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Research Papers

Singular Stress Fields in Anisotropic Bonded Joints Considering 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

Nubuyasu Suzuki

Nagaoka University of Technology,
1603-1 Kamitomioka,
Nagaoka, Niigata 940-2188,Japan
e-mail: s103054@stn.nagaokaut.ac.jp

Manuscript received January 11, 2014; final manuscript received February 8, 2014; accepted manuscript posted February 14, 2014; published online March 6, 2014. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 81(7), 071003 (Mar 06, 2014) (12 pages) Paper No: JAM-14-1029; doi: 10.1115/1.4026840 History: Received January 11, 2014; Revised February 08, 2014; Accepted February 14, 2014

Surface stress and surface elasticity are related to the organization of surface morphology, surface patterns, and surface atomic structures. As the size of the structure approaches the nanometer level, the surface-to-volume ratio increases. Generally the surface energy in deformable solids depends on the surface strain. The surface stress and elasticity influence the distribution of bulk stress near the surface. Interface stress and elasticity also exist at material interfaces and determine the interface properties. In the present study, the singular stress at a wedge corner in an anisotropic two-dimensional joint under tensile loading is analyzed using the molecular dynamic (MD) method and the anisotropic elasticity theory using a boundary condition with interface stress and interface elasticity. Not only the interface stress but also surface stress on the free surface are considered as a special case of an interface. The interface stress and interface elasticity are obtained through the MD analysis. In the case of a two-dimensional joint, the interface stress and elasticity depend on the distance from the wedge corner. In the analysis of anisotropic elasticity, the eigenequation used to determine the order of the stress singularity is newly derived using a boundary condition that considers the interface stress and interface elasticity. The order of the stress singularity varies with distance from the wedge corner. The stress distribution near the wedge corner can be expressed by the relation between the order of the stress singularity and the distance from the wedge corner.

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Figures

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Fig. 1

Composite wedge composed of n different materials

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Fig. 3

Maps of stress σyy after subtraction of initial residual stress: (a) incoherent interface model and (b) coherent interface model

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Fig. 4

Distributions of atomic stress at coherent interface and incoherent interface ω = 170 deg: (a) before subtraction of initial residual stress and (b) after subtraction of initial residual stress

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Fig. 5

Distributions of atomic stress σyy, with respect to distance from the apex for various angles ω: (a) before subtraction of initial residual stress and (b) after subtraction of initial residual stress

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Fig. 6

Variation of interface stress τ11: (a) ω = 170 deg and (b) ω = 120 deg

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Fig. 9

Variation of order of stress singularity with distance from the apex: (a) ω = 170 deg and (b) ω = 120 deg

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Fig. 10

Angular functions for λI, λII, and λIII

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Fig. 7

Variation of interface elastic moduli for ω = 170 deg: (a) d1111, (b) d1113, and (c) d3131

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Fig. 8

Variation of interface elastic moduli for ω = 120 deg: (a) d1111, (b) d1113, and (c) d3131

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Fig. 2

Wedge model for analysis

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Fig. 11

Distribution of atomic stress σyy: (a) ω = 170 deg and (b) ω = 120 deg

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