Bending of a bimetallic beam due to the Kirkendall effect

Abstract

The time-dependent bending of single-phase and two-phase bimetal strips due to interdiffusion is computed. The model couples simple beam theory and diffusion with bending due to the creation and/or annihilation of vacancies necessitated by unequal lattice diffusion rates of the two metals. The single-phase analysis employs a Fourier method for the diffusion analysis and predicts a beam curvature that is initially proportional to time and later reaches a constant value. The two-phase analysis, which involves a moving interphase boundary, employs an error function solution for the diffusion problem to model early times and a numerical solution for later time. Unlike the single-phase results, linear behavior is obtained at early time only if the original interface is centered in the beam. In general, the curvature initially is proportional to the square root of time. The numerical solution gives the gradual transition of the curvature to a constant value at late time. In some cases, nonmonotonic time dependence is obtained for the curvature for the two-phase beam. © 2009 ASM International.