Experimental analysis of rolling contact stresses in a viscoelastic strip

An experimental approach to two-dimensional, viscoelastic, steadily moving rolling contact is described. The photoviscoelastic technique is employed for the analysis of rolling contact stresses between a viscoelastic plate and a rigid rolling cylinder in which the principal axes of stress, strain and birefringence are not coincident with each other. Using an elliptically polarized white light, the distribution of isochromatic fringe order and the principal axes of birefringence at an instant are determined from a single photoviscoelastic image. The time variations of the differences of the principal stresses and strains, as well as their directions, are obtained by use of the optical constitutive equations of photoviscoelasticity. The experimental results involving the time variation of the stresses around the contact surface and their distributions are analyzed.     

Determination of the stress distribution in assemblies of photoelastic particles

An optical measuring method and a calculation procedure for determining the distribution of the stress tensor in a plane-strained three-dimensional assembly of random-shaped photoelastic particles are described. The stress tensor at an arbitrary point of the model is determined by an integration procedure, based on the equations of equilibrium of stresses. The distribution of the principal-stress direction and the relative principal-stress difference and at least two normal stresses in a plane have to be known to perform the integration. The distribution of the principal-stress directions and their difference are measured optically by scanning the model with an optical filter system with a single rotating polarizer.     

Magnetophotoelasticity—Photoelasticity in a magnetic field

The basic equations governing the propagation of polarized light in a three-dimensional photoelastic model located in a magnetic field are derived. Optical phenomena in this case can be adequately described by the aid of the theory of characteristic directions developed previously by the author. The case when the principal-stress difference, as well as the magnetic field, is constant is considered in detail. An algorithm is developed that permits the study of the optical phenomena in the case of arbitrary stress distribution along the wave normal. As an example, investigation of the bending of plates is considered; graphs are produced that permit the determination of the stress components on the basis of experimental data. Some considerations of the experimental technique are given.     

Integrated-plane photoelastic method—Application of photoelastic isodynes

It has been shown by Pindera and Mazurkiewicz that a new type of scattered-light modulation in the plane of a two-dimensional photoelastic object can be obtained when the stationary integrated photoelastic method developed by Pindera and Straka is applied in a scanning mode and when the transfer function of the photoelastic system satisfies certain conditions. The new type of light modulation, called field of isodynes by the authors, carries information on stress components normal to the direction of propagation of primary beam, and on corresponding total-force component. The points where this stress component is equal to zero can be easily determined. The classical scattered-light modulation along a chosen line represents a cross section of a corresponding isodynes field. It is shown that these features of the method of isodynes make it possible to easily determine the distribution and values of normal stress components at any arbitrary rectilinear cross section, and to check immediately the accuracy of measurements. The experimental determination of contact stresses and contact regions using the method of isodynes is especially simple and elegant.     

A numerical method for separation of stresses in photo-orthotropic elasticity

A numerical method is suggested for separation of stresses in photo-orthotropic elasticity using the numerical solution of compatibility equation for orthotropic case. The compatibility equation is written in terms of a stress parameter S analogous to the sum of principal stresses in two-dimensional isotropic case. The solution of this equation provides a relation between the normal stresses. The photoelastic data give the shear stress and another relation between the two normal stresses. The accuracy of the numerical method and its application to practical problems are illustrated with examples.     

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.     

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.     

Photoelastic analysis of a three-dimensional specimen by optical slicing and digital image processing

The authors show a nondestructive method for obtaining the isochromatic and isoclinic fringes in a three-dimensional photoelastic specimen. The basic idea is to delimit a slice between two plane laser beams. The properties of polarization of the scattered light (Rayleigh's law) and the interference possibilities of the diffused beams are used. By introducing speckle pattern properties, the correlation factor of the two scattered beams is similar to the illumination given in a plane polariscope for the investigation of a slice (in a classical frozen-stress technique). The authors use a monochromatic laser beam, a CCD camera and a personal computer. Because they cannot obtain the correlation factor directly, they do a statistical analysis of the speckle patterns. The variance (function of the correlation factor) is computed from the light intensities of three images corresponding to the speckle pattern for plane 1 alone, plane 2 alone, and both planes together.     

The double-light-beam method in three-dimensional scattered-light photoelasticity

This paper presents a new scattered-light photoelasticity technique which may be called the double-light-beam measurement method. Principal-stress directions and relative retardations related to the principal-stress differences can be measured at any point within an ordinary three-dimensional photoelastic model by this method. This method does not need double loading and the quantities to be measured depend only on the relative light intensity. Moreover, the output signals alternate, providing improved accuracy and stability. If supported by an appropriate program-control and digital processing system, the double-light-beam method can be used to quickly determine the internal stress distribution in ordinary three-dimensional photoelastic models.     

A scattered-light method in photoelasticity

The birefringence and, thereby, the stresses in a photoelastic model are investigated utilizing the light scattered from a beam of light propagating through the model. The retardance from the entry point of the beam into the model to a certain point along the beam is expressed in terms of the intensity of the scattered light. The retardance for a short distance along the light path within the model is determined as a function of the total retardances from the entry point of the model to the two end points of the distance investigated. The effects of retarders and polarizers on the state of polarization of the light beam are treated by Mueller calculus. It is not necessary to make other assumptions than those made in the usual stress-freezing and slicing method.     

Photoelastic Analysis of Edge Residual Stresses in Glass by Automated “Test Fringes” Methods

Since the glass is a birefringent material, the analysis of residual stress in glass is usually carried out by means of photoelastic methods. This paper considers the automation of the “test fringes” method which is based on the use of a Babinet compensator or of a beam subjected to bending. In particular, two automated methods are proposed: the first one is based on the use of the centre fringe method in monochromatic light and the second one is based on the use of RGB photoelasticity in white light. The proposed methods have been applied to the analysis of membranal residual stresses in some tempered glasses, showing that they can effectively replace manual methods of photoelastic analysis of residual stresses in glass.     

