An integrated crystal plasticity–phase field model for spatially resolved twin nucleation, propagation, and growth in hexagonal materials
C. Liu, P. Shanthraj, M. Diehl, F. Roters, S. Dong, J. Dong, W. Ding, D. Raabe,
Volume: 106. Pages: 203--227
DOI: 10.1016/j.ijplas.2018.03.009
Published: 2018
Abstract
Typical hexagonal engineering materials, such as magnesium and titanium,
deform extensively through shear strains and crystallographic re-orientations
associated with the nucleation, propagation, and growth of twins.
To accurately predict their deformation behavior it is, therefore,
critical for constitutive models to incorporate these mechanisms.
In this work an integrated approach for modeling the concurrent dislocation
mediated plasticity and heterogeneous twinning behavior in hexagonal
materials is presented. A dislocation density-based crystal plasticity
model is employed to predict the heterogeneous distribution of stress,
strain and dislocation activity and is coupled to a phase field model
for the description of the nucleation, propagation, and growth of
tensile twins. A stochastic model is used to nucleate twins at grain
boundaries, and their subsequent propagation and growth are driven
by the Ginzburg–Landau relaxation of the system free energy which
includes the orientation dependent twin interfacial energy and the
elastic strain energy. Application of this novel and fully coupled
model to the cases of magnesium single crystal, bicrystal, and polycrystal
deformation is shown to demonstrate its predictive capability. Numerical
simulations predict, in accordance with experimental observations,
twin nucleation at grain boundaries followed by twin propagation
into the grain interior and subsequent transverse twin thickening.
Through this new combination of modeling approaches it is possible
to systematically study the twin induced strain fields, the stress
distribution along twin boundaries, and the spatial evolution of
dislocation density within twins and parent grains.