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.     

Stresses in case-bonded solid-propellent rocket motors under transverse body-force loading

The stresses in rocket motors generated by transverse body forces during storage, shipping or in flight maneuvers become increasingly significant as motor size increases. An 8-ft-diam centrifuge was used to study these stresses in photoelastic models made from Hysol 4485. The models were 5.4-in. diameter, with an internal star-shaped boundary which was free, and an external circular boundary enclosed in an elastic case. The maximum stresses at each star point were studied as a function of load orientation, case stiffness and method of support. Three support conditions were considered—a point support and two types of slings. Stresses of a significant magnitude are predicted in the current large motors by this study.     

Shock-front loading method for studies in dynamic photoelasticity

A versatile technique for applying a well-defined dynamic load to models for studies in dynamic photoelasticity is described. The method utilizes the shock front produced in a gas-dynamic shock tube to apply a load to models by direct normal impact. The principles and scope of the method are described and some examples of the dynamic stresses arising from shock-front impact on a low-modulus photoelastic model are presented and discussed. The method is suited to studies where simple variation and accurate determination of the load-cycle parameters, as well as precise reproducibility, are necessary. The method, in addition, permits close-field study of the initial response of materials to dynamic loading to be undertaken.     

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.     

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.     

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.     

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.     

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.     

Stress Distribution in an Orthotropic Plate with Circular Holes under Impulsive Loading

The photoelastic method is used to analyze the stress–strain state induced by an impulsive load in an orthotropic plate with circular holes. The distribution of dynamic stress concentration factors along the periphery of the holes is studied, and stresses and strains in representative sections are determined     

New method to determine restrained-shrinkage stresses in propellant-grain models

This paper deals with the photoelastic determination of restrained-shrinkage stresses which may be produced by curing or by thermal effects in models of solid propellant grains bonded to the case. Use is made of the birefringence exhibited in the curing process of a restrained polyurethane rubber. The techniques developed to take advantage of this property are shown in detail. The method can also be applied to the determination of the residual stresses produced in the curing process of a propellant cast around a rigid insert. An example of this application is also given. The extension of the method, using epoxies, to three-dimensional analyses is pointed out.     

Photoelastic modeling of stresses caused by thermal shock

The paper describes and evaluates an easy experimental method for subjecting the edges of photoelastic plate models to severe and repeatable thermal shock. It presents the development, with time, of the photoelasticfringe pattern at the edge of a plate and shows that this method simulates thermal-shock conditions in metallic materials of an intensity that is exceeded only under the most severe practical conditions. The resultant edge stresses are shown to increase to maximum values and then decrease with time as conditions shift from essentially plane strain to plane stress.     

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.     

Separation of principal stresses in the freezing method

In order to separate principal stresses in the photoelastic freezing method, the stress sum is determined by measuring the dilatation or variation of specific weight of small particles of frozen-in models. A floating teat has proved to give very accurate results.     

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.     

Theory of elastic and photoelastic isodynes. Samples of application in composite structures

The theoretical foundations of a system of new methods which the authors call isodyne photoelasticity are presented. It is shown that the plane-elastic isodynes related to two-dimensional stress fields can be obtained experimentally using particular scattered-light techniques. The experimentally obtained photoelastic isodynes allow non-destructive analysis of stresses in structures with local three-dimensional stress states.Isodyne photoelasticity is used to determine stresses in composite structures, in particular the stresses at internal discontinuities and the delaminating stresses. The results are used to assess the reliability of some analytical solutions. The theories of isodynes and of the developed experimental techniques of isodyne photoelasticity are presented in a manner compatible with contemporary concepts of the models of reality—physical models, mathematical models, and experimental models constructed of matter and energy.Paper was presented at V International Congress on Experimental Mechanics held in Montreal, Quebec, Canada on June 10–15, 1985.     

