Scale transition using dislocation dynamics and the nudged elastic band method

Abstract Microstructural features such as precipitates or irradiation-induced defects impede dislocation motion and directly influence macroscopic mechanical properties such as yield point and ductility. Dislocation-defect interactions involve both atomic scale and long range elastic interactions. Thermally assisted dislocation bypass of obstacles occurs when thermal fluctuations and driving stresses contribute sufficient energy to overcome the energy barrier. The Nudged Elastic Band (NEB) method is typically used in the context of atomistic simulations to quantify the activation barriers for a given reaction. In this work, the NEB method is generalized to coarse-grain continuum representations of evolving microstructure states beyond the discrete particle descriptions of first principles and atomistics. This method enables the calculation of activation energies for a 1 / 2 [ 111 ] ( 1 1 ¯ 0 ) glide dislocation bypassing a [001] self-interstitial atom loop of size in the range of 4–10  nm with a spacing larger than 150  nm in α-iron for a range of applied stresses and interaction geometries. Further, the study is complemented by a comparison between atomistic and continuum based prediction of barriers.

[1]  S. Zinkle,et al.  Dose dependence of defect accumulation in neutron irradiated copper and iron , 2002 .

[2]  G. Schoeck The Activation Energy of Dislocation Movement , 1965, February 1.

[3]  Yunzhi Wang,et al.  Finding Critical Nucleus in Solid-State Transformations , 2008 .

[4]  Christopher R. Weinberger,et al.  A non-singular continuum theory of dislocations , 2006 .

[5]  G. Barkema,et al.  Traveling through potential energy landscapes of disordered materials: The activation-relaxation technique , 1997, cond-mat/9710023.

[6]  S. Dudarev,et al.  Theory and simulation of the diffusion of kinks on dislocations in bcc metals , 2012, 1210.8327.

[7]  T. Neeraj,et al.  Screw dislocation mobility in BCC Metals: a refined potential description for α-Fe , 2011 .

[8]  J. M. Perlado,et al.  MD modeling of defects in Fe and their interactions , 2003 .

[9]  D. McDowell A perspective on trends in multiscale plasticity , 2010 .

[10]  M. Meyers,et al.  Mechanical properties of nanocrystalline materials , 2006 .

[11]  G. Henkelman,et al.  Improved tangent estimate in the nudged elastic band method for finding minimum energy paths and saddle points , 2000 .

[12]  A. Takahashi,et al.  Interaction Analysis between Edge Dislocation and Self Interstitial Type Dislocation Loop in BCC Iron Using Molecular Dynamics , 2005 .

[13]  M. Makin,et al.  DISLOCATION MOVEMENT THROUGH RANDOM ARRAYS OF OBSTACLES , 1966 .

[14]  Blas P. Uberuaga,et al.  Efficient Annealing of Radiation Damage Near Grain Boundaries via Interstitial Emission , 2010, Science.

[15]  Samuel Forest,et al.  Micromorphic Approach for Gradient Elasticity, Viscoplasticity, and Damage , 2009 .

[16]  G. Vineyard Frequency factors and isotope effects in solid state rate processes , 1957 .

[17]  David L. McDowell,et al.  Viscoplasticity of heterogeneous metallic materials , 2008 .

[18]  David J Wales,et al.  Benchmarks for Characterization of Minima, Transition States, and Pathways in Atomic, Molecular, and Condensed Matter Systems. , 2014, Journal of chemical theory and computation.

[19]  M. E. Kassner,et al.  Five-power-law creep in single phase metals and alloys , 2000 .

[20]  P. Hirsch,et al.  Elastic interaction between prismatic dislocation loops and straight dislocations , 1964 .

[21]  Graeme Ackland,et al.  Development of an interatomic potential for phosphorus impurities in α-iron , 2004 .

[22]  E. Kuramoto,et al.  Thermally activated slip deformation of high purity iron single crystals between 4.2 K and 300 K , 1979 .

[23]  Graeme Henkelman,et al.  Paths to which the nudged elastic band converges , 2011, J. Comput. Chem..

[24]  Ignacio Martin-Bragado,et al.  MMonCa: An Object Kinetic Monte Carlo simulator for damage irradiation evolution and defect diffusion , 2013, Comput. Phys. Commun..

[25]  B. Devincre,et al.  Interaction of 〈1 0 0〉 dislocation loops with dislocations studied by dislocation dynamics in α-iron , 2015 .

[26]  C. V. Singh,et al.  Harnessing atomistic simulations to predict the rate at which dislocations overcome obstacles , 2016 .

[27]  D. Warner,et al.  Atomistic predictions of dislocation nucleation with transition state theory , 2011 .

[28]  William D. Nix,et al.  Plasticity of bcc micropillars controlled by competition between dislocation multiplication and depletion , 2013 .

