Giant compliance and spontaneous buckling of beams containing mobile solute atoms

Abstract

Recent experiments have shown that the elastic compliance of a porous metal can be substantially enhanced when mobile solute is alloyed into interstitial sites of the crystal lattice. The observations agree with predictions – due to Gorsky and to Larché and Cahn – for the elasticity of open systems in which the elastic responses is probed at constant chemical potential. The underlying mechanism involves an exchange of solute between tensile and compressive fibers in beam-like elements of the microstructure. Here, we analyze the elastic deformation of such elements in a continuum approach, accounting explicitly for the coupling between chemistry and mechanics. We consider a regular solution with linear elasticity in the limit of constant composition and with a linear composition-strain coupling. Materials parameters are matched to experiments on Pd-H, so as to realistically account for the balance between chemical and mechanical energies. At constant chemical potential, the elastic response can be strongly nonlinear. With decreasing temperature, the bending goes from a monotonic moment-curvature relation to one including a horizontal tangent and, hence, a state of giant bending compliance. Reducing the temperature further brings first a temperature interval with a simple bistability and finally one with degeneracy including – depending on the chemical potential or on the mean solute fraction – the possibility of finite curvature at zero moment. Quenching the uniform solution into a two-phase region of the alloy phase diagram can lead to spontaneous buckling at no load. Furthermore, degenerate moment-curvature relations allow for bending states in which the radius is not a constant along the beam axis. Intervals of lar ge strain at constant load are similar to superelasticity, but the underlying phase transformation is here not martensitic.