Andrei Errapart

Modern Photoelasticity for Residual Stress Measurement in Glass

Residual stress is one of the important indicators of the quality of any glass product. The paper gives a review of the methods, which are nowadays used in glass industry for measuring residual stress both in architectural and automotive glass panels and in hollow glassware.

Application of the Abel inversion in case of a tensor field

Abels integral equations arise in many areas of natural science and engineering, particularly in plasma diagnostics. The axisymmetric physical field is determined using the Abel inversion. Until now, the Abel inversion has been applied almost exceptionally for the determination of scalar fields, i.e. fields, which at a point are characterized by a scalar. In several areas of engineering, the need to determine axisymmetric tensor fields arises, for example by measuring residual stress in axisymmetric glass articles with photoelasticity. In this article, we show how the Abel inversion can be used for the determination of an axisymmetric stress tensor field. The peculiarity in determining the tensor field is that on every ray two integrals of the field are measured and for complete determination of all the components of the stress tensor, equations of the theory of elasticity are used. The method is illustrated by an example.

Photoelastic tomography for residual stress measurement in glass

The paper describes analgorithm of photoelastic tomography and its application for residual stress measurement in glass articles of complicated shape. The algorithm is based on a linearized solution of the equations of integrated photoelasticity. The problem of tensor field tomography is decomposed into several problems of scalar field tomography for normal stress components of the stress tensor. The method is implemented with an automated polariscope with a rotary stage. Several examples illustrateapplication of the method.

Generalized Onion-Peeling Method in Integrated Photoelasticity of Axisymmetric Problems

By measuring residual stress in axisymmetric glass articles, stress distribution is usually described with polynomials [1]. In case of cylinders, axial stress distribution can be measured also using a discrete algorithm, named “onion-peeling” [2]. In this method, the cylinder is considered as consisting of a number of concentric cylindrical rings (Fig. 1), in each of which the axial stress σz may be considered constant. Axial stress in the first ring σz(1) is determined through

Measuring residual stresses in homogeneous and composite glass materials using photoelastic techniques

Abstract: This chapter gives a review of the modern photoelastic techniques for residual stress measurement in homogeneous and composite glass articles, including glass articles of complicated shape. For residual stress measurement in axisymmetrical glass articles, integrated photoelasticity is being used. In the case of non-axisymmetrical glass articles of complicated shape, photoelastic tomography is to be used. As for automotive and architectural glass panels used in buildings, surface stress can be measured with the mirage method. More complete stress analysis can be carried out with the scattered light method.

Effects of Ray Bending in Scattered Light Photoelasticity for Tempered and Annealed Glass Plates

Residual stresses in tempered glass plates can be measured with the scattered light method. Usually a rectilinear propagation of light is assumed. However, due to the gradients of the refractive index, the light rays curve. We have experimentally demonstrated this for tempered (surface stress 120 MPa and more) and annealed glass plates. For a laser beam of finite width this also results in broadening and loss of photoelastic modulation. While some features of the experimental picture (dependence of the period of modulation on depth), can be captured in the simple model of rectilinear propagation, the other observations need development of more elaborated models.

Determination of All Stress Components of Axisymmetric Stress State in Photoelastic Tomography

In this paper we describe the application of photoelastic tomography for determining stresses in glass. The basic equations of linear approximation in photoelastic tomography are presented. Since these equations permit direct determination only of the axial and shear stress, a method for calculating the other stress components is described. In the case of the residual stresses, it uses the equilibrium equation and the generalized sum rule. In the case of stresses due to external loads, it uses the equilibrium and compatibility equations. It is shown, both graphically and analytically, that integration of these equations must start at the axis and proceed along the positive direction of the radial axis. As an example, residual stresses in the stem of a wine glass are determined. Results are verified by comparing the birefringence, calculated from the determined stress state, with measured birefringence. The numerical algorithm for the case of stresses due to external loads is verified by using the theoretical solution for a Hertzian contact stress problem.

Photoelastic tomography as hybrid mechanics

Photoelastic tomography is a non-destructive method of 3D stress analysis. It permits determination of normal stress distribution in an arbitrary section of a 3D test object. In case of axial symmetry also the shear stress distribution can be determined directly from the measurement data. To determine also the other stress components one can use equations of the theory of elasticity. Such a combined application of experimental measurements and numerical handling of the equations of the theory of elasticity is named hybrid mechanics. It is shown that if stresses are due to external loads, the hybrid mechanics algorithm is based on the equations of equilibrium and compatibility. In the case of the measurement of the residual stress in glass the compatibility equation can not be applied. In this case a new relationship of axisymmetric thermoelasticity, the generalized sum rule can be applied. 1 Classical tomography Tomography is a powerfull method for the analysis of the internal structure of different objects, from human bodies to parts of atomic reactors [1]. In tomography, some radiation (X-rays, protons, acoustic waves, light, etc.) is passed through a section of the object in many directions, and properties of the radiation after it has passed the object (intensity, phase, deflection, etc.) are measured on many rays (Figure 1). Experimental data g(l,θ*) for different values of the angle θ* are called projections. Fig. 1. Scheme of tomographic measurements. a e-mail : aben@cs.ioc.ee

Linear and Non-Linear Algorithms of Photoelastic Tomography

Photoelastic tomography in linear approximation is based on the formulas [1]