Apparent Hall-Petch effects in polycrystalline lamellar TiAl

The mechanisms responsible for the extremely high Hall-Fetch slope of K-y approximate to 5MPa m(1/2), for grain sizes d in the range 3000-200 mu m, in fully lamellar (FL) and nearly lamellar (NL) TiAl microstructures are explored. It is shown that the constraints exerted by the neighbouring crystals, particularly those oriented in the hard mode, are the dominant factors controlling the yield stress. At large grain sizes (and small sample dimensions), these constraints are largely relaxed, because of free boundary conditions, thereby severely underestimating the true yield stress. Numerically computed flow stress curves illustrate that the sample gauge diameter D, for approximating bulk behaviour, for Hall-Fetch measurements, scales with the hard-mode (g(2) degrees) against soft-mode (g(1) degrees) critical resolved shear stress anisotropy. Thus, while D/d approximate to 10 meets the bulk requirement for nearly isotropic, fully gamma alloys, the minimum number of crystals required to approach bulk behaviour is 400 or more (i.e. D/d greater than or equal to 20) for nominal plastic anisotropy (g(2) degrees/g(1) degrees approximate to 12) of the (FL, NL) lamellar alloys. This requirement is expected to be further exacerbated as the ratio increases, with the limit (g(2) degrees/g(1) degrees --> infinity, as g(2) degrees --> infinity) of having only one slip system as input. A similar high Hall-Fetch slope (K-y approximate to 4.42 MFa m(1/2)) is derived from computed results by simply considering the geometrical factors pertaining to material constraint for D/d in the range 1-20 for lamellar microstructures. Thus, increasing constrained volume fraction, as the grain size decreases, is concomitant with the increase in yield stress, and the ensuing Hall-Fetch slope.