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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

Professor
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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Figures

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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. 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. 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. 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. 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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