An analysis of key characteristics of the Frank-Read source process in FCC metals

Abstract A well-known intragranular dislocation source, the Frank-Read (FR) source plays an important role in size-dependent dislocation multiplication in crystalline materials. Despite a number of studies in this topic, a systematic investigation of multiple aspects of the FR source in different materials is lacking. In this paper, we employ large scale quasistatic concurrent atomistic-continuum (CAC) simulations to model an edge dislocation bowing out from an FR source in Cu, Ni, and Al. First, a number of quantities that are important for the FR source process are quantified in the coarse-grained domain. Then, two key characteristics of the FR source, including the critical shear stress and critical dislocation configuration, are investigated. In all crystalline materials, the critical stresses and the aspect ratio of the dislocation half-loop height to the FR source length scale well with respect to the FR source length. In Al, the critical stress calculated by CAC simulations for a given FR source length agrees reasonably well with a continuum model that explicitly includes the dislocation core energy. Nevertheless, the predictions of the isotropic elastic theory do not accurately capture the FR source responses in Cu and Ni, which have a relatively large stacking fault width and elastic anisotropy. Our results highlight the significance of directly simulating the FR source activities using fully 3D models and shed light on developing more accurate continuum models.

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

[2]  W. Cai,et al.  Dislocation dynamics simulation of Frank-Read sources in anisotropic α-Fe , 2012 .

[3]  J Li,et al.  Anisotropic elastic interactions of a periodic dislocation array. , 2001, Physical review letters.

[4]  R. H. Wagoner,et al.  On precipitate induced hardening in crystal plasticity: theory , 2004 .

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

[6]  Youping Chen,et al.  Edge dislocations bowing out from a row of collinear obstacles in Al , 2016 .

[7]  Youping Chen,et al.  Nucleation and growth of dislocation loops in Cu, Al and Si by a concurrent atomistic-continuum method , 2012 .

[8]  L. M. Brown.  A proof of lothe's theorem , 1967 .

[9]  M. Parrinello,et al.  Polymorphic transitions in single crystals: A new molecular dynamics method , 1981 .

[10]  A. Stukowski.  Structure identification methods for atomistic simulations of crystalline materials , 2012, 1202.5005.

[11]  William Schroeder,et al.  The Visualization Toolkit: An Object-Oriented Approach to 3-D Graphics , 1997 .

[12]  S. S. Shishvan,et al.  A dislocation-dynamics-based derivation of the Frank–Read source characteristics for discrete dislocation plasticity , 2008 .

[13]  D. Dini,et al.  The mechanisms governing the activation of dislocation sources in aluminum at different strain rates , 2015 .

[14]  Marc Legros,et al.  Atomic-scale simulation of screw dislocation/coherent twin boundary interaction in Al, Au, Cu and Ni , 2011 .

[15]  William E. Lorensen,et al.  The visualization toolkit (2nd ed.): an object-oriented approach to 3D graphics , 1998 .

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

[17]  Youping Chen,et al.  Reformulation of microscopic balance equations for multiscale materials modeling. , 2009, The Journal of chemical physics.

[18]  David L. McDowell,et al.  A quasistatic implementation of the concurrent atomistic-continuum method for FCC crystals , 2015 .

[19]  Atomistic simulations for the evolution of a U-shaped dislocation in fcc Al , 2006 .

[20]  Nancy Wilkins-Diehr,et al.  XSEDE: Accelerating Scientific Discovery , 2014, Computing in Science & Engineering.

[21]  P. Gumbsch,et al.  Atomistic study of drag, surface and inertial effects on edge dislocations in face-centered cubic metals , 2004 .

[22]  David L. McDowell,et al.  Coarse-grained atomistic simulation of dislocations , 2011 .

[23]  David L. McDowell,et al.  Sequential slip transfer of mixed-character dislocations across Σ3 coherent twin boundary in FCC metals: a concurrent atomistic-continuum study , 2016 .

[24]  W. Curtin,et al.  Analysis of spurious image forces in atomistic simulations of dislocations , 2015 .

[25]  A. Cottrell.  Commentary. A brief view of work hardening , 2002 .

[26]  D. Bacon.  A Method for Describing a Flexible Dislocation , 1967, October 1.

[27]  V. Bulatov,et al.  Automated identification and indexing of dislocations in crystal interfaces , 2012 .

[28]  S. Fitzgerald.  Frank–Read sources and the yield of anisotropic cubic crystals , 2010 .

[29]  Molecular dynamics investigation of dislocation pinning by a nanovoid in copper , 2004, cond-mat/0412697.

[30]  W. Curtin,et al.  Operation of a 3D Frank–Read source in a stress gradient and implications for size-dependent plasticity , 2013 .

[31]  X. Markenscoff,et al.  Configurational force on a lattice dislocation and the Peierls stress , 2007 .

[32]  Michael J. Mehl,et al.  Interatomic potentials for monoatomic metals from experimental data and ab initio calculations , 1999 .

[33]  David L. McDowell,et al.  Concurrent atomistic–continuum simulations of dislocation–void interactions in fcc crystals , 2015 .

