A phase field model for the growth and characteristic thickness of deformation-induced twins

Nicolò Grilli*, Alan C.F. Cocks, Edmund Tarleton

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

18 Citations (Scopus)


Deformation-induced twinning is an important mechanism in metals with a limited number of slip deformation modes. The mechanisms for twin nucleation and growth are not completely understood, and modelling these processes is challenging because of the different length and time scales involved. Twins grow at the speed of sound up to a length of several millimetres and thickness of only a few microns. We present a phase field model for twinning, coupled with a dislocation-density based model for slip, implemented within the crystal plasticity finite element method. Softening of the critical resolved shear stress for twinning is used to reproduce the shear localisation that is typical of twin bands. Two interaction terms are introduced. The first one is a non-local term that models the interaction between residual dislocations at the twin interface and mobile dislocations in untwinned regions. The second is a local term that models the hardening of the twin system due to the presence of dislocations. By introducing these interaction terms, it is possible to reproduce a discrete pattern of twin bands after deformation. These interaction terms and interaction strength parameters determine the nucleation and spatial position of twins, twin thickness and number density of twins as a function of strain. The model is validated by comparing the simulated twin phase field with the dynamic formation of twins in tension, as measured by electron backscatter diffraction experiments on α-uranium. This model sheds light on the mechanism that determines twin growth and twin thickness. Specifically, twins stop thickening after a critical density of residual dislocations at the twin interface is reached. The interaction coefficients are interpreted in terms of the stacking fault energy in order to apply the model to different metals.

Original languageEnglish
Article number104061
JournalJournal of the Mechanics and Physics of Solids
Publication statusPublished - Oct 2020

Bibliographical note

Funding Information:
The authors acknowledge financial support from AWE plc for this research, program manager: Dr John Askew. ET acknowledges support from the Engineering and Physical Sciences Research Council under Fellowship grant EP/N007239/1 .

Publisher Copyright:
© 2020 Elsevier Ltd


  • Crystal plasticity
  • Dislocations
  • EBSD
  • Tensile test
  • Twinning
  • Uranium


Dive into the research topics of 'A phase field model for the growth and characteristic thickness of deformation-induced twins'. Together they form a unique fingerprint.

Cite this