A New Criterion of Yielding in Metals

Abstract

SEVERAL theoretical criteria of yielding have been proposed^1,2 and tested by comparing the stress values found experimentally just as yielding began under simple stress systems. For example, the ratio of simple shear yield stress to simple tensile yield stress T₀/S₀ is given variously by older theories as 1, 0.77, 0.50, 0.62, while experimentally for common engineering materials this ratio is found to be 0.56 approximately. A better fit to experiment is the theory credited jointly to Huber, von Mises and Hencky (ref. 1, p. 478), which for the above ratio gives . This theory stated in Hencky's form for the stress system S_ii, etc., when i = 1, 2, 3, j = 2, 3, 1, is just as yielding is beginning. If the system of stresses is two-dimensional simple shear together with simple tension, then the Huber criterion gives an ellipse by plotting shear stress as ordinate and simple tension as abscissa. Experimental examination^3,4 shows the experimental values to lie approximately on the theoretical ellipse.