A piezoelectric screw dislocation in a bimaterial with surface piezoelectricity. (English) Zbl 1329.74089

Wang, Xu; Fan, Hui

Acta Mech. 226, No. 10, 3317-3331 (2015).

Summary: We study the contribution of surface piezoelectricity to the interaction between a screw dislocation and a hexagonal piezoelectric bimaterial interface. The screw dislocation suffers a finite discontinuity in the displacement and in the electric potential across the slip plane, and meanwhile is subjected to a line force and a line charge at its core. The surface piezoelectricity is incorporated by using an extended version of the continuum-based surface/interface model of Gurtin and Murdoch. An elementary solution in terms of the exponential integral is obtained. In addition, we present an explicit and concise expression of the image force acting on the piezoelectric screw dislocation. Several special cases are discussed in detail to demonstrate and validate the obtained solution. The associated problem of a piezoelectric screw dislocation interacting with a circular inclusion with surface piezoelectricity is also solved. The dislocation can be located either in the surrounding matrix or in the circular inclusion.

MSC:

74F15

Electromagnetic effects in solid mechanics

References:

[1]	Dundurs, J.: Elastic interaction of dislocations with inhomogeneities. In: Mura, T. (ed.) Mathematical Theory of Dislocations, pp. 70-115. ASME, New York (1969) · Zbl 0208.27503
[2]	Ting T.C.T.: Anisotropic Elasticity-Theory and Applications. Oxford University Press, New York (1996) · Zbl 0883.73001
[3]	Shilkrot, L.E.; Srolovitz, D.J., Elastic analysis of finite stiffness bimaterial interfaces: applications to dislocation-interface interactions, Acta Mater., 46, 3063-3075, (1998)
[4]	Wang, X.; Shen, Y.P., An edge dislocation in a three-phase composite cylinder model with a sliding interface, ASME J. Appl. Mech., 69, 527-538, (2002) · Zbl 1110.74745
[5]	Fan, H.; Wang, G.F., Screw dislocation interacting with imperfect interface, Mech. Mater., 35, 943-953, (2003)
[6]	Wang, X.; Sudak, L.J., A piezoelectric screw dislocation interacting with an imperfect piezoelectric bimaterial interface, Int. J. Solids Struct., 44, 3344-3358, (2007) · Zbl 1121.74366
[7]	Hashin, Z., The spherical inclusion with imperfect interface, ASME J. Appl. Mech., 58, 444-449, (1991)
[8]	Fan, H.; Sze, K.Y., A micro-mechanics model for imperfect interface in dielectric materials, Mech. Mater., 33, 363-370, (2001)
[9]	Sharma, P.; Ganti, S., Size-dependent eshelby’s tensor for embedded nano-inclusions incorporating surface/interface energies, ASME J. Appl. Mech., 71, 663-671, (2004) · Zbl 1111.74629
[10]	Gurtin, M.E.; Murdoch, A., A continuum theory of elastic material surfaces, Arch. Ration. Mech. Anal., 57, 291-323, (1975) · Zbl 0326.73001
[11]	Gurtin, M.E.; Murdoch, A.I., Surface stress in solids, Int. J. Solids Struct., 14, 431-440, (1978) · Zbl 0377.73001
[12]	Gurtin, M.E.; Weissmuller, J.; Larche, F., A general theory of curved deformable interface in solids at equilibrium, Philos. Mag. A, 78, 1093-1109, (1998)
[13]	Steigmann, D.J.; Ogden, R.W., Plane deformations of elastic solids with intrinsic boundary elasticity, Proc. R. Soc. Lond. A, 453, 853-877, (1997) · Zbl 0938.74014
[14]	Chen, T.; Dvorak, G.J.; Yu, C.C., Size-dependent elastic properties of unidirectional nano-composites with interface stresses, Acta Mech., 188, 39-54, (2007) · Zbl 1107.74010
[15]	Markenscoff, X.; Dundurs, J., Annular inhomogeneities with eigenstrain and interphase modeling, J. Mech. Phys. Solids, 64, 468-482, (2014)
[16]	Huang, G.Y.; Yu, S.W., Effect of surface piezoelectricity on the electromechanical behaviour of a piezoelectric ring, Phys. Status Solidi (b), 243, r22-r24, (2006)
[17]	Dai, S.; Gharbi, M.; Sharma, P.; Park H., S., Surface piezoelectricity: size effects in nanostructures and the emergence of piezoelectricity in non-piezoelectric materials, J. Appl. Phys., 110, 104305, (2011)
[18]	Pan, X.; Yu, S.; Feng, X., A continuum theory of surface piezoelectricity for nanodielectrics, Sci. China, 54, 564-573, (2011)
[19]	Wang, X., Zhou, K.: A crack with surface effects in a piezoelectric material. Math. Mech. Solids (in press) · Zbl 1371.74251
[20]	Abramovitz M., Stegun I.A.: Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. Dover, New York (1972)
[21]	Suo, Z.; Kuo, C.M.; Barnett, D.M.; Willis, J.R., Fracture mechanics for piezoelectric ceramics, J. Mech. Phys. Solids, 40, 739-765, (1992) · Zbl 0825.73584
[22]	Ru, C.Q., Simple geometrical explanation of Gurtin-murdoch model of surface elasticity with clarification of its related versions, Sci. China, 53, 536-544, (2010)
[23]	Pak, Y.E., Force on a piezoelectric screw dislocation, ASME J. Appl. Mech., 57, 863-869, (1990) · Zbl 0735.73072
[24]	Lee, K.Y.; Lee, W.G.; Pak, Y.E., Interaction between a semi-infinite crack and a screw dislocation in a piezoelectric material, ASME J. Appl. Mech., 67, 165-170, (2000) · Zbl 1110.74537
[25]	Liu, J.X.; Du, S.Y.; Wang, B., A screw dislocation interacting with a piezoelectric bimaterial interface, Mech. Res. Commun., 26, 415-420, (1999) · Zbl 0973.74032
[26]	Xiao, Z.M.; Bai, J., On piezoelectric inhomogeneity related problems—part II: a circular piezoelectric inhomogeneity interacting with a nearby crack, Int. J. Eng. Sci., 37, 961-976, (1999)
[27]	Chen, B.J.; Xiao, Z.M.; Liew, K.M., A screw dislocation in a piezoelectric bi-material wedge, Int. J. Eng. Sci., 40, 1665-1685, (2002)