Holographic photoelasticity: Determination of absolute retardations by a single hologram

In this paper, real-time holographic interferometry is applied to determine the absolute-retardation fringes in the photoelastic analysis of plane models. The method requires only one hologram recorded with the model unloaded. In the reconstruction process, the mcdel is loaded and the polarizers on the reference and object beams are rotated through the same angle. At the points of the model where the polarization direction is parallel to one of the principal stresses, only the corresponding family of absolute retardations is obtained. The technique is demonstrated experimentally using a deep beam centrally loaded.     

Further applications of holography to photoelasticity

A holographic method for reconstructing the polarization of light emitted by a photoelastic model is presented. Isochromatic and the entire family of isoclinic fringe patterns may be obtained by examining the holographic image, a posteriori. This is accomplished by using two orthogonally polarized reference beams so arranged that the reconstructed crosstalk images do not overlap. An analysis is preseted crosstalk images do not overlap. An analysis is presented which shows that, to reconstruct polarization, the phase relationship between the two reference beams must be maintained. This requirement is more stringent than that normally required in holography. Experimental verification is presented.The use of double-exposure holography to obtain isopachic-isochromatic fringe patterns in the reconstructed image is discussed. An analytic treatment of the method is presented. Expressions relating the isopachic-isochromatic fringe pattern in the reconstructed virtual image to the principal stresses are developed. Differences between this analysis and that presented in a recent paper are discussed. Experimental results are obtained and compared to theory and to other experimental results with good agreement.Paper was presented at 1969 SESA Spring Meeting held in Philadelphia, Pa., on May 13–16.The study reported herein was supported in part by NASA Grant No. NsG-401.     

Single-strand strainwire technique: Comparison with existing methods and a proposed photostrain technique

This paper is the third of three papers evaluating a refined internal strainwire technique. This final paper evaluates the technique by comparing it with two elastic solutions, with a photoelastic solution, and with a new proposed photostrain technique. The problem chosen as the basis of comparison was a plane-stress problem of a plate with a circular hole under uniform tension. The proposed technique is experimental in nature and combines parts of the results of a photoelastic solution with those yielded by a three-wire internal strain-gage-rosette analysis to completely fix the state of stress in the model. The scientific techniques used to compare the three-wire strain technique and photostrain technique are as follows: two elastic solutions, one evaluated at a point and one arrived at by integrating the stress functions over a finite length; a finite-element solution; a photoelastic analysis using the shear-difference technique to separate the principal stresses; and a three-wire-rosette analysis. A comparison is made of the values of principal stresses yielded by these methods.     

刚构连续梁桥墩梁固节点结构的光弹性试验及有限元分析

某铁路特大桥的主桥部分采用预应力混凝土刚构连续梁桥,本文采用光弹性模型冻结应力法对该刚构连续梁桥墩梁固节点结构进行了应力分析,给出了结构边界应力分布和主应力迹线。应用ANSYS软件对墩梁固节点实际结构进行了有限元计算。将实验与有限元分析结果进行了比较,结果表明,实验应力分析法与有限元数值法吻合较好。在有限元分析中,对墩梁固节点结构梁端加载边界的影响区进行了研究,通过合理选择梁的长度可以有效减小局部应力。模型实验和有限元计算的结果为结构的优化设计提供了重要的依据。     

Stress separation in the photoelastic study of centrifugal stresses

This technical note refers to the problem of stress separation in the photoelastic analysis of plane models under centrifugal stresses. Two methods are described in order to determine the sum of principal stresses. These methods, which are based on the compatibility equation, reduce the determination of the sum of principal stresses to the solution of a Laplace's or Poisson's equations. As an example of application, the separation of stresses in a rotating disk with two eccentric holes is shown and comparison with the stresses obtained by using the shear-difference method is made.     

Identification of residual stresses by instrumented elliptical indentation and inverse analysis

The residual stress tensor near the surface of a metal structural component or products of metallurgical processes (particularly welding) is considered in view of the estimation of its governing components. These are: the two principal stresses if the directions are “a priori” known as assumed here for the preliminary optimization of the indenter shape; otherwise two normal stresses and a shear stress according to a preselected reference system. In both situations the material is assumed to be endowed with known elastic–plastic properties. The novel parameter identification procedure investigated herein can be outlined as follows, when the unknown stresses are three: an instrumented indenter is adopted with elliptical section across the axis of an originally conical, or, as an alternative, of an originally spherical shape; three indentations are performed with the ellipse axis rotated by 45° in a sequence, in three locations near to each other at minimal distances apt to avoid interference; the three digitalized indentation curves (loading–unloading force versus penetration) are the source of the experimental data set used as input of inverse analysis; this is carried out by a fast method consisting of finite element simulations of the tests, “proper orthogonal decomposition”, “radial basis function” interpolation, and a first-order algorithm for the minimization of the discrepancy function. When the unknowns are the two principal stresses (directions known) two orthogonal indentations turn out to be sufficient.     

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.     

单层纤维复合材料的光弹模型初探

本文总结了用显微激光分析仪对一般纤维增强复合材料进行透射式光弹性研究的近期工作.针对纤维复合材料违反传统光弹理论的偏振光学行为,讨论了纤维,基体的双折射率不同及由纤维,基体界面两侧出射的光在Airy斑重叠区发生干涉等问题,从更一般的角度探讨了最近的文章中所提出的新光弹公式中所含两个滞后量的存在性.