Young's Modulus Interpreted from Compression Tests with End Friction

Abstract

This paper derives an approximate expression for the true Young's modulus of a solid circular cylinder under compression between two end blocks with friction, provided that the Poisson's ratio is known. The conventional method of evaluating the Young's modulus assumes that uniform stress and deformation fields exist inside the specimen. However, if friction exists between the loading platens and the end surfaces of the specimen, a correction factor must be applied to the apparent Young's modulus. A correction factor with calculable error is obtained through the use of the Prager-Synge function space concept. The amount of friction is quantified by proposing a measurable parameter to model partial slip conditions. Numerical results show that the correction factor increases with both the slenderness ratio and the Poisson's ratio; these observations agree qualitatively with Filon's classical result. For the cases of partial slip, tables are provided for quick calculation of the correction factor.