Dislocation Modelling of Elasto-Plastic Cracks

In various fracture processes, including fatigue and stress corrosion cracking, the crack takes an often complex path following specific microstructural features such as slip bands and grain boundaries as it propagates through the material. Micromechanical modelling must take account of the effects of multiple crack deflections in calculating the driving force for crack advance. We have developed dislocation dipole based boundary element models to analyse such problems. Climb and glide dipoles are distributed along the crack path to represent the mode I and mode II opening. Similarly glide dipoles are placed along slip planes to represent plastic flow. The ‘strength’ of these dipoles is found by imposing stress based boundary conditions at collocation points at the centre of each element, and solving through an iterative scheme. This is really a numerical/discrete extension of the classic Bilby-Cottrell-Swinden model. The approach is very flexible in being able to capture complex two dimensional cracks. We have validated the implementation of the model by analysing some simple geometries for which analytic solutions are available, and then extending these to situations where obvious trends in the results are to be expected. We have then moved on to look at the more complex problem of a grain boundary crack propagating through a two dimensional microstructure. Here the model is used within a Monte Carlo framework to assess statistical aspects as cracks are propagated through many virtual microstructures.

BEM crack model schematic
mode I stress field
crack path through random microstructure
stress intensity factor along crack path

Contact: Anke Stoll and Angus Wilkinson

Discrete Dislocation Based Simulations of Plasticity associated with Stationary and Quasi-Statically Advancing Cracks
Anke Stoll and Angus J Wilkinson
Int. J. Fracture, (2010), available on-line