混合光载波法分离动静态主应力

本文将等差载波位相调制原理与夹层全息术结合形成的混合光载波法,可同时获得等差载波条纹图与混合载波条纹图.对混合载波纹图进行光学付里叶变换,利用空间滤波技术可将等和载波条纹从中分离出来.利用图象处理技术实现了对两种载波条纹图从预处理到应力计算的自动化处理.将混合光载波法应用于动态全息光弹性,分离了动态主应力. 文中还提出了一个经济实用的大尺寸载波片制作技术.     

Cyclic-stress studies by time-averaged photoelasticity

This paper describes an experimental method whereby the amplitude of cyclic stresses may be readily determined by time-averaged photoelasticity. Using an ordinary polariscope with a monochromatic-light source, ‘time-averaged isochromatics fringes’ are formed if the photographic film in the camera is exposed with an exposure time equal to one or several periods while the photoelastic model is undergoing steady-state cyclic loading. The fringe pattern depicts amplitudes of the oscillating stresses according to the zeroth-order Bessel function. These properties permit the determination of a time-averaged cyclic stress-optic law. It is also possible to use the method to determine time-averaged isoclinics. The method has great potentiality in the study of in-plane vibrations.     

多幅动态等和线及等差线的分离和图象处理

提出用夹层光载波法分离多幅动态等和线与等差线,将VAX机及Model75用于图象的自动处理,求出用每一载面分离了的主应力。     

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.     

A rational theory of oblique incidence and its extension to stress-separation in birefringent composites

A rational theory of oblique incidence for a birefringent medium is developed. The theory rules out the concept of secondary principal stresses as an arbitrary one and provides more adequate interpretation of isochromatics and isoclinics in oblique incidence. The method is shown to be applicable for stress-separation in an anisotropic-birefringent composite, and the stress-optical equations deduced require an additional stress-fringe constant to those involved in normal incidence. The stress-birefringence relations for isotropic photoelasticity are obtained as a particular case of the general theory.     

Linear and Nonlinear Algorithms for Stress Separation in Photoelasticity

An experimental-numerical hybrid method for the stress separation in photoelasticity is proposed in this study. In the proposed method, boundary conditions for a local finite element model, that is, tractions along boundaries are inversely determined from photoelastic fringes. Two algorithms are proposed for determining the boundary condition. One is a linear algorithm in which the tractions are obtained by the method of linear least-squares from both principal stress difference and principal direction. Another is the nonlinear algorithm in which the tractions are determined only from the principal stress difference. After determining the boundary conditions for the local finite element model, the stresses can be obtained by finite element direct analysis. The effectiveness is demonstrated by applying the proposed method to a perforated plate under tension and contact problems. Results show that the boundary conditions of the local finite element model can be determined from the photoelastic fringes and then the individual stresses can be obtained by the proposed method. Furthermore, the stresses can be evaluated even if the boundary condition is complicated such as at the contact surface. It is expected that the proposed method can be powerful tool for stress analysis.     

Towards RGB photoelasticity: Full-field automated photoelasticity in white light

In this paper a new full-field method for the automatic analysis of isochromatic fringes in white light is presented. The method, named RGB photoelasticity, eliminates the typical drawbacks of the classical approach to photoelasticity in white light which requires a subjective analysis of colors and an experienced analyst to acquire and interpret the results. The proposed method makes it possible to determine retardations uniquely in the range of 0–3 fringe orders. For this purpose the isochromatics are acquired by means of a color video camera and the colors are decomposed in the three primary colors (red, green and blue) and compared to those stored in a calibration array in the system. Furthermore, the influence of various spurious effects on the accuracy of the proposed method is experimentally evaluated.     

Full-field separation of principal stresses by combined thermo- and photoelasticity

The combined use of thermoelastic stress analysis and full-field reflection photoelasticity based on the phase-stepping technique has been developed for twodimensional problems. The first method determines the sum of the principal stresses, the latter evaluates the difference of the principal stresses. Thus the principal stresses were separated at each point in the field of view without reference to neighboring points. An evaluation of this approach has been performed using a tensile plate with a central circular hole. The results show that the analysis carried out combining thermo- and photoelasticity incurred errors no larger than those of each system working independently.     

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.     

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.     

An experimental investigation on isoclinic parameters in viscoelastoplastic materials under cyclic stresses

Photovisco-elastoplasticity has been developed and applied to various problems in nonlinear stress analysis as an extension of photoelasticity into nonlinear photomechanics. In photoelasticity, because stress is simply related to strain, isochromatics are proportional to either the principal stress difference or the principal strain difference and isoclinics indicate the directions of either principal stresses or principal strains separately. However, in photovisco-elastoplasticity, these optical responses are nonlinearly related to both stress and strain state simultaneously. Thus isochromatics are related nonlinearly with both the principal stress and strain differences. Isoclinics depend on the direction of principal strain as well as that of principal stress. Concerning now isoclinic parameter: according to the results of experiments performed by us for the deformation state where the directions of principal stress and strain do not coincide with one another, it has been found that isoclinic parameter moves gradually from the direction of principal stress to that of principal strain with increasing viscous deformation under constant stress. In the present research, extending our previous investigations, the behavior of isoclinic parameter has been examined experimentally under cyclic stressing, where the direction of principal stress changes alternately. In the course of an experiment, the variation of isoclinic parameter in relation to the number of cycles was measured together with the corresponding strain state on the thin-walled tubular specimen of celluloid softened by heating, subjected to combined loading conditions consisting of constant axial tension and cyclic torsion. The results obtained may be summarized as follows.

