Robb Thomson

Theory of Strain Percolation in Metals: Mean Field and Strong Boundary Universality Class

For the percolation model of strain in a deforming metal proposed earlier, we develop sum rule and mean field approximations which predict a critical point. The numerical work is restricted to the simpler of two cases proposed in the earlier work, in which the cell walls are “strong”, and unzipping of the dislocation entities which lock the walls into the lattice is not permitted. For this case, we find that strain percolation is a new form of correlated percolation, but that it is in the same universality class as standard percolation.

In-situ observation of small-angle X-ray scattering by dislocations

Ultra-small-angle X-ray scattering by dislocations in single-crystal aluminum has been observed in situ as a function of plastic deformation. The scattering is strongly dependent upon sample orientation, with single dislocations, dislocation dipoles, and the dislocation distribution within walls each exhibiting distinct scattering profiles. Among the microstructural features that have been observed are: the correlations between the ordered fraction of dislocations, the presence of dislocation dipoles, the increasing dislocation content with increasing strain, and the decreasing width of the interface between dislocation walls and the surrounding nearly-dislocation-free material with increasing deformation.

Self-organized critical behavior in a deforming metal

It has been shown that the transport of mobile dislocations through blocking dislocation walls in a deforming metal can be treated by a simple percolation theory. Two different mechanisms for strain propagation are proposed in the strain percolation model. In the first case, the strain propagates between adjacent dislocation cells by activation of sources within the walls. In the second case, as an additional mechanism, unstable locks can be unzipped by a nearby dislocation pileup which can lead to a large localized strain. Previous simulations have shown that both cases belong to the same universality class as standard percolation. Further extensive simulations of the model have been performed to understand how the geometrical aspects of a strained percolating cluster are related to the strain itself. In our case, the strain is an additional variable not present in standard percolation theory. We find that the total strain and the mean strain per strained cell show power-law behavior in the critical regime, and obtain a scaling function which explains its critical behavior. Other percolation and critical aspects of the model are also discussed in terms of the initial strain, correlation length (which is a characteristic length scale), and model parameters.

Critical behavior of a strain percolation model for metals with unstable locks

Using a strain percolation model proposed for the transport of mobile dislocations through a dislocation cell structure in a deforming metal, we have further explored the critical behavior of the model when there are some unstable locks present in the system that may be broken by the stress field of incident dislocations. The presence of such locks changes dramatically some of the characteristic features of the system. One such change is a fractal distribution of broken locks within a strained cluster leading to a model parameter-dependent critical point. In the critical regime, growth of a strained cluster as well as the distribution of broken locks within the cluster exhibits universal power-law behavior well explained by ordinary two-dimensional percolation theory. This random aspect of the model at large scales appears to arise from a self-organizing critical behavior of cells that evolve into a state of a minimum stable strain.

Asymptotic Behavior of a Strain Percolation Model for a Deforming Metal

In this paper, we present a recent advance in theoretical understanding of a deforming metal, using a strain percolation model which possibly explains spasmodic, fine slip line burst events occurring in the metal. The model addresses how the additional strain nucleated in a cell propagates through a dislocation cell structure, and predicts that near the critical point, the system exhibits critical power-law behavior. It is found that although the model displays long-transient behavior associated with the initial strain in the model, asymptotically critical behavior observed in the system is well explained by standard percolation theory. The long-transient behavior suggests that finite-size effects could be an important factor for the stress-strain relation in the metal. A detailed study reveals that the universal aspects of the model, i.e., the evolution into an initial condition- independent, critical state, arise from collective behavior of a huge number of self- organizing critical cells that develop the minimum or at least marginally stable strain

Strain Percolation in Metal Deformation

In previous papers, we have introduced a percolation model for the transport of strain through a deforming metal. In this paper, we summarize the results from that model, and discuss how the model can be applied to the deformation problem. In particular, we outline the primary experimental features of deformation which the model must address, and discuss how the model is to be used in such a program. It is proposed that the discrete percolation events correspond to slip line formation in a deforming metal, and it is shown that the deforming solid is a self organizing system. It is recognized that deformation is localized in space and time, that deformation is fundamentally rate dependent, that hardening depends upon relaxation processes associated with discrete percolating events, and that secondary slip is an essential part of band growth and relaxation processes.