PIRE - mathematics, mechanics, materials science

Science at the triple point between
mathematics, mechanics and materials science

Publication 8

Nucleation barriers for the cubic-to-tetragonal phase transformation


BonnHans Knupfer
Bonn University

NYURobert V Kohn
Courant Institute of Mathematical Sciences
New York University

MaxPlanckFelix Otto
Max Planck Institute for Mathematics in the Sciences (MIS) in Leipzig

We are interested in the phase transformation from austenite to marten- site. This transformation is typically accompanied by the generation and growth of small inclusions of martensite. We consider a model from geometrically linear elasticity with sharp energy penalization for phase boundaries. Focusing on a cubic-to-tetragonal phase transformation, we show that the minimal energy for an inclusion of martensite scales like $\max\{V^{\;2}/3,V^{\;9}/11 \}$ in terms of the volume V . Moreover, our arguments illustrate the role of self-accommodation to achieve the minimal scaling of the energy. The analysis is based on Fourier representation of the elastic energy.
Get the paper in its entirety

Back to Publications