Analysis of turbine blades using a rapid three-dimensional photoelastic method

Abstract

A new fast-curing photoelastic material formulation is presented that, when used with recommended curing and loading cycles, reduces the time needed to obtain three-dimensional stress results to the order of a week or less. The new formulation allows models to be cast to shape (replicated from a prototype) rather than machined. This is a major factor in the reduction of time. The stress analysis of the dovetail joint of a turbine blade and fan disk is reported as an example of the new method. INCE its inception in the last century, photoelasticity has been used as an alternate to theoretical methods to determine the stresses in bodies under load. Like other ex- perimental methods of measurement, photoelasticity has been found most useful for problems in which the geometry of loading, or the geometry per se, was too complicated to permit solution of the boundary value problem of the governing partial differential equations. For those problems which do lend themselves to mathematical expression, theoretical solutions usually have a generality far surpassing the corresponding photoelastic solution. So both theory and experiment serve different classes of problems, with a certain amount of overlapping. The introduction of three-dimensional photoelasticity broadened the scope of experimental stress analysis. The invention of the computer greatly widened the scope of theoretical stress analysis methods. It was felt by some that the introduction of computer-base d methods, and the finite- element method in particular, rendered two-dimensional photoelasticity obsolete and as well three-dimensional photoelastic analysis of axisymmetric problems. The only exception was the use of photoelastic methods to check the finite-element methods. Note should be taken of the fact that numerical stress analysis methods, while usually considered theoretical, have taken on several of the traits of experimental methods. As with experimental methods they often provide only a single (nonparametric) solution, and as with some measurement methods they provide the average stress over some finite area. Three-dimensional stress analysis of nonaxisymmetric problems is difficult, experimentally or theoretically . Thus, for the historic reasons cited above and because of developments in three-dimensi onal photoelasticity, it has become a major area of interest in experimental stress analysis. A singular difficulty in three-dimensional photoelasticity is the manufacture of the model. In most studies in order to avoid the rind effect, it has been felt necessary to machine the