An Alternative Decomposition of the Strain Gradient Tensor

[+] Author and Article Information
H. Jiang, T. F. Guo, K. C. Hwang

Failure Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China

Y. Huang

Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801

J. Appl. Mech 69(2), 139-141 (Jul 18, 2001) (3 pages) doi:10.1115/1.1430666 History: Received January 18, 2001; Revised July 18, 2001
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Fleck,  N. A., and Hutchinson,  J. W., 1997, “Strain Gradient Plasticity,” Adv. Appl. Mech., 33, pp. 295–361.
De Guzman,  M. S., Neubauer,  G., Flinn,  P., and Nix,  W. D., 1993, “The Role of Indentation Depth on the Measured Hardness of Materials,” Mat. Res. Sym. Proc., 308, pp. 613–618.
Stelmashenko,  N. A., Walls,  M. G., Brown,  L. M., and Milman,  Y. V., 1993, “Microindentation on W and Mo Oriented Single Crystals: An STM Study,” Acta Metall. Mater., 41, pp. 2855–2865.
Fleck,  N. A., Muller,  G. M., Ashby,  M. F., and Hutchinson,  J. W., 1994, “Strain Gradient Plasticity: Theory and Experiments,” Acta Metall. Mater., 42, pp. 475–487.
Lloyd,  D. J., 1994, “Particle Reinforced Aluminum and Magnesium Matrix Composites,” Int. Mater. Rev., 39, pp. 1–23.
Ma,  Q., and Clarke,  D. R., 1995, “Size Dependent Hardness of Silver Single Crystals,” J. Mater. Res., 10, pp. 853–863.
Poole,  W. J., Ashby,  M. F., and Fleck,  N. A., 1996, “Micro-hardness of Annealed and Work-Hardened Copper Polycrystals,” Scr. Metall. Mater., 34, pp. 559–564.
McElhaney,  K. W., Vlassak,  J. J., and Nix,  W. D., 1998, “Determination of Indenter Tip Geometry and Indentation Contact Area for Depth-Sensing Indentation Experiments,” J. Mater. Res., 13, pp. 1300–1306.
Stolken,  J. S., and Evans,  A. G., 1998, “A Microbend Test Method for Measuring the Plasticity Length Scale,” Acta Mater., 46, pp. 5109–5115.
Smyshlyaev,  V. P., and Fleck,  N. A., 1996, “Role of Strain Gradients in the Grain Size Effect for Polycrystals,” J. Mech. Phys. Solids, 44, pp. 465–495.
Gao,  H., Huang,  Y., Nix,  W. D., and Hutchinson,  J. W., 1999, “Mechanism-Based Strain Gradient Plasticity—I. Theory,” J. Mech. Phys. Solids, 47, pp. 1239–1263.
Huang,  Y., Gao,  H., Nix,  W. D., and Hutchinson,  J. W., 2000, “Mechanism-Based Strain Gradient Plasticity—II. Analysis,” J. Mech. Phys. Solids, 48, pp. 99–128.
Huang,  Y., Xue,  Z., Gao,  H., Nix,  W. D., and Xia,  Z. C., 2000, “A Study of Micro-Indentation Hardness Tests by Mechanism-Based Strain Gradient Plasticity,” J. Mater. Res., 15, pp. 1786–1796.
Gao,  H., Huang,  Y., and Nix,  W. D., 1999, “Modeling Plasticity at the Micrometer Scale,” Naturwissenschaften, 86, pp. 507–515.
Hwang,  K. C., and Inoue,  T., 1998, “Recent Advances in Strain Gradient Plasticity,” Mat. Sci. Res. Int., 4, pp. 227–238.
Acharya,  A., and Bassani,  J. L., 2000, “Lattice Incompatibility and a Gradient Theory of Crystal Plasticity,” J. Mech. Phys. Solids, 48, pp. 1565–1595.
Acharya,  A., and Beaudoin,  A. J., 2000, “Grain-Size Effect in Viscoplastic Polycrystals at Moderate Strains,” J. Mech. Phys. Solids, 48, pp. 2213–2230.
Dai, H., and Parks, D. M., 2001, “Geometrically Necessary Dislocation Density in Continuum Crystal Plasticity Theory and FEM Implementation,” unpublished manuscript.
Qiu, X., Huang, Y., Wei, Y., Gao, H., and Hwang, K. C., 2001, “The Flow Theory of Mechanism-Based Strain Gradient Plasticity,” submitted for publication.
Hutchinson,  J. W., 1968, “Singular Behavior at the End of a Tensile Crack in a Hardening Material,” J. Mech. Phys. Solids, 16, pp. 13–31.
Rice,  J. R., and Rosengren,  G. F., 1968, “Plane Strain Deformation Near a Crack Tip in a Power Law Hardening Material,” J. Mech. Phys. Solids, 16, pp. 1–12.


Grahic Jump Location
The effective stress σe normalized by the uniaxial yield stress σY versus the normalized distance to the crack tip, r/l, ahead of the crack tip, where l is the intrinsic material length in strain gradient plasticity; the plastic work hardening exponent N=0.2, Poisson’s ratio ν=0.3, the ratio of yield stress to elastic modulus σY/E=0.2percent, and the remotely applied elastic stress intensity factor KIYl1/2=20



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In