Epl Draft

EPL (Europhysics Letters), 2008

A novel analysis of homogeneous nucleation of dislocations in sheared twodimensional crystals described by periodized discrete elasticity models is presented. When the crystal is sheared beyond a critical strain F = Fc, the strained dislocation-free state becomes unstable via a subcritical pitchfork bifurcation. Selecting a fixed final applied strain F f > Fc, different simultaneously stable stationary configurations containing two or four edge dislocations may be reached by setting F = F f t/tr during different time intervals tr. At a characteristic time after tr, one or two dipoles are nucleated, split, and the resulting two edge dislocations move in opposite directions to the sample boundary. Numerical continuation shows how configurations with different numbers of edge dislocation pairs emerge as bifurcations from the dislocation-free state.

Handbook of Materials Modeling, 2005

Plastic deformation of crystalline solids is of both scientific and technological interest. Over a wide temperature range, the principal mechanism of plastic deformation in crystalline solids involves the glide of large numbers of dislocations. As a consequence, since the 1930s, when dislocations were identified as carriers of plastic deformation in crystalline solids, there has been considerable interest in elucidating the physics of individual dislocations and of dislocation structures. Major effort has also been devoted to developing tools to solve boundary value problems based on phenomenological continuum descriptions in order to predict the plastic deformations that result in structures and components from some imposed loading. Since the 1980s these two approaches have grown toward each other, driven by, for instance, miniaturization and the need for more accurate models in engineering design. The approaches meet at a scale where the collective behavior of individual dislocations controls phenomena. This encounter, together with continuously increasing computing power, has fostered the development of an approach where boundary value problems are solved with plastic flow modeled in terms of the collective motion of discrete dislocations represented as line defects in a linear elastic continuum . This is the field of discrete dislocation plasticity.

IOP Conference Series: Materials Science and Engineering, 2009

In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study two cases: i) the particular case of parallel straight dislocations and ii) the general case of curved dislocations. In each case, we perform rigorously the homogenization of the dynamics and predict the corresponding effective macroscopic elasto-visco-plastic flow rule.

Modelling and Simulation in Materials Science and Engineering, 1995

A method for solving small-stnin plasticity problem 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 h e a r elastic medium. At each instant, superposition is used to represent the solution in terms of the infinitemedium 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 nuclealion 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-swain boundary value problem are solved for a solid having edge dislocaUons on parallel slip planes. Monophase and compasite materials subject to simple shear p d i e l to the slip plme are analysed. Typically, a peak in the shear stress versus shear strain C U N~ is found, &er which the svess falls to a plateau at which the material deforms steadily. The plateau is associated with the localization of dislocation activity on more or less isalated systems. The results for composite malerials are compared with solutions for a phenomenological continuum slip characterivtion of plastic flow.

Journal of Engineering Materials and Technology, 2009

Discrete dislocation dynamics is a numerical tool developed to model the plasticity of crystalline materials at an intermediate length scale, between the atomistic modeling and the crystal plasticity theory. In this review we show, using examples from the literature, how a discrete dislocation model can be used either in a hierarchical or a concurrent multiscale framework. In the last section of this review, we show through the uniaxial compression of microcrystal application, how a concurrent multiscale model involving a discrete dislocation framework can be used for predictive purposes.

Materials Science and Engineering: A, 2008

Continuum frameworks of dislocation-based plasticity theories are gaining prominence in the research community. In these theories, the underlying discrete lattice defects are represented by an averaged continuous description of a signed dislocation density. The long-range stress fields are accurately characterized but the short-range interactions are modeled phenomenologically. In this paper, we demonstrate by a rigorous analysis that short-range interactions resulting from certain aspects of the underlying discreteness cannot be neglected. An idealized problem of dislocation pile-ups against a hard obstacle is used to illustrate this observation. It is also demonstrated that the modeling of short-range interactions by a local gradient of dislocation distribution has limitations. It is realized that even though the stress contribution for distant dislocations is relatively small, it is the accumulation of these stress contributions from numerous such dislocations which culminates in substantial contributions. It would be inaccurate to neglect these effects. Our benchmark problem can be used for calibration of current and future theories of plasticity that attempt to accurately model short-range interactions.

Journal of the Mechanics and Physics of Solids, 2001

The question of the description of the elastic ÿelds of dislocations and of the plastic strains generated by their motion is central to the connection between dislocation-based and continuum approaches of plasticity. In the present work, the homogenization of the elementary shears produced by dislocations is discussed within the frame of a discrete-continuum numerical model. In the latter, a dislocation dynamics simulation is substituted for the constitutive form traditionally used in ÿnite element calculations. As an illustrative example of the discrete-continuum model, the stress ÿeld of single dislocations is obtained as a solution of the boundary value problem. The hybrid code is also shown to account for size e ects originating from line tension e ects and from stress concentrations at the tip of dislocation pile-ups.

2007

A dislocation ensemble is a system of objects with long range i teraction. So the traditional methods developed for atomic sys tem to derive a continuum theory from the equation of motion of the individual objects cannot be directly applied. We consider a set of parallel edge dislocations representin g the simplest possible, but already rather complex system. It is shown, that based on dis crete dislocation simulation results, a link between the microscopic and mesoscopic length-scale description of the collective behavior of dislocations can be establish ed. It is found that the continuum theory of dislocations can be formulated as a phase fie ld th ory.

Philosophical Magazine, 2010

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Fundamentals - Microstructures - Process Applications, 2005