Research Papers

Stress and Displacement Fields Around Misfit Dislocation in Anisotropic Dissimilar Materials With Interface Stress and Interface Elasticity

[+] Author and Article Information
Hideo Koguchi

Department of Mechanical Engineering,
Nagaoka University of Technology,
1603-1 Kamitomioka,
Nagaoka, Niigata 940-2188, Japan
e-mail: koguchi@mech.nagaokaut.ac.jp

Yuki Hirasawa

Graduate School of Nagaoka
University of Technology,
1603-1 Kamitomioka,
Nagaoka, Niigata 940-2188, Japan
e-mail: hirasawayuki1@gmail.com

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received March 14, 2015; final manuscript received May 1, 2015; published online June 9, 2015. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 82(8), 081005 (Aug 01, 2015) (12 pages) Paper No: JAM-15-1140; doi: 10.1115/1.4030522 History: Received March 14, 2015; Revised May 01, 2015; Online June 09, 2015

Interfaces frequently exist in polycrystalline and multiphase materials. In nanoscale joints, interface properties, such as interface stresses and interface elasticity, influence the stress and displacement field near the interface. Generally, a misfit dislocation exists in the interface due to the mismatch of lattice length in crystals composing the joints. In the present paper, a misfit dislocation is introduced to a coherent interface in order to calculate the stress and displacement distributions in an incoherent interface. A model with an interface zone transferring traction only in the zone from one region to the opposite region is proposed, because these regions slip against each other due to the misfit dislocation. The traction in the interface depends on the displacement and the interface properties. Stresses and displacements considering the interface properties are deduced using a three-dimensional Stroh’s formalism. Bulk stress and displacements around the misfit dislocation are shown to increase with increasing the values of the interface stress and the interface elastic moduli. The stresses and displacements obtained from the derived solutions are compared with those obtained through molecular dynamic (MD) analysis. It is shown that the proposed interface zone model can adequately express the displacement and stress near the misfit dislocation.

