Experimental investigation of transient thermal stresses in a solid sphere

An experimental investigation was made to determine if a transient-thermal-stress distribution could be effectively analyzed using scattered-light photoelasticity. the problem selected for investigation was a solid sphere at one temperature subjected to a spherical symmetric temperature distribution at a different temperature. The results and techniques are discussed.     

Photothermoelastic analysis of transient thermal stresses

Photothermoelasticity by means of heating is used to obtain an experimental solution to the quasi-static problem of transient thermal stresses around elliptical holes. Empirical equations are obtained for the maximum stresses due to step temperature changes at the edges of the plates.     

Photoelastic analysis of microelectric-component thermal stresses

Integrated circuit components are subject during manufacture and in service to three-dimensional thermal-stress concentrations from differential thermal expansion between the thin film and wafer (base). A typical microelectronic device is photoelastically modeled by isotropically prestraining the thin-film material that is later cemented to an annealed wafer. Stresses in the model assembly are then redistributed during a final stress-freezing cycle, as they would be in a prototype subjected to a typical thermal environment, and observed by slicing. Four additional models are also tested to observed the effects of different film-corned and edge configurations and to permit making analytical comparisons to verify the modeling approach. Experimental techniques and test results are reported and some suggestions are incorported for microelectronic-circuitry design.     

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.     

On thermal stresses and displacements in finned-tube panels

The end stresses in a finned-tube panel subjected to transverse temperature gradients are shown to be substantially different than those of a flat plate. Important differences occur due to the local bending of the tube and the extension of the tube beyond the end of the fin. On the other hand, stresses not near the ends and the in-plane deflections of a finned-tube panel are similar to those of a flat plate. These results are obtained by means of a review of flat-plate analysis and comparison with measurements made on two finned-tube panels with a step-transverse temperature gradient.     

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.     

2D and 3D separation of stresses using automated photoelasticity

A procedure for the separation of full-field photoelastic images for use with an automated polariscope is described. Regions of background in the image are identified thus producing the boundary of the model. The shear difference method is used to calculate the components of stress along all raster lines in the image using photoelastic parameters at the boundary points to calculate the initial values of stress. Algorithms were also used to evaluate the stress components along raster lines which did not contain boundary points. A plastic template was used to evaluate the efficiency of the boundary routine. It was found that it was able to identify edges to within approximately one pixel on screen. The complete procedure for stress separation was evaluated using a stress frozen disc in compression and a turbine slot. The values of stress found using the automated polariscope with the stress-separation procedure were found to agree well with theory and with results determined using the method of Tardy compensation and manual analysis. The automated polariscope was also used to analyze three-dimensional stress components along arbitrary lines of a 3D model. A two-model slicing regime was used to analyze a strut subjected to a vertical load. This work was compared to results obtained by Frocht and Guernsey on an identical model machined from Fosterite and subjected to a higher load. Good agreement was found between the results for points away from the region of loading. Significant differences were found near to the load point, however. A finite element analysis of the same problem suggested that this was due to the effects of plasticity.     

Photoelastic simulation of thermal stresses by mechanical prestraining

Several experiments are reported in which thermal stresses were simulated in photoelastic models by a mechanical-prestraining method. This method permitted the study of complex stress distributions arising from simple thermal-expansion conditions. The validity of the method is demonstrated by providing a comparison between theoretical and experimental results obtained for a fundamental disk problem. The usefulness of the method is illustrated by presenting some results of a tube-sheet experiment pertaining to a difficult engineering problem. Additional applications are described to indicate the variety of problems that may be studied by the prestraining method.Thomas Slot was formerly associated with Advanced Technology Laboratories, General Electric Co., Schenectady N.Y.; is now with Nuclear Materials and Propulsion Operation, General Electric Co., Cincinnati, Ohio.Paper was presented at 1965 SESA Spring Meeting held in Denver, Colo., on May 5–7.     

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.     

