On screw dislocation in a multiphase lamellar inclusion

Journal of Applied Physics, 1986

The dislocation-modeling technique and complex variable method are used to analyze the interaction between the general parallel screw dislocations and a surface crack. For the case of one dislocation, the dislocation distribution in the crack, the stress field, the strain energy, the image force, the stress intensity factor, and the crack extension force are obtained. The results are compared with various special cases of other papers. Under the applied stress without the frictional force, there are two metastable points and no stable point in the strain energy diagram. Therefore, the dislocation will move to the free surface, crack surface, or infinity depending on its location. The two-dislocation system or the even dislocation dipole is analyzed. Although this approach gets the same results as the conformal mapping method, the former is superior in analyzing two or more dislocations.

Journal of Mechanics of Materials and Structures, 2008

Exact closed-form solutions in terms of elementary functions are derived for the problem of a screw dislocation embedded in an unbounded piezoelectric matrix interacting with a piezoelectric circular inclusion with a linear viscous interface. By means of the complex variable method, the original boundary value problem is reduced to an inhomogeneous first-order partial differential equation whose solution can be expressed in terms of elementary functions. The time dependent electroelastic fields such as stresses, strains, electric fields, and electric displacements are then obtained. In particular the image force acting on the piezoelectric screw dislocation, due to its interaction with the circular viscous interface, is presented. Some special cases of practical importance are discussed to verify and to illustrate the obtained solution. Finally we present a specific example of a screw dislocation located in a piezoelectric PZT-5 matrix interacting with a piezoelectric BaTiO 3 fiber to graphically demonstrate the influence of the viscosity of the interface on the mobility of the screw dislocation.

Scripta Materialia, 1996

Modelling and Simulation in Materials Science and Engineering, 2014

An analytical formulation of the nodal forces induced by a dislocation segment on a surface element is presented. The determination of such nodal forces is a critical step when associating dislocation dynamics simulations with continuum approaches to simulate the plastic behaviour of finite domains. The nodal force calculation starts from the infinite-domain stress field of a dislocation and involves a triple integration over the dislocation ensemble and over the surface element at the domain boundary. In the case of arbitrary oriented straight segments of dislocations and a linear rectangular surface element, the solution is derived by means of a sequence of integrations by parts that present specific recurrence relations. The use of the non-singular expression for the infinitedomain stress field ensures that the traction field is finite everywhere even at the dislocation core. A specific solution is provided for virtual semi-infinite segments that can be used to enforce global mechanical equilibrium in the infinite domain. The proposed model for nodal forces is fully analytical, exact and very efficient computationally. A discussion on how to adapt the proposed methodology to more complex shape functions and surface element geometry is presented at the end of the paper.

Archive of Applied Mechanics, 2013

The interaction of a screw dislocation with a circular inhomogeneity near the free surface is discussed in this paper. By using the complex potential and conformal mapping technique, an explicit series solution is obtained. Then, the solution is cast into a new expression to separate the interaction effects between the dislocation, inhomogeneity, and free surface. The new expression is not only convenient to reveal the coupling interaction effects, but also helpful to improve the convergence of the solution. As an application of the new expression, a simple approximate formula is presented with high accuracy. Finally, the full-field interaction energy and image force are evaluated and studied graphically. It is found that when the screw dislocation, inhomogeneity, and free surface are close to each other, their interaction effects strongly and intricately couple in the near field. In the case of a soft inhomogeneity or a hole, there is an unstable equilibrium point of the screw dislocation between the inhomogeneity and free surface, whereas in the case of a hard or rigid inhomogeneity, there is an unstable equilibrium point on the opposite side of the inhomogeneity.

Theoretical and Applied Mechanics, 2017

Pileups of screw dislocations against an inclined bimetallic interface are considered. It is assumed that differently oriented pileups are either under the same remote uniform loading, or under the same resolved shear stress along the pileup direction for any orientation of the interface. The distributions of dislocations and the lengths of pileups are substantially different for differently oriented interfaces, particularly in the case of the same remote loading. The interface stresses are also strongly depended on the pileup orientation. The maximum stress can be higher for a pileup along an inclined direction than along the direction orthogonal to the interface. The back stress behind a pileup is evaluated and discussed.

Molecular Physics, 2011

arXiv: Analysis of PDEs, 2017

This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semi-discrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and collision events and (ii) the confinement inside the domain when a suitable Dirichlet-type boundary condition is imposed. In the first case, we analytically prove that free boundaries attract dislocations and we provide an expression for the Peach--Koehler force on a dislocation near the boundary. Moreover, we use this to prove an upper bound on the collision time of a dislocation with the boundary, provided certain geometric conditions are satisfied. An upper bound on the collision time for two dislocations with opposite Burgers vectors hitting each other is also obtained. In the second case, we turn to domains whose boundaries are subject to an external stress. In this situation, we prove that dislocations find it energetically favourable to st...

International Journal of Engineering Science, 1977

A simple model of a screw dislocation with first neighbours interactions is presented. The interaction energy of atoms is a piece-wisely parabolic function of distortions. The equilibrium configurations of weak bonds as a function of the model parameter y and the quasi-static motion of the dislocation are examined. Sessile and glissile configurations of weak bonds and symmetric and asymmetric equilibrium positions of the dislocation are found. The dependence of the Peierls stress on the model parameter y is discussed.

2003

Interface and interfacial cracks interacting with screw dislocations in piezoelectric bimaterials subjected to antiplane mechanical and in-plane electrical loadings are studied within the framework of linear piezoelectricity theory. Straight dislocations with the Burgers vector normal to the isotropic basal plane near the interface or interfacial crack are considered. The dislocations are characterized by a discontinuous electric potential across the slip plane and are subjected to a line-force and a line-charge at the core. An explicit solution for the screw dislocation in piezoelectric bimaterial with straight interface is found based on the solution of a similar problem for infinite homogenous medium. The obtained relation is independent of the nature of singularity. This fundamental result is used to analyze dislocation interacting with a set of collinear interfacial cracks in piezoelectric bimaterials. Three solutions for the screw dislocation interacting with a semi-infinite c...