Statistical micro-mechanics of dislocations.

Описание: 2025-10-16 Lecture by prof Raf Schouwenaars.

Abstract:
Traditionally, the micro-mechanics of defects in solids has focused on the stress fields and elastic strains induced by inclusions and dislocations. The strength of alloys is then assumed to depend on the interaction between the stress fields of crystal defects, with the dislocation pileup at grain boundaries being the classical example.
To explain strain hardening, dislocation slip and storage must be included, leading to the Kocks-Mecking (KM) model, which calculates the stress from dislocation density through the Taylor equation.

This lecture revisits the KM model and presents its mathematical foundations, to investigate how it can be modified to include additional hardening effects. The Taylor equation will be derived from a balance equation for dislocation emission and storage, based on the statistical properties of a plane Poisson process. The resulting ordinary differential equation (ODE) inherently provides a way to include particle hardening. Then, the role of grain boundaries (GB) as sources and sinks for dislocations will be explained. By calculating how the slip length is affected by the presence of the GBs, a modification of the KM equation is found without the introduction of additional fitting parameters. Comparison with literature data shows that the new ODE correctly predicts the grain size effect (GSE).

It is concluded that strain hardening, particle strengthening and the GSE can be modelled by a set of two ODEs. The role of shearable precipitates and solid solution can be included in a lattice friction term, which will be studied in more detail in future research.