Photoelastic stress analysis

Abstract

This work deals with stress problems solved by Photoelastic Techniques. The problems that can be solved range from the most simple, to a highly complex industrial problem and the ease with which a solution can be obtained shows the method's versatility. Unfortunately, photoelasticity is not always appreciated, and the great potential offered by this method of solution is lost. Stress distribution problems are always encountered in engineering, and a variety of methods of solution are offered. Many may prefer a mathematical approach, which is ideal for relatively simple shapes, but as the complexity of the problem is increased, and unless the mathematical solution is supported by experiment, variations to the correct solution occur even when simplifications are undertaken. Since the advent of computers finite element analysis was introduced, and stress problems could be solved, as long as economic problems, with regards to time and money have no limit. Solution of such problems by a proved finite element package must still be regarded with caution, since conditions within the boundary and at the boundary must at all times obey the rules set by stress distribution problems and the tendency that a finite element user may become detached from the real problem must also be avoided. Also, the stress analysis of a full-sized construction by strain gauges is expensive so that alternative methods are developed in which a solution is obtained by tests on small scaled models. This work on photoelasticity, shows that by using small scaled models, manufactured from materials which have special mechanical and optical properties, and examined in polarized light, the stress distribution can easily be deduced. Photoelasticity is a rapid and economical method of stress analysis giving a reliable quantitative solution of the problem. One of the chief advantages of this method is that it gives the engineer an immediate and tangible picture of the stress conditions in the whole component being investigated. This work is not intended to expand into the full mathematics of photoelastici ty, but rather to give a detailed account of how one would approach stress solutions. The techniques, as such, are not complicated, but one would require some experience with regards to apparatus set up, manufacturing of the models, correct load application and analysis of stress distributions before a quantitative reliable solution can be obtained. The models analysed are not of any high complex industrial component. Since it must be appreciated that attaining the skills for this technique requires much time, effort and patience. One cannot simply plunge into stress distribution problems, but must gradually attain the skill, by starting from the simplest models. It is only by doing this can one truly appreciate the method's versatility when problems of a complex nature can then be solved. On accomplishing this, photoelasticity will prove the ease with which a solution is obtained, and once it is fully appreciated and understood, mathematical or other methods of solution will soon be regarded as second to photoelasticity. A brief summary of this thesis is as follows: Chapter One describes the basic apparatus necessary for any photoelastic analysis, and gives a detailed procedure of the apparatus set up. Other components, which are not compulsory but will facilitate the analysis, such as the ·tilting stage, oven frame and loading attachments are also described. Chapter Two gives a detailed account of the photoelastic theory, since it is very important that one may understand the principles involved and hence be ·able to visualise an overall picture whilst working. Both a descriptive and mathematical approach is considered when explaining the nature of plane and circular polarized light, and the effects of a stressed model in this light path. lsoclinics, lines of principal stress and methods of compensation are also described. Chapter Three explains how one would choose a good photoelastic material, which has optimal mechanical and optical properties, besides other conditions which must be satisfied. It also gives the reasons why the epoxy resin CT200 material of thickness 3, 6 and 9 mm were chosen. Chapter Four· deals with the various methods of manufacturing models starting from polished sheets of material. The optimal conditions of the model manufacturing and defects which can be produced during manufacture are also explained. Chapter Five deals with the loading of both two and three dimensional models. It explains the rules which must be followed, the difficulties encountered and defects observed. Reasons why some models were manufactured and why others were not is also given. attachments and their use is also described. Special loading Chapter Six give the technique for fabricating complex models from epoxy resin sheet using the adhesive cycle. Chapter Seven gives an account of the stress freezing cycle, the thermal requirements during this operation, the ·behaviour of the material at the critical temperature and slicing of the model for analysis. Chapter Eight shows and gives the equations of how the photoelastic results can be transferred and applied to stresses in the prototype, by using dimensional analysis on the scaled photoelastic models. Chapter Nine explains how one would calibrate the material by means of a disc in diametrical compression.to obtain the material fringe value. Chapter Ten shows how one is able to interpret the isochromatic or fringe patterns to obtain boundary stresses, stresses at points within the boundary and individual principal stress by the oblique incidence method in both two or three dimensional models. Chapter Eleven expresses the photoelastic results as a series of fringe/stress patterns, isoclinics and stress trajectories, from which any type of stress solution can be obtained for that particular model and loading condition. Chapter Twelve shows various applications for photoelasticity which vary from simple educational applications. problems to highly industrial Chapter Thirteen gives a comparison with advantages and disadvantages of photoelasticity and finite element analysis by means of two examples.