Analysis of the Deformation of Cosserat Elastic Shells Using the Dislocation Density Tensor

2017 ◽  
pp. 13-30
Author(s):  
Mircea Bîrsan ◽  
Patrizio Neff
Keyword(s):  
Dislocation Density ◽  
Elastic Shells ◽  
Density Tensor ◽  
Dislocation Density Tensor

Dislocation core investigation by geometric phase analysis and the dislocation density tensor

2008 ◽  
Vol 41 (3) ◽  
pp. 035408 ◽  
Author(s):  
J Kioseoglou ◽  
G P Dimitrakopulos ◽  
Ph Komninou ◽  
Th Karakostas ◽  
E C Aifantis
Keyword(s):  
Dislocation Density ◽  
Phase Analysis ◽  
Geometric Phase ◽  
Dislocation Core ◽  
Density Tensor ◽  
Geometric Phase Analysis ◽  
Dislocation Density Tensor

A complete list of invariants for defective crystals

1991 ◽  
Vol 432 (1886) ◽  
pp. 341-365 ◽  
Keyword(s):  
Dislocation Density ◽  
Classical Theory ◽  
Infinite Number ◽  
Basic Mechanism ◽  
Crystal Defects ◽  
Complete List ◽  
Density Tensor ◽  
Dislocation Density Tensor ◽  
Defective Crystals ◽  
Tensor Densities

The classical theory of continuous distributions of dislocations has traditionally focused on the Burgers’ vectors and the dislocation density tensor as descriptions of defectiveness. We prove that, generally, there is an infinite number of tensor densities with similarly descriptive properties, and that there is a functional basis for this list which strictly includes the Burgers’ vectors and dislocation density. Moreover the changes of state which preserve these densities turn out to represent slip in certain surfaces associated with crystal geometry, so that the basic mechanism of plasticity emerges naturally from abstract ideas which neither anticipate nor involve the kinematics of particular types of crystal defects.

Statistics of Internal Elastic Fields and Dislocation Density Tensor in Deformed FCC Crystals

2008 ◽  
Vol 1130 ◽  
Author(s):  
Jie Deng ◽  
Anter El-Azab ◽  
B.C. Larson
Keyword(s):  
Probability Density Function ◽  
Dislocation Density ◽  
Probability Density ◽  
Density Function ◽  
Dislocation Dynamics ◽  
Dynamics Simulation ◽  
Pair Correlations ◽  
Density Tensor ◽  
Elastic Fields ◽  
Dislocation Density Tensor

ABSTRACTThe statistics of internal elastic fields and dislocation density tensor associated with arbitrary 3D dislocation distributions have been modeled using probability density function and pair correlations. Numerical results for these quantities have been obtained for dislocation structures generated by the method of dislocation dynamics simulation.

The Weighted Burgers Vector: A Quantity for Constraining Dislocation Densities and Types Using Electron Backscatter Diffraction on 2D Sections through Crystalline Materials

2012 ◽  
Vol 715-716 ◽  
pp. 732-736 ◽  
Author(s):  
John Wheeler ◽  
Elisabetta Mariani ◽  
Sandra Piazolo ◽  
David J. Prior ◽  
P.J. Trimby ◽  
...  
Keyword(s):  
Dislocation Density ◽  
Coordinate System ◽  
Lattice Distortion ◽  
Local Lattice Distortion ◽  
Burgers Vector ◽  
Density Tensor ◽  
The Third ◽  
Third Dimension ◽  
Dislocation Density Tensor ◽  
Local Misorientation

The Weighted Burgers Vector (WBV) is defined as the sum, over all types of dislocations, of [(density of intersections of dislocation lines with a map) x (Burgers vector)]. It can be calculated, for any crystal system, solely from orientation gradients in a map view, unlike the full dislocation density tensor, which requires gradients in the third dimension. No assumption is made about gradients in the third dimension and they may be non-zero. The only assumption involved is that elastic strains are small so the lattice distortion is entirely due to dislocations. Orientation gradients can be estimated from gridded orientation measurements obtained by EBSD mapping, so the WBV can be calculated as a vector field on an EBSD map. The magnitude of the WBV gives a lower bound on the magnitude of the dislocation density tensor when that magnitude is defined in a coordinate invariant way. The direction of the WBV can constrain the types of Burgers vectors of geometrically necessary dislocations present in the microstructure, most clearly when it is broken down in terms of lattice vectors. The WBV has five advantages over other measures of local lattice distortion. 1. It is a vector and hence carries more information than any scalar measure of local misorientation. 2. It has an explicit mathematical link to the individual Burgers vectors of dislocations. 3. Since it is derived via tensor calculus, it is not dependent on the map coordinate system, in contrast to existing measures of local misorientation which are not only scalar but dependent on the coordinate system used. 4. Calculation involves no assumptions about energy minimisation. 5. The numerical differentiation involved in calculating the WBV may introduce errors, but there is a direct mathematical link to a contour integral. The net Burgers vector content of dislocations intersecting an area of a map can be simply calculated by an integration round the edge of that area, a method which is fast and complements point-by-point WBV calculations. Errors in orientation measurement will have a much smaller effect here, and dislocations can be detected which are otherwise lost in the noise of any local calculation.

scholarly journals On Plastic Dislocation Density Tensor

2019 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Dislocation Density ◽  
Density Tensor ◽  
Proper Definition ◽  
Definition Of ◽  
Dislocation Density Tensor

This letter attempts to clarify an issue regarding the proper definition of plastic dislocation density tensor. This study shows that the Ortiz’s and Berdichevsky’s plastic dislocation density tensor are equivalent with each other, but not with Kondo’s one. To fix the problem, we propose a modified version of Kondo’s plastic dislocation density tensor.

scholarly journals Dislocation Density Tensor of Thin Elastic Shells at Finite Deformation

2018 ◽  
Author(s):  
Bohua Sun
Keyword(s):  
Dislocation Density ◽  
Curvature Tensor ◽  
Finite Deformation ◽  
Middle Surface ◽  
Gauss Curvature ◽  
Riemann Curvature ◽  
Riemann Curvature Tensor ◽  
Metric Tensor ◽  
Elastic Shells ◽  
Dislocation Density Tensor

The dislocation density tensors of thin elastic shells have been formulated explicitly in terms of the Riemann curvature tensor. The formulation reveals that the dislocation density of the shells is  proportional to KA3=2, where K is the Gauss curvature and A is the determinant of metric tensor ofthe middle surface.

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