Linear limit stresses of some photoelastic and mechanical model materials

Certain laws of similarity must be observed in structural-model analyses. In this paper, one aspect of model similarity—that of linearity—is examined quite extensively. Most model analyses assume that both prototype and model materials obey Hooke's law. But the plastics often used for structural or photoelastic models are viscoelastic or photoviscoelastic. The stress-strain and stress-birefringence relations are time dependent and may be nonlinear. Through careful calibration of model materials and proper design of model tests, potential errors due to the time dependence of material properties can usually be avoided. If the results of the test are to be interpreted conveniently and accurately, the stresses in the model material must be within the linear range. This range is limited and time dependent for most plastics. The linear range may extend only to stresses considerably below the ultimate or fracture strength of the material. Hence, analyses based don linearity may be in error if the initial stresses are too high and/or if given stresses are sustained too long before desired information is collected. The stresses which limit the linear range, called linear limit stresses, were determined for both stress-strain and stress-birefringence relations for four commonly used plastics: CR-39 (Cast Optics Co.), PS-1 and PS-2 (Photolastic, Inc.) and P6-K (B.A.S.F., Germany). A graphical presentation of the time-dependent photoelastic and mechanical properties is employed. It was concluded that linear limit stresses for birefringence are approximately equal to those based on strain and can therefore be used to establish, within reasonable bounds of accuracy, the linear range of behavior of the material.     

The effect of out-of-plane restraint on plane-stress solutions near straight boundaries

The existence of out-of-plane displacement restraint where thin photoelastic plates are bonded to relaively rigid boundaries or inclusions will induce transverse stress components whose presence can cause the in-plane stresses to deviate significantly from the plane-stress solution. The extended generalized planestress formulation, which was developed in a previous paper to study the effect of out-of-plane restraint on the through-the-thickness averages of the in-plane stresses and displacements in thin plates, is applied here to obtain correction factors by which the photoelastically determined in-plane stress components at a straight restrained boundary can be multiplied to recover the desired twodimensional solution. Cases of mechanical and thermal loadings which vary sinusoidally in the direction parallel to the restrained boundary are treated. The stress-field alterations due to out-of-lane restraint are shown to depend strongly on Poisson's ratiov and the ratioL/H of the half-wavelength of the load variation to the plate thickness, and can be minimized by choosing a photoelastic material with the smallest values ofv andH possible. The simple asymptotic form of the stress-field alterations for large values ofL/H has enabled us to prescribe simple correction factors in this range. Finally, it is observed that, although the normal stress component which is parallel to the restrained boundary is altered to a greater degree than are the other in-plane stress components, the effect on this stress component penetrates into the plate a distance of only about one plate thickness, whereas the effect on the other components penetrates a distance of approximately one half-wavelength of the load variation.     

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.     

An approximate method of orthotropic photoelastic analysis

An approximate strain-optic law has been derived for photoelastic analysis of orthotropic model materials. Principal-strain difference and the direction of major principal strain can be obtained from only two photoelastic measurements (isochromatic-fringe order and isoclinic angle) by means of this strain-optic law. Limited experiments on models subjected to uniaxial and biaxial stresses indicate good agreement between the experimental results and predictions of the strain-optic law. A parametric study demonstrates that the direction of major principal strain can be predicted to within a few degrees of the exact value and that the principalstrain difference can be predicted within ±20 percent for most practical values of degree of orthotropy and ratio of principal strains. The error levels are quite acceptable considering the significant ease in analysis provided by the new law and the fact that such error levels are not uncommon in experimental investigations.     

On the studies of residual stresses in glass plates

The theoretical foundation of the photoelastic methods being presently used for measuring and analyzing residual stresses in glass is insufficient for studying development of transient viscoelastic stress states in glass plates during tempering process and for an explanation of the actual material behavior. It is shown that the basic knowledge of photoviscoelastic effect in glass over a wide range of electromagnetic radiation and temperature is necessary for such on analysis. Some photoelastic properties of plate glass are presented.