Elastic deformation of twinned microstructures

Pfeiffer, S.; Wagner, M.F.-X.

doi:10.1098/rspa.2017.0330

Elastic deformation of twinned microstructures (bibtex)

by S. Pfeiffer, M.F.-X. Wagner

Abstract:

Many crystalline materials exhibit twinned microstructures, where well-defined orientation relationships define the special symmetry between different, elastically anisotropic twin variants. When such twins are subjected to external loading, additional internal stresses necessarily occur at the twin boundaries in order to maintain compatibility. These compatibility stresses are constant inside each variant in repeating stacks of twins and considerably affect the local stress state. In this paper, we use anisotropic linear elasticity to derive general analytical solutions for compatibility stresses in a stack of twin variants in arbitrary materials, for arbitrary variant volume fractions and twin types, subjected to arbitrary applied stresses. By considering two examples, growth twins in electrodeposited Cu and B19' martensite twins in the shape memory alloy NiTi, we further demonstrate that compatibility stresses can considerably alter the preferred slip systems for dislocation plasticity as well as the effective macroscopic behaviour of twinned microstructures.

Reference:

Pfeiffer, S., Wagner, M.F.-X.: Elastic deformation of twinned microstructures, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 473, 20170330, 2017.

Bibtex Entry:

@Article{Pfeiffer20170330,
  author    = {Pfeiffer, S. and Wagner, M.F.-X.},
  title     = {Elastic deformation of twinned microstructures},
  journal   = {Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences},
  year      = {2017},
  volume    = {473},
  number    = {2204},
  pages     = {20170330},
  month     = aug,
  issn      = {1364-5021},
  abstract  = {Many crystalline materials exhibit twinned microstructures, where well-defined orientation relationships define the special symmetry between different, elastically anisotropic twin variants. When such twins are subjected to external loading, additional internal stresses necessarily occur at the twin boundaries in order to maintain compatibility. These compatibility stresses are constant inside each variant in repeating stacks of twins and considerably affect the local stress state. In this paper, we use anisotropic linear elasticity to derive general analytical solutions for compatibility stresses in a stack of twin variants in arbitrary materials, for arbitrary variant volume fractions and twin types, subjected to arbitrary applied stresses. By considering two examples, growth twins in electrodeposited Cu and B19' martensite twins in the shape memory alloy NiTi, we further demonstrate that compatibility stresses can considerably alter the preferred slip systems for dislocation plasticity as well as the effective macroscopic behaviour of twinned microstructures.},
  doi       = {10.1098/rspa.2017.0330},
  eprint    = {http://rspa.royalsocietypublishing.org/content/473/2204/20170330.full.pdf},
  publisher = {The Royal Society},
}