A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses

Xu Wang; Liang Chen; Peter Schiavone

doi:10.1016/j.crme.2018.12.003

A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses

Xu Wang ¹ ; Liang Chen ¹; Peter Schiavone ²

¹ School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
² Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada

Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 181-190.

Abstract

We consider the anti-plane shear deformation of a three-phase inhomogeneity-coating-matrix composite containing a coated non-elliptical inhomogeneity whose surrounding matrix is subjected to the action of a screw dislocation and uniform remote anti-plane shear stresses. Our objective is to establish conditions under which the inhomogeneity maintains an internal uniform stress field. Our analysis, which is based on a carefully chosen conformal mapping function, clearly indicates that such an internal uniform stress distribution can be achieved independently of the action of the screw dislocation, which influences the shape of the inhomogeneity depending on its proximity to the dislocation. In fact, we find that when the screw dislocation is located far from the coated inhomogeneity, the corresponding material interfaces become two confocal ellipses as reported previously in the literature. A simple criterion for the convergence of the series in the conformal mapping function is established.

Received: 2018-09-21
Accepted: 2018-12-14
Published online: 2019-01-22

DOI: 10.1016/j.crme.2018.12.003

Keywords: Conformal mapping, Complex variable method, Anti-plane elasticity, Coating, Non-elliptical inhomogeneity, Internal uniform stress field

Author's affiliations:

Xu Wang ¹; Liang Chen ¹; Peter Schiavone ²

¹ School of Mechanical and Power Engineering, East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, China
² Department of Mechanical Engineering, University of Alberta, 10-203 Donadeo Innovation Centre for Engineering, Edmonton, Alberta T6G 1H9, Canada

@article{CRMECA_2019__347_2_181_0,
     author = {Xu Wang and Liang Chen and Peter Schiavone},
     title = {A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {181--190},
     publisher = {Elsevier},
     volume = {347},
     number = {2},
     year = {2019},
     doi = {10.1016/j.crme.2018.12.003},
     language = {en},
}

TY  - JOUR
AU  - Xu Wang
AU  - Liang Chen
AU  - Peter Schiavone
TI  - A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses
JO  - Comptes Rendus. Mécanique
PY  - 2019
SP  - 181
EP  - 190
VL  - 347
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crme.2018.12.003
LA  - en
ID  - CRMECA_2019__347_2_181_0
ER  -

%0 Journal Article
%A Xu Wang
%A Liang Chen
%A Peter Schiavone
%T A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses
%J Comptes Rendus. Mécanique
%D 2019
%P 181-190
%V 347
%N 2
%I Elsevier
%R 10.1016/j.crme.2018.12.003
%G en
%F CRMECA_2019__347_2_181_0

Xu Wang; Liang Chen; Peter Schiavone. A screw dislocation near a coated non-elliptical inhomogeneity with internal uniform stresses. Comptes Rendus. Mécanique, Volume 347 (2019) no. 2, pp. 181-190. doi : 10.1016/j.crme.2018.12.003. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.12.003/

References
Cited by

[1] Y. Mikata; M. Taya Stress field in and around a coated short fiber in infinite matrix subjected to uniaxial and biaxial loading, ASME J. Appl. Mech., Volume 52 (1985), pp. 19-24

[2] Y.P. Qiu; G.J. Weng Elastic moduli of thickly coated particle and fiber-reinforced composites, ASME J. Appl. Mech., Volume 58 (1991), pp. 388-398

[3] C.Q. Ru Three-phase elliptical inclusions with internal uniform hydrostatic stresses, J. Mech. Phys. Solids, Volume 47 (1999), pp. 259-273

[4] R. Hashemi; G.J. Weng; M.H. Kargarnovin; H.M. Shodja Piezoelectric composites with periodic multi-coated inhomogeneities, Int. J. Solids Struct., Volume 47 (2010), pp. 2893-2904

[5] Y. Benveniste Exact results for the local fields and the effective moduli of fibrous composites with thickly coated fibers, J. Mech. Phys. Solids, Volume 71 (2014), pp. 219-238

[6] C.Q. Ru; P. Schiavone A circular inclusion with circumferentially inhomogeneous interface in anti-plane shear, Proc. R. Soc. Lond. A, Volume 453 (1997), pp. 2551-2572

[7] C.Q. Ru; P. Schiavone; A. Mioduchowski Uniformity of stresses within a three-phase elliptic inclusion in anti-plane shear, J. Elast., Volume 52 (1999), pp. 121-128

[8] X. Wang; X.L. Gao On the uniform stress state inside an inclusion of arbitrary shape in a three-phase composite, Z. Angew. Math. Phys., Volume 62 (2011), pp. 1101-1116

[9] Z.M. Xiao; B.J. Chen A screw dislocation interacting with a coated fiber, Mech. Mater., Volume 32 (2000), pp. 485-494

[10] X. Wang; P. Schiavone Two inhomogeneities of irregular shape with internal uniform stress fields interacting with a screw dislocation, C. R. Mecanique, Volume 344 (2016), pp. 532-538

[11] X. Wang; L. Chen; P. Schiavone Uniform stress field inside an anisotropic non-elliptical inhomogeneity interacting with a screw dislocation, Eur. J. Mech. A, Solids, Volume 70 (2018), pp. 1-7

[12] T.C.T. Ting Anisotropic Elasticity – Theory and Applications, Oxford University Press, New York, 1996

Cited by Sources:

Comments - Policy