Fotoelasticidad

Manual on Experimental Stress Analysis
Fifth Edition
James F. Doyle and James W. Phillips, eds.

Society for Experimental Mechanics

6. PHOTOELASTICITY Daniel Post1 6. 1. INTRODUCTION

Photoelasticity is an experimental technique for stress and strain analysis that is particularly useful for members having complicated geometry, complicated loading conditions, or both. For such cases,analytical methods (that is, strictly mathematical methods) may be cumbersome or impossible, and analysis by an experimental approach maybe more appropriate. While the virtues of experimental solution of static, elastic, two-dimensional problems are now largely overshadowed by analytical methods, problems involving three-dimensional geometry, multiple-component assemblies, dynamic loading andinelastic material behavior are usually more amenable to experimental analysis. The name photoelasticity reflects the nature of this experimental method: photo implies the use of light rays and optical techniques, while elasticity depicts the study of stresses and deformations in elastic bodies. Through the photoelastic-coating technique, its domain has extended to inelastic bodies, too. Photoelasticanalysis is widely used for problems in which stress or strain information is required for extended regions of the structure. It provides quantitative evidence of highly stressed areas and peak stresses at surface and interior points of the structure — and often equally important, it discerns areas of low stress level where structural material is utilized inefficiently. This chapter is intended tointroduce the basic concepts — to emphasize those elements that are fundamental to the photoelastic method. The details involving characteristics of specific photoelastic materials — their formulation, optical and mechanical properties, machining techniques, etc. — and the details involved in the use of specialized auxiliary instruments and accessories are not included. While such information isvitally important to the student of photoelasticity, it quickly becomes obsolete and is better disseminated by current technical papers and current manufacturers' literature. 6.2. PHOTOELASTIC BEHAVIOR

The photoelastic method is based upon a unique property of some transparent materials, in particular, certain plastics. Consider a model of some structural part made from a photoelastic material.When the model is stressed and a ray of light enters along one of the directions of principal stress, a remarkable thing happens. The light is divided into two component waves, each with its plane of vibration (plane of polarization) parallel to one of the remaining two principal planes (planes on which shear stress is zero). Furthermore, the light travels along these two paths with differentvelocities, which depend upon the magnitudes of the remaining two principal stresses in the material. Figure 6.1 illustrates this phenomenon. The incident light is resolved into components having planes of vibration parallel to the directions of the principal stresses σ1 and σ2. Since these waves traverse the body with different velocities, the waves emerge with a new phase relationship, or relativeretardation. 2 Specifically, the relative retardation is the difference between the number of wave cycles experienced by the two rays traveling inside the body.

1Professor of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, Blacksburg VA 2 The frequency of a monochromatic light wave is constant, regardless of the material being traversed by the wave.24061.

Therefore, the two waves have different wavelengths inside the body.

Fig. 6.1. Plane-polarized light waves double
3 refracting model. 3 4 waves are shown for one

plane, 3 1 waves for the other; relative 2 retardation is 1 wave. 4

This phenomenon is called double refraction or birefringence, and is the same as exhibited by certain optical crystals — but in photoelasticity the...