基于染料的光弹性涂层方法回顾与展望

光弹性涂层法是最常用的实验应变分析测试技术之一,但其实际应用受到诸如准备时间长、基底加强效应、复杂的数据后期处理等固有局限性的影响。近年来,出现了两种通过在光弹性聚合物材料中添加非发光染料或发光染料的新的光弹性涂层制作方法。这种基于染料的光弹性涂层使新方法能够克服上述传统光弹性涂层法应用中的许多局限性,并有望成为重要的应变测量工具。论文回顾了这两种新的基于染料的光弹性涂层方法的提出与发展过程,分别介绍了两种测量方法的实验装置、基本原理及一些实际应用,总结了两种新方法各自的优点与不足。最后指出了基于添加发光染料的发光光弹性涂层的未来发展方向和技术改进。     

A stress-optic law for photoelastic analysis of orthotropic composites

The feasibility for utilizing transparent filament-resin composites for photoelastic stress analysis was investigated. Satisfactory photoelastic stress patterns were demonstrated in simple models with undirectional and bidirectional fiber orientations. A stress-optic law was formulated, based on the concept that the birefringence components contributed by each component of plane stress are combined according to a Mohr circle of birefringence. Applying this concept, the difference of the physical and optical principal directions was accounted for, and a general method of photoelastic solution for the plane-stress problem in orthotropic sheets was developed. The method of analysis is little more complex than the well-known procedures for isotropic materials, but at least three experimental measurements are required to characterize the optical response of the material to plane stress. Partial confirmation of the proposed stress-optic law was obtained by comparison of the theory to limited experimental data obtained in uniaxial-stress samples. It remains to establish a more positive verification by experiments in a variety of biaxial-stress conditions.     

Construction of complex photoelastic models using thin molded-epoxy sheets

The construction and analysis of complex thin-shell photoelastic models are discussed. Examples of both two- and three-dimensional applications are presented. The first example concerns an investigation of the structural supports of a new and unique blastfurnace design. The second example is directly related to the design and analysis of complex thin-shell pressure vessels and manifolds. Existing laboratory techniques were used successfully to construct the photoelastic models. The construction method is basically an extension of the techniques previously associated with the contour-sheet method of preparing photoelastic coatings. As such, it does not involve new or untried concepts, but rather it extends the existing in-house capabilities of many laboratories.     

Twisting stresses in tape

An analysis is presented of the stresses induced in a thin tape by bending over pulleys, by axial tension and by twisting of the tape when running between two out-of-plane pulleys. Analytical results are compared with some photoelastic tests on tape models made of epoxy resin. The weak retardation produced by the thin tape is multiplied by repeated light passage through the tape and is measured by a bent-beam compensator. The tests are of especial interest because the rate of rotation of the principal stresses is higher than had been encountered before. Surprisingly, the experimental results uncorrected for rotation are in good agreement with the calculated stresses.     

Effects of the thickness of birefringent coatings

It is known that birefringent coatings are a powerful experimental technique for the determination of surface strains of metals or other opaque bodies. In this paper the complete state of strain in such a coating is determined for an arbitrary one-dimensional variation of the displacement at the metal surface. It is shown that strain gradients or curvature of the surface have a pronounced effect on the observed birefringence, and must be taken into consideration. This can be done by means of two correction factors derived in the paper which take into account the elastic properties of the coating and its thickness. An experimental procedure is outlined for determining an unknown distribution of strain at the metal surface on the basis of the observed photoelastic pattern.     

Experimental stress analysis of a nuclear-reactor pressure vessel

The stresses from internal pressure in a nuclear-reactor pressure vessel were investigated using both strain-gaged and photoelastic models. The methods used in obtaining complete stress distributions along the nozzles from strain-gage data are described, and comparisons are made between the distributions obtained from the photoelastic model and those derived from strain-gage data. The effects of nonradial attachment of a nozzle to a spherical shell upon the stresses in the nozzle and in the shell are shown. Finally, comprisons are made between the experimental results and those for simplified analytical models.     

