TY - JOUR
T1 - Slip and Twinning in Bravais Lattices
AU - Ball, John M.
N1 - Funding Information:
This paper grew out of an invitation to give the 2019 Leçons Jacques-Louis Lions at Sorbonne Université Paris, and was developed during visits to the Hong Kong Institute for Advanced Study and the Hausdorff Institute of Mathematics (funded by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy – EXC-2047/1 – 390685813). The research forms part of the project Mathematical theory of polycrystalline materials supported by the EPSRC grant EP/V00204X.
Publisher Copyright:
© 2023, The Author(s).
PY - 2023/9/5
Y1 - 2023/9/5
N2 - A unified treatment of slip and twinning in Bravais lattices is given, focussing on the case of cubic symmetry, and using the Ericksen energy well formulation, so that interfaces correspond to rank-one connections between the infinitely many crystallographically equivalent energy wells. Twins are defined to be such rank-one connections involving a nontrivial reflection of the lattice across some plane. The slips and twins minimizing shear magnitude for cubic lattices are rigorously calculated, and the conjugates of these and other slips analyzed. It is observed that all rank-one connections between the energy wells for the dual of a Bravais lattice can be obtained explicitly from those for the original lattice, so that in particular the rank-one connections for fcc can be obtained explicitly from those for bcc.
AB - A unified treatment of slip and twinning in Bravais lattices is given, focussing on the case of cubic symmetry, and using the Ericksen energy well formulation, so that interfaces correspond to rank-one connections between the infinitely many crystallographically equivalent energy wells. Twins are defined to be such rank-one connections involving a nontrivial reflection of the lattice across some plane. The slips and twins minimizing shear magnitude for cubic lattices are rigorously calculated, and the conjugates of these and other slips analyzed. It is observed that all rank-one connections between the energy wells for the dual of a Bravais lattice can be obtained explicitly from those for the original lattice, so that in particular the rank-one connections for fcc can be obtained explicitly from those for bcc.
KW - Rank-one connections
KW - Slip
KW - Twinning
UR - http://www.scopus.com/inward/record.url?scp=85169815223&partnerID=8YFLogxK
U2 - 10.1007/s10659-023-10034-9
DO - 10.1007/s10659-023-10034-9
M3 - Article
AN - SCOPUS:85169815223
SN - 0374-3535
JO - Journal of Elasticity
JF - Journal of Elasticity
ER -