The Complexity in Materials group conducts both theoretical and experimental research into complex phenomena in material science. Particular areas of interest include: hysteresis and noise in ferromagnetic material, fluctuations in fracture and plasticity, collective transport in nanostructured materials and deformation in soft condensed matter physics. We are particularly active in the statistical analysis of the Barkhausen noise in ferromagnetic thin films and strips, and in the study of computational models for magnetic domain walls in disordered media. We perform large scale numerical simulations of lattice models for the fracture and plasticity of heterogeneous materials. Another subject of current investigation is the topological properties of deformed colloidal and vortex crystals, which we study by molecular dynamics simulations.
Domain wall dynamics in ferromagnetic materials:
The Barkhausen effect is the name given to the noise in the magnetic output generated in a ferromagnetic material when the magnetising field applied to it is changed. It is understood that the origin of this noise is due to the fact that the domain wall, which moves in response to the externally applied magnetic field, moves in a jerky manner. This irregular motion is due to the fact that the domain wall can become pinned, at various points, by impurities in the material. By increasing the strength of the external field the domain wall can become locally depined and moves forward, only to become trapped once again by more impurities further ahead. The study of the Barkhausen effect is currently one of the most active fields in the science of soft magnetic materials. There is considerable interest from an applied perspective, since the amount of Barkhausen noise for a given material is linked with the amount of impurities and defects it contains. This effect can be used as a non-destructive means of analysing the mechanical properties of a material. However, the success of this approach is contingent on having a flexible and accurate simulation method. The method must be able to incorporate a number of effects which can yeild a dramatic change in the morphological and dynamic properties of the domain wall. These include: (i) a cross over in the presence of long range dipolar forces acting on the domain wall, (ii) a cross over upon going from a strictly 1D interface (in a 2D space) to a 2D interface (in 3D space).
The above image (from our recent paper) shows the effect on the morphology of the domain wall depending on the strength of the long range dipolar forces. These long range forces are weak for low values of the saturation magnetisation (left image) and strong for high values of the saturation magnetisation (right image). It is found that the behaviour of Barkhausen avalanches can be described by two separate universality classes depending on the value of the saturation magnetization. On the one hand, when the long range diploar interaction is strong the domain wall has saw toothed morphology which has the effect of reducing the magnetic charge density. On the other hand, by increasing the temperature of the sample it is possible to study the regime in which the saturation magnetization is negligible. In this case the morphology of the domain wall is dominated by line tension and is observed to form a rough interface free of large zigzags.
Statistical models for fracture and plasticity
The average damage concentration around a notch in a disordered medium allows to identify a fracture process zone, in red.
The comparison between an optimal path (ME) and a perfectly plastic yield surface in a model for plasticity in a disordered medium.
The complexity in materials group has been working in the characterization of fracture and plasticity in disordered media through the use of statistical lattice models, which allow for relatively simple descriptions of disorder and elasticity. The cornerstone in this respect has been for the last twenty years the Random Fuse Model (RFM) a lattice model for the fracture of solid materials in which as a further key simplification vectorial elasticity has been substituted with a scalar field. Recently, we have used the RFM to study the crossover from deterministic to statistical size effects when the sample has a large notch (1). This is a central problem in materials science and engineering, since the dependence on the sample size of the fracture strength has important implication for the safety and reliability of components and structures. In our study, we were able to show that statistical size effects always prevail at sufficiently large sizes even if a large flaw is present in the sample. We have also characterized the elusive fracture process zone ahead of the crack tip, where most of the damage processes take place (Figure). While brittle materials show dramatic size effects, with the strength going to zero as the sampe size increases, ductile materials show much smaller size effects. A plastic version of the RFM has been used to study ductile yielding of disordered media and the relation to optimization (2). It has been argued in the past that yielding is an optimization process and that the yield surface, where the plastic deformation is concentrated, corresponds to a minimum energy surface. We have shown that this claim does not apply (see Figure) and the two surfaces differ. As a result, the global yield stress is lower than expected from naive optimization and the difference persists as the sample size increases. We have provided a theoretical argument that explains how this behavior arises from the very different nature of the optimization problem in both cases.