Improvement in use of photometric methods for measurement of birefringence

Visual or graphical determination of isochromatic order in photoelastic models is not sufficiently accurate for many photoelastic observations. This is especially true in the long-wavelength spectral region where fringe orders are low and photometric devices must be used for observation. In such cases, some method of fractional-fringe measurement is required. The Tardy and Sénarmont methods are often chosen for convenience, with preference given to the Sénarmont method because of smaller system error. These methods are based on detection of the analyzer angle at which the light transmitted through the given point in the model is minimum. The experimental problem is poorly conditioned, and the procedure is incompatible with nonideal light-sensing apparatus. The equations of the Sénarmont technique show that the intensity of radiation is an even function of the rotation of the analyzer from the position which produces minimum intensity. The indeterminacy in the measurement of minimum-intensity angle may be reduced by observing the angles at which the intensity reaches arbitrary values greater than minimum. The average of two such readings on both sides of the minimum-intensity angle provides an improved measurement of this angle. Best results are obtained if observations are made where the intensity reaches half its maximum value. For a signal-to-noise ratio of 1000, this procedure improves results by a factor of 16. Improvement is greater asS/N is increased.     

Aluminum-reinforced epoxy models

This paper discusses test applications, fabrication methods, and stress-analysis techniques which have been developed on aluminum-filled epoxy models. The use of aluminum-reinforced epoxy models as a preliminary design tool has found extensive application in the development and modification of aircraft structures and related components. The range of uses has varied from the effects of adding or removing material in order to optimize a design, to a full experimental stress analysis of a complete part under multiple-loading conditions. This technique when used in conjunction with photoelastic coatings and/or strain gages, provides complete kinematic and design information before production, tooling, manufacturing and engineering expenses are incurred. The paper discusses machined and molded models, material properties including time-modulus criteria and viscoelastic-creep phenomena, model rework, photoelastic-coating reinforcement and strain-gage effects.     

New model materials for photoelasticity and photoplasticity

Two new materials are proposed as models for photoelasticity and photoplasticity. One is cast resin fully cured epoxy-phenol alloy which is made by the mutual cross linking of pre-condensed resins of epoxy and phenol. While epoxy-phenol alloy resin is available only for photoelasticity, the other, polycarbonate resin, is useful not only for photoelasticity, but also for photoplasticity. Polycarbonate is very tough and has large values of both photoelastic stress sensitivity and modulus of elasticity. The excellent cold workability of polycarbonate is proved by a deep-drawing test. Hence the photoplastic results obtained from a polycarbonate model can be applied by analogy to the plastic stress analysis in other ductile materials. Both resins are very transparent even in the plastic state.     

Remarks on properties of photoviscoelastic model materials

One of the basic problems of structural-model analysis, model photoelasticity and photoelastic coatings in the problem of mechanical and optical creep, relaxation and related phenomena. It is pointed out that, in spite of creep or relaxation, it is possible to achieve physical similarity between model and object if the model material behaves in a certain range as a linear viscoelastic material. Such a material is called a “momentarily linear material.” Several model materials behave in this way in a certain range of stress and time. Because of creep and relaxation, the common tensile tests are, in general, not quite adequate for evaluation of physical properties of plastics used for models. Also the bending test is not always adequate. It is shown how to obtain sufficiently accurate relations between stress, strain, birefringence and time, using tapered specimens. The problem of biaxial creep of model materials is discussed, and a simple method of evaluating the suitability of a given plastic as a model material is shown. Some conclusions concerning time-dependent factors are formulated, and some possible areas of investigation are shown.     

Experimental stress analysis in the design of a liquid-hydrogen pump rotor

A design optimization of the cross section of a high-speed rotor to pump liquid hydrogen was accomplished by means of photoelastic evaluations and model tests. The photoelastic models were rotated in the field of a polariscope with stroboscopic light synchronized to this rotation to evaluate the stresses. Differential radial growths were measured from model tests.     

