By Anton Peterlin (auth.), H. H. Stadelmaier, W. W. Austin (eds.)
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Hence, the virtual work for deformation is given by equation (18) as a d€ = :l:Ti dyi = :l:Tt* dyi* John E. Dorn and Jim. D. Mote 38 where Tt* is the resolved shear stress for the equivalent set of slips. For the operative set Tt = Tc, but since the resolved shear stress on the equivalent set cannot exceed the critical resolved shear stress for slip, Tc ~ Tt*· Consequently, and (21) Equation (21) asserts that the sum of the absolute values of the operative shear set of shear strains is never greater than the set of geometrically equivalent shear strains.
Stress vs. 5 %Al: Experimental ( - - ) and theoretical (- - -)[54 • 27 ). 10 stroin On the Plastic Behavior of Polycrystalline Aggregates .... ~. 4 True atrain Fig. 22. Stress vs. strain curves of polycrystalline aluminum for various grain sizes . It is possible, of course, that some of the observed decrease in flow strength with increasing grain size arises not from a grain-size effect per se but rather as a result of modification of the substructure of the grains. For, when a metal is annealed for a Ionger time or at a higher temperature in an attempt to coarsen the grain size, the pattern of dislocations can well change as a result of cross-slip or climb to provide a more dislocation-free and, therefore, softer metal.
With the assumption of an average imposed increment of strain dEt 1, that set of stresses which provides the greatest work can, by the application of the principle of maximum plastic strain energy, be identified as the operative set. 06 Tc for simple tension. They further demonstrated that the plastic potential calculated on the basis of their theory lies between the Tresca and von Mises criteria for yielding under combined stresses, a deduction which is in good agreement with the best current experimental evidence.