scholarly journals Analytical prediction of yield stress and strain hardening in a strain gradient plasticity material reinforced by small elastic particles

2022 ◽  
pp. 103200
Author(s):  
Philip Croné ◽  
Peter Gudmundson ◽  
Jonas Faleskog
Keyword(s):  
Strain Hardening ◽  
Yield Stress ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Stress And Strain ◽  
Analytical Prediction ◽  
Gradient Plasticity ◽  
Elastic Particles

scholarly journals Size Scaling of Plastic Deformation in Simple Shear: Fractional Strain-Gradient Plasticity and Boundary Effects in Conventional Strain-Gradient Plasticity

2020 ◽  
Vol 87 (3) ◽  
Author(s):  
Carl F. O. Dahlberg ◽  
Michael Ortiz
Keyword(s):  
Boundary Condition ◽  
Yield Stress ◽  
Simple Shear ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Scaling Exponent ◽  
Gradient Plasticity ◽  
Size Scaling ◽  
Model Extension ◽  
Shear Problem

Abstract A recently developed model based on fractional derivatives of plastic strain is compared with conventional strain-gradient plasticity (SGP) models. Specifically, the experimental data and observed model discrepancies in the study by Mu et al. (2016, “Dependence of Confined Plastic Flow of Polycrystalline Cu Thin Films on Microstructure,” MRS Com. Res. Let. 20, pp. 1–6) are considered by solving the constrained simple shear problem. Solutions are presented both for a conventional SGP model and a model extension introducing an energetic interface. The interface allows us to relax the Dirichlet boundary condition usually assumed to prevail when solving this problem with the SGP model. We show that the particular form of a relaxed boundary condition does not change the underlying size scaling of the yield stress and consequently does not resolve the scaling issue. Furthermore, we show that the fractional strain-gradient plasticity model predicts a yield stress with a scaling exponent that is equal to the fractional order of differentiation.

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.

Experimental Verification of the Strain-Gradient Plasticity Model for Indentation

2005 ◽  
Vol 20 (11) ◽  
pp. 3150-3156
Author(s):  
Linmao Qian ◽  
Hui Yang ◽  
Minhao Zhu ◽  
Zhongrong Zhou
Keyword(s):  
Size Effect ◽  
Yield Stress ◽  
Strain Gradient ◽  
Indentation Size Effect ◽  
Linear Increase ◽  
Strain Gradient Plasticity ◽  
Plasticity Model ◽  
Gradient Plasticity ◽  
Indentation Size ◽  
Tensile Yield Stress

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.

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.

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