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.     

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.     

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.     

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.     

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.     

Polarimetry for spatiotemporal photoelastic analysis

This paper describes a new photoelastic technique for the spatiotemporal stress analysis. In a polarimeter developed, an elliptically polarized signal beam of light, modulated in state of polarization by two-dimensional principal-stress distributions interferes with a reference beam of light consisting of orthogonal linearly polarized two components. A time-sequential series of two-dimensional interference patterns are received one after another by a MOS video camera, followed by a computer. Of the elliptically polarized signal beam, the orthogonal field components along the directions of the principal stresses in a two-dimensional photoelastic sample can be computed from a recorded interference pattern, which offer the data needer for mapping the spatiotemporal principal-stress distribution over the sample. Not only each of the two orthogonal principal stresses but also the principal-stress difference are mapped in a time-sequential diagram. No use of any movable polarization element such as a rotating analyzer allows us to follow a rapid change in stress distribution within the maximum frame rate 2066 s⁻¹ of the MOS video camera.     

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.     

DYNAMIC STRESS ANALYSIS OF GAS TURBINE ROTOR AIRFOILS USING THERMOELASTIC TECHNIQUES

The SPATE system provided a means for experimental ther-moelastic analysis of high frequency modes of vibration of a complicated turbine impeller which did not facilitate analysis with conventional methods due to low stress response and high modal density.
Testing also demonstrated a unique experimental stress analysis technique which was applied to a blade and vane airfoil and exhibited excellent stress distribution correlation with an established experimental technique (brittle lacquer) and with analytical stress distributions predicted by NASTRAN.
Full field dynamic stress analysis of gas turbine compressor airfoils accomplished using thermoelastic techniques provided an efficient method of determining optimum strain gage locations for monitoring rig and engine vibratory stress.
Significant cost savings could be realized using this technique from: (1) reduction in the amount of instrumentation required to characterize airfoil dynamic behavior and (2) increased vibratory response mode coverage thereby preventing the re-running of engine test programs to measure vibratory stress response levels of unexpected resonances encountered during initial engine testing.
Care is required when using SPATE results for vibratory modes resulting in high bi-axial stress distributions since the system output indicated stress magnitudes based on the sum of the principal stresses which could be significantly higher than either of the individual principal stresses.     

Acoustical birefringence and the use of ultrasonic waves for experimental stress analysis

Stress-induced optical birefringence in transparent materials has long been a common technique of stress analysis. Although stress-induced acoustic birefringence was discovered more than 20 years ago, its development and actual applications are still limited. This paper will look at the similarities and differences between the propagation of light waves in photoelastic materials and the propagation of ultrasonic waves in deformed solids. Critical comparisons of the experimental methods employed in photoelasticity with those available in modern ultrasonic measuring technique show why previous studies on ultrasonic measurement of stresses were not very successful. A new experimental technique is devised for using ultrasonic waves for stress analysis. The technique employs a single rotatable 10-MHz shear transducer as the transmitter and receiver of ultrasonic pulses. The enlarged display of the 10-MHz modulated-pulse pattern of reflected echoes provides a convenient way to determine the directions of principal axis of the stress within ±3 deg. The pulse-echo-overlap method is used to measure the absolute velocities of the two principal shear waves. The difference in principal stresses is then calculated from the velocity measurements. Test results of common structural-aluminum and steel specimens under uniaxial compression show a linear relation between the velocity changes and the applied stress. Ultrasonic measurements of stress distribution in a 6.35-cm diameter, 1.9-cm-thick aluminum disk under diametric compression are also reported. Paper was presented at Third SESA International Congress on Experimental Mechanics held in Los Angeles, CA on May 13–18, 1973.     

Data analysis in dynamic photoelasticity

A method to separate the principal stresses and to obtain displacements from dynamic photoelastic fringe patterns is presented. The method utilizes geometric characteristics of either the model or the stress wave to provide the additional equation necessary for separation. The method is illustrated in ten specific cases.     