Photoelasticity for stress analysis under high hydrostatic pressure

Experimental research relative to pressure effects on the mechanical behavior of materials is frequently handicapped by the difficulties associated with making load and deformation measurements in a hostile environment. The application of photoelasticity in high-pressure experiments provides a means for studying the effect of hydrostatic stress on varying stress fields. The purpose of this paper is to examine the feasibility of using the photoelastic method of stress analysis in a high-pressure environment. The unusual feature of this application is the finite elastic deformations suffered by the photoelastic model under high pressure. As a result, the mechanical and stress-optical properties of the model materials are functions of pressure. Another important feature in this study is the selection of a suitable model material. Since the model must come into contact with the liquid pressure media, chemical and absorption resistance are essential considerations. Although it was found that photoelastic investigations can be carried out at high pressure, limitations are imposed by the presence of the optical vessel and pressurized fluid.     

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.     

Residual Stress Determination by Hole Drilling Combined with Optical Methods

An overview is provided of the use of eight different optical methods with hole drilling to determine residual stresses. The methods considered are: brittle and photoelastic coatings, Moire interferometry, holographic interferometry, electronic speckle pattern interferometry, interferometric strain rosette, digital image correlation and shearography. A number of applications are summarized, such as the use of hole drilling with holographic interferometry to investigate stresses in rock structures accessed by deep boreholes and to determine manufacturing-induced residual stresses in fillets of small radii.     

Simplifications for scattered-light photoelasticity when using the unpolarized incident beam

A method is presented for obtaining scettered-light photoelastic data in three-dimensional problems using an unpolarized incident light beam. Using simplifying optical assumptions, the scattered-light observation path is considered tobe a series of half-wave retarders. Data are obtained through rotation of the optical analyzer and translation of the incident light beam with respect to the model. The method is applied to obtain data in problems where the secondary principal directions are: (1) fixed and (2) rotate. Results compare favorably with those obatained using a polarized incident beam.     

Photoelastic investigation of large deflections by low-modulus photoelastic materials

Information is given to enable the experimental analysis of large deformations by application of photoelastic techniques. Promising photoelastic materials having low elastic modulus and high optical sensitivity were obtained for practical use at room temperature. The time and temperature dependence of the stress-fringe order and stress-strain relations of one of these viscoelastic materials is discussed. Photoelastic investigations of large deflected straight and circular beams are reported. Photoelastic technique seems to be a useful method for analysis of large deformations of models with complicated shapes.     

Model interferometry with air-holograms

An “air-hologram” is formed by the superposition of collimated object and reference light beams in a standard transmission holographic bench. Since no model is initially placed in the system, the reconstruction is simply the collimated beam that had passed through the model space. Insertion of transparent model material changes the optical path-length profile causing interference between the existing beam, which traverses the model, and the reconstructed beam which had traversed air only—hence, the designation “air-hologram”. Using this method, model material can be inspected and selected for optical flatness. Interference in the unloaded models can then be eliminated by simple rotation of the hologram. Real-time holographic interferometry is performed in the same manner as is photoelasticity. Further, it is shown how errors caused by large model displacements can be minimized.     

Determination of the full-field stress and displacement using photoelasticity and sampling moiré method in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials. Various optical measurement techniques such as photoelasticity, moiré and digital image correlation methods have been developed to achieve this goal. However, these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement; however, these elements will disturb the light passing through the tested models using photoelasticity. In this study, by combining photoelasticity and the sampling moiré method, we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional (3D)-printed photoelastic model with orthogonal grating. Then, the full-field stress was determined by analyzing 10 photoelastic patterns, and the displacement fields were calculated using the sampling moiré method. The results indicate that the developed method can simultaneously determine the stress and displacement fields.