Geometrically necessary dislocations and strain gradient plasticity––a dislocation dynamics point of view

2003 ◽  
Vol 48 (2) ◽  
pp. 133-139 ◽  
Author(s):  
Michael Zaiser ◽  
Elias C Aifantis
Keyword(s):  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Point Of View ◽  
Dislocation Dynamics ◽  
Gradient Plasticity

A Retrospective Account of Seminal Research by H. M. Zbib

2021 ◽  
pp. 1-5
Author(s):  
John Hirth
Keyword(s):  
Multiscale Modeling ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Dislocation Dynamics ◽  
Gradient Plasticity ◽  
Discrete Dislocation Dynamics ◽  
Discrete Dislocation ◽  
Retrospective Account

Abstract Throughout his career, Zbib was innovative, originating models in seminal papers that anticipated areas of subsequent increased interest. These include strain-gradient plasticity, discrete dislocation dynamics, multiscale modeling, Arrays of Somigliana ring dislocations, and nanoscale plasticity. We comment here on these aspects of his work. Many of the papers in this volume represent applications of these ideas.

Analysis of particle induced dislocation structures using three-dimensional dislocation dynamics and strain gradient plasticity

2012 ◽  
Vol 52 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Hyung-Jun Chang ◽  
Anaïs Gaubert ◽  
Marc Fivel ◽  
Stéphane Berbenni ◽  
Olivier Bouaziz ◽  
...  
Keyword(s):  
Strain Gradient ◽  
Three Dimensional ◽  
Strain Gradient Plasticity ◽  
Dislocation Dynamics ◽  
Gradient Plasticity ◽  
Induced Dislocation

Questioning size effects as predicted by strain gradient plasticity

2013 ◽  
Vol 22 (3-4) ◽  
pp. 101-110 ◽  
Author(s):  
Samuel Forest
Keyword(s):  
Strain Gradient ◽  
Size Effects ◽  
Shear Loading ◽  
Strain Gradient Plasticity ◽  
Point Of View ◽  
Plastic Behavior ◽  
Gradient Plasticity ◽  
Two Phase ◽  
Elastic Plastic ◽  
The Individual

AbstractThe analytical solution of the elastic-plastic response of a two-phase laminate microstructure subjected to periodic simple shear loading conditions is derived considering strain gradient and micromorphic plasticity models successively. One phase remains purely elastic, whereas the second one displays an isotropic elastic-plastic behavior. Although no classic hardening is introduced at the individual phase level, the laminate is shown to exhibit an overall linear hardening scaling with the inverse of the square of the cell size. The micromorphic model leads to a saturation of the hardening at small length scales in contrast to Aifantis strain gradient plasticity model displaying unlimited hardening. The models deliver qualitatively relevant size effects from the physical metallurgical point of view, but fundamental quantitative discrepancy is pointed out and discussed, thus requiring the development of more realistic nonlinear equations in strain gradient plasticity.

scholarly journals AN ANALYTIC SOLUTION FOR ONE-DIMENSIONAL DISSIPATIONAL STRAIN-GRADIENT PLASTICITY

2009 ◽  
Vol 50 (3) ◽  
pp. 407-420
Author(s):  
ROGER YOUNG
Keyword(s):  
Boundary Condition ◽  
Strain Gradient ◽  
Analytic Solution ◽  
Strain Gradient Plasticity ◽  
Numerical Results ◽  
Gradient Plasticity ◽  
One Dimensional ◽  
Numerical Result ◽  
Formulation Analysis ◽  
The One

AbstractAn analytic solution is developed for the one-dimensional dissipational slip gradient equation first described by Gurtin [“On the plasticity of single crystals: free energy, microforces, plastic strain-gradients”, J. Mech. Phys. Solids48 (2000) 989–1036] and then investigated numerically by Anand et al. [“A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results”, J. Mech. Phys. Solids53 (2005) 1798–1826]. However we find that the analytic solution is incompatible with the zero-sliprate boundary condition (“clamped boundary condition”) postulated by these authors, and is in fact excluded by the theory. As a consequence the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al. also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.

A Study of Microindentation Hardness Tests by Mechanism-based Strain Gradient Plasticity

2000 ◽  
Vol 15 (8) ◽  
pp. 1786-1796 ◽  
Author(s):  
Y. Huang ◽  
Z. Xue ◽  
H. Gao ◽  
W. D. Nix ◽  
Z. C. Xia
Keyword(s):  
Strain Gradient ◽  
Size Dependence ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Hierarchical Framework ◽  
Microindentation Hardness ◽  
Dislocation Hardening ◽  
Hardness Tests ◽  
Micro Indentation

We recently proposed a theory of mechanism-based strain gradient (MSG) plasticity to account for the size dependence of plastic deformation at micron- and submicronlength scales. The MSG plasticity theory connects micron-scale plasticity to dislocation theories via a multiscale, hierarchical framework linking Taylor's dislocation hardening model to strain gradient plasticity. Here we show that the theory of MSG plasticity, when used to study micro-indentation, indeed reproduces the linear dependence observed in experiments, thus providing an important self-consistent check of the theory. The effects of pileup, sink-in, and the radius of indenter tip have been taken into account in the indentation model. In accomplishing this objective, we have generalized the MSG plasticity theory to include the elastic deformation in the hierarchical framework.

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