Continuum Dislocation Dynamics Based on the Second Order Alignment Tensor

2014 ◽  
Vol 1651 ◽  
Author(s):  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Evolution Equations ◽  
Continuum Theory ◽  
Orientation Distribution ◽  
Line Length ◽  
Second Order ◽  
Dislocation Dynamics ◽  
Alignment Tensor ◽  
Length Changes ◽  
Edge Dislocations

ABSTRACTIn the current paper we present a continuum theory of dislocations based on the second-order alignment tensor in conjunction with the classical dislocation density tensor (Kröner-Nye-tensor) and a scalar dislocation curvature measure. The second-order alignment tensor is a symmetric second order tensor characterizing the orientation distribution of dislocations in elliptic form. It is closely connected to total densities of screw and edge dislocations introduced in the literature. The scalar dislocation curvature density is a conserved quantity the integral of which represents the total number of dislocations in the system. The presented evolution equations of these dislocation density measures partly parallel earlier developed theories based on screw-edge decompositions but handle line length changes and segment reorientation consistently. We demonstrate that the presented equations allow predicting the evolution of a single dislocation loop in a non-trivial velocity field.

Three-Dimensional Continuum Dislocation Dynamics Simulations of Dislocation Structure Evolution in Bending of a Micro-Beam

MRS Advances ◽  
2016 ◽  
Vol 1 (24) ◽  
pp. 1791-1796 ◽  
Author(s):  
Alireza Ebrahimi ◽  
Thomas Hochrainer
Keyword(s):  
Dislocation Density ◽  
Slip System ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Dislocation Dynamics ◽  
Structure Evolution ◽  
Internal Variables ◽  
Plastic Shear ◽  
Continuum Dislocation Dynamics ◽  
Dynamics Simulations

ABSTRACTA persistent challenge in multi-scale modeling of materials is the prediction of plastic materials behavior based on the evolution of the dislocation state. An important step towards a dislocation based continuum description was recently achieved with the so called continuum dislocation dynamics (CDD). CDD captures the kinematics of moving curved dislocations in flux-type evolution equations for dislocation density variables, coupled to the stress field via average dislocation velocity-laws based on the Peach-Koehler force. The lowest order closure of CDD employs three internal variables per slip system, namely the total dislocation density, the classical dislocation density tensor and a so called curvature density.In the current work we present a three-dimensional implementation of the lowest order CDD theory as a materials sub-routine for Abaqus®in conjunction with the crystal plasticity framework DAMASK. We simulate bending of a micro-beam and qualitatively compare the plastic shear and the dislocation distribution on a given slip system to results from the literature. The CDD simulations reproduce a zone of reduced plastic shear close to the surfaces and dislocation pile-ups towards the center of the beam, which have been similarly observed in discrete dislocation simulations.

TEM investigation of defect reduction and etch pit formation in GaN

2003 ◽  
Vol 798 ◽  
Author(s):  
Angelika Vennemann ◽  
Jens Dennemarck ◽  
Roland Kröger ◽  
Tim Böttcher ◽  
Detlef Hommel ◽  
...  
Keyword(s):  
Electron Microscopy ◽  
Dislocation Density ◽  
Line Tension ◽  
Threading Dislocations ◽  
Dislocation Loops ◽  
Etch Pits ◽  
Defect Reduction ◽  
Transmission Electron ◽  
Order Of Magnitude ◽  
Edge Dislocations

ABSTRACTGaN samples of this study were chemically wet etched to gain easier access to the dislocation sturcture. The scanning electron microscopy and transmission electron microscopy investigations revealed four different types of etch pits. After brief etching, several dislocations with screw component showed large etch pits, which may be correlated with the core of the screw dislocation. By means of SiNx micromasking the dislocation density could be reduced by more than one order of magnitude. The reduction of threading dislocations in the SiNx region in GaN grown on 〈0001〉 sapphire is due to bending of the threading dislocations into the {0001} plane, such that they form dislocation loops if they meet dislocations with opposite Burgers vectors. Accordingly, the achievable reduction of the dislocation density is limited by the probability that these dislocations interact. Edge dislocations bend more easily on account of their low line tension. This results in a preferential bending and reduction of dislocations with edge character.

Plastic Ploughing of a Sinusoidal Asperity on a Rough Surface

2015 ◽  
Vol 82 (7) ◽  
Author(s):  
H. Song ◽  
R. J. Dikken ◽  
L. Nicola ◽  
E. Van der Giessen
Keyword(s):  
Friction Stress ◽  
Dislocation Dynamics ◽  
Two Dimensional ◽  
Unit Process ◽  
Contact Models ◽  
Self Similar ◽  
Dynamics Simulations ◽  
Micrometer Scale ◽  
Edge Dislocations ◽  
Flat Contact

Part of the friction between two rough surfaces is due to the interlocking between asperities on opposite surfaces. In order for the surfaces to slide relative to each other, these interlocking asperities have to deform plastically. Here, we study the unit process of plastic ploughing of a single micrometer-scale asperity by means of two-dimensional dislocation dynamics simulations. Plastic deformation is described through the generation, motion, and annihilation of edge dislocations inside the asperity as well as in the subsurface. We find that the force required to plough an asperity at different ploughing depths follows a Gaussian distribution. For self-similar asperities, the friction stress is found to increase with the inverse of size. Comparison of the friction stress is made with other two contact models to show that interlocking asperities that are larger than ∼2 μm are easier to shear off plastically than asperities with a flat contact.

Subharmonic resonance of short internal standing waves by progressive surface waves

1996 ◽  
Vol 321 ◽  
pp. 217-233 ◽  
Author(s):  
D. F. Hill ◽  
M. A. Foda
Keyword(s):  
Surface Wave ◽  
Internal Wave ◽  
Surface Waves ◽  
Internal Waves ◽  
Growth Rates ◽  
Evolution Equations ◽  
Standing Waves ◽  
Second Order ◽  
Inviscid Limit ◽  
Initial Growth

Experimental evidence and a theoretical formulation describing the interaction between a progressive surface wave and a nearly standing subharmonic internal wave in a two-layer system are presented. Laboratory investigations into the dynamics of an interface between water and a fluidized sediment bed reveal that progressive surface waves can excite short standing waves at this interface. The corresponding theoretical analysis is second order and specifically considers the case where the internal wave, composed of two oppositely travelling harmonics, is much shorter than the surface wave. Furthermore, the analysis is limited to the case where the internal waves are small, so that only the initial growth is described. Approximate solution to the nonlinear boundary value problem is facilitated through a perturbation expansion in surface wave steepness. When certain resonance conditions are imposed, quadratic interactions between any two of the harmonics are in phase with the third, yielding a resonant triad. At the second order, evolution equations are derived for the internal wave amplitudes. Solution of these equations in the inviscid limit reveals that, at this order, the growth rates for the internal waves are purely imaginary. The introduction of viscosity into the analysis has the effect of modifying the evolution equations so that the growth rates are complex. As a result, the amplitudes of the internal waves are found to grow exponentially in time. Physically, the viscosity has the effect of adjusting the phase of the pressure so that there is net work done on the internal waves. The growth rates are, in addition, shown to be functions of the density ratio of the two fluids, the fluid layer depths, and the surface wave conditions.

scholarly journals Second order evolution equations with parameter

1994 ◽  
Vol 59 (1) ◽  
pp. 41-52
Author(s):  
Jan Bochenek ◽  
Teresa Winiarska
Keyword(s):  
Evolution Equations ◽  
Second Order
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