scholarly journals A dislocation-based model for twin growth within and across grains

2018 ◽  
Vol 474 (2210) ◽  
pp. 20170709 ◽  
Author(s):  
J. T. Lloyd
Keyword(s):  
Grain Boundaries ◽  
Elastic Solid ◽  
Computational Method ◽  
Reasonable Approximation ◽  
Analytical Approximations ◽  
Statics And Dynamics ◽  
Discrete Dislocations ◽  
Twin Growth ◽  
Twin Thickness ◽  
Misorientation Angles

A computational method is presented for representing twins via two-dimensional dislocation statics in an isotropic elastic solid. The method is compared with analytical approximations of twin shape and is used to study how twins evolve within grains subjected to an arbitrary external shear stress. Twin transfer across grains is then studied using the same computational method. The dislocation-based model for twin growth gives the following dependencies: twin thickness increases linearly with grain size and external stress, and increases substantially as the grain is able to traverse multiple grain boundaries with low misorientation angles; the model also predicts that twin transfer becomes less prominent across grain boundaries with high misorientation angles. These predictions are consistent with experimentally measured extension twin growth in magnesium polycrystals. This study suggests that representing twins via discrete dislocations provides a physically reasonable approximation of twinning that can be naturally incorporated into existing dislocation statics and dynamics codes.

Recursive Linearization of Multibody Dynamics and Application to Control Design

1990 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Linear Equations ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

Abstract The non-linear equations of motion in multi-body dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

Using the Explicit Dynamic Method to Simulate Pile Dynamical Driving Process

2010 ◽  
Vol 163-167 ◽  
pp. 366-371
Author(s):  
Jian Bing Lv ◽  
He Lin Fu ◽  
Hua Zhi Li ◽  
Zhe Liu
Keyword(s):  
Method Development ◽  
Elastic Solid ◽  
Computational Method ◽  
Dynamical Analysis ◽  
Pile Driving ◽  
Past Study ◽  
Analysis Method ◽  
The Past ◽  
Explicit Dynamic ◽  
Dynamical Stress

The dynamic pile driving process is so complex that till now the analysis on the process had been focusing on the filed test or laboratory test. However, the past study about the dynamic process is a time consuming one; with the computational method development, the numerical simulation on this process is possible. In this paper, explicit dynamical analysis method is adopted, the pile is simulated using the elastic solid element, two computational cases are considered and finally the pile driving process dynamical stress is studied.

A computational method for earthquake cycles within anisotropic media

2019 ◽  
Vol 219 (2) ◽  
pp. 816-833 ◽  
Author(s):  
Maricela Best Mckay ◽  
Brittany A Erickson ◽  
Jeremy E Kozdon
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Elastic Solid ◽  
Elliptic Partial Differential Equation ◽  
Computational Method ◽  
Parameter Study ◽  
Time Step ◽  
Time Stepping ◽  
Static Elasticity ◽  
Earthquake Cycles

SUMMARY We present a numerical method for the simulation of earthquake cycles on a 1-D fault interface embedded in a 2-D homogeneous, anisotropic elastic solid. The fault is governed by an experimentally motivated friction law known as rate-and-state friction which furnishes a set of ordinary differential equations which couple the interface to the surrounding volume. Time enters the problem through the evolution of the ordinary differential equations along the fault and provides boundary conditions for the volume, which is governed by quasi-static elasticity. We develop a time-stepping method which accounts for the interface/volume coupling and requires solving an elliptic partial differential equation for the volume response at each time step. The 2-D volume is discretized with a second-order accurate finite difference method satisfying the summation-by-parts property, with boundary and fault interface conditions enforced weakly. This framework leads to a provably stable semi-discretization. To mimic slow tectonic loading, the remote side-boundaries are displaced at a slow rate, which eventually leads to earthquake nucleation at the fault. Time stepping is based on an adaptive, fourth-order Runge–Kutta method and captures the highly varying timescales present. The method is verified with convergence tests for both the orthotropic and fully anisotropic cases. An initial parameter study reveals regions of parameter space where the systems experience a bifurcation from period one to period two behaviour. Additionally, we find that anisotropy influences the recurrence interval between earthquakes, as well as the emergence of aseismic transients and the nucleation zone size and depth of earthquakes.

