Singularities at Grain Triple Junctions in Two-Dimensional Polycrystals With Cubic and Orthotropic Grains

Stress singularities at grain triple junctions are evaluated for various asymmetric grain boundary configurations and random orientations of cubic and orthotropic grains. The analysis is limited to elastic plane-strain deformation and carried out using the Eshelby-Stroh formalism for anisotropic elasticity. For both the cubic and orthotropic grains, the most singular configuration corresponds to the fully symmetric case with grain boundaries 120 deg apart, and with symmetric orientations of the material axes. The magnitude of the singularities are obtained for several engineering polycrystals.

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Two-Dimensional Grain Growth Simulation by Local Curvature Multi-Vertex Model

Materials Science Forum ◽

10.4028/www.scientific.net/msf.715-716.551 ◽

2012 ◽

Vol 715-716 ◽

pp. 551-556 ◽

Cited By ~ 3

Author(s):

Teruyuki Tamaki ◽

Kenichi Murakami ◽

Hotaka Homma ◽

Kohsaku Ushioda

Keyword(s):

Grain Boundary ◽

Boundary Energy ◽

Two Dimensional ◽

Vertex Model ◽

Triple Junctions ◽

Local Curvature ◽

Misorientation Distribution ◽

Grain Boundary Character ◽

Random Microstructure ◽

Physical Principles

A local curvature multi-vertex model was developed. This model is the straightforward two-dimensional topological network model based on the physical principles which are the curvatures of grain boundaries and the grain boundary tensions at triple junctions. The model was applied to the artificial random microstructure under some conditions of grain boundary characters. The misorientation distribution was changed very little under constant grain boundary energy and mobility, but it was change much under grain boundary character dependent on misorientation. Therefore, in order to discuss actual textures, it is important to take grain boundary characters into account.

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Displacements and Stress Functions of Straight Dislocations and Line Forces in Anisotropic Elasticity: A New Derivation and Its Relation to the Integral Formalism

Symmetry ◽

10.3390/sym13091721 ◽

2021 ◽

Vol 13 (9) ◽

pp. 1721

Author(s):

Markus Lazar

Keyword(s):

Plane Strain ◽

Stress Function ◽

Function Fields ◽

Three Dimensional ◽

Anisotropic Elasticity ◽

Green Tensor ◽

Two Dimensional ◽

Integral Formalism ◽

Stress Functions ◽

Generalized Plane Strain

The displacement and stress function fields of straight dislocations and lines forces are derived based on three-dimensional anisotropic incompatible elasticity. Using the two-dimensional anisotropic Green tensor of generalized plane strain, a Burgers-like formula for straight dislocations and body forces is derived and its relation to the solution of the displacement and stress function fields in the integral formalism is given. Moreover, the stress functions of a point force are calculated and the relation to the potential of a Dirac string is pointed out.

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The finite elastic plane strain deformation of a mooney-rivlin body

International Journal of Engineering Science ◽

10.1016/0020-7225(64)90018-7 ◽

1964 ◽

Vol 2 (4) ◽

pp. 405-411

Author(s):

P.J. Blatz

Keyword(s):

Plane Strain ◽

Elastic Plane ◽

Plane Strain Deformation

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The evolution of stress intensity factors in the propagation of two dimensional cracks

European Journal of Applied Mathematics ◽

10.1017/s0956792500004265 ◽

2000 ◽

Vol 11 (5) ◽

pp. 453-471 ◽

Cited By ~ 1

Author(s):

AVNER FRIEDMAN ◽

BEI HU ◽

JUAN J. L. VELAZQUEZ

Keyword(s):

Stress Intensity ◽

Elastic Medium ◽

Plane Strain ◽

Asymptotic Expansions ◽

Stress Intensity Factors ◽

Matched Asymptotic Expansions ◽

Two Dimensional ◽

Intensity Factors ◽

Plane Strain Deformation ◽

Isotropic Elastic Medium

The aim of this paper is to describe a technique based on matched asymptotic expansions that allows us to derive the variation of the stress intensity factors in a homogeneous isotropic elastic medium under plane strain deformation. The case of antiplane shearing is also considered.

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Generalized plane strain analysis of a bimaterial composite containing a free surface normal to the interface

Journal of Materials Research ◽

10.1557/jmr.1991.2609 ◽

1991 ◽

Vol 6 (12) ◽

pp. 2609-2622 ◽

Cited By ~ 3

Author(s):

V.K. Tewary ◽

R.D. Kriz

Keyword(s):

Free Surface ◽

Grain Boundary ◽

Integral Representation ◽

Plane Strain ◽

Displacement Field ◽

Strain Analysis ◽

Elastic Plane ◽

Surface Normal ◽

Out Of Plane ◽

Generalized Plane Strain

The elastic plane strain Green's function calculated in earlier papers is modified to account for generalized plane strain and applied to calculating the stress and the displacement field in a bimaterial composite containing a free surface normal to the interface and subjected to an out-of-plane load. The result is obtained in terms of a closed integral representation which is evaluated numerically as well as analytically. The method is applied to a cubic solid containing a Σ-5 grain boundary and to fiber-reinforced laminated composites. The singularities in the stress are identified and discussed.

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Multiphase microstructure evolution model including dislocation plasticity

Journal of Materials Research ◽

10.1557/jmr.2002.0286 ◽

2002 ◽

Vol 17 (8) ◽

pp. 1932-1940 ◽

Cited By ~ 1

Author(s):

Fabrizio Cleri ◽

Gregorio D'Agostino

Keyword(s):

Monte Carlo ◽

Grain Boundary ◽

Numerical Simulations ◽

Microstructure Evolution ◽

Evolution Model ◽

Monte Carlo Algorithm ◽

Two Dimensional ◽

Triple Junctions ◽

Multiphase Microstructure ◽

Dislocation Plasticity

We present the recent extensions of our stochastic microstructure evolution model including multiphase domain evolution and dislocation plasticity. The model was implemented by means of numerical simulations based on the velocity Monte Carlo algorithm. It describes the evolution of a two-dimensional microstructure by tracking the motion of triple junctions, i.e., the vertices where three grain boundaries (GBs) meet. GBs can be modeled as straight, curved, or discretized segments; the misorientation dependence of both grain-boundary energies and mobilities can be included to represent different textures.

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Anisotropic Elasticity

10.1093/oso/9780195074475.001.0001 ◽

1996 ◽

Cited By ~ 35

Author(s):

T. T. C. Ting

Keyword(s):

Composite Materials ◽

Elastic Constants ◽

Piezoelectric Materials ◽

Anisotropic Materials ◽

Anisotropic Elasticity ◽

Stress Singularities ◽

Comprehensive Survey ◽

The Subject ◽

Key Topics ◽

First Time

Anisotropic Elasticity offers for the first time a comprehensive survey of the analysis of anisotropic materials that can have up to twenty-one elastic constants. Focusing on the mathematically elegant and technically powerful Stroh formalism as a means to understanding the subject, the author tackles a broad range of key topics, including antiplane deformations, Green's functions, stress singularities in composite materials, elliptic inclusions, cracks, thermo-elasticity, and piezoelectric materials, among many others. Well written, theoretically rigorous, and practically oriented, the book will be welcomed by students and researchers alike.

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