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Taylor, G. I., 1934, “The Mechanism of Plastic Deformation of Crystals. Part I. Theoretical,” Proc. R. Soc. London, Ser. A, 145(855), pp. 362–387. [CrossRef]
Burgers, J. M., 1940, “Geometrical Considerations Concerning the Structural Irregularities to be Assumed in a Crystal,” Proc. Phys. Soc., 52(1), pp. 23–33. [CrossRef]
Bonnet, R., 1996, “Elasticity Theory of Straight Dislocation in a Multilayer,” Phys. Rev. B, 53(16), pp. 10978–10982. [CrossRef]
Bonnet, R., 2000, “A Biperiodic Network of Misfit Dislocations in a Thin Bicrystalline Foil,” Phys. Status Solidi A, 180(487), pp. 487–497. [CrossRef]
Yao, Y., Wang, T., and Wang, C., 1999, “Peierls–Nabarro Model of Interfacial Misfit Dislocation: An Analytic Solution,” Phys. Rev. B, 59(12), pp. 8232–8236. [CrossRef]
Bonnet, R., Youssef, S. B., and Fnaiech, M., 2001, “Simulation of the Free Surface Deformation Due to Subsurface Dislocations Arranged in Trigonal Networks,” Mater. Sci. Eng.: A, 297(1–2), pp. 286–289. [CrossRef]
Outtas, T., Adami, L., Derardja, A., Madani, S., and Bonnet, R., 2001, “Anisotropic Elastic Field of a Thin Bicrystal Deformed by a Biperiodic Network of Misfit Dislocations,” Phys. Status Solidi A, 188(3), pp. 1041–1045. [CrossRef]
Outtas, T., Adami, L., and Bonnet, R., 2002, “A Biperiodic Interfacial Pattern of Misfit Dislocation Interacting With Both Free Surfaces of a Thin Bicrystalline Sandwich,” Solid State Sci., 4(2), pp. 161–166. [CrossRef]
Yuan, J. H., Pan, E., and Chen, W. Q., 2013, “Line-Integral Representations for the Elastic Displacements, Stresses and Interaction Energy of Arbitrary Dislocation Loops in Transversely Isotropic Biomaterials,” Int. J. Solids Struct., 50(20–21), pp. 3472–3489. [CrossRef]
Wang, X., Pan, E., and Albrecht, J. D., 2007, “Anisotropic Elasticity of Multilayered Crystals Deformed by a Biperiodic Network of Misfit Dislocations,” Phys. Rev. B, 76(13), p. 134112. [CrossRef]
Vattre, A. J., and Demkowicz, M. J., 2013, “Determining the Burgers Vectors and Elastic Strain Energies of Interface Dislocation Arrays Using Anisotropic Elasticity Theory,” Acta Mater., 61(14), pp. 5172–5187. [CrossRef]
Wang, Y., Ruterana, P., Kret, S., Chen, J., El Kazzi, S., Desplanque, L., and Wallart, X., 2012, “Mechanism of Formation of the Misfit Dislocations at the Cubic Materials Interfaces,” Appl. Phys. Lett., 100(26), p. 262110. [CrossRef]
Gurtin, M. E., and Murdoch, A. I., 1975, “A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57(4), pp. 291–323 [CrossRef].
Koguchi, H., 1992, “Stress Analysis for Nano-Scaled Elastic Materials (1st Report, Formulation of Boundary Condition for Interface With Surface Stress),” Trans. Jpn. Soc. Mech. Eng., 58(555), pp. 2132–2137. [CrossRef]
Koguchi, H., 1996, “Stress Analysis for Nano-Scaled Elastic Materials: Elastic Contact Problems Considering Surface Stresses,” JSME Int. J., Ser. A, 39(3), pp. 3337–3345.
Ibach, H., 1997, “The Role of Surface Stress in Reconstruction, Epitaxial Growth and Stabilization of Mesoscopic Structures,” Surf. Sci. Rep., 29(5–6), pp. 195–263. [CrossRef]
Muller, P., and Saul, A., 2004, “Elastic Effects on Surface Physics,” Surf. Sci. Rep., 54(5–8), pp. 157–258. [CrossRef]
Koguchi, H., 2007, “Effects of Surface Stresses on Elastic Fields Near Surface and Interface,” J. Solid Mech. Mater. Eng., 1(2), pp. 152–168. [CrossRef]
Hanbucken, M., Muller, P., and Wehrspohn, R. B., 2011, Mechanical Stress on the Nanoscale, Wiley-VCH Verlag, Weinheim, Germany.
Koguchi, H., 2008, “Surface Green Function With Surface Stresses and Surface Elasticity Using Stroh’s Formalism,” ASME J. Appl. Mech., 75(6), p. 061014. [CrossRef]
Miller, R. E., and Shenoy, V. B., 2000, “Size-Dependent Elastic Properties of Nanosized Structural Elements,” Nanotechnology, 11(3), pp. 139–147. [CrossRef]
Shenoy, V. B., 2002, “Size-Dependent Rigidities of Nanosized Torsional Elements,” Int. J. Solids Struct., 39(15), pp. 4039–4052. [CrossRef]
Koguchi, H., 2003, “Surface Deformation Induced by a Variation in Surface Stresses in Anisotropic Half-Regions,” Philos. Mag., 83(10), pp. 1205–1226. [CrossRef]
Koguchi, H., 2004, “Contact and Adhesion Analysis Considering a Variation of Surface Stresses (2nd Report, A Comparison of the Present Theory and JKR Theory),” Trans. Jpn. Soc. Mech. Eng., 70(697), pp. 1332–1340. [CrossRef]
Duan, H. L., Wang, J., Huang, Z. P., and Karihaloo, B. L., 2005, “Size-Dependent Effective Elastic Constants of Solids Containing Nano-Inhomogeneities With Interface Stress,” J. Mech. Phys. Solids, 53(7), pp. 1574–1596. [CrossRef]
Dingreville, R., Qu, J., and Cherkaoui, M., 2005, “Surface Free Energy and Its Effect on the Elastic Behavior of Nano-Sized Particles, Wires and Films,” J. Mech. Phys. Solids, 53(8), pp. 1827–1854. [CrossRef]
Kim, C. I., Schiavone, P., and Ru, C.-Q., 2010, “The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution,” ASME J. Appl. Mech., 77(2), p. 021011. [CrossRef]
Kim, C. I., Ru, C.-Q., and Schiavone, P., 2010, “Analysis of Plane-Strain Crack Problems (Mode-I & Mode-II) in the Presence of Surface Elasticity,” J. Elasticity, 104(1–2), pp. 397–420. [CrossRef]
Ladan, P., and Hossein, M. S., 2011, “Surface and Interface Effects on Torsion of Eccentrically Two-Phase fcc Circular Nanorods: Determination of the Surface/Interface Elastic Properties Via an Atomistic Approach,” ASME J. Appl. Mech., 78(1), p. 011011. [CrossRef]
Gutkin, M. Yu., Enzevaee, C., and Shodja, H. M., 2013, “Interface Effects on Elastic Behavior of an Edge Dislocation in a Core–Shell Nanowire Embedded to an Infinite Matrix,” Int. J. Solids Struct., 50(7–8), pp. 1177–1186. [CrossRef]
Dingreville, R., Hallil, A., and Berbenni, S., 2014, “From Coherent to Incoherent Mismatched Interfaces: A Generalized Continuum Formulation of Surface Stresses,” J. Mech. Phys. Solids, 72, pp. 40–60. [CrossRef]
Ting, T. C. T., 1996, Anisotropic Elasticity—Theory and Application, Oxford University Press, New York.
Wadley, H. N. G., Zhou, X., Johnson, R. A., and Neurock, M., 2001, “Mechanisms, Models and Methods of Vapor Deposition,” Prog. Mater. Sci., 46(3–4), pp. 329–377. [CrossRef]