From meandering to straight grain boundaries: Improving the structures of artificially induced grain boundaries in superconducting YBa2Cu3Oy bicrystals

1997 ◽  
Vol 12 (11) ◽  
pp. 3029-3035 ◽  
Author(s):  
Xiao-Feng Zhang ◽  
Volk R. Todt ◽  
Dean J. Miller
Keyword(s):  
Thin Film ◽  
Grain Boundaries ◽  
Film Deposition ◽  
Ybco Bulk ◽  
Transmission Electron ◽  
Ybco Superconductors ◽  
Film Deposition Rate ◽  
Melt Texture ◽  
Key Aspects ◽  
Misorientation Angles

This paper presents several key aspects of our approach to preparing artificially induced [001] tilt grain boundaries (GB's) with uniform, well-defined structures in YBa2Cu3Oy (YBCO) superconductors. GB structures formed in thin film and bulk bicrystals, respectively, will be compared. In YBCO thin film bicrystals, meandering rather than planar GB's are formed. Using a low film deposition rate has been demonstrated to reduce the magnitude of meander significantly, but complete elimination of the meander has not yet been accomplished. Thus, we have developed a dual-seeded-melt-texture process to produce uniform, planar GB's with controllable misorientation angles in YBCO bulk bicrystals. Transmission electron microscopy (TEM) studies reveal a remarkably planar and simple configuration on different length scales. Such a simple structure allows for an insightful interpretation of transport behavior across individual GB's.

Characterization of Zinalco Alloy Superplastically Deformed Using Orientation Imaging Microscopy

2009 ◽  
Vol 1242 ◽  
Author(s):  
Ramos A. Mitsuo ◽  
Martínez F. Elizabeth ◽  
Negrete S. Jesús ◽  
Torres-Villaseñor G.
Keyword(s):  
Grain Size ◽  
Grain Boundary ◽  
Grain Boundaries ◽  
Superplastic Deformation ◽  
Orientation Imaging Microscopy ◽  
Grain Boundary Sliding ◽  
Boundary Misorientation ◽  
Average Grain Size ◽  
Grain Boundary Misorientation ◽  
Misorientation Angles

ABSTRACTZinalco alloy (Zn-21mass%Al-2mass%Cu) specimens were deformed superplastically with a strain rate (ε) of 1×10-3 s-1 at homologous temperature (TH) of 0.68 (5 ). It was observed neck formation that indicate nonhomegeneus deformation. Grain size and grain boundaries misorientation changes, due superplastic deformation, were characterized by Orientation Imagining Microscopy (OIM) technique. It was studied three regions in deformed specimens and the results were compared with the results for a specimen without deformation. Average grain size of 1 mm was observed in non-deformed specimen and a fraction of 82% for grain boundary misorientation angles with a grain boundaries angles between 15° and 55° was found. For deformed specimen, the fraction of angles between 15° and 55° was decreced to average value of 75% and fractions of low angle (<5°) and high angle (>55°) misorientations were 10% and 15% respectively. The grain size and high fraction of grain boundary misorientation angles between 15° and 55° observed in the alloy without deformation, are favorable for grain rotation and grain boundary sliding (GBS) procces. The changes observed in the fraction of favorable grain boundary angles during superplastic deformation, shown that the superplastic capacity of Zinalco was reduced with the deformation.

scholarly journals The five-dimensional parameter space of grain boundaries

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150442 ◽  
Author(s):  
A. P. Sutton ◽  
E. P. Banks ◽  
A. R. Warwick
Keyword(s):  
Grain Boundaries ◽  
Degrees Of Freedom ◽  
Geodesic Distance ◽  
Rotational Symmetry ◽  
Boundary Misorientation ◽  
Dimensional Parameter ◽  
Orthogonal Subspace ◽  
The Mean ◽  
Misorientation Angles ◽  
Three Degrees Of Freedom

