Dislocation-based continuum models of crystal plasticity on the micron scale

Abstract

The miniaturization trends on electronic components manufacturing, have challenged conventional knowledge on materials strength and deformation behavior. ”The smaller the stronger” has become a commonplace expression summarizing a multitude of experimental findings in micro-scale plasticity, and modelling tools capable of capturing this distinctive reality are in urgent demand. The thesis investigates the ubiquitous size effects in plastic deformation of micron-scale specimens. Tracing the source of such a behavior to the constituent elements of plastic deformation, we use as starting point the dynamics of discrete dislocations and try to embody them into a continuum framework. The thesis is structured in two independent parts. In the first part the question why size effects occur in constrained geometries is addressed. A systematic investigation of the connection between internal and external length scales is carried out in a system where dislocations, in the form of continuous lines embedded in a threedimensional isotropic medium, move, expand, interact, and thus create plastic distortion on the deforming body. Our modelling strategy utilizes a set of deterministic evolution equations on dislocation densities for describing the stress-driven evolution of the material’s internal state. These transport-like equations simultaneously serve the role of constitutive laws describing the deformation of the stressed body. Subsequent application to three benchmark problems is found to give good agreement both with experiment and discrete dislocation dynamics simulation. The second part of this thesis focuses on the heterogeneity and intermittency of deformation processes on the micro scale. Recent experimental results question the concept of smooth and homogeneous plastic flow with fluctuations that average out above a certain scale. Bursts of activity, which follow power-law size distributions and produce long-range correlated deformation patterns, seem to pertain even on scales far greater than the atomic one. In short, plasticity in this view appears as a ’crackling noise’ phenomenon similar to other irregular and burst-like processes such as earthquakes or granular avalanches. But then why do we witness smooth stress-strain curves on macroscopic sample testing? Concepts originating from Self Organized Criticality and pinning theories are employed for producing an efficient continuum description which is then used to study the effect of intrinsic and extrinsic deformation parameters on the fluctuation phenomena. It is deduced that hardening, load driving and specimen size, are all decisive on constraining fluctuating behavior, and limits of classical theory’s applicability can be drawn.