussed.     

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.     

Dynamic stress-intensity factors for unsymmetric dynamic isochromatics

The mixed mode, near-field state of stresses sourrounding a crack propagating at constant velocity is used to derive a relation between the dynamic stress-intensity factorsK _I,K _II, the remote stress component σ _ox and the dynamic isochromatics. This relation, together with an over-deterministic least-square method, form the basis of a datareduction procedure for extracting dynamic,K _I,K _II and σ _ox from the recorded dynamic photoelastic pattern surrounding a running crack. The overdeterministic least-square method is also used to fit static isochromatics to the numerically generated dynamic isochromatics. The resultant staticK _I,K _II and σ _ox are compared with the corresponding dynamic values and estimats of errors involved in using static analysis to process dynamic isochromatic data are obtained. The data-reduction procedure is then used to evaluate the branching stress-intensity factor associated with crack branching and the mixed-mode stress-intensity factors associated with crack curving.     

Characteristic relations of flow birefringence

The general problems of the flow-induced birefringence in liquids have been presented and discussed in Part 1 of this paper, in which some particular responses of an aqueous solution of NGS 1828 were presented, namely, the pertinent mechanical responses and the birefringence responses in transmitted radiation. This paper presents the optical responses of NGS 1828 observed in the scattered radiation. It is shown that the scattered-light techniques can become a powerful and indispensable tool of flow-birefringence techniques, if the actual patterns of light scattering are taken into account. Proof is given that the light scattering and the related birefringence cannot be described by Rayleigh's mathematical model of scattering (Part 1, Ref. 51). The optical effects of the modulation of the primary beam and the scattered beam, called scattered primary isochromatics and scattered secondary isochromatics, are described in terms of the parameters of the system. A practical example is presented. Samples of typical recordings of light-intensity modulation by typical flow patterns are given in the form of scattered primary and secondary isochromatics and integrated isochromatics. One type of intensity modulation enables the determination of shear-strain rate at an interior point in the flow field. Using the determined shear-strain rates at the interior points, a velocity profile along the axis of symmetry of a rectangular-conduit flow was obtained. The results so obtained were satisfactory when compared with the results of direct volumetric measurement. The other type of intensity modulation reveals the nonuniform distribution of birefringence along the path of the transmitted light in the rectangular-conduit flow. The results presented in Part 1 of this paper, are complementary to the results presented below.     

Full-field isopachic generation in photoelastic coatings

A method has been developed for the generation of isopachic fringes in photoelastic coatings. This method requires that the front (outer) surface of the coating be deposited with a thin metallic film to increase the front-surface reflellctivity. The light which penetrotes the photoelastic coating reflects from the rear surface, emerges from the front surface and then combines with the frontsurface reflection to yield a system of “carrier” fringes. When the model is loaded, the carrier-fringer system is modulated by the principal-strain sums and the principalstrain differences. Superposition of the modulate carrierfringer system with the original one (by double exposure or by superposition) yields isopachic and isochromatic fringes. The isochromatics can be suppressed by proper selection of the photoelastic material to yield only isopachics for the unambiguous determination of principal-strain sums over the full field.     

On the effect of quarter-wave-plate errors in stress-holo-interferometry

The purpose of this paper is to analyze the influence of imperfect quarter-wave plates on the fringe configuration which is obtained in holographic interferometry. It has been found that isopachics may be substantially shifted by very small errors in the retardation of the quarter-wave plates. An alternative multiexposure technique using plane-polarized light is proposed. This technique eliminates the quarter-wave-plate error and preserves the full-field character of the interferometic method. The technique is proven analytically and experimentally.     

On the limit velocity and buckling phenomena of axially moving orthotropic membranes and plates

In this paper, we consider the static stability problems of axially moving orthotropic membranes and plates. The study is motivated by paper production processes, as paper has a fiber structure which can be described as orthotropic on the macroscopic level. The moving web is modeled as an axially moving orthotropic plate. The original dynamic plate problem is reduced to a two-dimensional spectral problem for static stability analysis, and solved using analytical techniques. As a result, the minimal eigenvalue and the corresponding buckling mode are found. It is observed that the buckling mode has a shape localized in the regions close to the free boundaries. The localization effect is demonstrated with the help of numerical examples. It is seen that the in-plane shear modulus affects the strength of this phenomenon. The behavior of the solution is investigated analytically. It is shown that the eigenvalues of the cross-sectional spectral problem are nonnegative. The analytical approach allows for a fast solver, which can then be used for applications such as statistical uncertainty and sensitivity analysis, real-time parameter space exploration, and finding optimal values for design parameters.     

Holographic velocimetry for flow diagnostics

Currently, there are a number of flow diagnostic tools available for the evaluation of fluid dynamic systems. In spite of its great potential, holographic velocimetry is one technique which has not been widely used. It does, however, have great potential in this area due to its inherent three-dimensionality. As demonstrated in this study of fully developed turbulent flow in a pipe, full three-dimensional mapping can be achieved at any instant in a flow cycle. Comparisons of holographic results with analytical predictions and laser-Doppler-anemometry (LDA) measurements demonstrate the accuracy of the technique as well as some of its advantages and disadvantages relative to LDA. Although relatively poor spatial resolution is obtained, the fact that holographic velocimetry is both an instantaneous and full volume measuring tool makes it useful for a range of complex and high-speed flow-measurement applications.     

AN IMPROVED IRS METHOD FOR STRUCTURE MODEL CONDENSATION1)

模型缩聚法在结构的静力和动力特性分析中有着广泛的应用。应用模型缩聚法,可以有效降低结构的有限元计算规模,节省计算时间和成本,并能获得和实验测量自由度相匹配的有限元模型。本文在改进模型缩聚方法(improved reduced system, IRS)的基础上,提出一种考虑二阶惯性量的改进IRS方法,有效改进了IRS方法的计算精度,和模型缩聚迭代法(iterated IRS, IIRS)相比,此方法计算量更小且计算精度更高。以桁架结构和框架结构为例对所提二阶IRS方法进行了验证,并将计算结果与精确值、Guyan缩聚解、IRS缩聚解和IIRS缩聚解进行了比较,结果表明了所提方法计算精度最好,具有良好的工程应用前景。     

静刚性分布动力载荷下半空间的表面位移

本文用积分变换及Ｃａｇｎｉａｒｄ－Ｄｅ Ｈｏｏｐ方法获得静刚性分布脉冲载荷作用下半空间表面中心点位移的解析表达式。利用此闭合表达式可以进一步研究土五结构物的动力相互作用问题及动力接触问题。