Fluctuation phenomena in crystal plasticity - a continuum model

On microscopic and mesoscopic scales, plastic flow of crystals is characterized by large intrinsic fluctuations. Deformation by crystallographic slip occurs in a sequence of intermittent bursts ('slip avalanches') with power-law size distribution. In the spatial domain, these avalanches produce characteristic deformation patterns in the form of slip lines and slip bands which exhibit long-range spatial correlations. We propose a generic continuum model which accounts for randomness in the local stress-strain relationships as well as for long-range internal stresses that arise from the ensuing plastic strain heterogeneities. The model parameters are related to the local dynamics and interactions of lattice dislocations. The model explains experimental observations on slip avalanches as well as the associated slip and surface pattern morphologies

Some Limitations of Dislocation Walls as Models for Plastic Boundary Layers

It has recently become popular to analyze the behavior of excess dislocations in plastic deformation under the assumption that such dislocations are arranged into walls with periodic dislocation spacing along the wall direction. This assumption is made plausible by the fact that periodic walls represent minimum energy arrangements for dislocations of the same sign, and it allows to use the analytically known short-ranged stress fields of such walls for analyzing the structure of plastic boundary layers. Here we show that unfortunately both the idea that dislocation walls are low-energy configurations and the properties of their interactions depend critically on the assumption of a periodic arrangement of dislocations within the walls. Once this assumption is replaced by a random arrangement, the properties of dislocation walls change completely.Comment: To appear in: Proceedings of the International conference on numerical analysis and applied mathematics (ICNAAM) 2011, 4 pages, to appear in APS proceeding

Depinning of a dislocation: the influence of long-range interactions

The theory of the depinning transition of elastic manifolds in random media provides a framework for the statistical dynamics of dislocation systems at yield. We consider the case of a single flexible dislocation gliding through a random stress field generated by a distribution of immobile dislocations threading through its glide plane. The immobile dislocations are arranged in a "restrictedly random" manner and provide an effective stress field whose statistical properties can be calculated explicitly. We write an equation of motion for the dislocation and compute the associated depinning force, which may be identified with the yield stress. Numerical simulations of a discretized version of the equation confirm these results and allow us to investigate the critical dynamics of the pinning-depinning transition.Comment: 8 pages, 4 figures. To appear in the proceedings of the Dislocations2000 meeting (published by Materials Science and Engeneering A

Determining Cosserat constants of 2D cellular solids from beam models

We present results of a two-scale model of disordered cellular materials where we describe the microstructure in an idealized manner using a beam network model and then make a transition to a Cosserat-type continuum model describing the same material on the macroscopic scale. In such scale transitions, normally either bottom-up homogenization approaches or top-down reverse modelling strategies are used in order to match the macro-scale Cosserat continuum to the micro-scale beam network. Here we use a different approach that is based on an energetically consistent continuization scheme that uses data from the beam network model in order to determine continuous stress and strain variables in a set of control volumes defined on the scale of the individual microstructure elements (cells) in such a manner that they form a continuous tessellation of the material domain. Stresses and strains are determined independently in all control volumes, and constitutive parameters are obtained from the ensemble of control volume data using a least-square error criterion. We show that this approach yields material parameters that are for regular honeycomb structures in close agreement with analytical results. For strongly disordered cellular structures, the thus parametrized Cosserat continuum produces results that reproduce the behavior of the micro-scale beam models both in view of the observed strain patterns and in view of the macroscopic response, including its size dependence

Slip avalanches in crystal plasticity: scaling of the avalanche cutoff

Plastic deformation of crystals proceeds through a sequence of intermittent slip avalanches with scale-free (power-law) size distribution. On macroscopic scales, however, plastic flow is known to be smooth and homogeneous. In the present letter we use a recently proposed continuum model of slip avalanches to systematically investigate the nature of the cut-off which truncates scale-free behavior at large avalanche sizes. The dependence of the cut-off on system size, geometry, and driving mode, but also on intrinsic parameters such as the strain hardening rate is established. Implications for the observability of avalanche behavior in microscopic and macroscopic samples are discussed.Comment: 12 pages, 4 figure