Scattered-light rosette

A newly developed concept, called thescattered-light, rosette, is used to determine the state of stress on a free surface. Three simultaneous, polarized-light beams intersecting at a surface point yield sufficient scattered-light photoelastic data to evaluate the stresses at a surface point. After initial calibration, the surface-stress analysis consists of a series of photographs, one photograph for each point of interest. General equations are derived which are valid for any three light beams intersecting at a surface point on a stressed, photoelastic material. Simplifications of the general equations and techniques are also noted. Stresses obtained from the scattered-light-rosette analysis are compared with the known solutions for two problems.     

A new photoelastic model for studying fatigue crack closure

The photoelastic analysis of crack tip stress intensity factors has been historically developed for use on sharp notches in brittle materials that idealize the cracked structure. This approach, while useful, is not applicable to cases where residual effects of fatigue crack development (e.g., plasticity, surface roughness) affect the applied stress intensity range. A photoelastic model of these fatigue processes has been developed using polycarbonate, which is sufficiently ductile to allow the growth of a fatigue crack. The resultant stress field has been modeled mathematically using the stress potential function approach of Muskhelishvili to predict the stresses near a loaded but closed crack in an elastic body. The model was fitted to full-field photoelastic data using a combination of a generic algorithm and the downhill simplex method. The technique offers a significant advance in the ability to characterize the behavior of fatigue cracks with plasticity-induced closure, and hence to gain new insights into the associated mechanisms.     

数字光弹性法综述

将光弹性法与计算机图像处理技术相结合 ,来自动采集光弹性数据和分析应力的方法 ,称为数字光弹性法 ,与传统光弹性法相比 ,它可以进一步提高实验速度和精度。本文详细讨论了以下两个方面 :一是光弹性条纹的细化和倍增处理技术 ;二是自动确定光弹性参数的技术 ,包括相移法、傅立叶变换法、逐步载荷法、广谱分析法和RGB光弹性法等。通过对近二十年来国内外在这些方面的研究、应用和进展作了综述 ,认为采用白光的彩色域相移技术计算光弹性等倾角 ,结合采用白光源或三色光源的相移法来确定光弹性等色线级数 ,有望成为解决静态二维和三维冻结模型薄切片应力分析的最佳方法 ;另外 ,设计一种能实时和同步采集多幅条纹图的实验装置 ,通过相移法来自动获取动态光弹性数据 ,是数字动态光弹性法很有前景的发展方向     

An Experimental-Numerical Hybrid Method for Elastic Contact Problems*

ABSTRACT

An experimental-numerical hybrid technique for determining the contact stress distribution between two elastic bodies having both frictionless as well as bonded contact is discussed in this paper. The hybrid method makes use of experimental data collected at a section far from the contact surface and the numerically generated influence coefficients, in terms of the applied unit normal and shear stresses. The experimental data, i.e., the differences in normal stresses and the shear stress, are obtained using photoelastic analysis for the examples illustrated in this paper. When substituted into equations corresponding to the unit normal and shear stress applied in the contact region, this results in a set of algebraic equations which, when solved, allow the contact stress distribution to be obtained. This method is illustrated with examples involving simple and complex geometries of the contacting bodies.     

Simultaneous stress separation,smoothing of measured thermoelastic isopachic information and enhanced boundary data

A new thermoelastic hybrid method of stress analysis is demonstrated experimentally which simultaneously smooths the measured isopachic data, enhances the boundary information, and separates the stresses at nonboundary locations using only the isopachics. The technique is illustrated by application to a tensile plate containing a hole.     

Photoelastic analysis of a thin-walled compressor housing

The fabrication, testing, and analysis of a full-sized photoelastic model of a thin-walled compressor housing are presented. The conical model and connecting bolts were stress frozen under axial and bending loads to simulate severe in-flight manoeuver loads of a jet aircraft sufficient to cause flange separation. Results and discussion are presented for stresses in and near the flange, for stresses experienced by the bolts, and for the fabrication techniques used.     

