Recent Developments in Gradient Plasticity—Part I: Formulation and Size Effects

[+] Author and Article Information
Ioannis Tsagrakis

Laboratory of Mechanics and Materials (LMM), Polytechnic School, Aristotle University of Thessaloniki, Thessaloniki, GR-54006 Greece   e-mail: mom@mom.gen.auth.gr

Elias C. Aifantis

Laboratory of Mechanics and Materials (LMM), Polytechnic School, Aristotle University of Thessaloniki, Thessaloniki, GR-54006 GreeceCenter for the Mechanics of Material Instabilities and Manufacturing Processes (MMINMP), Michigan Tech, Houghton, MI 49931

J. Eng. Mater. Technol 124(3), 352-357 (Jun 10, 2002) (6 pages) doi:10.1115/1.1479695 History: Received January 19, 2002; Revised February 19, 2002; Online June 10, 2002
Copyright © 2002 by ASME
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Aifantis,  E. C., 1999, “Gradient Deformation Models at Nano, Micro, and Macro Scales,” ASME J. Eng. Mater. Technol., 121, pp. 189–202.
Aifantis, E. C., 1981, “Elementary Physicochemical Degradation Processes” Mechanics of Structured Media, A. P. S. Selvadurai, ed., Elevier, Amsterdam, pp. 301–317.
Aifantis, E. C., 1983, “Dislocation Kinetics and the Formation of Deformation Bands,” Defects Fracture and Fatigue, G. C. Sih and J. W. Provan, eds., Martinus-Nijhoff, The Hague, pp. 75–84.
Bammann,  D. J., and Aifantis,  E. C., 1982, “On a Proposal for a Continuum with Microstructure,” Acta Mech., 45, pp. 91–121.
Walgraef,  D., and Aifantis,  E. C., 1985, “Dislocation Patterning in Fatigued Metals as a Result of Dynamical Instabilities,” J. Appl. Phys., 58, pp. 688–691.
Bulatov,  V., Abraham,  F. F., Kubin,  L., Devincre,  B., and Yip,  S., 1998, “Connecting Atomistic and Mesoscopic Simulations of Crystal Plasticity,” Nature (London), 391, pp. 669–672.
Zbib,  H. M., Rhee,  M., and Hirth,  J. P., 1998, “On Plastic Deformation and the Dynamics of 3D Dislocations,” Int. J. Mech. Sci., 40, pp. 113–127.
Romanov,  A. E., and Aifantis,  E. C., 1993, “On the Kinetic and Diffusional Nature of Linear Defects,” Scr. Metall. Mater., 29, pp. 707–712.
Liosatos,  N., Romanov,  A. E., Zaiser,  M., and Aifantis,  E. C., 1998, “Non-local Interactions and Patterning of Misfit Dislocations in Thin Films,” Scr. Mater., 38, pp. 819–826.
Romanov,  A. E., Pompe,  W., Mathis,  S., Beltz,  G. E., and Speck,  J. S., 1999, “Threading Dislocation Reduction in Strained Layers,” J. Appl. Phys., 85, pp. 182–192.
Zaiser, M., and Aifantis, E. C., 1999, “Materials Instabilities and Deformation Patterning in Plasticity,” Recent Res. Devel. Metallurg. & Materials Sci., Vol. 3 , S. G. Pandalai, ed., Research Signpost, pp. 79–103.
Zaiser, M., and Aifantis, E. C., “Avalanches in Plastic Deformation,” J. Mech. Behav. Mater., (in press).
Zaiser, M., and Aifantis, E. C., 2001, “Modeling the Crushing of a Cellular Material,” Proc. 6th National Congress of Mechanics, III, E. C. Aifantis and A. N. Kounadis, eds., Giahoudi-Giapouli Publ., Thessaloniki, pp. 102–108.
Aifantis,  E. C., 1984, “On the Microstructural Origin of Certain Inelastic Models,” ASME J. Eng. Mater. Technol., 106, pp. 326–330.
Aifantis,  E. C., 1987, “The Physics of Plastic Deformation,” Int. J. Plast. 3, pp. 211–247.
Aifantis,  E. C., 1992, “On the Role of Gradients on the Localization of Deformation and Fracture,” Int. J. Eng. Sci., 30, pp. 1279–1299.
Aifantis,  E. C., 1995, “Pattern Formation in Plasticity,” Int. J. Eng. Sci., 33, pp. 2161–2178.
Aifantis,  E. C., 1996, “Non-linearity, Periodicity and Patterning in Plasticity and Fracture,” Int. J. Non-Linear Mech., 31, pp. 797–809.
Zbib,  H. M., and Aifantis,  E. C., 1988, “On the Structure and Width of Shear Bands,” Scr. Metall., 22, pp. 703–708.
Zbib,  H. M., and Aifantis,  E. C., 1988, “A Gradient-dependent Model for the Portevin-Le Chatelier Effect,” Scr. Metall., 22, pp. 1331–1336.
