Generalized continuum modeling of scale-dependent crystalline plasticity

[1]  R. Naghdabadi,et al.  Computational aspects of the Cosserat finite element analysis of localization phenomena , 2006 .

[2]  P. Neff,et al.  Well-Posedness of Dynamic Cosserat Plasticity , 2007 .

[3]  K. Garikipati.  Couple stresses in crystalline solids: origins from plastic slip gradients, dislocation core distortions, and three-body interatomic potentials , 2003 .

[4]  M. Ashby,et al.  Strain gradient plasticity: Theory and experiment , 1994 .

[5]  P. Steinmann.  An improved FE expansion for micropolar localization analysis , 1994 .

[6]  V. Tvergaard,et al.  Simulations of micro-bending of thin foils using a scale dependent crystal plasticity model , 2006 .

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

[8]  Norman A. Fleck,et al.  Strain gradient crystal plasticity: size-dependentdeformation of bicrystals , 1999 .

[9]  W. Brekelmans,et al.  A three-dimensional dislocation field crystal plasticity approach applied to miniaturized structures , 2007 .

[10]  W. Brekelmans,et al.  Overall behaviour of heterogeneous elastoviscoplastic materials: effect of microstructural modelling , 2000 .

[11]  J. Kysar,et al.  High strain gradient plasticity associated with wedge indentation into face-centered cubic single crystals: Geometrically necessary dislocation densities , 2007 .

[12]  Mgd Marc Geers,et al.  Non-local crystal plasticity model with intrinsic SSD and GND effects , 2004 .

[13]  A. Acharya,et al.  Finite element approximation of field dislocation mechanics , 2005 .

[14]  Patrizio Neff,et al.  Simple shear in nonlinear Cosserat elasticity: bifurcation and induced microstructure , 2009 .

[15]  Dierk Raabe,et al.  On the consideration of interactions between dislocations and grain boundaries in crystal plasticity finite element modeling – Theory, experiments, and simulations , 2006 .

[16]  Wenge Yang,et al.  Experimental characterization of the mesoscale dislocation density tensor , 2007 .

[17]  E. Kröner,et al.  On the physical reality of torque stresses in continuum mechanics , 1963 .

[18]  E. Holm,et al.  Polycrystalline kinematics: An extension of single crystal kinematics that incorporates initial microstructure , 2007 .

[19]  Arun R. Srinivasa,et al.  A dynamical theory of structures solids. I Basic developments , 1993, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[20]  R. Yassar,et al.  Micromechanics of hardening of elastic-plastic crystals with elastic inclusions: I - Dilute concentration , 2007 .

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

[22]  S. Reese,et al.  Continuum Thermodynamic Modeling and Simulation of Additional Hardening due to Deformation Incompatibility , 2003 .

[23]  Chung-Souk Han,et al.  A Finite Element approach with patch projection for strain gradient plasticity formulations , 2007 .

[24]  P. Steinmann.  Theory and numerics of ductile micropolar elastoplastic damage , 1995 .

[25]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[26]  Mgd Marc Geers,et al.  A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity , 2006 .

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

[28]  M. Gurtin,et al.  Gradient single-crystal plasticity with free energy dependent on dislocation densities , 2007 .

[29]  István Groma,et al.  Link between the microscopic and mesoscopic length-scale description of the collective behavior of dislocations , 1997 .

[30]  Norman A. Fleck,et al.  The role of strain gradients in the grain size effect for polycrystals , 1996 .

[31]  V. Tvergaard,et al.  Effects of microscopic boundary conditions on plastic deformations of small-sized single crystals , 2009 .

[32]  Soo-Ik Oh,et al.  Finite element analysis of grain-by-grain deformation by crystal plasticity with couple stress , 2003 .

[33]  Mohammed A. Zikry,et al.  Single void morphological and grain-boundary effects on overall failure in F.C.C. polycrystalline systems , 2003 .

[34]  Hui Wang,et al.  Quadrilateral isoparametric finite elements for plane elastic Cosserat bodies , 2005 .

[35]  K. Shizawa,et al.  Multiscale crystal plasticity modeling based on geometrically necessary crystal defects and simulation on fine-graining for polycrystal , 2007 .

[36]  R. Lakes,et al.  Finite element analysis of stress concentration around a blunt crack in a Cosserat elastic solid , 1988 .

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

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

[39]  David L. McDowell,et al.  A multiscale multiplicative decomposition for elastoplasticity of polycrystals , 2003 .

[40]  Minsheng Huang,et al.  Discrete dislocation plasticity analysis of single crystalline thin beam under combined cyclic tension and bending , 2008 .

