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1.
GENERALIZATION OF ESHELBY''S METHOD TO THE ANISOTROPIC ELASTICITY THEORY OF DISLOCATIONS IN QUASICRYSTALS 下载免费PDF全文
The general expressions of the elastic fields induced by straight dislocations in quasicrystals have been given according to Eshelby's method which was used to treat the anisotropic elasticity of dislocations in crystals. As an example, the elastic displacement vector, the stress tensor and the elastic energy density of a screw dislocation line lying on the quasiperiodic plane of decagonal quasicrystals are calculated. 相似文献
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M. Ricker J. Bachteler H.-R. Trebin 《The European Physical Journal B - Condensed Matter and Complex Systems》2001,23(3):351-363
In quasicrystals, there are not only conventional, but also phason displacement fields and associated Burgers vectors. We
have calculated approximate solutions for the elastic fields induced by two-, three- and fivefold straight screw- and edge-dislocations
in infinite icosahedral quasicrystals by means of a generalized perturbation method. Starting from the solution for elastic
isotropy in phonon and phason spaces, corrections of higher order reflect the two-, three- and fivefold symmetry of the elastic
fields surrounding screw dislocations. The fields of special edge dislocations display characteristic symmetries also, which
can be seen from the contributions of all orders.
Received 21 February 2001 and Received in final form 27 June 2001 相似文献
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The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended displacement vector for an arbitrary extended force are derived. Next, in the framework of dislocation theory of quasicrystals, the solutions of the field equations for the extended displacement vector and the extended elastic distortion tensor are given; that is, the generalized Burgers equation for arbitrary sources and the generalized Mura–Willis formula, respectively. Moreover, important quantities of the theory of dislocations as the Eshelby stress tensor, Peach–Koehler force, stress function tensor and the interaction energy are derived for general dislocations. The application to dislocation loops gives rise to the generalized Burgers equation, where the displacement vector can be written as a sum of a line integral plus a purely geometric part. Finally, using the Green tensor, all other dislocation key-formulas for loops, known from the theory of anisotropic elasticity, like the Peach–Koehler stress formula, Mura–Willis equation, Volterra equation, stress function tensor and the interaction energy are derived for quasicrystals. 相似文献
5.
《Comptes Rendus Physique》2014,15(1):82-89
In this article we interpret the mechanical properties of icosahedral quasicrystals with the dislocation theory. After having defined the concept of dislocation in a periodic crystal, we extend this notion to quasicrystals in the 6-dimensional space. We show that perfect dislocations and imperfect dislocations trailing a phason fault can be defined and observed in transmission electron microscopy (TEM). In-situ straining TEM experiments at high temperature show that dislocations move solely by climb, a non-conservative motion-requiring diffusion. This behavior at variance with that of crystals which deform mainly by glide is explained by the atypical nature of the atomic structure of icosahedral quasicrystals. 相似文献
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Wang R 《Micron (Oxford, England : 1993)》2000,31(5):475-486
Principles, method and some application examples of determining Burgers vectors of dislocations in crystals and quasicrystals by means of defocus convergent-beam electron diffraction (CBED) technique are described and reviewed and compared with contrast experiment techniques. By using defocus CBED technique, dislocation reactions during high-temperature plastic deformation of face-centered icosahedral quasicrystals have been studied. These studies lead to a preliminary understanding to the micromechanism of high-temperature plastic deformation of quasicrystals. 相似文献
9.
P. Gong C.-Z. Hu X. Zhou L. Miao X. Wang 《The European Physical Journal B - Condensed Matter and Complex Systems》2006,52(4):477-481
Since quasicrystals have positional and orientational
long-range order, they are essentially anisotropic. However, the
researches show that some physical properties of quasicrystals are
isotropic. On the other hand, quasicrystals have additional phason
degrees of freedom which can influence on their physical behaviours.
To reveal the quasicrystal anisotropy, we investigate the
quasicrystal elasticity and other physical properties, such as
thermal expansion, piezoelectric and piezoresistance, for which one
must consider the contributions of the phason field. The results indicate that:
for the elastic properties, within linear phonon domain all
quasicrystals are isotropic, and within nonlinear phonon domain the
planar quasicrystals are still isotropic but the icosahedral
quasicrystals are anisotropic. Moreover, the nonlinear elastic
properties due to the coupling between phonons and phasons may
reveal the anisotropic structure of QCs. For the other physical
properties all quasicrystals behave like isotropic media except for
piezoresistance properties of icosahedral
quasicrystals due to the phason field. 相似文献
10.
