Effect of Couple-Stress on the Pure Bending of a Prismatic Bar

摘要

An evaluation of the applicability of the couple-stress theory to the stress analysis of graphite structures is performed by solving a pure bending problem. The differences between solutions from the couple-stress theory and from the classical theory of elasticity are compared. It is found that the differences are sufficient to account for the inconsistencies which have often been observed between the classical elasticity theory and actual behavior of graphite under bend and tensile loadings. An experimental procedure to measure the material constants in the couple-stress theory is also suggested. The linear couple-stress theory, the origins of which go back to the turn of the last century, adds linear relations between couple-stresses and rotation gradients to the classical stress-strain law. By adopting the classical assumption that the plane cross section remains plane after deformation, the pure-bending problem is reduced to a plane couple-stress problem with traction-free boundary conditions. A general solution for an isotropic elastic prismatic bar under pure bending is then obtained using the Airy stress function and another stress function wich accounts for the couple-stresss. For a cylindrical bar, it reduces to a simple series solution. The moment-curvature and stress-curvature relations derived for a cylindrical bar from the general solution are used to examine the effect of couple-stresses. Numerical compilation of relations indicates that the couple stress parameters can be practically determined by measuring the moment-curvature ratio of various diametered specimens under bending. Although there is not sufficient data for such evaluation at present, it appears that the theory is consistent with the limited bend and tensile strength data of cylindrical specimens for H-451 graphite. (ERA citation 81:025946)