On strain gradients and size-dependent hardening descriptions in crystal plasticity frameworks

2006 ◽  
Vol 12 (5) ◽  
pp. 407-411 ◽  
Author(s):  
Chung -Souk Han ◽  
Franz Roters ◽  
Dierk Raabe
Keyword(s):  
Crystal Plasticity ◽  
Strain Gradients ◽  
Size Dependent

scholarly journals Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1935 ◽  
Author(s):  
Mohammad Malikan ◽  
Victor A. Eremeyev ◽  
Krzysztof Kamil Żur
Keyword(s):  
Material Properties ◽  
Gradient Elasticity ◽  
Small Scale ◽  
Stability Equation ◽  
Strain Gradients ◽  
Size Dependent ◽  
Different Types ◽  
Dependent Property ◽  
The Stability ◽  
Transverse Deflection

We investigated the stability of an axially loaded Euler–Bernoulli porous nanobeam considering the flexomagnetic material properties. The flexomagneticity relates to the magnetization with strain gradients. Here we assume both piezomagnetic and flexomagnetic phenomena are coupled simultaneously with elastic relations in an inverse magnetization. Similar to flexoelectricity, the flexomagneticity is a size-dependent property. Therefore, its effect is more pronounced at small scales. We merge the stability equation with a nonlocal model of the strain gradient elasticity. The Navier sinusoidal transverse deflection is employed to attain the critical buckling load. Furthermore, different types of axial symmetric and asymmetric porosity distributions are studied. It was revealed that regardless of the high magnetic field, one can realize the flexomagnetic effect at a small scale. We demonstrate as well that for the larger thicknesses a difference between responses of piezomagnetic and piezo-flexomagnetic nanobeams would not be significant.

Lattice Rotation Patterns and Strain Gradient Effects in Face-Centered-Cubic Single Crystals Under Spherical Indentation

2015 ◽  
Vol 82 (6) ◽  
Author(s):  
Y. F. Gao ◽  
B. C. Larson ◽  
J. H. Lee ◽  
L. Nicola ◽  
J. Z. Tischler ◽  
...  
Keyword(s):  
Single Crystals ◽  
Crystal Plasticity ◽  
Strain Gradient ◽  
Lattice Rotation ◽  
Spherical Indentation ◽  
Strain Gradients ◽  
Discrete Dislocation ◽  
Rotation Field ◽  
Strain Gradient Effects ◽  
Gradient Effects

Strain gradient effects are commonly modeled as the origin of the size dependence of material strength, such as the dependence of indentation hardness on contact depth and spherical indenter radius. However, studies on the microstructural comparisons of experiments and theories are limited. First, we have extended a strain gradient Mises-plasticity model to its crystal plasticity version and implemented a finite element method to simulate the load–displacement response and the lattice rotation field of Cu single crystals under spherical indentation. The strain gradient simulations demonstrate that the forming of distinct sectors of positive and negative angles in the lattice rotation field is governed primarily by the slip geometry and crystallographic orientations, depending only weakly on strain gradient effects, although hardness depends strongly on strain gradients. Second, the lattice rotation simulations are compared quantitatively with micron resolution, three-dimensional X-ray microscopy (3DXM) measurements of the lattice rotation fields under 100 mN force, 100 μm radius spherical indentations in 〈111〉, 〈110〉, and 〈001〉 oriented Cu single crystals. Third, noting the limitation of continuum strain gradient crystal plasticity models, two-dimensional discrete dislocation simulation results suggest that the hardness in the nanocontact regime is governed synergistically by a combination of strain gradients and source-limited plasticity. However, the lattice rotation field in the discrete dislocation simulations is found to be insensitive to these two factors but to depend critically on dislocation obstacle densities and strengths.

Fracture Mechanics Analysis of Size-Dependent Piezoelectric Solids under a Thermal Load

2017 ◽  
Vol 754 ◽  
pp. 165-168
Author(s):  
Jan Sladek ◽  
Vladimir Sladek ◽  
Michael Wünsche ◽  
Choon Lai Tan
Keyword(s):  
Strain Gradient ◽  
Thermal Load ◽  
Heat Conduction Problem ◽  
Electric Displacement ◽  
The Finite Element Method ◽  
Governing Equations ◽  
Strain Gradients ◽  
Size Dependent ◽  
Piezoelectric Solids ◽  
Order Stress

General 2D boundary value problems of piezoelectric nanosized structures with cracks under a thermal load are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nanosized structures is described by the strain-gradient effect. The strain gradients are considered in the constitutive equations for electric displacement and the high-order stress tensor. For this model, the governing equations are derived with the corresponding boundary conditions using the variational principle. Uncoupled thermoelasticity is considered, thus, the heat conduction problem is analyzed independently of the mechanical fields in the first step. A numerical example is presented and discussed to demonstrate the effects of the strain-gradient.

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