[41]  Phillips,et al.  Mesoscopic analysis of structure and strength of dislocation junctions in fcc metals , 2000, Physical review letters.

[42]  P. Steinmann.  A micropolar theory of finite deformation and finite rotation multiplicative elastoplasticity , 1994 .

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

[44]  Morton E. Gurtin,et al.  Boundary conditions in small-deformation, single-crystal plasticity that account for the Burgers vector , 2005 .

[45]  A. Needleman,et al.  A tangent modulus method for rate dependent solids , 1984 .

[46]  D. Parks,et al.  Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density , 1999 .

[47]  C. Tsakmakis,et al.  Micropolar plasticity theories and their classical limits. Part I: Resulting model , 2007 .

[48]  J. Kysar,et al.  Strain gradient crystal plasticity analysis of a single crystal containing a cylindrical void , 2007 .

[49]  Brent L. Adams,et al.  Mesoscale investigation of the deformation field of an aluminum bicrystal , 1998 .

[50]  P. Neff,et al.  The Cosserat couple modulus for continuous solids is zero viz the linearized Cauchy‐stress tensor is symmetric , 2006 .

[51]  A. Eringen.  Microcontinuum Field Theories , 2020, Advanced Continuum Theories and Finite Element Analyses.

[52]  P. M. Naghdi,et al.  Characterization of dislocations and their influence on plastic deformation in single crystals , 1994 .

[53]  V. Tvergaard,et al.  A finite deformation theory of higher-order gradient crystal plasticity , 2008 .

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

[55]  H. Stumpf,et al.  A MODEL OF ELASTOPLASTIC BODIES WITH CONTINUOUSLY DISTRIBUTED DISLOCATIONS , 1996 .

[56]  Morton E. Gurtin,et al.  On the plasticity of single crystals: free energy, microforces, plastic-strain gradients , 2000 .

[57]  Anthony G. Evans,et al.  A microbend test method for measuring the plasticity length scale , 1998 .

[58]  Ladislas P. Kubin,et al.  Mesoscopic simulations of dislocations and plasticity , 1997 .

[59]  René de Borst,et al.  A generalisation of J 2 -flow theory for polar continua , 1993 .

[60]  A. Zaoui,et al.  Multislip in FCC and BCC Crystals: a Theoretical Approach Compared with Experimental Data , 1982 .

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

[62]  Rhj Ron Peerlings,et al.  Continuum modeling of dislocation interactions: why discreteness matters? , 2008 .

[63]  R. Borst.  Numerical modelling of bifurcation and localisation in cohesive-frictional materials , 1991 .

[64]  Amit Acharya,et al.  New Perspectives in Plasticity Theory: Dislocation Nucleation, Waves, and Partial Continuity of Plastic Strain Rate , 2008 .

[65]  P. Neff,et al.  A NUMERICAL SOLUTION METHOD FOR AN INFINITESIMAL ELASTO-PLASTIC COSSERAT MODEL , 2007 .

[66]  Jobie M. Gerken,et al.  A crystal plasticity model that incorporates stresses and strains due to slip gradients , 2008 .

[67]  Size Effects in Micro-bending Deformation of MEMS Devices Based on the Discrete Dislocation Theory , 2002 .

[68]  H. Zbib,et al.  A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals , 1999 .

[69]  E. Cosserat,et al.  Théorie des Corps déformables , 1909, Nature.

[70]  David L. McDowell,et al.  Modeling Dislocations and Disclinations With Finite Micropolar Elastoplasticity , 2006 .

[71]  G. Voyiadjis,et al.  Evolving internal length scales in plastic strain localization for granular materials , 2005 .

[72]  A. Needleman,et al.  An analysis of equilibrium dislocation distributions , 1993 .

[73]  T. Ariman,et al.  Stress concentration effects in micropolar elasticity , 1967 .

[74]  N. Fleck,et al.  FINITE ELEMENTS FOR MATERIALS WITH STRAIN GRADIENT EFFECTS , 1999 .

[75]  Joost J. Vlassak,et al.  Mechanical Behavior of Thin Films , 1996 .

[76]  W. Brekelmans,et al.  Second-order crystal plasticity: internal stress effects and cyclic loading , 2006 .

[77]  D. McDowell,et al.  A Multiscale Gradient Theory for Single Crystalline Elastoviscoplasticity , 2004 .

[78]  Lorenzo Bardella,et al.  A deformation theory of strain gradient crystal plasticity that accounts for geometrically necessary dislocations , 2006 .

[79]  U. Borg.  A strain gradient crystal plasticity analysis of grain size effects in polycrystals , 2007 .

[80]  Amit Acharya,et al.  Size effects and idealized dislocation microstructure at small scales: Predictions of a Phenomenological model of Mesoscopic Field Dislocation Mechanics: Part I , 2006 .

