A stress-gradient based criterion for dislocation nucleation in crystals

Dislocations are the main lattice defects responsible for the strength and ductility of crystalline solids. The generation of new dislocations is an essential aspect of crystal defect physics, but a fundamental understanding of the mechanical conditions which lead to dislocation nucleation has remained elusive. Here, we present a nucleation criterion motivated from continuum thermomechanical considerations of a crystalline solid undergoing deformation, and demonstrate the criterion's ability to correctly predict dislocation nucleation via direct atomistic simulations. We further demonstrate that the commonly held notion of a nucleation criterion based on the magnitude of local stress components is incorrect.

[1]  James R. Rice,et al.  Dislocation Nucleation from a Crack Tip" an Analysis Based on the Peierls Concept , 1991 .

[2]  Khantha,et al.  Dislocation screening and the brittle-to-ductile transition: A Kosterlitz-Thouless type instability. , 1994, Physical review letters.

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

[4]  Hussein M. Zbib,et al.  On plastic deformation and the dynamics of 3D dislocations , 1998 .

[5]  Ellad B. Tadmor,et al.  Nucleation of dislocations beneath a plane strain indenter , 2000 .

[6]  Donald E. Carlson.  On Gunther’s stress functions for couple stresses , 1967 .

[7]  F. Nabarro,et al.  Dislocations in solids , 1979 .

[8]  M. Baskes,et al.  Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals , 1984 .

[9]  J. Willis,et al.  Second-order effects of dislocations in anisotropic crystals , 1967 .

[10]  V. Vítek,et al.  Plastic anisotropy in b.c.c. transition metals , 1998 .

[11]  van der Erik Giessen,et al.  Discrete dislocation plasticity: a simple planar model , 1995 .

[12]  John R. Rice,et al.  The activation energy for dislocation nucleation at a crack , 1994 .

[13]  V. Vítek,et al.  Effect of Non-Glide Components of the Stress Tensor on Deformation Behavior of Bcc Transition Metals , 1998 .

[14]  L E Shilkrot,et al.  Coupled atomistic and discrete dislocation plasticity. , 2002, Physical review letters.

[15]  J. Rice.  Localization of plastic deformation , 1976 .

[16]  Amit Acharya,et al.  Constitutive analysis of finite deformation field dislocation mechanics , 2004 .

[17]  M. Born,et al.  Dynamical Theory of Crystal Lattices , 1954 .

[18]  B. Wirth,et al.  Atomistic Simulation of Dislocation-Defect Interactions in Cu , 2000 .

[19]  Amit Acharya.  Driving forces and boundary conditions in continuum dislocation mechanics , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[20]  Peter Gumbsch,et al.  On the continuum versus atomistic descriptions of dislocation nucleation and cleavage in nickel , 1995 .

[21]  L. P. Kubin,et al.  The modelling of dislocation patterns , 1992 .

[22]  R. Hill.  Acceleration waves in solids , 1962 .

[23]  M. Ortiz,et al.  Nucleation of dislocations from crack tips under mixed modes of loading: Implications for brittle against ductile behaviour of crystals , 1995 .

[24]  Ting Zhu,et al.  Atomistic mechanisms governing elastic limit and incipient plasticity in crystals , 2002, Nature.

[25]  Simon R. Phillpot,et al.  Length-scale effects in the nucleation of extended dislocations in nanocrystalline Al by molecular-dynamics simulation , 2001 .

[26]  V. Vítek,et al.  The brittle-to-ductile transition - I: A cooperative dislocation generation instability , 1994 .

[27]  J. Rice,et al.  Estimates from atomic models of tension-shear coupling in dislocation nucleation from a crack tip , 1993 .

[28]  S. Suresh,et al.  Nanoindentation: Simulation of defect nucleation in a crystal , 2001, Nature.

[29]  J. C. Hamilton,et al.  Dislocation nucleation and defect structure during surface indentation , 1998 .

[30]  Ting Zhu,et al.  Quantifying the early stages of plasticity through nanoscale experiments and simulations , 2003 .

[31]  Amit Acharya,et al.  A model of crystal plasticity based on the theory of continuously distributed dislocations , 2001 .

[32]  J C Hamilton,et al.  Dislocation emission around nanoindentations on a (001) fcc metal surface studied by scanning tunneling microscopy and atomistic simulations. , 2002, Physical review letters.

[33]  James B. Adams,et al.  Interatomic Potentials from First-Principles Calculations: The Force-Matching Method , 1993, cond-mat/9306054.

[34]  Foiles,et al.  Embedded-atom-method functions for the fcc metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys. , 1986, Physical review. B, Condensed matter.

[35]  M. Kakihana,et al.  Materials Research Society Symposium - Proceedings , 2000 .

[36]  J. Rice.  Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity , 1971 .

[37]  Toshio Mura,et al.  Continuous distribution of moving dislocations , 1963 .

[38]  V. Vítek,et al.  Atomic Level Stresses in Solids and Liquids , 1987 .

[39]  P. Hirsch,et al.  Cooperative nucleation of shear dislocation loops. , 2002, Physical review letters.

[40]  J. C. Hamilton,et al.  Surface step effects on nanoindentation. , 2001, Physical review letters.