On couple stress in the mechanics of materials

Abstract

The couple stress theory as presented by Mindlin, Koiter, Stokes and others is reviewed with particular attention being given to stress concentration and size effects. That theory is compared on a qualitative and quantitative basis with Neuber's theory for stress concentration for very small or sharp notches and with observed notch sensitivity effects in aluminum and steel.

It is established that, in order to explain observed elastic size effects in these materials, the new material constant ℓ which is characteristic of the couple stress theory must be on the order of magnitude of .02". In order to determine order of magnitude of the constant, a series of experiments was designed based on a thin plate analysis developed here.

The plate theory uses the basic assumptions of classical plate theory as well as several, as explained in the text, necessary when couple stress is included. The formulation resulted in a set of equations for plate deflection including classical and couple stress terms in such a way that when the constant ℓ was allowed to be zero, the classical equations resulted.

Experimentally, it was found that the couple stress effect in steel and aluminum is at least one order of magnitude too small to account for observed size effects as was suggested by Mindlin. In addition, the magnitude of ℓ was found to be such that its effect would undoubtedly be clouded by inhomogeneity and anisotropy of metals at the microstructural level.

The results represent the only known experimental data at the time of publication dealing with couple stress in metals and would seem to be the next obvious step in the development of the theory which has proceeded on a purely mathematical plane.

An alternate approach to account for the effects of microstructure in notch sensitivity is discussed.