Abstract
This work deals with the coupling interaction of a screw dislocation with a bimaterial interface and a nearby circular inclusion. Explicit series solutions are obtained by the complex potential and conformal mapping technique. Then the solutions are cast into new expressions with the coupling interaction effects separated. The new expressions converge rapidly and provide good first-order approximation formulae. The interaction energy and image force fields are formulated, evaluated, and shown graphically. It is found that the inclusion severely distorts the neighboring interaction energy contours and image force lines. There must be one unstable equilibrium point in Material 2 where the inclusion is located, whereas there may be zero, one or two equilibrium points (stable or unstable) in Material 1 without any inclusion, which depends on a combination of three material shear moduli and the nondimensional distance between the inclusion and bimaterial interface. It is interesting to notice that the direction of some local image forces in Material 1 may be inversed by a nearby inclusion in Material 2, and the inverse region is close to but not connected to the bimaterial interface.
Similar content being viewed by others
References
Bonilla, L.L., Carpio, A.: Driving dislocations in grapheme. Science 337, 161–162 (2012)
Head, A.K.: The interaction of dislocations and boundaries. Philos. Mag. 44, 92–94 (1953)
Dundurs, J.: Elastic interaction of dislocations with inhomogeneities. In: Mura, T. (ed.) Mathematical Theory of Dislocations. ASME, New York (1969)
Huang, H., Kardomateas, G.A.: Mixed-mode stress intensity factors for cracks located at or parallel to the interface in bimaterial half planes. Int. J. Solids Struct. 38, 3719–3734 (2001)
Kuo, C.H.: Elastic field due to an edge dislocation in a multilayered composite. Int. J. Solids Struct. 51, 1421–1433 (2014)
Hejazi, A.A., Ayatollahi, M., Bagheri, R., Monfared, M.M.: Dislocation technique to obtain the dynamic stress intensity factors for multiple cracks in a half-plane under impact load. Arch. Appl. Mech. 84, 95–107 (2014)
Fan, H., Wang, G.F.: Screw dislocation interacting with imperfect interface. Mech. Mater. 35, 943–953 (2003)
Shen, Y., Anderson, P.M.: Transmission of a screw dislocation across a coherent, slipping interface. Acta Mater. 54, 3941–3951 (2006)
Wang, X., Pan, E.: Interaction between a screw dislocation and a viscoelastic piezoelectric bimaterial interface. Int. J. Solids Struct. 45, 245–257 (2008)
Smith, E.: The interaction between dislocations and inhomogeneities-I. Int. J. Eng. Sci. 6, 129–143 (1968)
Sendeckyj, G.P.: Screw dislocations near circular inclusions. Phys. Status Solidi (a) 3, 529–535 (1970)
Li, Z.H., Shi, J.Y.: The interaction of a screw dislocation with inclusion analyzed by Eshelby equivalent inclusion method. Scr. Mater. 47, 371–375 (2002)
Gutkin, M.Y., Sheinerman, A.G., Smirnov, M.A.: Elastic behavior of screw dislocations in porous solids. Mech. Mater. 41, 905–918 (2009)
Shen, M.H., Chen, S.N., Lin, C.P.: The interaction between a screw dislocation and a piezoelectric fiber composite with a wedge crack. Arch. Appl. Mech. 82, 215–227 (2012)
Zeng, X., Fang, Q.H., Liu, Y.W.: Exact solutions for piezoelectric screw dislocations near two asymmetrical edge cracks emanating from an elliptical hole. Arch. Appl. Mech. 83, 1097–1107 (2013)
Zhang, J., Qu, Z., Huang, Q.Q., Xie, L.C., Xiong, C.B.: Interaction between cracks and a circular inclusion in a finite plate with the distributed dislocation method. Arch. Appl. Mech. 83, 861–873 (2013)
Sudak, L.J.: On the interaction between a dislocation and a circular inhomogeneity with imperfect interface in antiplane shear. Mech. Res. Commun. 30, 53–59 (2003)
Wang, X., Pan, E.: Interaction between an edge dislocation and a circular inclusion with interface slip and diffusion. Acta Mater. 59, 797–804 (2011)
Xiao, Z.M., Chen, B.J.: A screw dislocation interacting with a coated fiber. Mech. Mater. 32, 485–494 (2000)
Shen, M.H.: A magnetoelectric screw dislocation interacting with a circular layered inclusion. Eur. J. Mech. A Solids 27, 429–442 (2008)
Chen, F.M.: Edge dislocation interacting with a nonuniformly coated circular inclusion. Arch. Appl. Mech. 81, 1117–1128 (2011)
Li, B., Liu, Y.W., Fang, Q.H.: Interaction of an anti-plane singularity with interfacial anti-cracks in cylindrically anisotropic composites. Arch. Appl. Mech. 78, 295–309 (2008)
Luo, J., Xiao, Z.M.: Analysis of a screw dislocation interacting with an elliptical nano inhomogeneity. Int. J. Eng. Sci. 47, 883–892 (2009)
Ahmadzadeh-Bakhshayesh, H., Gutkin, M.Y., Shodja, H.M.: Surface/interface effects on elastic behavior of a screw dislocation in an eccentric core–shell nanowire. Int. J. Solids Struct. 49, 2422–2440 (2012)
Ye, W., Ougazzaden, A., Cherkaoui, M.: Analytical formulations of image forces on dislocations with surface stress in nanowires and nanorods. Int. J. Solids Struct. 50, 4341–4348 (2013)
Muskhelishvili, N.I.: Some Basic Problems of the Mathematical Theory of Elasticity. Noorhoff, Groningen (1953)
Jiang, C.P., Chai, H., Yan, P., Song, F.: The interaction of a screw dislocation with a circular inhomogeneity near the free surface. Arch. Appl. Mech. 84, 343–353 (2014)
Gong, S.X., Meguid, S.A.: A screw dislocation interacting with an elastic elliptical inhomogeneity. Int. J. Eng. Sci. 32, 1221–122 (1994)
Gutkin, M.Y., Romanov, A.E.: Straight edge dislocation in a thin two-phase plate, II. impurity-vacancy polarization of plate, interaction of a dislocation with interface and free surfaces. Phys. Status Solidi (a) 129, 363–377 (1992)
Gouldstone, A., Van Vliet, K.J., Suresh, S.: Nanoindentation Simulation of defect nucleation in a crystal. Nature 411, 656–656 (2001)
Schall, P., Cohen, I., Weitz, D.A., Spaepen, F.: Visualizing dislocation nucleation by indenting colloidal crystals. Nature 440, 319–323 (2006)
Acknowledgments
The work was supported by the National Natural Science Foundation of China (Grants Nos. 11172023 and 11232013).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chai, H., Jiang, C., Song, F. et al. The coupling interaction of a screw dislocation with a bimaterial interface and a nearby circular inclusion. Arch Appl Mech 85, 1733–1742 (2015). https://doi.org/10.1007/s00419-015-1015-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00419-015-1015-6