Theories of Strength

Abstract

A metallic material will begin to deform plastically under a tensile or a compressive stress (i.e. a uniaxial stress system), after the yield stress has been reached. It has been seen that simple tensile or compressive yielding can be avoided when the introduction of a safety factor imposes a maximum allowable elastic stress limit for a material. In practice stress states are often biaxial or triaxial, e.g. a plate with forces distributed over its edges is two-dimensional while a point in the wall of a thick-walled cylinder under internal pressure is three-dimensional. The question arises as to what magnitudes of these combined stresses will produce yielding? This requires that a suitable criterion be found, based upon stress, strain or strain energy, that connects yielding under combined stresses to uniaxial yielding. It will be shown that any such criterion can be related to the uniaxial yield stress Y, which is most conveniently measured from a tension test. In the following section a summary is given of the yield criteria that have been proposed over the past two centuries. Of these, it is now accepted that those attributed to von Mises and Tresca are most representative of initial yielding in metallic materials. Experimental evidence is presented in support of this.