Transient stress relaxation around spherical inclusions by interfacial diffusion and sliding

He, Liqun

doi:10.1007/bf01261667

Cited by 14 publications

(7 citation statements)

References 26 publications

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“…where the overdot denotes differentiation with respect to the time t , D ( ≥ 0 ) is the interface diffusion constant, η ( ≥ 0 ) is the viscosity for interface sliding, σ rr + and σ r θ + are the normal and tangential stresses on the surface of the inclusion. In addition, D = M Ω 2 and η = h 2 / 4 M Ω 2 where M is the atomic mobility on the interface, Ω is the volume per diffusing atom and h is the height of the asperity of the interface [2,3].…”

Section: Analytical Solutionmentioning

confidence: 99%

“…0) is the viscosity for interface sliding, s + rr and s + ru are the normal and tangential stresses on the surface of the inclusion. In addition, D = MO 2 and h = h 2 4MO 2 where M is the atomic mobility on the interface, O is the volume per diffusing atom and h is the height of the asperity of the interface [2,3].…”

Section: Analytical Solutionmentioning

confidence: 99%

“…The stress relaxation caused by the combination of interfacial diffusion and sliding around an elastic or rigid spherical inclusion has been studied by several authors from the mechanical point of view [1][2][3][4]. As the radius of the spherical inclusion shrinks to the nanoscale, surface stresses, tension, and energies come into play [5,6].…”

Section: Introductionmentioning

confidence: 99%

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A nanosized rigid spherical inclusion with interfacial diffusion and sliding

Wang

2017

Mathematics and Mechanics of Solids

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We examine the time-dependent deformations around a nanosized rigid spherical inclusion in an infinite elastic matrix under uniaxial tension at infinity. The elastic matrix is first endowed with separate Gurtin–Murdoch surface elasticity. Furthermore, interfacial diffusion and sliding both occur on the inclusion–matrix interface. Closed-form expressions of the time-dependent displacements and stresses in the matrix are derived by using Papkovich–Neuber displacement potentials. A concise and elegant expression of the steady-state normal stress on the surface of the inclusion is also obtained. It is seen that the displacements and stresses in the matrix evolve with two relaxation times which are reliant on three size-dependent parameters, one from surface elasticity and the other two from interfacial diffusion and sliding. Numerical results are presented to demonstrate the influence of surface elasticity on the relaxation times and on the stress distribution near the inclusion. It is observed that the surface elasticity can alter the nature of the steady state normal stress on the surface of the inclusion from tension to compression. When the radius of the inclusion is not greater than the ratio of residual surface tension to remote tension, the steady state normal stress on the surface of the inclusion is always compressive. The related problem of a nanosized rigid spherical inclusion with a spring-type imperfect interface is also solved. We find that it is feasible to design a neutral spherical inclusion that does not disturb a prescribed uniform uniaxial stress field or even any uniform stress field outside the inclusion through a judicious choice of the four imperfect interface parameters.

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Section: Analytical Solutionmentioning

confidence: 99%

Section: Analytical Solutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A nanosized rigid spherical inclusion with interfacial diffusion and sliding

Wang

2017

Mathematics and Mechanics of Solids

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“…Transient stress relaxation caused by the combination of interfacial diffusion and sliding in particulate and fibrous composites and in polycrystalline solids has been investigated (see, for example, Sofronis and McMeeking [1], Onaka et al [2,3], He [4], He and Hu [5], Wang and Pan [6], Wang et al [7] and Wei et al [8]). The long-range interfacial diffusion is driven by the chemical potential gradients on the interface [9], whilst interfacial sliding is due to short-range diffusion on a length scale comparable to the size of the asperities of the interface [10].…”

Section: Introductionmentioning

confidence: 99%

Transient response of bilayered elastic strips with interfacial diffusion and sliding in cylindrical bending

Wang

2017

Mathematics and Mechanics of Solids

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Time-dependent deformations of bilayered elastic strips with interfacial diffusion and sliding in cylindrical bending are studied. A film–substrate system is also addressed by letting the thickness of one layer approach infinity. Our solution clearly indicates that the stresses and displacements in the strip evolve with two relaxation times when its upper surface is subjected to a sinusoidal pressure. Explicit and elementary expressions of the relaxation times are derived. The steady-state displacement jumps across the interface are found independent of the elastic property and thickness of the lower layer free of external loading. When the film is extremely thin, the relaxation times are independent of the elastic property of the substrate; when the film is extremely thick, the relaxation times are found independent of the film thickness. Detailed numerical results are presented to show the influence of the material, geometric and interface parameters on the relaxation times and on the evolving displacements and stresses in the strip or in the film–substrate system. Finally, the state-space method is proposed to determine the transient elastic field in simply supported multilayered elastic strips with interfacial diffusion and sliding under thermomechanical loads.

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“…This model of viscous interface has been adopted to investigate inelastic responses of fiberand particle-reinforced as well as laminated composites [15][16][17][18]. As a primary effort to damping analysis, we constrain ourselves here to the case that the composites are under longitudinal deformations.…”

Section: Introductionmentioning

confidence: 99%

Damping behavior of fibrous composites with viscous interface under longitudinal shear loads

Liu

2005

Composites Science and Technology

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Transient stress relaxation around spherical inclusions by interfacial diffusion and sliding

Cited by 14 publications

References 26 publications

A nanosized rigid spherical inclusion with interfacial diffusion and sliding

A nanosized rigid spherical inclusion with interfacial diffusion and sliding

Transient response of bilayered elastic strips with interfacial diffusion and sliding in cylindrical bending

Damping behavior of fibrous composites with viscous interface under longitudinal shear loads

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