[34]  D. Bacon.  Dislocation – Obstacle Interactions at the Atomic Level , 2009 .

[35]  K. T. Ramesh,et al.  Nanomaterials: Mechanics and Mechanisms , 2009 .

[36]  Julia R. Weertman,et al.  Elementary Dislocation Theory , 1992 .

[37]  T. Shimokawa,et al.  Dislocation Multiplication from the Frank–Read Source in Atomic Models , 2014 .

[38]  David L. McDowell,et al.  Coarse-grained elastodynamics of fast moving dislocations , 2016 .

[39]  A. Strachan,et al.  Effect of core energy on mobility in a continuum dislocation model , 2011 .

[40]  A. J. E. Foreman,et al.  The bowing of a dislocation segment , 1967 .

[41]  J. Hirth,et al.  Dislocation core parameters , 2005 .

[42]  Yang Xiang,et al.  A level set method for dislocation dynamics , 2003 .

[43]  A. Benzerga.  An analysis of exhaustion hardening in micron-scale plasticity , 2008 .

[44]  A. Arsenlis,et al.  Methods to compute dislocation line tension energy and force in anisotropic elasticity , 2013 .

[45]  K. Ho,et al.  Core energy and Peierls stress of a screw dislocation in bcc molybdenum: A periodic-cell tight-binding study , 2004 .

[46]  J. Koehler,et al.  Interaction of Dislocations with an Applied Stress in Anisotropic Crystals , 1959 .

[47]  W. T. Read,et al.  Multiplication Processes for Slow Moving Dislocations , 1950 .

[48]  A. Stukowski.  Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool , 2009 .

[49]  H. Matsui,et al.  Void-induced cross slip of screw dislocations in fcc copper , 2007, 0710.5811.

[50]  U. F. Kocks,et al.  The effect of dislocation self-interaction on the Orowan stress , 1973 .

[51]  David L. McDowell,et al.  A concurrent scheme for passing dislocations from atomistic to continuum domains , 2012 .

[52]  Minsheng Huang,et al.  Dislocation Dissociation Strongly Influences on Frank—Read Source Nucleation and Microplasticy of Materials with Low Stacking Fault Energy , 2014 .

[53]  T. Germann,et al.  Dislocation nucleation mechanisms from fcc/bcc incoherent interfaces , 2011 .

[54]  L. M. Brown.  The self-stress of dislocations and the shape of extended nodes , 1964 .

[55]  W. Curtin,et al.  Robust atomistic calculation of dislocation line tension , 2015 .

[56]  Jian Wang,et al.  Atomic-scale study of nucleation of dislocations from fcc–bcc interfaces , 2012 .

[57]  C. Sinclair,et al.  Phase field crystal modeling as a unified atomistic approach to defect dynamics , 2014, 1403.0601.

[58]  J. Cantrell.  Substructural organization, dislocation plasticity and harmonic generation in cyclically stressed wavy slip metals , 2004, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[59]  Sidney Yip,et al.  Chapter 64 – Dislocation Core Effects on Mobility , 2004 .

[60]  A. Needleman,et al.  Discrete dislocation plasticity analysis of the grain size dependence of the flow strength of polycrystals , 2008 .

[61]  Martin Ostoja-Starzewski,et al.  Universal elastic anisotropy index. , 2008, Physical review letters.

[62]  Y. H. Zhao,et al.  Compact and dissociated dislocations in aluminum: implications for deformation. , 2005, Physical review letters.

[63]  Arthur F. Voter,et al.  Structural stability and lattice defects in copper: Ab initio , tight-binding, and embedded-atom calculations , 2001 .

[64]  T. Hatano.  Dynamics of a dislocation bypassing an impenetrable precipitate: The Hirsch mechanism revisited , 2005, cond-mat/0511358.

[65]  Maurice de Koning,et al.  Anomalous dislocation multiplication in FCC metals. , 2003, Physical review letters.

[66]  Joshua C. Crone,et al.  Capturing the effects of free surfaces on void strengthening with dislocation dynamics , 2015 .

[67]  M. Alava,et al.  Multiscale modeling of dislocation-precipitate interactions in Fe: From molecular dynamics to discrete dislocations. , 2016, Physical review. E.

[68]  C. S. Hartley,et al.  Characterization and visualization of the lattice misfit associated with dislocation cores , 2005 .

[69]  A. Needleman,et al.  Plasticity size effects in tension and compression of single crystals , 2005 .

[70]  D. Hull,et al.  Introduction to Dislocations Ed. 5 , 2011 .

[71]  A. Benzerga.  Micro-pillar plasticity: 2.5D mesoscopic simulations , 2009 .

[72]  R. Scattergood,et al.  The strengthening effect of voids , 1982 .

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

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

[75]  D. McDowell,et al.  Mesh refinement schemes for the concurrent atomistic-continuum method , 2016 .

[76]  Enrique Martínez,et al.  Atomistically informed dislocation dynamics in fcc crystals , 2006, Journal of the Mechanics and Physics of Solids.