To specify a grain boundary at a macroscopic length scale requires the specification of five degrees of freedom. We use a specification in which three degrees of freedom associated with the boundary misorientation are in an orthogonal subspace from two associated with the mean boundary plane. By using Rodrigues vectors to describe rotations, we show how paths through these subspaces may be characterized. Some of these paths correspond to physical processes involving grain boundaries during microstructural evolution. Exploiting the orthogonality of the subspaces, a metric to measure ‘distance’ between two boundaries is defined in terms of the minimum set of rotations required to map one boundary on to the other. We compare our metric with others that have appeared. The existence of rotational symmetry in face-centred cubic crystals leads to as many as 2304 equivalent specifications of a boundary. We illustrate this multiplicity of descriptions for the (111) twin and a more general boundary. We present an algorithm to evaluate the geodesic distance between two boundaries, and apply it to identify the path along which the distance between these two boundaries is minimized. In general, the shortest path does not involve descriptions of boundary misorientations with the smallest misorientation angles.

scholarly journals Particularities of changes in internal structure of nanocrystalline Ni under mechanical loading

2019 ◽  
Vol 221 ◽  
pp. 01025
Author(s):  
Dmitrij Kryzhevich ◽  
Aleksandr Korchuganov ◽  
Konstantin Zolnikov
Keyword(s):  
Grain Boundaries ◽  
Triple Junction ◽  
Shear Loading ◽  
Stacking Fault ◽  
Grain Sizes ◽  
Compressive Stresses ◽  
Nucleation Mechanisms ◽  
Constrained Conditions ◽  
Misorientation Angles ◽  
Nanocrystalline Sample

Molecular dynamics study of the plasticity nucleation mechanisms in a Ni nanocrystalline sample under shear loading in the constrained conditions was carried out. The studied Ni sample consisted of nine grains of the same size with large misorientation angles relative to each other. In one of the directions, grippers were simulated, to which compressive forces and shear with a constant velocity were applied. In two other directions, periodic boundary conditions were used. It is shown that plasticity nucleation occurs in the region of the triple junction. At the same time, in the region of the triple junction, in the zone of which the stacking fault will be formed, tensile stresses are realized along one of the adjacent grain boundaries, and compressive stresses occur along the other. An increase in stresses in the triple junction zone leads to the formation of a stacking fault, which moves to the volume of one of the grains. Another mechanism of plasticity in nanocrystalline nickel is the migration of grain boundaries, which leads to a significant change in grain sizes.

Recursive Linearization of Multibody Dynamics and Application to Control Design

1994 ◽  
Vol 116 (2) ◽  
pp. 445-451 ◽  
Author(s):  
Tsung-Chieh Lin ◽  
K. Harold Yae
Keyword(s):  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Control Design ◽  
Numerical Differentiation ◽  
Difficult Problem ◽  
General Purpose ◽  
Computational Method ◽  
Computational Error ◽  
Dynamics Modeling ◽  
Analytical Approximations

The nonlinear equations of motion in multibody dynamics pose a difficult problem in linear control design. It is therefore desirable to have linearization capability in conjunction with a general-purpose multibody dynamics modeling technique. A new computational method for linearization is obtained by applying a series of first-order analytical approximations to the recursive kinematic relationships. The method has proved to be computationally more efficient. It has also turned out to be more accurate because the analytical perturbation requires matrix and vector operations by circumventing numerical differentiation and other associated numerical operations that may accumulate computational error.

In-Situ 1Mev Tem and Hrem Study of the Deformation and the Transformation of Symmetrical Tilt Grain Boundaries in Ge and Si.

1993 ◽  
Vol 319 ◽  
Author(s):  
Jany. Thibault ◽  
X. Baillin ◽  
J. Pelissier ◽  
J.L. Putaux ◽  
H.M. Michaud
Keyword(s):  
Grain Boundaries ◽  
Deformation Temperature ◽  
In Situ Tem ◽  
Final Structure ◽  
Different Types ◽  
Symmetrical Tilt ◽  
Misorientation Angles

AbstractThe evolution under deformation of symmetrical GBs in Si and Ge has been studied both by in-situ TEM and HREM. The influence of the strain conditions (tension or compression) on the final structure through the entrance of different types of dislocations will be discussed. The influence of the deformation temperature on the multiplicity of the structures has been observed in a particular range of misorientation angles.

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