Coherency stresses in lamellar Ti−Al

Abstract

General formulas are given for the coherency strains and stresses in a multilayer far from the free surfaces. The multilayer is assumed to be a periodic stack of different elastically isotropic materials, but there may be any number of layers in the stack and they may each have any thickness and any elastic constants. The results are applied to lamellar Ti−Al alloys, in which there are shear misfits between different γ layers and both shear and biaxial misfits between the γ and α2 layers. In a fully coherent multilayer, the stresses would be large, in the GPa range, and in high strength, thin lamella alloys, the coherency stresses are a substantial fraction of a GPa. The shear stresses act principally on hard mode deformation systems, and the biaxial stresses place every α2 lamella in biaxial compression. This biaxial compression, which, for dislocation glide, is equivalent to a uniaxial tension normal to the lamella, is particularly large when the α2 volume fraction is small.