Multiple slip in a strain-gradient plasticity model motivated by a statistical-mechanics description of dislocations

The indentation size effect of pure iron samples with various pre-plastic tensile strains has been experimentally investigated and analyzed. With the increase in the strain, the indentation size effect of iron samples becomes weak, accompanied by the multiplication of the statistically stored dislocations. All of the hardness (H) versus indentation depth (h) curves fit the strain-gradient plasticity model for indentation of Nix and Gao well. Two fitting parameters, the hardness in the limit of infinite depth (H0) and the characteristic length (h*), were obtained for each curve. The hardness (H0) of iron samples can also be estimated as the microhardness (H) at a very large depth, h ≅ 10h*. Both the fitted H0 and the measured H0′ increase linearly with the tensile yield stress σy of iron samples, indicating a dependence of H0 on the statistically stored dislocation density through σy. Furthermore, 1/√h* shows a linear increase with the tensile yield stress σy, which also agrees qualitatively with the general prediction of the Nix and Gao theory. Therefore, our experiments and analysis demonstrate that the strain-gradient plasticity model for indentation of Nix and Gao can interpret the indentation size effect with satisfied precision.

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Bilinear Behavior in the Indentation Size Effect: A Consequence of Strain Gradient Plasticity

MRS Proceedings ◽

10.1557/proc-750-y1.7 ◽

2002 ◽

Vol 750 ◽

Author(s):

A. A. Elmustafa ◽

J. Lou ◽

O. Adewoye ◽

W. O. Soboyejo ◽

D. S. Stone

Keyword(s):

Strain Gradient ◽

Stacking Fault ◽

Strain Gradient Plasticity ◽

Stacking Fault Energy ◽

Face Centered Cubic ◽

Plasticity Model ◽

Gradient Plasticity ◽

Abrupt Decrease ◽

Linear Behavior ◽

Face Centered

ABSTRACTThis paper examines the effects of stacking fault energy on the micro- and nano-indentation behavior of face-centered-cubic thin films. These include: LIGA nickel MEMS structures, alpha brass, copper and high purity aluminum. The measured hardness are then fitted to a strain gradient plasticity model based on the Taylor dislocation hardening model. Hardness is shown to exhibit a size dependence with different characteristic slopes in the micron and nano-scale regimes. Deep indents are shown to exhibit classical linear behavior. However, shallow indents exhibit an abrupt decrease in slope (almost by a factor of 10), giving rise to a bi-linear behavior. Furthermore, as the gradients become less sharp, the trends in the nano-hardness data become similar to those of the microhardness data predicted by the strain gradient plasticity model. Finally, the effects of stacking fault energy are then discussed within the context of cross-slip and hardening associated with Shockly partials.

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Higher-Order Thermomechanical Gradient Plasticity Model With Energetic and Dissipative Components

Journal of Engineering Materials and Technology ◽

10.1115/1.4035293 ◽

2017 ◽

Vol 139 (2) ◽

Cited By ~ 11

Author(s):

George Z. Voyiadjis ◽

Yooseob Song ◽

Taehyo Park

Keyword(s):

Finite Element ◽

Strain Gradient ◽

Loading Condition ◽

Strain Gradient Plasticity ◽

Plasticity Model ◽

Gradient Plasticity ◽

Jump Phenomenon ◽

Stress Jump ◽

Dissipation Potential ◽

Nonproportional Loading

The thermodynamically consistent framework accounting for the thermomechanical behavior of the microstructure is addressed using the finite-element implementation. In particular, two different classes of the strain gradient plasticity (SGP) theories are proposed: In the first theory, the dissipation potential is dependent on the gradient of the plastic strain, as a result, the nonrecoverable microstresses do not have a value of zero. In the second theory, the dissipation potential is independent of the gradient of the plastic strain, in which the nonrecoverable microstresses do not exist. Recently, Fleck et al. pointed out that the nonrecoverable microstresses always generate the stress jump phenomenon under the nonproportional loading condition. In this work, a one-dimensional finite-element solution for the proposed strain gradient plasticity model is developed for investigating the stress jump phenomenon. The proposed strain gradient plasticity model and the corresponding finite-element code are validated by comparing with the experimental data from the two sets of microscale thin film experiments. In both experimental validations, it is shown that the calculated numerical results of the proposed model are in good agreement with the experimental measurements. The stretch-passivation problems are then numerically solved for investigating the stress jump phenomenon under the nonproportional loading condition.

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Investigation of the Hall-Petch Relationship Using Strain Gradient Plasticity Model for Finite Deformation Framework

Journal of Materials and Applications ◽

10.32732/jma.2020.9.2.55 ◽

2020 ◽

Vol 9 (2) ◽

pp. 55-69

Author(s):

Yooseob Song

Keyword(s):

Strain Gradient ◽

Finite Deformation ◽

Strain Gradient Plasticity ◽

Plasticity Model ◽

Gradient Plasticity ◽

Equilibrium Conditions ◽

Petch Relationship ◽

Proposed Model ◽

Constitutive Formulation ◽

Strain Gradient Plasticity Theory

The Hall-Petch relationship in metals is investigated using the strain gradient plasticity theory within the finite deformation framework. For this purpose, the thermodynamically consistent constitutive formulation for the coupled thermomechanical gradient-enhanced plasticity model is developed. The corresponding finite element method is performed to investigate the characteristics of the Hall-Petch relationship in metals. The proposed model is established based on an extra Helmholtz-type partial differential equation, and the nonlocal quantity is calculated in a coupled method based on the equilibrium conditions. An excellent agreement between the simulation results and the test data is resulted in the Hall-Petch graph. Furthermore, it is observed that the Hall-Petch constants do not remain unchanged but vary with the strain level.

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