The α-factor in the Taylor flow-stress law in monotonic, cyclic and quasi-stationary deformations: Dependence on slip mode, dislocation arrangement and density

The aim of the present work is to assess in a formal manner “effective” values of the geometrical factor α which takes into account the arrangement of the dislocation pattern in the classical Taylor flow-stress law. For this purpose, selected experimentally well-documented cases of unidirectional and cyclic plastic deformation were analyzed. It is shown that, in both monotonic and cyclic deformation, the α-factor depends on the mode of deformation (single slip versus multiple slip). For examples of dominant primary slip interaction, a value α ≈ 0.1 is found. However, more frequently, α ≈ 0.3-0.4, typical of forest interaction, obtains. As deformation proceeds, the dislocation pattern frequently becomes more heterogeneous (cell formation) and approaches a state of lower energy, with increasing lattice misorientations which arise from an increasing density of geometrically necessary dislocations (GNDs). In these cases, α is generally lowered, for example from an initial value of 0.35 down to values around 0.2. This behaviour is explicable in terms of the composite model in which the heterogeneity is explicitly taken into account. Very similar developments of the dislocation arrangement, accompanied by a decrease of the α-value, are also noted during so-called “steady-state” cyclic and high-temperature creep deformations. In both cases, deformation is shown to be only quasi-stationary due to the fact that well-documented small but non-negligible microstructural changes, associated with a mild increase of the density of the GNDs, persist during deformation. The overall behaviour is readily described in an empirical manner in a unified picture. From the results obtained follows the requirement for a more general flow-stress model which considers explicitly the interaction of different slip systems and the heterogeneity of the dislocation pattern.