[81]  Samuel Forest,et al.  Finite deformation Cosserat-type modelling of dissipative solids and its application to crystal plasticity , 1998 .

[82]  E. Werner,et al.  Plastic deformation of a composite and the source-shortening effect simulated by a continuum dislocation-based model , 2006 .

[83]  Ronald W. Armstrong,et al.  The (cleavage) strength of pre-cracked polycrystals , 1987 .

[84]  Holger Steeb,et al.  The size effect in foams and its theoretical and numerical investigation , 2002, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[85]  D. Clarke,et al.  Size dependent hardness of silver single crystals , 1995 .

[86]  M. A. Kattis,et al.  Finite element method in plane Cosserat elasticity , 2002 .

[87]  N. O'Dowd,et al.  Finite element implementation of a generalised non-local rate-dependent crystallographic formulation for finite strains , 2001 .

[88]  S. Forest,et al.  Strain Localization Patterns at a Crack Tip in Generalized Single Crystal Plasticity , 2001 .

[89]  W. Brekelmans,et al.  Scale dependent crystal plasticity framework with dislocation density and grain boundary effects , 2004 .

[90]  C. Tsakmakis,et al.  Finite element implementation of large deformation micropolar plasticity exhibiting isotropic and kinematic hardening effects , 2005 .

[91]  Milan Jirásek,et al.  Nonlocal integral formulations of plasticity and damage : Survey of progress , 2002 .

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

[93]  M. Zikry,et al.  Effects of grain boundaries and dislocation density evolution on large strain deformation modes in fcc crystalline materials* , 2000 .

[94]  P. Neff.  A finite-strain elastic–plastic Cosserat theory for polycrystals with grain rotations , 2006 .

[95]  R. Sedláček.  Bending of thin crystalline strips: Comparison of continuum dislocation-based models , 2005 .

[96]  P. M. Naghdi,et al.  A dynamical theory of structures solids. II Special constitutive equations and special cases of the theory , 1993, Philosophical Transactions of the Royal Society of London. Series A: Physical and Engineering Sciences.

[97]  Amit Acharya,et al.  Lattice incompatibility and a gradient theory of crystal plasticity , 2000 .

[98]  C. Hartley.  A method for linking thermally activated dislocation mechanisms of yielding with continuum plasticity theory , 2003 .

[99]  F. Roters,et al.  Studying the effect of grain boundaries in dislocation density based crystal-plasticity finite element simulations , 2006 .

[100]  Darby J. Luscher,et al.  A hierarchical framework for the multiscale modeling of microstructure evolution in heterogeneous materials. , 2010 .

[101]  Morton E. Gurtin,et al.  A theory of grain boundaries that accounts automatically for grain misorientation and grain-boundary orientation , 2008 .

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

[103]  Peter Gumbsch,et al.  Micro-bending tests: A comparison between three-dimensional discrete dislocation dynamics simulations and experiments , 2008 .

[104]  H. Mughrabi,et al.  On the current understanding of strain gradient plasticity , 2004 .

[105]  L. P. Eversa,et al.  Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation , 2002 .

[106]  U. F. Kocks,et al.  Kinetics of flow and strain-hardening☆ , 1981 .

[107]  M. Becker.  Incompatibility and instability based size effects in crystals and composites at finite elastoplastic strains , 2006 .

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

[109]  A. Acharya.  Philosophical Magazine, , 2006 .

[110]  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.

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

[112]  W. King,et al.  Observations of lattice curvature near the interface of a deformed aluminium bicrystal , 2000 .

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

[114]  John L. Bassani,et al.  Plastic flow of crystals , 1993 .

[115]  V. Tvergaard,et al.  Studies of scale dependent crystal viscoplasticity models , 2006 .

[116]  H. Stumpf,et al.  Nonlinear continuum theory of dislocations , 1996 .

[117]  F. Roters,et al.  The mechanical size effect as a mean-field breakdown phenomenon: Example of microscale single crystal beam bending , 2010 .

[118]  Vasily V. Bulatov,et al.  On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals , 2004 .

[119]  Victor A. Eremeyev,et al.  On natural strain measures of the non-linear micropolar continuum , 2009 .

[120]  S. Xie,et al.  Finite element method for linear micropolar elasticity and numerical study of some scale effects phenomena in MEMS , 2004 .

[121]  M. Zikry,et al.  Grain boundary effects and void porosity evolution , 2003 .

[122]  van der Erik Giessen,et al.  COMPARISON OF DISCRETE DISLOCATION AND CONTINUUM PLASTICITY PREDICTIONS FOR A COMPOSITE MATERIAL , 1997 .

