Shape deformation by moving a glissile interface with one set of misfit dislocations

Abstract Transformation and misfit dislocations are used to describe the motion of glissile interfaces with one set of misfit dislocations in the framework of the Frank−Bilby equation. The sweep of these glissile interfaces brings about an invariant-plane-strain type shape deformation. Our approach explains the glissile motion of martensitic interfaces and small-angle symmetrical tilt grain boundaries. It is consistent with the phenomenological theory of martensite crystallography but more flexible. Keywords: transformation dislocationsmisfit dislocationsgrain boundariesinterfacesmartensitic transformations Acknowledgements This work was partially supported by Grant-in-Aids for Scientific Research of the Ministry of Education, Science and Culture (Nos. 17002009, 18686077, and 15106015). Z.G. Yang would like to acknowledge the support of the National Natural Science Foundation of China (No. 50871059). Notes Note 1. A bold upper-case letter denotes a 3 × 3 matrix; a bold small italic letter denotes a 3 × 1 column vector; superscript "−1" is the inverse of a matrix; and "′" indicates the transpose of a matrix or vector. |A| is the determinant of a matrix A, and | a | is the length of a vector a . All the vectors and matrix operations are described in the crystallographic coordinate system of the reference lattice except those with subscripts "f" and "b" (they are defined in face-centered cubic (FCC) and body-centered cubic (BCC) lattices. The length unit is selected as the lattice parameter of the reference lattice.