PERTURBATION METHOD SOLVING ELASTIC PROBLEMS OF ICOSAHEDRAL QUASICRYSTALS CONTAINING A CIRCULAR CRACK 下载免费PDF全文
Perturbation method for solving elastic three-dimensional (3D) problems for 3D icosahedral quasicrystals is proposed. Considering an infinite 3D icosahedral quasicrystal weakened by a circular crack, we obtain the uniformly valid asymptotic solutions up to O(R2) for the mode I loading, where R is the elastic constant of phonon-phason coupling. 相似文献
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The application of group theory to elasticity in two-dimensional (2D)quasicrystals is presented. The expression of elastic energy as a function of gradients of the phonon and phason fields has been derived to quadratic order. The phonon response to an external stress is isotropic, but the response of phason field is anisotropic for eightfold and twelvefold symmetries. 相似文献
12.
J. Bachteler H.-R. Trebin 《The European Physical Journal B - Condensed Matter and Complex Systems》1998,4(3):299-306
The elastic theory of quasicrystals considers, in addition to the “normal” displacement field, three “phason” degrees of freedom.
We present an approximative solution for the elastic Green's function of icosahedral quasicrystals, assuming that the coupling
between the phonons and phasons is small.
Received: 18 December 1997 / Accepted: 6 March 1998 相似文献
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Jianlin Lei Renhui Wang Chengzheng Hu Di-hua Ding 《The European Physical Journal B - Condensed Matter and Complex Systems》2000,13(1):21-30
General formulae for thermal diffuse scattering from quasicrystals are applied to the case of dodecagonal quasicrystals from
corresponding elasticity theory. Contours of constant diffuse scattering intensity are illustrated. Unlike ordinary crystals,
shapes of isointensity contours are much more complicated and vary even among the collinear Bragg spots. Diffuse scattering
patterns in the plane perpendicular to a given zone axis are associated with corresponding specific elastic constants. Information
about elastic constants can be extracted from quantitative analysis of diffuse scattering patterns.
Received 7 December 1998 and Received in final form 12 March 1999 相似文献
15.
Interaction between infinitely many dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal 下载免费PDF全文
By means of analytic function theory, the problems of interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are studied. The analytic solutions of stress fields of the interaction between infinitely many parallel dislocations and a semi-infinite crack in one-dimensional hexagonal quasicrystal are obtained. They indicate that the stress concentration occurs at the dislocation source and the tip of the crack, and the value of the stress increases with the number of the dislocations increasing. These results are the development of interaction among the finitely many defects of quasicrystals, which possesses an important reference value for studying the interaction problems of infinitely many defects in fracture mechanics of quasicrystal. 相似文献
16.
A model is developed for describing phason defects in quasicrystals in the form of dilation filaments. This model is used
to calculate the energy of edge dislocations in quasicrystals including the interaction of this type of dislocation with its
“intrinsic” phason defects and with the equilibrium phason defects present in a quasicrystal. It is shown that the contribution
of “intrinsic” phason defects to the total energy of an edge dislocation in a quasicrystal is substantial.
Fiz. Tverd. Tela (St. Petersburg) 39, 2003–2007 (November 1997) 相似文献
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General complex variable function method for solving plane elasticity and the dislocation problems of quasicrystals with point group 10 mm has been proposed. All the fields variables are expressed by four arbitrary analytic functions. Analytical displacement expressions for the dislocation problem of the quasicrystal is obtained. The interaction between two parallel dislocations is also discussed in detail. 相似文献
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Elastic analysis of an elliptic notch in quasicrystals of point group 10 subjected to shear loading 下载免费PDF全文
Based on the stress potential and complex variable
function method, this paper makes an elastic analysis of an
elliptic notch subjected to uniform shear stress at infinity in
quasicrystals with point group 10. With the aid of conformal
transformation, an exact solution for the elliptic notch of the
quasicrystals is obtained. The solution of the mode {\rm II}
Griffith crack as a special case is constructed. The stress
intensity factor and energy release rate have been also obtained as
a direct result of the crack solution. 相似文献
19.
According go the group representation theory, we derive the character formulae of representation-matrices of the期physical property gensors for the one-dimensional (1D) quasicrysgals. Based on this, we have calculated the numbers of independent components of representation-matrices for thermal expansion coefficient gensors, piezoelectric coefficient tensors and elastic constant tensors under 31 point-groups for the 1D quasicrystals. Moreover, we have deduced the particular matrix forms of these gensors under the 31 point-groups. This is an important complement of quasicrysgal physical property. 相似文献
20.
Markus Lazar 《哲学杂志》2013,93(25):3327-3342
We investigate the non-uniform motion of straight dislocations in infinite media using the theory of incompatible elastodynamics. The equations of motion are derived for non-uniformly moving screw dislocations, gliding edge and climbing edge dislocations. The exact closed-form solutions of the elastic fields are calculated. The fields of the elastic velocity and elastic distortion surrounding the arbitrarily moving dislocations are given explicitly in the form of integral representations free of non-integrable singularities. The elastic fields describe the response in the form of non-uniformly moving elastic waves caused by the motion of the dislocation. 相似文献