[123]  E. Kröner,et al.  Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen , 1959 .

[124]  Wenjun Liu,et al.  Dislocation Density Tensor Characterization of Deformation Using 3D X-Ray Microscopy , 2008 .

[125]  M. Zikry,et al.  Prediction of Grain-Boundary Interfacial Mechanisms in Polycrystalline Materials , 2002 .

[126]  Amit Acharya,et al.  Size effects and idealized dislocation microstructure at small scales: predictions of a phenomenological model of Mesoscopic Field Dislocation Mechanics: Part II , 2005 .

[127]  H. Zbib,et al.  Multiscale modelling of size effect in fcc crystals: discrete dislocation dynamics and dislocation-based gradient plasticity , 2007 .

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

[129]  Marisol Koslowski,et al.  Direct calculations of material parameters for gradient plasticity , 2008 .

[130]  V. Tvergaard,et al.  On the formulations of higher-order strain gradient crystal plasticity models , 2008 .

[131]  R. Bullough,et al.  Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[132]  P. Grammenoudis,et al.  Hardening rules for finite deformation micropolar plasticity: Restrictions imposed by the second law of thermodynamics and the postulate of Il'iushin , 2001 .

[133]  Stephen C. Cowin,et al.  Stress functions for cosserat elasticity , 1970 .

[134]  K. Schwarz,et al.  Simulation of dislocations on the mesoscopic scale. I. Methods and examples , 1999 .

[135]  H. Mughrabi.  On the role of strain gradients and long-range internal stresses in the composite model of crystal plasticity , 2001 .

[136]  A. Acharya,et al.  Dislocation transport using an explicit Galerkin/least-squares formulation , 2006 .

[137]  R. Toupin.  Elastic materials with couple-stresses , 1962 .

[138]  P. Dawson,et al.  A finite element formulation to solve a non-local constitutive model with stresses and strains due to slip gradients , 2008 .

[139]  Amit Acharya,et al.  Continuum theory and methods for coarse-grained, mesoscopic plasticity , 2006 .

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

[141]  Kondo Kazuo.  On the analytical and physical foundations of the theory of dislocations and yielding by the differential geometry of continua , 1964 .

[142]  David L. McDowell,et al.  Equivalent continuum for dynamically deforming atomistic particle systems , 2002 .

[143]  W. Brekelmans,et al.  Size effects in miniaturized polycrystalline FCC samples: Strengthening versus weakening , 2006 .

[144]  C. Sansour.  A unified concept of elastic-viscoplastic Cosserat and micromorphic continua , 1998 .

[145]  E. Hall,et al.  The Deformation and Ageing of Mild Steel: III Discussion of Results , 1951 .

[146]  E. Aifantis,et al.  Dislocation patterning in fatigued metals as a result of dynamical instabilities , 1985 .

[147]  C. F. Niordson,et al.  Size effects on void growth in single crystals with distributed voids , 2008 .

[148]  O. Bouaziz,et al.  Cosserat continuum modelling of grain size effects in metal polycrystals , 2005 .

[149]  Vikram Deshpande,et al.  Size effects in the bending of thin foils , 2009 .

[150]  R. Sedláček.  Orowan-type size effect in plastic bending of free-standing thin crystalline strips , 2005 .

[151]  Dierk Raabe,et al.  A dislocation density based constitutive model for crystal plasticity FEM including geometrically necessary dislocations , 2006 .

[152]  C. Tsakmakis,et al.  Predictions of microtorsional experiments by micropolar plasticity , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[153]  M. Gurtin,et al.  Thermodynamics with Internal State Variables , 1967 .

[154]  E. Holm,et al.  Predicting the Hall-Petch Effect in FCC Metals Using Non-Local Crystal Plasticity , 2006 .

[155]  J. Weertman,et al.  Anomalous work hardening, non-redundant screw dislocations in a circular bar deformed in torsion, and non-redundant edge dislocations in a bent foil , 2002 .

[156]  Koichi Masaki,et al.  Tensile and microbend tests of pure aluminum foils with different thicknesses , 2009 .

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

[158]  Bob Svendsen,et al.  Continuum thermodynamic models for crystal plasticity including the effects of geometrically-necessary dislocations , 2002 .

[159]  K. Bathe.  Finite Element Procedures , 1995 .

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

[161]  Alan Needleman,et al.  Material rate dependence and localized deformation in crystalline solids , 1983 .

[162]  A. Cemal Eringen,et al.  NONLINEAR THEORY OF SIMPLE MICRO-ELASTIC SOLIDS-I , 1964 .

[163]  Gérard A. Maugin,et al.  The method of virtual power in continuum mechanics: Application to coupled fields , 1980 .

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