Effect of grip constraints on the tensile deformation of f.c.c. single crystals

Abstract

It has been found experimentally that the slope and the length of easy glide of a single crystal are orientation dependent. When a single crystal shears on a slip plane, this shear has in general a component on a plane perpendicular to the tensile axis, and the shear component will tend to displace one grip laterally relative to the other. As lateral displacement of one grip relative to another is impossible during a tensile test, this shear tendency interacts with the grips to produce a shear stress assumed to be proportional to the shear strain tendency. This shear stress, referred to as total grip effect, can be resolved on all the slip systems. The total grip effect resolved onto the active slip plane, always opposes the applied shear stress and therefore gives rise to a slope. When the total grip effect adds to the applied shear stress on a latent slip system, it will force this system to be activated. When the secondary system activated by the total grip effect forms Cottrell-Lomer locks with the primary slip system, it will terminate easy glide. The total grip effect being orientation dependent, the same is true for the slope and the length of easy glide. The most striking result is that the total grip effect is zero for the so-called “0.5” orientation (0.5 = Schmid factor). It is precisely in the neighbourhood of this orientation that f.c.c. single crystals are found to have the largest easy glide associated with the lowest slope. This theoretical analysis leads to the conclusion that the easy glide region depends on the shape of the specimen, the resolved shear stress, the grip effect on the primary system and the grip effect on the systems which form Cottrell-Lomer locks with the primary, on the lattice rotation as it changes these grip effects and on the grip effect created by lattice rotation itself. The same kind of formalism has been applied to single crystals deforming on many equally stressed systems. By requiring that the grip effect be zero, it was possible to establish the number of slip systems really operating and thereby distinguish qualitatively between the different cases of polyslip.