scholarly journals Strain Localization Modes within Single Crystals Using Finite Deformation Strain Gradient Crystal Plasticity

Crystals ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1235
Author(s):  
Lei Cai ◽  
Mohamed Jebahi ◽  
Farid Abed-Meraim
Keyword(s):  
Single Crystals ◽  
Crystal Plasticity ◽  
Strain Gradient ◽  
Finite Deformation ◽  
Small Deformation ◽  
Higher Order ◽  
Extended Model ◽  
Kink Bands ◽  
Dissipative Effects ◽  
Slip Bands

The present paper aims at providing a comprehensive investigation of the abilities and limitations of strain gradient crystal plasticity (SGCP) theories in capturing different kinds of localization modes in single crystals. To this end, the small deformation Gurtin-type SGCP model recently proposed by the authors, based on non-quadratic defect energy and the uncoupled dissipation assumption, is extended to finite deformation. The extended model is then applied to simulate several single crystal localization problems with different slip system configurations. These configurations are chosen in such a way as to obtain idealized slip and kink bands as well as general localization bands, i.e., with no particular orientation with respect to the initial crystallographic directions. The obtained results show the good abilities of the applied model in regularizing various kinds of localization bands, except for idealized slip bands. Finally, the model is applied to reproduce the complex localization behavior of single crystals undergoing single slip, where competition between kink and slip bands can take place. Both higher-order energetic and dissipative effects are considered in this investigation. For both effects, mesh-independent results are obtained, proving the good capabilities of SGCP theories in regularizing complex localization behaviors. The results associated with higher-order energetic effects are in close agreement with those obtained using a micromorphic crystal plasticity approach. Higher-order dissipative effects led to different results with dominant slip banding.

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.

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