Microstructure evolution in deformed polycrystals predicted by a diffuse interface Cosserat approach

Formulating appropriate simulation models that capture the microstructure evolution at the mesoscale in metals undergoing thermomechanical treatments is a formidable task. In this work, an approach combining higher-order dislocation density based crystal plasticity with a phase-field model is used to predict microstructure evolution in deformed polycrystals. This approach allows to model the heterogeneous reorientation of the crystal lattice due to viscoplastic deformation and the reorientation due to migrating grain boundaries. The model is used to study the effect of strain localization in subgrain boundary formation and grain boundary migration due to stored dislocation densities. It is demonstrated that both these phenomena are inherently captured by the coupled approach.

[1]  T. Blesgen.  Deformation patterning in three-dimensional large-strain Cosserat plasticity , 2014 .

[2]  M. Ashby.  The deformation of plastically non-homogeneous materials , 1970 .

[3]  G. Cailletaud,et al.  Hardening description for FCC materials under complex loading paths , 2009 .

[4]  T. Blesgen.  A variational model for dynamic recrystallization based on Cosserat plasticity , 2017 .

[5]  S. Forest,et al.  Subgrain formation during deformation: Physical origin and consequences , 2002 .

[6]  Samuel Forest,et al.  Modeling slip, kink and shear banding in classical and generalized single crystal plasticity , 1998 .

[7]  M. Gurtin.  Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance , 1996 .

[8]  D. McDowell,et al.  A comparison of Gurtin type and micropolar theories of generalized single crystal plasticity , 2014 .

[9]  D. Wolf,et al.  Structure-energy correlation for grain boundaries in F.C.C. metals—III. Symmetrical tilt boundaries , 1990 .

[10]  W. Carter,et al.  A continuum model of grain boundaries , 2000 .

[11]  Markus Bambach,et al.  Modelling of static recrystallization kinetics by coupling crystal plasticity FEM and multiphase field calculations , 2013 .

[12]  S. Forest,et al.  Intragranular localization induced by softening crystal plasticity: Analysis of slip and kink bands localization modes from high resolution FFT-simulations results , 2019, Acta Materialia.

[13]  B. Appolaire,et al.  Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part II: Application to recrystallisation , 2012 .

[14]  Markus Bambach,et al.  Coupling of Crystal Plasticity Finite Element and Phase Field Methods for the Prediction of SRX Kinetics after Hot Working , 2014 .

[15]  Georges Cailletaud,et al.  Cosserat modelling of size effects in the mechanical behaviour of polycrystals and multi-phase materials , 2000 .

[16]  Louise Poissant.  Part I , 1996, Leonardo.

[17]  A. L. Titchener,et al.  The Stored Energy of Cold Work , 1973 .

[18]  Håkan Hallberg,et al.  A modified level set approach to 2D modeling of dynamic recrystallization , 2013 .

[19]  Esteban P. Busso,et al.  Discrete dislocation density modelling of single phase FCC polycrystal aggregates , 2004 .

[20]  S. Forest,et al.  Cosserat crystal plasticity with dislocation-driven grain boundary migration , 2018, Journal of Micromechanics and Molecular Physics.

[21]  R. Quey,et al.  Large-scale 3D random polycrystals for the finite element method: Generation, meshing and remeshing , 2011 .

[22]  R. J.,et al.  I Strain Localization in Ductile Single Crystals , 1977 .

[23]  Morton E. Gurtin,et al.  A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations , 2002 .

[24]  Georges Cailletaud,et al.  A Cosserat theory for elastoviscoplastic single crystals at finite deformation , 1997 .

[25]  David L. McDowell,et al.  Dislocation-based micropolar single crystal plasticity: Comparison of multi- and single criterion theories , 2011 .

[26]  Morton E. Gurtin,et al.  Sharp-interface and phase-field theories of recrystallization in the plane , 1999 .

[27]  C. Fressengeas,et al.  An elasto-plastic theory of dislocation and disclination fields , 2011 .

[28]  W. Missol.  Orientation dependence of grain-boundary energy in metals in the view of a pseudoheterophase dislocation core model , 1975 .

[29]  Thomas Böhlke,et al.  Strain gradient plasticity modeling of the cyclic behavior of laminate microstructures , 2015 .

[30]  S. Forest,et al.  A Cosserat–phase-field theory of crystal plasticity and grain boundary migration at finite deformation , 2018, Continuum Mechanics and Thermodynamics.

[31]  R. Pippan,et al.  Direct evidence for grain boundary motion as the dominant restoration mechanism in the steady-state regime of extremely cold-rolled copper , 2014, Acta materialia.

[32]  S. Forest,et al.  Size-dependent energy in crystal plasticity and continuum dislocation models , 2015, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[33]  G. Po,et al.  A unified framework for polycrystal plasticity with grain boundary evolution , 2017, International Journal of Plasticity.

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

[35]  Akinori Yamanaka,et al.  Phase-field model during static recrystallization based on crystal-plasticity theory , 2007 .

[36]  S. Forest,et al.  Non‐Local Plasticity at Microscale: A Dislocation‐Based and a Cosserat Model , 2000 .

[37]  M. Cherkaoui,et al.  A micromechanics-based model for shear-coupled grain boundary migration in bicrystals , 2013 .

[38]  S. Forest,et al.  Plastic slip distribution in two-phase laminate microstructures: Dislocation-based versus generalized-continuum approaches , 2003 .

[39]  W. Carter,et al.  Extending Phase Field Models of Solidification to Polycrystalline Materials , 2003 .

[40]  Samuel Forest,et al.  Elastoviscoplastic constitutive frameworks for generalized continua , 2003 .

[41]  B. Nestler,et al.  Combined crystal plasticity and phase-field method for recrystallization in a process chain of sheet metal production , 2015 .

[42]  D. J. Jensen,et al.  Grain boundary mobility during recrystallization of copper , 1997 .

[43]  S. Forest,et al.  Phase field modelling of grain boundary motion driven by curvature and stored energy gradients. Part I: theory and numerical implementation , 2012 .

[44]  Dierk Raabe,et al.  Coupling of a crystal plasticity finite-element model with a probabilistic cellular automaton for simulating primary static recrystallization in aluminium , 2000 .

[45]  S. Forest,et al.  A Cosserat crystal plasticity and phase field theory for grain boundary migration , 2018, Journal of the Mechanics and Physics of Solids.

[46]  A. Brahme,et al.  Coupled crystal plasticity – Probabilistic cellular automata approach to model dynamic recrystallization in magnesium alloys , 2015 .

[47]  Sharp interface limit of a phase-field model of crystal grains. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[49]  Yoshikazu Giga,et al.  Equations with Singular Diffusivity , 1998 .

[50]  N. Ohno,et al.  Higher-order stress and grain size effects due to self-energy of geometrically necessary dislocations , 2007 .

[51]  A. Cental Eringen,et al.  Part I – Polar Field Theories , 1976 .

[52]  S. Forest.  Some links between Cosserat, strain gradient crystal plasticity and the statistical theory of dislocations , 2008 .

[53]  J. Nye.  Some geometrical relations in dislocated crystals , 1953 .

[54]  D. McDowell,et al.  Symmetric and asymmetric tilt grain boundary structure and energy in Cu and Al (and transferability to other fcc metals) , 2015, Integrating Materials and Manufacturing Innovation.