Analytical modelling of thermal stresses in anisotropic composites

This paper represents a continuation of the author's previous work which deals with an analytical model of thermal stresses which originate during a cooling process of an anisotropic solid elastic continuum. This continuum consists of anisotropic spherical particles which are periodically distributed in an anisotropic infinite matrix. The infinite matrix is imaginarily divided into identical cubic cells with central particles. This multi-particle–matrix system represents a model system which is applicable to two-component materials of the precipitate–matrix type. The thermal stresses, which originate due to different thermal expansion coefficients of components of the model system, are determined within the cubic cell. The analytical modelling results from fundamental equations of continuum mechanics for solid elastic continuum (Cauchy's, compatibility and equilibrium equations, Hooke's law). This paper presents suitable mathematical procedures which are applied to the fundamental equations. These mathematical procedures lead to such final formulae for the thermal stresses which are relatively simple in comparison with the final formulae presented in the author's previous work which are extremely extensive. Using these new final formulae, the numerical determination of the thermal stresses in real two-component materials with anisotropic components is not time-consuming.     

Transient thermal stresses and thermal deformations in a solid cylinder with a moving boundary

Summary This paper is concerned with transient thermal stresses and thermal deformations of the axisymmetric problem of a solid cylinder on consideration of a moving boundary. Assuming that a heated edge of the cylinder which is kept at a constant temperature moves with a constant velocity, the temperature distribution of the cylinder is analyzed using a moving coordinate system. Thereafter, the associated thermal stress distributions and thermal displacements are determined with aid of the method of the thermoelastic potential function and Love's displacement function. As an illustration, numerical calculations are carried out for several values of the velocity of the moving boundary, and the influence of the velocity on the temperature distribution and the stress distribution are examined precisely.

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Wärmespannungen und Verformungen in einem Zylinder mit bewegter Wärmequelle

Übersicht Es werden die Wärmespannungen und Verformungen in einem Zylinder untersucht, bei dem sich eine Wärmequelle mit konstanter Geschwindigkeit in axialer Richtung bewegt. Zunächst wird dabei die Temperaturverteilung im Zylinder mit Hilfe eines bewegten Koordinatensystems ermittelt. Dann werden die Wärmespannungen und die Verformungen mit der thermoelastischen Potentialfunktion und mit der Loveschen Verschiebungsfunktion bestimmt. Numerische Beispiele zeigen den Einfluß der Geschwindigkeit der Wärmequelle auf die Temperatur- und die Spannungsverteilung.

     

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.     

Experimental determination of residual stresses in paperboard

A method for the experimental determination of the through-thickness residual stress distribution in paperboard is presented. The successive removal of thin layers from strips of board through surface grinding changes the stress-state and the bending stiffness resulting in a changed curvature, which is measurable. From tests of strips in both in-plane directions, stress distributions can then be evaluated using the Treuting-Read method. Geometrically nonlinear effects at the large deformations taking place are avoided through a proper choice of strip dimensions. Typical results are presented and factors influencing the accuracy of the determination are thoroughly discussed.     

A note on thermal stresses in hollow cylinders

Conclusions The extensions of Trostel's solutions derived in this paper may be employed tor general over wide conditions with a resulting error less than 3%, the stress values being too small in magnitude by this amount. The error decreases as the variation of physical properties of the media decreases or as 1/2. M. M. Stanii, Lectures in Mathematical Elasticity during summer semester 1958, Purdue University.     

Transient thermal stresses in fully and partly cooled circular rings

The constraint associated with the direction of the thickness of a thin photoelastic circular-ring model is experimentally proved to occur and it is compared with the theoretical result; the constraint is induced by thermal loads. The method for dealing with the constraint and for obtaining a transient thermal stress under plane-stress conditions is applied to study the thermal stress of the circular ring partly cooled from the inside cylindrical surface. It is found that the thermal stress of the fully cooled circular ring is not always greater than the partly cooled one.