The indenter tip radius effect in micro- and nanoindentation hardness experiments.

Nix and Gao established an important relation between the microindentation hardness and indentation depth. Such a relation has been verified by many microindentation experiments (indentation depths in the micrometer range), but it does not always hold in nanoindentation experiments (indentation depths approaching the nanometer range). Indenter tip radius effect has been proposed by Qu et al. and others as possibly the main factor that causes the deviation from Nix and Gao's relationship. We have developed an indentation model for micro- and nanoindentation, which accounts for two indenter shapes, a sharp, conical indenter and a conical indenter with a spherical tip. The analysis is based on the conventional theory of mechanism-based strain gradient plasticity established from the Taylor dislocation model to account for the effect of geometrically necessary dislocations. The comparison between numerical result and Feng and Nix's experimental data shows that the indenter tip radius effect indeed causes the deviation from Nix-Gao relation, but it seems not be the main factor.

[1]  J. Joubert,et al.  a comprehensive treatment , 1985 .

[2]  M. Saif,et al.  Strain gradient effect in nanoscale thin films , 2003 .

[3]  Zhenyu Xue,et al.  The Influence of Indenter Tip Radius on the Micro-Indentation Hardness , 2002 .

[4]  G. Pharr,et al.  The indentation size effect in the spherical indentation of iridium: A study via the conventional theory of mechanism-based strain gradient plasticity , 2006 .

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

[6]  Huajian Gao,et al.  The flow theory of mechanism-based strain gradient plasticity , 2003 .

[7]  Norman A. Fleck,et al.  A reformulation of strain gradient plasticity , 2001 .

[8]  Chuan-jiang Liu,et al.  Fracture analysis in the conventional theory of mechanism-based strain gradient (CMSG) plasticity , 2004 .

[9]  M. R. Douglass,et al.  Lifetime estimates and unique failure mechanisms of the Digital Micromirror Device (DMD) , 1998, 1998 IEEE International Reliability Physics Symposium Proceedings. 36th Annual (Cat. No.98CH36173).

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

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

[12]  A. Needleman,et al.  Discrete dislocation simulations and size dependent hardening in single slip , 1998 .

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

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

[15]  Esteban P. Busso,et al.  A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts , 2004 .

[16]  John L. Bassani,et al.  Incompatibility and a simple gradient theory of plasticity , 2001 .

[17]  van der Erik Giessen,et al.  A discrete dislocation analysis of bending , 1999 .

[18]  D. Tortorelli,et al.  A polycrystal plasticity model based on the mechanical threshold , 2002 .

[19]  Huajian Gao,et al.  A conventional theory of mechanism-based strain gradient plasticity , 2004 .

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

[21]  D. Tortorelli,et al.  A finite element model for the Portevin–Le Chatelier effect based on polycrystal plasticity , 2002 .

[22]  H. Wiedersich,et al.  Hardening mechanisms and the theory of deformation , 1964 .

[23]  M. M. Chaudhri,et al.  The effect of the indenter load on the nanohardness of ductile metals : an experimental study on polycrystalline work-hardened and annealed oxygen-free copper , 1999 .

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

[25]  Pranav Shrotriya,et al.  On the measurement of the plasticity length scale parameter in LIGA nickel foils , 2003 .

[26]  T. Siegmund,et al.  A study of particle size effect and interface fracture in aluminum alloy composite via an extended conventional theory of mechanism-based strain-gradient plasticity , 2005 .

[27]  D. Tortorelli,et al.  On the development of stage IV hardening using a model based on the mechanical threshold , 2002 .

[28]  A. Acharya,et al.  A model for rate-dependent flow of metal polycrystals based on the slip plane lattice incompatibility , 2001 .

[29]  Zhenyu Xue,et al.  Indentation of a soft metal film on a hard substrate: strain gradient hardening effects , 2001 .

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

[31]  J. E. Bailey,et al.  The dislocation distribution, flow stress, and stored energy in cold-worked polycrystalline silver , 1960 .

[32]  Huajian Gao,et al.  Effect of intrinsic lattice resistance in strain gradient plasticity , 2001 .

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

[34]  Yueguang Wei,et al.  Size effect measurement and characterization in nanoindentation test , 2004 .

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

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

[37]  Huajian Gao,et al.  A finite deformation theory of strain gradient plasticity , 2002 .

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

[39]  van der Erik Giessen,et al.  A discrete dislocation analysis of residual stresses in a composite material , 1999 .

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

[41]  K. Hsia,et al.  A study of microbend test by strain gradient plasticity , 2003 .

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

[43]  W. Nix,et al.  Indentation size effect in MgO , 2004 .

[44]  D. Stone,et al.  Nanoindentation and the indentation size effect: Kinetics of deformation and strain gradient plasticity , 2003 .

[45]  Huajian Gao,et al.  Taylor-based nonlocal theory of plasticity , 2001 .

[46]  F. Zhang,et al.  A Three-Dimensional Strain Gradient Plasticity Analysis of Particle Size Effect in Composite Materials , 2007 .

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

[48]  P. L. Pratt,et al.  Plastic Deformation and Work-Hardening in NaCl , 1964 .

[49]  G. Pharr,et al.  The correlation of the indentation size effect measured with indenters of various shapes , 2002 .

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

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

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

[53]  D. Parks,et al.  Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation , 2002 .

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

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

[56]  Huajian Gao,et al.  Geometrically necessary dislocation and size-dependent plasticity , 2003 .

[57]  Huajian Gao,et al.  Finite deformation analysis of mechanism-based strain gradient plasticity: torsion and crack tip field , 2003 .

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

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

[60]  G. Taylor.  The Mechanism of Plastic Deformation of Crystals. Part I. Theoretical , 1934 .

[61]  John W. Hutchinson,et al.  The mechanics of size-dependent indentation , 1998 .

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

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

[64]  U. F. Kocks,et al.  Physics and phenomenology of strain hardening: the FCC case , 2003 .

[65]  K. Hwang,et al.  Indenter tip radius effect on the Nix–Gao relation in micro- and nanoindentation hardness experiments , 2004 .

[66]  Huajian Gao,et al.  The J-integral and geometrically necessary dislocations in nonuniform plastic deformation , 2004 .

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

[68]  J. Hutchinson,et al.  Hardness trends in micron scale indentation , 2003 .

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

[70]  K. Hwang,et al.  The finite deformation theory of Taylor-based nonlocal plasticity , 2004 .

[71]  Amit Acharya,et al.  Grain-size effect in viscoplastic polycrystals at moderate strains , 2000 .

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