Taylor-based nonlocal theory of plasticity

A Taylor-based nonlocal theory of plasticity is proposed to account for the size dependence of plastic deformation at micron and submicron length scales. This theory is intended to link Taylor's model of dislocation hardening to a nonlocal theory of plasticity in which the density of geometrically necessary dislocations is expressed as a nonlocal integral of the strain field. We make application of this theory to void growth, cavitation instabilities and particle-reinforced composites, as well as comparison with experiments on micro-torsion, micro-bending and micro-indentation.

[1]  Zdeněk P. Bažant,et al.  Non-local yield limit degradation , 1988 .

[2]  Ted Belytschko,et al.  Continuum Theory for Strain‐Softening , 1984 .

[3]  Z. Bažant.  Mechanics of Distributed Cracking , 1986 .

[4]  David R. Clarke,et al.  The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites , 1996 .

[5]  R. Hill,et al.  CXXVIII. A theoretical derivation of the plastic properties of a polycrystalline face-centred metal , 1951 .

[6]  A. Cemal Eringen,et al.  On nonlocal plasticity , 1981 .

[7]  Yonggang Huang,et al.  Accurate Dilatation Rates for Spherical Voids in Triaxial Stress Fields , 1991 .

[8]  John W. Hutchinson,et al.  Void Growth in Plastic Solids , 1992 .

[9]  Alan Cottrell,et al.  Mechanical Properties of Matter , 1964 .

[10]  W. Nix,et al.  Modeling Plasticity at the Micrometer Scale , 1999, Naturwissenschaften.

[11]  W. T. Koiter.  Couple-stresses in the theory of elasticity , 1963 .

[12]  E. Aifantis.  On the Microstructural Origin of Certain Inelastic Models , 1984 .

[13]  A. S. Argon,et al.  Topics in fracture and fatigue , 1992 .

[14]  Yiu-Wing Mai,et al.  Advances in Fracture Research , 1997 .

[15]  J. Rice.  On the Structure of Stress-Strain Relations for Time-Dependent Plastic Deformation in Metals , 1970 .

[16]  Huajian Gao,et al.  Mechanism-based strain gradient plasticity—II. Analysis , 2000 .

[17]  Matti Ristinmaa,et al.  FE-formulation of a nonlocal plasticity theory , 1996 .

[18]  William D. Nix,et al.  The Role of Indentation Depth on the Measured Hardness of Materials , 1993 .

[19]  D. M. Tracey,et al.  On the ductile enlargement of voids in triaxial stress fields , 1969 .

[20]  H. Dai.  Geometrically-necessary dislocation density in continuum plasticity theory, FEM implementation and applications , 1997 .

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

[22]  Huajian Gao,et al.  A study of microindentation hardness tests by mechanism-based strain gradient plasticity , 2000 .

[23]  William D. Nix,et al.  Mechanical properties of thin films , 1989 .

[24]  Hussein M. Zbib,et al.  On the localization and postlocalization behavior of plastic deformation. II: On the evolution and thickness of shear bands , 1988 .

[25]  Z. Bažant,et al.  Nonlocal damage theory , 1987 .

[26]  Hussein M. Zbib,et al.  On the localization and postlocalization behavior of plastic deformation. I: On the initiation of shear bands , 1988 .

[27]  Norman A. Fleck,et al.  A phenomenological theory for strain gradient effects in plasticity , 1993 .

[28]  Y. Milman,et al.  Microindentations on W and Mo oriented single crystals: An STM study , 1993 .

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

[30]  R. Hill,et al.  XLVI. A theory of the plastic distortion of a polycrystalline aggregate under combined stresses. , 1951 .

[31]  A. Eringen.  Theories of nonlocal plasticity , 1983 .

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

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

[34]  D. Lloyd.  Particle reinforced aluminium and magnesium matrix composites , 1994 .

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

[36]  M. Ashby,et al.  Micro-hardness of annealed and work-hardened copper polycrystals , 1996 .

[37]  J. Vlassak,et al.  Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments , 1998 .

[38]  Huajian Gao,et al.  Indentation size effects in crystalline materials: A law for strain gradient plasticity , 1998 .

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

[40]  Michael Lane,et al.  Adhesion and debonding of multi-layer thin film structures , 1998 .

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

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

[43]  D. McLean,et al.  The Mechanical Properties of Metals , 1963 .

[44]  Manfred Rühle,et al.  The influence of interface impurities on fracture energy of UHV diffusion bonded metal-ceramic bicrystals , 1994 .

[45]  R. Hill.  The mathematical theory of plasticity , 1950 .

[46]  Huajian Gao,et al.  Mechanism-based strain gradient plasticity— I. Theory , 1999 .

[47]  A. Gurson.  Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part I—Yield Criteria and Flow Rules for Porous Ductile Media , 1977 .

[48]  Viggo Tvergaard,et al.  Cavitation instabilities in elastic-plastic solids , 1991 .

[49]  N. Mott,et al.  The theory of indentation and hardness tests , 1945 .

[50]  V. Tvergaard.  Material Failure by Void Growth to Coalescence , 1989 .

[51]  U. F. Kocks.  The relation between polycrystal deformation and single-crystal deformation , 1970 .

[52]  H. Zbib,et al.  On the localization and postlocalization behavior of plastic deformation. III: On the structure and velocity of the Portevin-Le Chatelier bands , 1988 .

[53]  René de Borst,et al.  Gradient-dependent plasticity: formulation and algorithmic aspects , 1992 .

[54]  N. Fleck,et al.  Strain gradient plasticity , 1997 .

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

[56]  R. D. Mindlin.  Micro-structure in linear elasticity , 1964 .

[57]  E. P. Chen,et al.  Non-local effects on dynamic damage accumulation in brittle solids , 1999 .