It was shown in Chapters 1 and 2 that the resolved shear stress in a single slip system is related to the applied stress by the Schmid factor, M. For a poly crystal, σ = MTτ, where MT is commonly referred to as the Taylor factor. The value of MT is computed such that the continuity of slip at the grain boundary satisfies the requirement for five independent slip systems to operate in each grain. The values of MT are computed by invoking the principle of virtual work. Convince yourself, by consulting appropriate references and standard textbooks on mechanical metallurgy, that for random orientations of grains,
(a) For FCC polycrystals, MT = 3.06.
(b) For BCC polycrystals, MT = 2.00.
(c) Taylor-type calculations are not possible for HCP polycrystals where twinning and nonbasal slip influence deformation.