Using complex variable methods and conformal mapping techniques, we demonstrate rigorously that two inhomogeneities of irregular shape interacting with a screw dislocation can indeed maintain uniform internal stress distributions. Our analysis indicates that while the internal uniform stresses are independent of the existence of the screw dislocation, the shapes of the two inhomogeneities required to achieve this uniformity depend on the Burgers vector, the location of the screw dislocation, and the size of the inhomogeneities. In addition, we find that this uniformity of the internal stress field is achievable also when the two inhomogeneities interact with an arbitrary number of discrete screw dislocations in the matrix.

Accepted:

Published online:

Xu Wang ^{1};
Peter Schiavone ^{2}

@article{CRMECA_2016__344_7_532_0, author = {Xu Wang and Peter Schiavone}, title = {Two inhomogeneities of irregular shape with internal uniform stress fields interacting with a screw dislocation}, journal = {Comptes Rendus. M\'ecanique}, pages = {532--538}, publisher = {Elsevier}, volume = {344}, number = {7}, year = {2016}, doi = {10.1016/j.crme.2016.02.008}, language = {en}, }

TY - JOUR AU - Xu Wang AU - Peter Schiavone TI - Two inhomogeneities of irregular shape with internal uniform stress fields interacting with a screw dislocation JO - Comptes Rendus. Mécanique PY - 2016 SP - 532 EP - 538 VL - 344 IS - 7 PB - Elsevier DO - 10.1016/j.crme.2016.02.008 LA - en ID - CRMECA_2016__344_7_532_0 ER -

Xu Wang; Peter Schiavone. Two inhomogeneities of irregular shape with internal uniform stress fields interacting with a screw dislocation. Comptes Rendus. Mécanique, Volume 344 (2016) no. 7, pp. 532-538. doi : 10.1016/j.crme.2016.02.008. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2016.02.008/

[1] Inclusion pairs satisfying Eshelby's uniformity property, SIAM J. Appl. Math., Volume 69 (2008), pp. 577-595

[2] Solution to the Eshelby conjectures, Proc. R. Soc. A, Volume 464 (2008), pp. 573-594

[3] Uniform fields inside two non-elliptical inclusions, Math. Mech. Solids, Volume 17 (2012), pp. 736-761

[4] Uniform strain fields inside multiple inclusions in an elastic infinite plane under anti-plane shear, Math. Mech. Solids (2014) | DOI

[5] Uniform stress fields inside multiple inclusions in an elastic infinite plane under plane deformation, Proc. R. Soc. A, Volume 471 (2015)

[6] The mechanism of plastic deformation of crystals. Part I. Theoretical, Proc. R. Soc. A, Volume 145 (1934), pp. 362-387

[7] Continuous distribution of dislocations and the mathematical theory of plasticity, Phys. Status Solidi, Volume 10 (1965), pp. 447-453

[8] Continuum theory of plasticity and dislocations, Int. J. Eng. Sci., Volume 5 (1967), pp. 341-351

[9] Dynamic theory of continuously distributed dislocations. Its relation to plasticity theory, J. Appl. Math. Mech., Volume 31 (1967), pp. 981-1000

[10] Link between the microscopic and mesoscopic length-scale description of the collective behavior of dislocations, Phys. Rev. B, Volume 56 (1997), pp. 5807-5813

[11] Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Mater., Volume 51 (2003), pp. 1271-1281

[12] The pair distribution function for an array of screw dislocations, Int. J. Solids Struct., Volume 45 (2008), pp. 3726-3738

[13] The pair distribution function for an array of screw dislocations: implications for gradient plasticity, Math. Mech. Solids, Volume 14 (2009), pp. 161-178

[14] Anisotropic Elasticity-Theory and Applications, Oxford University Press, New York, 1996

*Cited by Sources: *

Comments - Policy