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Research Papers

On a Screw Dislocation Interacting With Two Viscous Interfaces

[+] Author and Article Information
X. Wang1

Department of Civil Engineering, and Department of Applied Mathematics, University of Akron, Akron, OH 44325-3905xuwang_sun@hotmail.com

E. Pan

Department of Civil Engineering, and Department of Applied Mathematics, University of Akron, Akron, OH 44325-3905pan2@uakron.edu

1

Corresponding author.

J. Appl. Mech 76(5), 051004 (Jun 17, 2009) (6 pages) doi:10.1115/1.3112743 History: Received May 02, 2008; Revised October 03, 2008; Published June 17, 2009

We investigate a screw dislocation interacting with two concentric circular linear viscous interfaces. The inner viscous interface is formed by the circular inhomogeneity and the interphase layer, and the outer viscous interface by the interphase layer and the unbounded matrix. The time-dependent stresses in the inhomogeneity, interphase layer, and unbounded matrix induced by the screw dislocation located within the interphase layer are derived. Also obtained is the time-dependent image force on the screw dislocation due to its interaction with the two viscous interfaces. It is found that when the interphase layer is more compliant than both the inhomogeneity and the matrix, three transient equilibrium positions (two are unstable and one is stable) for the dislocation can coexist at a certain early time moment. If the inhomogeneity and matrix possess the same shear modulus, and the characteristic times for the two viscous interfaces are also the same, a fixed equilibrium position always exists for the dislocation. In addition, when the interphase layer is stiffer than the inhomogeneity and matrix, the fixed equilibrium position is always an unstable one; on the other hand, when the interface layer is more compliant than the inhomogeneity and matrix, the nature of the fixed equilibrium position depends on the time: the fixed equilibrium position is a stable one if the time is below a critical value, and it is an unstable one if the time is above the critical value. In addition, a saddle point transient equilibrium position for the dislocation can also be observed under certain conditions.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

A screw dislocation in a three-phase circular inhomogeneity with two concentric circular linear viscous interfaces

Grahic Jump Location
Figure 2

The normalized time-dependent image force F̃=aFx/μ2bz2 on the screw dislocation at five different times t̃=t/t0=0.005, 0.01, 0.02, 0.0329, 0.1 with t1=t2=t0, Γ1=Γ2=Γ=1.8, and b=1.1a

Grahic Jump Location
Figure 3

The normalized time-dependent image force F̃=aFx/μ2bz2 on the screw dislocation at four different times t̃=t/t0=0.005, 0.0109, 0.02, 0.1 with t1=t2=t0, Γ1=1.8, Γ2=1.5, and b=1.1a

Grahic Jump Location
Figure 4

The normalized time-dependent image force F̃=aFx/μ2bz2 on the screw dislocation at four different times t̃=t/t0=0.005, 0.0109, 0.02, 0.1 with t1=t2=t0, Γ1=1.5, Γ2=1.8, and b=1.1a

Grahic Jump Location
Figure 5

The different situations for the transient equilibrium positions of the dislocation at a certain fixed normalized time t̃=t/t0 with t1=t2=t0 and b=1.1a

Grahic Jump Location
Figure 6

The variation in t̃c as a function of the relative thickness (b−a)/a of the interphase layer with the assumption that t1=t2=t0

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