scholarly journals Novel cloaking lamellar structures for a screw dislocation dipole, a circular Eshelby inclusion and a concentrated couple

2020 ◽  
Vol 476 (2241) ◽  
pp. 20200095
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Conformal Mapping ◽  
Screw Dislocation ◽  
Lamellar Structure ◽  
Stress Fields ◽  
Uniform Stress ◽  
Dislocation Dipole ◽  
Lamellar Structures ◽  
Eshelby Inclusion ◽  
Mapping Techniques ◽  
Concentrated Couple

Using conformal mapping techniques, we design novel lamellar structures which cloak the influence of any one of a screw dislocation dipole, a circular Eshelby inclusion or a concentrated couple. The lamellar structure is composed of two half-planes bonded through a middle coating with a variable thickness within which is located either the dislocation dipole, the circular Eshelby inclusion or the concentrated couple. The Eshelby inclusion undergoes either uniform anti-plane eigenstrains or uniform in-plane volumetric eigenstrains. As a result, the influence of any one of the dislocation dipole, the circular Eshelby inclusion or the concentrated couple is cloaked in that their presence will not disturb the prescribed uniform stress fields in both surrounding half-planes.

A circular Eshelby inclusion interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2019 ◽  
Vol 25 (3) ◽  
pp. 573-581 ◽  
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Conformal Mapping ◽  
Stress Distributions ◽  
Uniform Stress ◽  
Elastic Deformations ◽  
Surrounding Matrix ◽  
Eshelby Inclusion ◽  
The Matrix ◽  
Uniform Stress Field ◽  
Mapping Techniques

Using conformal mapping techniques and analytic continuation, we prove that when subjected to anti-plane elastic deformations, a non-parabolic open inhomogeneity continues to admit an internal uniform stress field when a circular Eshelby inclusion is placed in its vicinity and the surrounding matrix is subjected to uniform remote stresses. Explicit expressions for the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion are obtained. The internal uniform stress field is independent of the shape of the inhomogeneity and the presence of the circular Eshelby inclusion, whereas the existence of the circular Eshelby inclusion exerts a significant influence on the shape of the non-parabolic open inhomogeneity as well as on the non-uniform stress distributions in the matrix and in the circular Eshelby inclusion itself.

A hole of irregular shape interacting with a non-parabolic open inhomogeneity with internal uniform anti-plane stresses

2020 ◽  
pp. 108128652097024
Author(s):  
Xu Wang ◽  
Ping Yang ◽  
Peter Schiavone
Keyword(s):  
Free Boundary ◽  
Stress Field ◽  
Conformal Mapping ◽  
Analytic Continuation ◽  
Uniform Stress ◽  
Surrounding Matrix ◽  
Parabolic Shape ◽  
Uniform Stress Field ◽  
Elastic Inhomogeneity ◽  
Mapping Techniques

We use conformal mapping techniques together with analytic continuation to show that a non-parabolic open elastic inhomogeneity continues to admit a state of uniform internal stress when a hole with closed curvilinear traction-free boundary is placed in its vicinity and the surrounding matrix is subjected to uniform remote anti-plane stresses. The internal uniform stress field inside the inhomogeneity is found to be independent of the existence of the nearby hole and the specific non-parabolic shape of the inhomogeneity. In contrast, the non-parabolic shape of the inhomogeneity is influenced solely by the existence of the nearby hole.

A New Defect in Polyethylene Single Crystals

1973 ◽  
Vol 31 ◽  
pp. 70-71
Author(s):  
E. L. Thomas ◽  
S. L. Sass
Keyword(s):  
Single Crystals ◽  
Screw Dislocation ◽  
Small Distance ◽  
Dipole Model ◽  
Dislocation Dipole ◽  
Chain Folding ◽  
Black And White ◽  
Polymer Crystal ◽  
Different Types

In polyethylene single crystals pairs of black and white lines spaced 700-3,000Å apart, parallel to the [100] and [010] directions, have been identified as microsector boundaries. A microsector is formed when the plane of chain folding changes over a small distance within a polymer crystal. In order for the different types of folds to accommodate at the boundary between the 2 fold domains, a staggering along the chain direction and a rotation of the chains in the plane of the boundary occurs. The black-white contrast from a microsector boundary can be explained in terms of these chain rotations. We demonstrate that microsectors can terminate within the crystal and interpret the observed terminal strain contrast in terms of a screw dislocation dipole model.