Zbib,  H. M., and Aifantis,  E. C., 1988, “On the Localization and Post-localization Behavior of Plastic Deformation-I,II,III,” Res. Mech., 23, pp. 261–305.
Belytschko,  T., and Kulkarni,  M., 1991, “On the Effect of Imperfections and Spatial Gradient Regularization in Strain Softening Viscoplasticity,” Mech. Res. Commun., 18, pp. 335–343.
de Borst,  R., and Mühlhaus,  H. B., 1992, “Gradient-dependent Plasticity: Formulation and Algorithmic Aspects,” Int. J. Numer. Methods Eng., 35, pp. 521–539.
Tomita,  Y., 1994, “Simulations of Plastic Instabilities in Solid Mechanics,” Appl. Mech. Rev., 47, pp. 171–205.
Fleck,  N. A., Müller,  G. M., Ashby,  M. F., and Hutchinson,  J. W., 1994, “Strain Gradient Plasticity: Theory and Experiment,” Acta Metall. Mater., 42, pp. 475–487.
Fleck, N. A., and Hutchinson, J. W., 1997, “Strain Gradient Plasticity,” Advances in Applied Mechanics, Vol. 33, J. W. Hutchinson and T. W. Wu, eds., pp. 295–361.
Gao,  H., Huang,  Y., Nix,  W. D., and Hutchinson,  J. W., 1999, “Mechanism-based Strain Gradient Plasticity-I,” 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,” J. Mech. Phys. Solids, 48, pp. 99–128.
Aifantis, E. C., 2001, “Gradient Plasticity,” Handbook of Materials Behavior Models, J. Lemaitre, ed., Academic Press, New York, pp. 281–297.
Fleck,  N. A., and Hutchinson,  J. W., 2001, “A Reformulation of Strain Gradient Plasticity,” J. Mech. Phys. Solids, 49, pp. 2245–2271.
Avlonitis,  M., Ioannidou,  T., Frantziskonis,  G., and Aifantis,  E. C., 2001, “Statistical and Stochastic Aspects of Gradient Theory,” J. Mech. Behav. Mater., 12, pp. 77–84.
Frantziskonis, G., and Aifantis, E. C., “On the Stochastic Interpretation of Gradient-dependent Constitutive Equations,” Eur. J. Mech. A/Solids, (in press).
Tsagrakis, I., 2001, “The Role of Gradients in Elasticity and Plasticity. Analytical and Numerical Applications,” Ph.D. thesis, Aristotle University of Thessaloniki, Thessaloniki (in Greek).
Stölken,  J. S., and Evans,  A. G., 1998, “A Microbend Test Method for Measuring the Plasticity Length Scale,” Acta Mater., 46, pp. 5109–5115.
Aifantis,  E. C., 1999, “Strain Gradient Interpretation of Size Effects,” Int. J. Fract., 95, pp. 299–314.
Lu,  Y. Y., Belytschko,  T., and Gu,  L., 1994, “A New Implementation of Element-Free Galerkin Method,” Comput. Methods Appl. Mech. Eng., 113, pp. 397–414.
Askes,  H., Pamin,  J., and de Borst,  R., 2000, “Dispersion Analysis and Element-Free Galerkin Solutions of Second- and Fourth-Order Gradient-Enhanced Damage Models,” Int. J. Numer. Methods Eng., 49, pp. 811–832.
Imamura,  S., and Sato,  Y., 1986, “The Size Effect on Yielding of a Mild Steel Strip with a Hole under Tension” (in Japanese), Trans. Jpn. Soc. Mech. Eng., Ser. A, 52, pp. 1440–1444.
Malmberg,  T., Tsagrakis,  I., Eleftheriadis,  I., and Aifantis,  E. C., 2001, On the Gradient Plasticity Approach to Size Effects, Part II: Applications, Forschungszentrum Karlsruhe, Scientific Report FZKA 6322.


Grahic Jump Location
Size effects in torsion. If size effects were absent or strain gradient effects were neglected, all curves would fall on a single curve.
Grahic Jump Location
Size effects in bending. If size effects were absent or strain gradient effects were neglected, all curves would fall on a single curve.
Grahic Jump Location
(a) Tension of a perforated plate and (b) size effect on the normalized applied stress (σao) versus nominal strain (u/H) graph for geometrically similar perforated plates.
Grahic Jump Location
Size effect on the effective plastic strain distribution for geometrically similar perforated plates at a nominal strain u/H=6.666⋅10−3



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