scholarly journals Strain gradient crystal plasticity with evolving length scale: Application to voided irradiated materials

2019 ◽  
Vol 77 ◽  
pp. 103768 ◽  
Author(s):  
J.M. Scherer ◽  
J. Besson ◽  
S. Forest ◽  
J. Hure ◽  
B. Tanguy
Keyword(s):  
Crystal Plasticity ◽  
Strain Gradient ◽  
Length Scale

Scale-Dependent Crack Modeling for Investigation the Effect of Geometrically Necessary Dislocations in Micro/Nano Grain Size of Copper

2016 ◽  
Vol 15 ◽  
pp. 1-16 ◽  
Author(s):  
Amin Zaami ◽  
Ali Shokuhfar
Keyword(s):  
Grain Size ◽  
Stress Concentration ◽  
Strain Gradient ◽  
Stress Concentration Factor ◽  
Size Effects ◽  
Crack Tip ◽  
Length Scale ◽  
State Variables ◽  
Dependent Model ◽  
Homogeneous Strain

In this study, a scale-dependent model is employed to investigate the size effects of copper on the behavior of the crack-tip. This model includes the homogeneous and non-homogeneous strain hardening based on the wavelet interpretation of size effect. Introducing additional micro/nano structural considerations together with decreasing grain size, different size effects can be obtained. As the size dependency is not taken into account in conventional plasticity, an enhanced theory which is related to the strain gradient introduces a length scale will give more realistic representations of state variables near the crack-tip. Accordingly, the contribution of geometrically necessary dislocations (GNDs) activity on strengthening and stress concentration factor is identified in the crack-tip. Finally, the affected zone which is dominated by presence of GNDs is identified

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.

A Study on Length Scale Effects on Indentation Delamination of Thin Films

2004 ◽  
Author(s):  
W. Li ◽  
S. Qu ◽  
T. Siegmund ◽  
Y. Huang
Keyword(s):  
Plastic Deformation ◽  
Strain Gradient ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Scale Effects ◽  
Scale Dependence ◽  
Zone Model ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Elastic Substrates

Simulations of indentation delamination of ductile films on elastic substrates are performed. A cohesive zone model accounts for initiation and growth of interface delaminations and a strain gradient plasticity framework for the length scale dependence of plastic deformation. With the cohesive zone model and the strain gradient formulation two length scales are introduced in to the analysis.

Torsional Vibration Analysis of Carbon Nanotubes Based on the Strain Gradient Theory and Molecular Dynamic Simulations

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
R. Ansari ◽  
R. Gholami ◽  
S. Ajori
Keyword(s):  
Carbon Nanotubes ◽  
Boundary Conditions ◽  
Molecular Dynamic ◽  
Strain Gradient ◽  
Torsional Vibration ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Molecular Dynamic Simulations ◽  
Dynamic Simulations

In the current study, the torsional vibration of carbon nanotubes is examined using the strain gradient theory and molecular dynamic simulations. The model developed based on this gradient theory enables us to interpret size effect through introducing material length scale parameters. The model accommodates the modified couple stress and classical models when two or all material length scale parameters are set to zero, respectively. Using Hamilton's principle, the governing equation and higher-order boundary conditions of carbon nanotubes are obtained. The generalized differential quadrature method is utilized to discretize the governing differential equation of the present model along with two boundary conditions. Then, molecular dynamic simulations are performed for a series of carbon nanotubes with different aspect ratios and boundary conditions, the results of which are matched with those of the present strain gradient model to extract the appropriate value of the length scale parameter. It is found that the present model with properly calibrated value of length scale parameter has a good capability to predict the torsional vibration behavior of carbon nanotubes.

scholarly journals A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

2019 ◽  
Vol 40 (12) ◽  
pp. 1695-1722 ◽  
Author(s):  
Lu Lu ◽  
Li Zhu ◽  
Xingming Guo ◽  
Jianzhong Zhao ◽  
Guanzhong Liu
Keyword(s):  
Strain Gradient ◽  
Scale Parameter ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Length Scale ◽  
Proposed Model ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Material Length ◽  
Nonlocal Strain Gradient

AbstractIn this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton’s principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.

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