1. The cyclic-variation phase of isoclinic parameter lags behind the cyclic-variation phase of the direction of principal stress. The phase difference between these cyclic variations remains constant regardless of the number of cycles.
2. Isoclinic parameter has a value close to the direction of the principal stress within a range of a small number of cycles and decreases with an increase in the number of cycles. However, it does not approach the direction of principal strain but a value between the direction of the principal stress and that of the principal strain, with a certain constant ratio to them.

     

On the determination of the sum of the principal stresses in two-dimensional problems

The well-known principle of the determination of the sum of principal stresses in plates by measuring thickness changes is applied in this paper to “frozen” plates and to models made with low-modulus materials, such as rubbers, deformed inside portable frames. It is shown that a sufficiently precise measurement of thickness changes is possible with a machine-shop comparator, rather than with the more delicate laboratory-type instruments. The necessary corrections to be introduced to the comparator readings when rubber models are used are described in the Appendix. Two other methods based on moiré fringes, using the same two kinds of models, are also presented. The use of moiré on “frozen” specimens yields patterns of large response. Gratings on rubber models also yield precise moiré patterns that can be combined with isochromatics to separate the principal stresses. Two ways of conducting the moiré analyses are presented. The advantages and limitations of the several alternative methods are pointed out, and applications are given.     

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.     

Separation of principal stresses in dynamic photoelasticity

A new and effective method used to separate the transient principal stresses for dynamic photoelasticity is proposed. This is a hybrid method combining the optical method of dynamic caustics and the boundary element numerical method. Firstly, a modified Cranz-Schardin spark camera is used to record simultaneously the isochromatic fringe patterns of photoelasticity and the shadow spot patterns in the dynamic process. By means of the isochromatic fringe patterns, the difference between transient principal stresses in the whole domain and the principal stresses along the free boundary can be solved. In addition, the method of caustics is a very powerful technique for measuring the concentrative load. Then, the sum of the principal stresses is calculated by the boundary integral equation obtained from the Laplace integral transform of the wave equation. So, the transient principal stresses can be determined from the experimental and numerical results. As an example, the transient principal stresses in a polycarbonate disk under an impact load are resolved. Concurrently published in the Chinese Edition of Acta Mechanica Sinica, Vol. 26, No. 1, 1994     

Phase Shifting Full-Field Interferometric Methods for Determination of In-Plane Tensorial Stress

A new method that combines phase shifting photoelasticity and transmission Coherent Gradient Sensing (CGS) is developed to determine the tensorial stress field in thin plates of photoelastic materials. A six step phase shifting photoelasticity method determines principal stress directions and the difference of principal stresses. The transmission CGS method utilizes a standard four step phase shifting method to measure the x and y first derivatives of the sum of principal stresses. These stress derivatives are numerically integrated using a weighted preconditioned conjugate gradient (PCG) algorithm, which is also used for the phase unwrapping of the photoelastic and CGS phases. With full-field measurement of the sum and difference of principal stresses, the principal stresses may be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions. The method is demonstrated for a compressed polycarbonate plate with a side V-shaped notch. The experimental stress fields compare well with theoretical stress fields derived from Williams solution for a thin plate with an angular corner.     

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 measurement method of scattered light photoelasticity using unpolarized light

This paper describes an automatic measurement method for the stress analysis of a three-dirnensional photoelastic model having the rotation of the principal stress by scattered-light photoelasticity using unpolarized light. The relative phase retardation and the principal stress directions of a linear retarder for a distance in the solid model are expressed in terms of measurable Stokes parameters. The method was used for measurements on a frozen stress sphere under diametral compression.     

Characterizing Frictional Contact Loading via Isochromatics

Isochromatic patterns in the vicinity of frictional contacts furnish vital clues for characterizing friction. Though friction effects are evident in a diametrally loaded circular disk, three-point loading provides better results towards highlighting friction. In this paper, a new method of characterizing friction at loading contacts using photoelastic isochromatics patterns is presented. Location of isotropic points (IPs) formed in three-point and four-point loadings of circular disk is used as a main tool to quantify the friction component using theoretical analysis. Bifurcation of isochromatic fringe loops near the distributed loads is explained by the presence of anti-symmetric Hertzian shear traction in addition to Hertzian normal traction. The classical solution by Flamant for point load at the edge of half plane is used to derive stresses in circular disk for all required loading configurations. A semicircualr ring under three-point loading is examined using photoelasticity to understand the isochromatics pattern theoretically by considering normal and shear traction components at loaded regions.     

On the complete determination of dynamic states of stress

An attempt is made in dynamic photoelasticity to get the principal directions and principal stresses of a time-dependent two-dimensional state by three simultaneous photoelectric signals. The signals are obtained from birefringence and interference of light in the model itself. The described procedure is possible because a laser was used instead of a conventional light source. It applies essentially to the general case where the principal directions vary as a function of time during a transient state of stress and, probably, it may also be used for certain three-dimensional tests. A comparison with theoretical values in an example has proved a rather good accuracy.