Three-dimensional photoelastic study of stresses in rack gears

A three-dimensional photoelastic analysis using the stress-freezing and slicing techniques was employed in studying the stress distribution and concentration across the thickness of a thick rack-gear tooth. Full-size photoelastic models of about 25-mm thickness, having various teeth parameters were machined from PLM-4B plates. A special mounting fixture was designed to hold the models in the loading frame and a knife-edged line load was used in loading the models. In the analysis, the method of oblique incidence was adopted for the separation of the principal stresses. The intension was to determine the magnitude and location of the maximum stress at the tensile fillet and to establish the stress-concentration factors for various geometric tooth configurations.From this study, it was concluded that the fillet stresses depend largely upon the pressure angle, fillet radius and the position of the load. Maximum values of the tensile fillet stresses occur at the middle plane of the tooth thickness. Furthermore, the value of the stress-concentration factor increases with the increase of the tooth thickness. In general, this investigation gave values of stresses much higher than those values calculated by the simple-flexure theory.     

Measurement of thermal stresses within an experimental nuclear-reactor vessel head

This paper describes certain tests and techniques employed in measuring stresses within an experimental nuclear-reactor head of unusual design. The incorporation of certain desired design features necessitated that the head be extremely thick. Due to the thickness and its complex geometry, it was considered desirable to determine stress distribution within the head under conditions of steady-state pressure combined with rapid heating and cooling transients within the reactor, in order to determine safe limits for the operation of the head. A photoelastic study of a three-dimensional model of the reactor head was completed in 1956; this study permitted prediction of the stress distribution throughout the head as a function of internal pressure, but it was not possible to assimilate the head thermal stresses by photoelastic means. It is the purpose of this paper to describe the technique employed in measuring thermal stresses in the interior of the head, under simulated operating conditions of steady-state pressure and temperature transients.     

Photoelastic assessment of finite-element analysis of a pipe tee

A three-dimensional photoelastic analysis and a finite-element analysis of a pressurized pipe tee are compared. The pipe tee is a 152-mm typical commercial straight buttwelding tee, having a nominal wall thickness of 11.0 mm. The finite-element program employs a doubly curved shell element in which stresses vary linearly through the thickness. The three-dimensional photoelastic model was cast from the pattern of an actual pipe tee. The model was pressurized and stress-frozen. Its principal planes were analyzed for in-plane surface stresses, then subsliced and analyzed for transverse stresses. The photoelastic stresses are graphically compared to those from finite elements. For large regions of the tee there is substantial agreement in the stresses from the two methods. Considerable disagreement is revealed in the sharply curved corners between the main pipe and the stem. Paper was presented at the 1986 SEM Spring Conference on Experimental Mechanics held in New Orleans, LA on June 8–13.     

The Potential for Assessing Residual Stress Using Thermoelastic Stress Analysis: A Study of Cold Expanded Holes

Thermoelastic stress analysis (TSA) is a well established tool for non-destructive full-field experimental stress analysis. In TSA the change in the sum of the principal stresses is derived, usually when a component is subjected to a cyclic load. Therefore the mean stress or any residual stress in a component cannot be obtained from the thermoelastic response. However, modifications to the linear form of the thermoelastic equation that incorporate the mean stress may provide a means of establishing the residual stresses. It has also been shown that the application of plastic strain modifies the thermoelastic constant in some materials, causing a change in thermoelastic response, which may also be related to the residual stress. The changes in response due to plastic strain and mean stress are of the order of a few mK and are significantly less than those expected to be resolved in standard TSA. Recent developments in infra-red detector technology have enabled these small variations in the thermoelastic response to be identified, leading to renewed interest in the use of TSA for residual stress analysis in realistic components. The component studied in this work is an aluminium plate that contains a cold expanded hole, hence providing an opportunity to examine any changes in thermoelastic response caused by the residual stress in the neighbourhood of the hole. The variations in thermoelastic response due to residual stress are shown to be measurable and significant; validation of the residual stress field is provided by laboratory X-ray diffraction. The potential for a TSA based approach for residual stress analysis is revisited, and the feasibility of applying it to components containing realistic residual stress levels is assessed.