Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory

2004 ◽  
pp. 167-174 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid Abu Al-Rub
Keyword(s):  
Plasticity Theory ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Intrinsic Length

A Modified Gradient Plasticity Theory for Micro-Bending and Micro-Torsion Size Effects

2004 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid K. Abu Al-Rub
Keyword(s):  
Size Effects ◽  
Scale Parameter ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Non Local ◽  
Material Length Scale ◽  
Material Length

The definition and magnitude of the intrinsic length scale are keys to the development of the theory of plasticity that incorporates size effects. Gradient plasticity theory with a material length scale parameter is successfully in capturing the size dependence of material behavior at the micron scale. However, a fixed value of the material length-scale is not always realistic and that different problems could require different values. Moreover, a linear coupling between the local and non-local terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed. This model assesses the sensitivity of predictions in the way in which the local and non-local parts are coupled. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.

The correlation between the internal material length scale and the microstructure in nanoindentation experiments and simulations using the conventional mechanism-based strain gradient plasticity theory

2009 ◽  
Vol 24 (3) ◽  
pp. 1197-1207 ◽  
Author(s):  
B. Backes ◽  
Y.Y. Huang ◽  
M. Göken ◽  
K. Durst
Keyword(s):  
Yield Stress ◽  
Strain Gradient ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Hardening Behavior ◽  
Material Length Scale ◽  
Material Length ◽  
Strain Gradient Plasticity Theory

In the present work a new equation to determine the internal material length scale for strain gradient plasticity theories from two independent experiments (uniaxial and nanoindentation tests) is introduced. The applicability of the presented equation is verified for conventional grained as well as for ultrafine-grained copper and brass with different amounts of prestraining. A significant decrease of the experimentally determined internal material length scale is found for increasing dislocation densities due to prestraining. Conventional mechanism strain gradient plasticity theory is used for simulating the indentation response, using experimentally determined material input data as the yield stress, the work-hardening behavior and the internal material length scale. The work-hardening behavior and the yield stress were taken from the uniaxial experiments, whereas the internal material length scale was calculated using the yield stress from the uniaxial experiment, the macroscopic hardness H0 and the length scale parameter h* following from the nanoindentation experiment. A good agreement between the measured and calculated load–displacement curve and the hardness is found independent of the material and the microstructure.

Gradient plasticity used for modeling extrinsic and intrinsic size effects in the torsion of Au microwires

2016 ◽  
Vol 25 (1-2) ◽  
pp. 53-56
Author(s):  
Xiaokun Wei ◽  
Avraam Konstantinidis ◽  
Chengzhi Qi ◽  
Elias Aifantis
Keyword(s):  
Grain Size ◽  
Sample Size ◽  
Plasticity Theory ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Internal Length ◽  
Size Dependent ◽  
Internal Length Scale ◽  
Model Size ◽  
Phenomenological Coefficients

AbstractThe gradient plasticity theory proposed by Aifantis and coworkers has been successfully used to model size effect phenomena at the microscale and nanoscale, by introducing into the formulation an internal length scale associated with the phenomenological coefficients of the gradient plasticity model. In this paper, Aifantis’ gradient plasticity theory is applied to model the sample size-dependent torsion of thin wires, with a strain-dependent internal length scale as well as grain size dependence based on the Hall-Petch relationship. This study reveals that internal length scale is related with sample size and grain size, with such a connection determined by the ductility of the material.

On the use of local strain fields for the determination of the intrinsic length scale

1998 ◽  
Vol 08 (PR8) ◽  
pp. Pr8-167-Pr8-174 ◽  
Author(s):  
M. G.D. Geers ◽  
R. de Borst ◽  
W. A.M. Brekelmans ◽  
R. H.J. Peerlings
Keyword(s):  
Local Strain ◽  
Length Scale ◽  
Strain Fields ◽  
Intrinsic Length

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.

Strain gradient plasticity to study hardness behavior of magnetite (Fe3O4) under multicyclic indentation

2009 ◽  
Vol 24 (3) ◽  
pp. 749-759 ◽  
Author(s):  
D. Chicot ◽  
F. Roudet ◽  
V. Lepingle ◽  
G. Louis
Keyword(s):  
Strain Gradient ◽  
Peak Load ◽  
Scale Factor ◽  
Strain Gradient Plasticity ◽  
Dislocation Network ◽  
Length Scale ◽  
Relevant Parameter ◽  
Characteristic Scale ◽  
Gradient Plasticity ◽  
Scale Length

The hardness of a material is generally affected by the indentation size effect. The strain gradient plasticity (SGP) theory is largely used to study this load dependence because it links the hardness to the intrinsic properties of the material. However, the characteristic scale-length is linked to the macrohardness, impeding any sound discussion. To find a relevant parameter, we suggest introducing a hardness length-scale factor that only depends on the shear modulus and the Burgers vector of the material and is easily calculable from the relation of the SGP theory. The variation of the hardness length-scale factor is thereafter used to discuss the hardness behavior of a magnetite crystal, the objective being to study the effect of the cumulative plasticity resulting from cyclic indentation. As a main result, the hardness length-scale factor is found to be constant by applying repeated cycles at a constant peak load whereas the macrohardness and the characteristic scale-length are both cycle dependent. When using incremental loads, the hardness length-scale factor monotonically decreases between two limits corresponding to those obtained at high and low loading rates, while the dwell-load duration increases. The physical meaning of such behavior is based on the modification of the dislocation network during the indentation process depending on the deformation rate.

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