[29]  M. Gurtin On a framework for small-deformation viscoplasticity: free energy, microforces, strain gradients , 2003 .

[30]  I. Martín-Bragado,et al.  An Atomistically Informed Kinetic Monte Carlo Model of Grain Boundary Motion Coupled to Shear Deformation , 2015 .

[31]  Engineering,et al.  First-principles data for solid-solution strengthening of magnesium: From geometry and chemistry to properties , 2010, 1007.2585.

[32]  A. Granato,et al.  Entropy Factors for Thermally Activated Unpinning of Dislocations , 1964 .

[33]  Jianmin Qu,et al.  Dislocation nucleation from bicrystal interfaces and grain boundary ledges: Relationship to nanocrystalline deformation , 2007 .

[34]  G. Henkelman,et al.  Comparison of methods for finding saddle points without knowledge of the final states. , 2004, The Journal of chemical physics.

[35]  Lorenzo Malerba,et al.  Simulation of radiation damage in Fe alloys: an object kinetic Monte Carlo approach , 2004 .

[36]  N. Mott,et al.  Report of a Conference on Strength of Solids , 1948 .

[37]  L. Hector,et al.  Molecular dynamics study of solute strengthening in Al/Mg alloys , 2006 .

[38]  K. E. Easterling,et al.  Phase Transformations in Metals and Alloys (Revised Reprint) , 2009 .

[39]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[40]  Jens Lothe John Price Hirth,et al.  Theory of Dislocations , 1968 .

[41]  D. Hull,et al.  Introduction to Dislocations , 1968 .

[42]  D. Terentyev,et al.  Reactions between a 1/2⟨111⟩ screw dislocation and ⟨100⟩ interstitial dislocation loops in alpha-iron modelled at atomic scale , 2010 .

[43]  W. Spitzig,et al.  The effect of orientation and temperature on the plastic flow properties of iron single crystals , 1970 .

[44]  D. Dimiduk,et al.  Calculations of intersection cross-slip activation energies in fcc metals using nudged elastic band method , 2011 .

[45]  G. B. Gibbs Thermodynamic analysis of dislocation glide controlled by dispersed local obstacles , 1969 .

[46]  D. Bacon,et al.  An atomic-level model for studying the dynamics of edge dislocations in metals , 2003 .

[47]  Laurent Capolungo,et al.  On the strength of dislocation interactions and their effect on latent hardening in pure Magnesium , 2014 .

[48]  M. Cherkaoui,et al.  The effect of interfaces on the mechanical behaviour of multilayered metallic laminates , 2014 .

[49]  A. U. Seybolt,et al.  The mechanical properties of iron single crystals containing less than 5 × 10−3 ppm carbon☆ , 1963 .

[50]  Niels Grønbech-Jensen,et al.  A simple and effective Verlet-type algorithm for simulating Langevin dynamics , 2012, 1212.1244.

[51]  D. Bacon Simulation of the interaction between an edge dislocation and a '100' interstitial dislocation loop in alpha-iron , 2008 .

[52]  S. Biner,et al.  Molecular dynamics simulations of the interactions between screw dislocations and self-interstitial clusters in body-centered cubic Fe , 2008 .

[53]  David L. McDowell,et al.  Thermal activation of dislocations in large scale obstacle bypass , 2017 .

[54]  M. Hernández-Mayoral,et al.  Transmission electron microscopy study on neutron irradiated pure iron and RPV model alloys , 2010 .

[55]  G. Henkelman,et al.  A dimer method for finding saddle points on high dimensional potential surfaces using only first derivatives , 1999 .

[56]  H. Jónsson,et al.  Nudged elastic band method for finding minimum energy paths of transitions , 1998 .

[57]  Nasr M. Ghoniem,et al.  Parametric dislocation dynamics: A thermodynamics-based approach to investigations of mesoscopic plastic deformation , 2000 .

[58]  C. Tomé,et al.  On the measure of dislocation densities from diffraction line profiles: A comparison with discrete dislocation methods , 2012 .

[59]  M. Duesbery On kinked screw dislocations in the b.c.c. lattice—I. The structure and peierls stress of isolated kinks , 1983 .

[60]  D. Bacon,et al.  Computer simulation of reactions between an edge dislocation and glissile self-interstitial clusters in iron , 2006 .

[61]  O. Politano,et al.  A 3D mesoscopic approach for discrete dislocation dynamics , 2001 .

[62]  J. Hosson,et al.  Dislocation Dynamics in Al-Li Alloys. Mean Jump Distance and Activation Length of Moving Dislocations , 1984 .

[63]  D. Terentyev,et al.  Transfer of molecular dynamics data to dislocation dynamics to assess dislocation–dislocation loop interaction in iron , 2013 .

[64]  A. Bower Applied Mechanics of Solids , 2009 .