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

Professor Edmund Tarleton, together with Professor Alan Cocks and Dr Nicolo Grilli, explored the problems encountered with modelling twin nucleation and growth processes, taking account of the challenges caused by different length and time scales.  

This paper, published by the Journal of the Mechanics and Physics of Solids, introduced two interaction terms to the phase field model with twinning, coupled with a dislocation-density based model for slip, implemented within the crystal plasticity finite element method.  The first is a non-local term that modelled the interaction between residual dislocations at the twin interface and mobile dislocations in untwinned regions.  The second is a local term that modelled the hardening of the twin system due to the presence of dislocations.

This paper explains how introducing these interaction terms, it was possible to reproduce a discrete pattern of twin bands after deformation.  These interaction terms and interaction strength parameters determined the nucleation and spatial position of twins, twin thickness and number density of twins as a function of strain.

The model was validated by comparing the simulated twin phase field with the dynamic formation of twins in tension, as measured by electron backscatter diffraction experiments in uranium.