Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part II: Application to recrystallisation

In this work, the coupled phase field–crystal plasticity constitutive framework proposed in a companion publication [G. Abrivard, E.P. Busso, S. Forest and B. Apolaire, Phil. Mag. (2012) (this issue)] is applied to study the microstructural evolution driven by grain boundary curvature and/or stored energy. Different microstructures involving bicrystals and polycrystals of pure Al are studied and the results compared against experimental data and known analytical solutions. First, the study of a bicrystal with only curvature as the driving force for boundary migration enables the model to reproduce the different mobilities between low and high angle grain boundaries in the absence of Σ-type boundaries, and to identify the threshold misorientation below which the mobility is negligible. The growth of a small dislocation-free grain embedded within a highly deformed one is considered having both curvature and stored energy as the competing driving forces. A parametric study enabled the effect of the initial size of the nucleus on the minimum level of stored energy required for grain migration to be quantified. Finally, a study of recrystallisation and grain growth phenomena on a representative polycrystal aggregate revealed that grains with the lowest stored energy are dominant at the end of the recrystallisation process. The predicted recrystallised material volume fraction evolution and the kinetics of recrystallisation and grain growth were found to have the same dependence on deformation levels and temperature as those reported in the literature. Several outstanding modelling issues are identified and suggestions for further developments are discussed.

[1]  P. Biswas,et al.  Vacancies, microstructure and the moments of nuclear magnetic resonance: the case of hydrogenated amorphous silicon , 2011, Journal of physics. Condensed matter : an Institute of Physics journal.

[2]  Guillaume Abrivard,et al.  A coupled crystal plasticity - phase field formulation to describe microstructural evolution in polycrystalline aggregates during recrystallisation , 2009 .

[3]  A. Mallick,et al.  Phase field study of the effect of grain boundary energy anisotropy on grain growth , 2009 .

[4]  Akinori Yamanaka,et al.  Multi-phase-field simulations for dynamic recrystallization , 2009 .

[5]  S. V. Shevchenko,et al.  Implementation of exact grain-boundary geometry into a 3-D Monte-Carlo (Potts) model for microstructure evolution , 2009 .

[6]  Frédéric Feyel,et al.  Finite element formulation of a phase field model based on the concept of generalized stresses , 2009 .

[7]  G. Gottstein,et al.  Three-dimensional grain growth: Analytical approaches and computer simulations , 2008 .

[8]  Hidehiro Onodera,et al.  Phase field simulation of stored energy driven interface migration at a recrystallization front , 2007 .

[9]  G. Gottstein,et al.  Modelling of recrystallisation textures in aluminium alloys: I. Model set-up and integration , 2006 .

[10]  P. Streitenberger,et al.  Three-dimensional normal grain growth: Monte Carlo Potts model simulation and analytical mean field theory , 2006 .

[11]  W. C. Liu,et al.  Effect of initial texture on the recrystallization texture of cold rolled AA 5182 aluminum alloy , 2005 .

[12]  G. Gottstein,et al.  Modelling of recrystallization textures , 2001 .

[13]  A. Rollett,et al.  Measuring relative grain boundary energies and mobilities in an aluminum foil from triple junction geometry , 2001 .

[14]  András Roósz,et al.  Simulation of grain coarsening in two dimensions by cellular-automaton , 2001 .

[15]  Steve Marshall,et al.  Process , 2001 .

[16]  R. Becker,et al.  Coupling of a crystal plasticity finite element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminum , 2000 .

[17]  D. Srolovitz,et al.  Misorientation dependence of intrinsic grain boundary mobility: simulation and experiment , 1999 .

[18]  F. J. Humphreys,et al.  Measurements of grain boundary mobility during recrystallization of a single-phase aluminium alloy , 1999 .

[19]  G. Gottstein,et al.  Simulation of primary recrystallization using a modified three-dimensional cellular automaton , 1999 .

[20]  A. Cocks,et al.  A variational approach to two dimensional grain growth—II. Numerical results , 1996 .

[21]  V. Erukhimovitch,et al.  Modeling recrystallization kinetics , 1996 .

[22]  Danan Fan,et al.  Computer Simulation Model for Coupled Grain Growth and Ostwald Ripening—Application to Al2O3‐ZrO2 Two‐Phase Systems , 1996 .

[23]  F. J. Humphreys,et al.  Recrystallization and Related Annealing Phenomena , 1995 .

[24]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[25]  S. Papson,et al.  “Model” , 1981 .

[26]  J. Mackenzie,et al.  The distribution of rotation axes in a random aggregate of cubic crystals , 1964 .

[27]  W. Mullins.  Two‐Dimensional Motion of Idealized Grain Boundaries , 1956 .

[28]  P. Beck,et al.  Strain Induced Grain Boundary Migration in High Purity Aluminum , 1950 .

[29]  F. J. Humphreys,et al.  Recrystallization of Two-Phase Alloys , 2004 .

[30]  D. Srolovitz,et al.  Grain boundary migration: misorientation dependence , 2001 .

[31]  Esteban P. Busso,et al.  A continuum theory for dynamic recrystallization with microstructure-related length scales , 1998 .