Atomistic Study of Motion of Twin Boundaries: Nucleation, Initiation of Motion, and Steady Kinetics

The materials that exhibit martensite transformation have very important applications in engineering, and the microstructures of the materials play a key role for
affecting their mechanical behavior in macroscope. Therefore many attentions have
been drawn for studying the related problems. This work focuses on the motion of
twin boundaries. Three questions are being asked: how is a twin boundary is nucleated in a homogenous (untwinned) material? After the twin boundary is nucleated,
how is its motion initiated? How fast does it move? This study provides an atomistic
understanding for these three questions.

Linear stability analysis is firstly applied to capture the initiation of motion of a
twin boundary. When a twin boundary is about to move, the lowest eigenvalue of the
system Hessian drops to zero. And the corresponding eigenvector predicts accurately
the way in which the twin boundary is going to move. The same idea is applied to
investigate how motion of an irrational twin boundary is initiated. Atomic models
of irrational twin boundaries are constructed by employment of continuum models,
provided that the point group of rotations which relate two variants is extended to
any rotations in plane. The zero eigenvectors reveal the complicated behavior of
motion of irrational twin boundaries.

The problem of nonuniqueness of kinetic relations proposed by Schwetlick and
Zimmer is solved in a thermoelasticity framework. By calculating the net heat
flux
crossing the phase boundary which is carried by the phonons, a unique kinetic relation
can be determined. Finally, a nonlocal criterion for nucleation of twin boundaries
is proposed. By checking the stiffness of each unit cell evaluated with respect to a
single variable that represents the displacement along the unit cell diagonal direction,
locations and the orientations of nucleated twin boundaries can be predicted.