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Fig. 1

Model for analysis and a coordinate system

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Fig. 2

An interface zone model for incoherent interface with a misfit dislocation

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Fig. 3

Interface containing dislocation described by O-lattice vectors p1o and p2o. Large solid circles represent O-lattice points, and q1 and q2 are the basis vectors. The dotted line indicates a unit cell in the interface structure.

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Fig. 4

Atomic interface stress, τ11, and interface elasticity, d11, along the x3-coordinate for the rotation angle θ = 0 deg: (a) interface stress τ11 and (b) interface elasticity d11

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Fig. 5

Distributions of displacements and stress along the x1-coordinate at x2 = 5 nm: (a) u1 at x3 = 0.20 nm in Au, (b) u1 at x3 = −0.20 nm in Cu, (c) u3 at x3 = 0.20 nm in Au, (d) u3 at x3 = −0.20 nm in Cu, (e) σ33 at x3 = 0.20 nm in Au, (f) σ33 at x3 = −0.20 nm in Cu, (g) σ33 at x3 = 0.20 nm in Au: enlargement of (e), and (h) σ33 at x3 = −0.20 nm in Cu: enlargement of (f)

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Fig. 6

Maps of displacements calculated using theory and MD analysis in Cu; rotation angle θ = π/4: (a) u1 (theory), (b) u1 (MD), (c) u3 (theory), and (d) u3 (MD)

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Fig. 7

Maps of displacements calculated theoretically and by MD analysis for Au for a rotation angle of θ = π/4: (a) u1 (theory), (b) u1 (MD), (c) u3 (theory), and (d) u3 (MD)

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Fig. 8

Distributions of displacements and stress calculated theoretically and by MD analysis along the x1-coordinate and x2 = 5 nm for a rotation angle of θ = π/4: (a) u1, (b) u3, and (c) σ33



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