Displacement threshold energy change in uniform stress fields

1986 ◽  
Vol 135 (2) ◽  
pp. K113-K117
Author(s):  
V. V. Kirsanov ◽  
E. M. Kislitsina
Keyword(s):  
Threshold Energy ◽  
Energy Change ◽  
Stress Fields ◽  
Uniform Stress ◽  
Displacement Threshold

Additivity of Hardening by Nanolamellar Structure and Antiphase Domain in Ti-39at%Al Single Crystals

2008 ◽  
Vol 1086 ◽  
Author(s):  
Yuichiro Koizumi ◽  
Yoritoshi Minamino ◽  
Takayuki Tanaka ◽  
Kazuki Iwamoto
Keyword(s):  
Lamellar Structure ◽  
Antiphase Domain ◽  
Dislocation Motion ◽  
Additional Stress ◽  
Slip Direction ◽  
Prism Slip ◽  
Screw Dislocations ◽  
Lamellar Structures ◽  
Mixed Microstructure ◽  
Antiphase Domains

AbstractA mixed microstructure of antiphase domains (APD) and fine lamellar structure were introduced in a Ti-39at%Al single crystal and it was examined whether the APD hardening works even in nano-scaled lamellar structures. The hardness increases with decreasing APD size even where the L is smaller than 100 nm below which the hardening by lamellar refining saturates. The mechanism of the additivity of strengthening by APD and lamellar structure is discussed in the context of the geometries of slip direction, lamellar boundaries and APD boundaries (APDBs). For {1100}<1120> prism slip (the easiest slip system of α2-Ti3Al), the lamellar boundaries are parallel to the slip direction, and therefore they interrupt the motion of screw dislocations effectively. On the other hand, APDBs inclined from lamellar boundaries can effectively obstruct the dislocation motion regardless of the dislocation character because the shear of such APDBs results in the formation of step-like APDBs on the slip-plane and requires additional stress for dislocation motion whereas APDBs parallel to the slip direction can be sheared without forming such a step-like APDB. Accordingly, APDs and lamellar structure can contribute to the strengthening complementarily.

Internal uniform hydrostatic stresses in a three-phase non-elliptical inclusion subjected to a nearby concentrated couple

2019 ◽  
Vol 24 (9) ◽  
pp. 2931-2943 ◽  
Author(s):  
Xu Wang ◽  
Peter Schiavone
Keyword(s):  
Stress Field ◽  
Conformal Mapping ◽  
Hydrostatic Stress ◽  
Geometric Parameters ◽  
Interphase Layer ◽  
Infinite Matrix ◽  
Elliptical Inclusion ◽  
Three Phase ◽  
Uniform Hydrostatic Stress Field ◽  
Concentrated Couple

We apply conformal mapping techniques with analytic continuation to study the existence of a uniform hydrostatic stress field inside a non-elliptical inclusion bonded to an infinite matrix via a finite thickness interphase layer when the matrix is simultaneously subjected to a concentrated couple as well as uniform remote in-plane stresses. We show that the desired internal uniform hydrostatic stress field is possible for given material and geometric parameters provided a certain constraint is placed on the remote loading. Subsequently, when the single loading parameter, five material parameters and three geometric parameters are prescribed, all of the unknown complex coefficients appearing in the series representing the corresponding conformal mapping function can be uniquely determined from a set of nonlinear recurrence relations. We find that the internal uniform hydrostatic stress field, the constant mean stress in the interphase layer and the hoop stress along the inner interface on the interphase layer side are all unaffected by the existence of the concentrated couple whereas the non-elliptical shape of the (three-phase) inclusion is attributed solely to the influence of the nearby concentrated couple.

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