Three-dimensional simulation schemes for discrete dislocation dynamics (DDD) have been used successfully to investigate plasticity of bulk materials. The adaptation of these DDD schemes to a description of thin-film plasticity requires detailed modeling of the interfaces and surfaces of the film. One possible method is to compensate for the normal stresses that a dislocation distribution exerts on a surface by appropriate point loads. This traction-compensation method is extended to a free standing film (two opposing surfaces). The extension to a thin film on a substrate is possible.

Stress development and relaxation in polycrystalline thin films perfectly bonded to a stiff substrate is analyzed numerically. The calculations are carried out within a two-dimensional plane strain framework. The film-substrate system is subject to a prescribed temperature decrease, with the coefficient of thermal expansion of the metal film larger than that of the substrate. Plastic deformation arises solely from the glide of edge dislocations. The dislocations nucleate from pre-existing Frank-Read sources, with the grain boundaries and film-substrate interface acting solely as impenetrable barriers to dislocation glide. At each stage of loading, a boundary value problem is solved to enforce the boundary conditions and the stress field and the dislocation structure are obtained. The results of the simulations show both film-thickness and grain size dependent strengthening of polycrystalline films. Limited plasticity occurs in films with a sufficiently small grain-size, mainly due to a reduced nucleation rate in the constrained grain geometry. ? 2004 Elsevier B.V. All rights reserved.

An efficient numerical algorithm for discrete dislocation dynamics simulations in two-dimensional, finite polygonal domains is presented. The algorithm is based on a complex boundary integral equation method. By use of the fast multipole method, linear complexity and storage requirement are achieved. This method has not, to the present author?s knowledge, previously been used in such simulations. Convergence studies show that the algorithm is accurate and numerically stable. Results from uniaxial load and bending moment load simulations at different loading rates are presented. The effect of finite size is studied. The results show that higher loading rate gives less yielding, and that a smaller specimen is harder than a larger one. This is in agreement with well-known results, and demonstrates that the dislocation dynamics model can describe important features of the physical problem. The cut-off velocity, that is the maximum velocity of the dislocations, is an important model parameter. In the present paper, it is shown that a four times higher cut-off velocity than was previously deemed sufficient is needed to obtain results independent of the cut-off velocity for the bending moment load simulations. ? 2002 Elsevier Science B.V. All rights reserved.

In the finite-deformation, continuum theory of crystal plasticity, the lattice is assumed to distort only elastically, while generally the elastic deformation itself is not compatible with a single-valued displacement field. Lattice incompatibility is shown to be characterized by a certain skew-symmetry property of the gradient of the elastic deformation field, and this measure can play a natural role in a nonlocal, gradient-type theory of crystal plasticity. A simple constitutive proposal is discussed where incompatibility only enters the instantaneous hardening relations, and thus the incremental moduli, which preserves the classical structure of the incremental boundary value problem.

The dynamics behavior of an assembly of parallel dislocations is investigated at different length scales. In the first part, it is shown that a discrete dislocation system is able to reproduce several important features of plastic deformation. Then, a self-consistent field continuum model is derived. Finally, a stochastic approach is outlined, which can be considered as an intermediate scale description between the discrete and the continuum models. ? 2001 Elsevier Science B.V. All rights reserved.

We present an extension of the fast-multipole method of Greengard and Rokhlin to the case of the long-range interactions between parallel edge (in arbitrary orientations) and screw dislocations. By finding complex potentials from which the stress terms can be calculated, and expanding those potentials in multipole series, we convert a computationally difficult O(N2) poroblem into a much faster O(N) approach. To reach sufficient numerical accuracy, only a few terms are needed in the multipole expansions (four screws and six for edges) so that the interactions between millions of dislocations can be calculated in a few minutes on a workstation. We present results of a study of the relaxed configurations of 16384 edge dislocations of arbitrary orientations.

The stress and displacement fields of an edge dislocation near a semiinfinite or a finite interfacial crack are formulated by using the complex potential theory of Muskhelishvili?s elasticity treatment of plane strain problems. The image forces exerted on the dislocation have an oscillatory character (with respect to the dislocation position) if the dislocation is originated elsewhere and moves to the vicinity of a finite interfacial crack. There is no such oscillation of image forces if the edge dislocation is emitted from the finite interfacial crack or if the crack is semiinfinite. The stress intensity factors produced by the edge dislocation also have an oscillatory character for both semiinfinite and finite interfacial cracks. They also depend on whether the dislocation is emitted from the crack or comes from elsewhere.

A method for solving small-strain plasticity problems with plastic flow represented by the collective motion of a large number of discrete dislocations is presented. The dislocations are modelled as line defects in a linear elastic medium. At each instant, superposition is used to represent the solution in terms of the infinite-medium solution for the discrete dislocations and a complementary solution that enforces the boundary conditions on the finite body. The complementary solution is nonsingular and is obtained from a finite-element solution of a linear elastic boundary value problem. The lattice resistance to dislocation motion, dislocation nucleation and annihilation are incorporated into the formulation through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. The deformation history is calculated in a linear incremental manner. Plane-strain boundary value problems are solved for a solid having edge dislocations on parallel slip planes. Monophase and composite materials subject to simple shear parallel to the slip plane are analysed. Typically, a peak in the shear stress versus shear strain curve is found, after which the stress falls to a plateau at which the material deforms steadily. The plateau is associated with the localization of dislocation activity on more or less isolated systems. The results for composite materials are compared with solutions for a phenomenological continuum slip characterization of plastic flow.