The role of elasticity and disorder and their interplay in plastic deformation processes is investigated on different length scales. Random disorder, in the form of impurities, fluctuations of defect densities and spatial heterogeneities, is responsible for a wealth of phenomena including surface roughening, non-linear dynamic response, stick-slip behaviour and temporal intermittency, which are observed in a wide variety of physical systems. A theoretical description of these phenomena is provided by theories of pinning and depinning transitions. In this work, these aspects are investigated in the context of plastic deformation of random media, such as real crystals with disordered microstructures or disordered elastic continua. Under the effect of an external force, these systems exhibit a complex behaviour arising form the competition between elasticity and disorder. Disorder tends to perturb the system, which reacts by opposing elastic restoring forces. This complex small scale dynamics determines the macroscopic behaviour of irreversibly deforming materials. These aspects are studied on different length scales. The problem of the depinning transition occurring in dislocation assemblies is first investigated. Dislocations are microstructure defects mediating plastic deformation. Under the effect of external forces, they are driven through disordered landscapes and rearrange into complex assemblies. A theory of pinning and collective behaviour of linear and planar dislocation arrays is formulated. Non-local elastic properties arise naturally form long-range dislocation interactions and influence dramatically statics and dynamics of these systems in the presence of disorder. Comparison with numerical results and experimental data confirms the validity of this approach. An application to vortex lattices in Type II superconductors is then considered. Dislocation assemblies such as low angle grain boundaries are often observed in these systems, determining the emergence of a polycrystalline phase. A theory of vortex polycrystals is proposed, in the conceptual framework of grain boundary pinning. Several aspects, including grain growth, transport properties, hysteretic behaviour and vortex lattice melting are investigated. Results are found in agreement with numerical simulations and experimental observations. On larger length scales, a theory of plastic flow in the presence of random stress fluctuations is discussed. The problem proves to be described by a continuum mean-field pinning model, where disorder is produced by randomness in dislocation densities. Such a description provides a theoretical framework to understand the origin of the critical behaviour often observed in plastically deforming crystals in the form of self-affine surface roughening and intermittent avalanche motion.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:659577 |
| Date | January 2005 |
| Creators | Moretti, Paolo |
| Publisher | University of Edinburgh |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://hdl.handle.net/1842/15428 |
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