A dynamic phase-field model for structural transformations and twinning: Regularized interfaces with transparent prescription of complex kinetics and nucleation. Part II: Two-dimensional characterization and boundary kinetics

Abstract A companion paper presented the formulation of a phase-field model – i.e., a model with regularized interfaces that do not require explicit numerical tracking – that allows for easy and transparent prescription of complex interface kinetics and nucleation. The key ingredients were a re-parametrization of the energy density to clearly separate nucleation from kinetics; and an evolution law that comes from a conservation statement for interfaces. This enables clear prescription of nucleation through the source term of the conservation law and of kinetics through an interfacial velocity field. This model overcomes an important shortcoming of existing phase-field models, namely that the specification of kinetics and nucleation is both restrictive and extremely opaque. In this paper, we present a number of numerical calculations – in one and two dimensions – that characterize our formulation. These calculations illustrate (i) highly-sensitive rate-dependent nucleation; (ii) independent prescription of the forward and backward nucleation stresses without changing the energy landscape; (iii) stick–slip interface kinetics; (iii) the competition between nucleation and kinetics in determining the final microstructural state; (iv) the effect of anisotropic kinetics; and (v) the effect of non-monotone kinetics. These calculations demonstrate the ability of this formulation to precisely prescribe complex nucleation and kinetics in a simple and transparent manner. We also extend our conservation statement to describe the kinetics of the junction lines between microstructural interfaces and boundaries. This enables us to prescribe an additional kinetic relation for the boundary, and we examine the interplay between the bulk kinetics and the junction kinetics.

[1]  John D. Clayton,et al.  Nonlinear Mechanics of Crystals , 2010 .

[2]  Технология.  Springer Science+Business Media , 2013 .

[3]  K. Bhattacharya,et al.  Edge effects on the propagation of phase boundaries , 1999 .

[4]  T. Lookman,et al.  Heterogeneity and phase transformation in materials: Energy minimization, iterative methods and geometric nonlinearity , 2013 .

[5]  K. Bhattacharya,et al.  Kinetics of phase boundaries with edges and junctions in a three-dimensional multi-phase body , 2000 .

[6]  Srikanth Vedantam,et al.  A lattice-based model of the kinetics of twin boundary motion , 2003 .

[7]  V. Vitek,et al.  Multiscale modeling of plastic deformation of molybdenum and tungsten: I. Atomistic studies of the core structure and glide of 1/2〈1 1 1〉 screw dislocations at 0 K , 2008 .

[8]  Thomas Y. Hou,et al.  A Level-Set Approach to the Computation of Twinning and Phase-Transition Dynamics , 1999 .

[9]  I. Beyerlein,et al.  A probabilistic twin nucleation model for HCP polycrystalline metals , 2010, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  K. Bhattacharya.  Microstructure of martensite : why it forms and how it gives rise to the shape-memory effect , 2003 .

[11]  I. Beyerlein,et al.  An atomic and probabilistic perspective on twin nucleation in Mg , 2010 .

[12]  V. Levitas.  Phase field approach to martensitic phase transformations with large strains and interface stresses , 2014 .

[13]  Multiscale modeling of plastic deformation of molybdenum and tungsten: II. Yield criterion for single crystals based on atomistic studies of glide of 1/2〈111〉 screw dislocations , 2008, 0807.2771.

[14]  Dong-Wook Lee,et al.  Athermal resistance to interface motion in the phase-field theory of microstructure evolution. , 2007, Physical review letters.

[15]  Kaushik Bhattacharya,et al.  Kinetics of phase boundaries with edges andjunctions , 1998 .

[16]  V. Levitas,et al.  Interface Propagation and Microstructure Evolution in Phase Field Models of Stress-Induced Martensitic Phase Transformations , 2010 .

[17]  Haimin Yao,et al.  Journal of the Mechanics and Physics of Solids , 2014 .

[18]  J. Knap,et al.  A phase field model of deformation twinning: Nonlinear theory and numerical simulations , 2011 .

[19]  J. K. Knowles,et al.  Unstable kinetic relations and the dynamics of solid-solid phase transitions , 1997 .

[20]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[21]  R. D. James,et al.  Proposed experimental tests of a theory of fine microstructure and the two-well problem , 1992, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[22]  J. Ball,et al.  Fine phase mixtures as minimizers of energy , 1987 .

[23]  S. Kalidindi.  Incorporation of deformation twinning in crystal plasticity models , 1998 .