The elastic limit of metals exposed to tri-axial stress

The numerous investigations which have been carried out since the opening of the present century into the elastic breakdown of metals have resulted in the formulation of several hypotheses concerning the conditions of stress and strain necessary for its occurrence. The methods generally employed in the investigations have consisted in the application of combinations of tension and compression with torsion, and of bending with torsion, to solid bars and thin tubes, and of tension and compression combined with internal and external pressure to thin tubes; so that the stress system produced in the metal was essentially bi-axial in character, the third principal stress being either very small or zero. The results of these experiments have given general support to the shear stress hypothesis of Guest, although with deviations which in some cases are not insignificant. Experiments employing a tri-axial stress system, in which the relation to each other of the component stresses could be varied, have been comparatively few in number. Tests by Turner on thick walled cylinders of mild steel exposed simultaneously to internal pressure and axial tension, were inconclusive, possibly owing to the irregularity of the tubes. Those by Cook and Robertson, also on thick-walled tubes of varying dimensions, showed a reasonably constant value of the maximum shear stress at the instant of elastic breakdown at the internal surface; this stress was, however, considerably higher than the shear stress observed in the uni-axial state of stress in a simple tensile test of the same material, a result confirmed in more recent tests of a similar kind by the author. The newer hypotheses of Haigh and of von Mises require an effect of this kind; but it has been suggested by the author that the observed effect may nevertheless be associated more directly with the non-uniform character of the stress distribution, rather than as an indication of the inapplicability of the hypothesis which regards failure as due to the existence of a critical value of the shear stress.