Shear Stress-Strain Relation Obtained from Torque-Twist Data

摘要

One method of establishing the shear stress-strain relation of a material involves applying torsion to a circular cylinder. This approach has the advantage of experimental simplicity, but the disadvantage that the specimen is nonuniformly loaded, thus requiring a somewhat sophisticated data analysis. Fortunately the required analysis has already been worked out for the case of solid cylinders made of an isotropic elastic material. Such an analysis was furnished by Nadai. Unfortunately, sometimes only an approximate analysis is performed, and results are only reported as the resulting approximate shear stress-strain relation. Fortunately however, as we shall show, this type of approximate result can be easily corrected to get the proper result without having to go back to the original torque-twist data, which may no longer be available. A second contribution of the paper is to extend the analysis to the case of hollow cylinders. A third is to call attention to the fact that some cases of combined loads can also be analyzed in essentially the same manner. This is of particular interest in the case of highly anisotropic materials, in which compression-shear interaction may be large. We first derive the standard result, using an approach that emphasizes the physical aspects of the problem, and serves as the basis of the extension to hollow cylinders.