In this project the propagation of fatigue cracks is modeled by a novel Strain Gradient Plasticity and a novel Cohesive Surfaces model.
This work was carried out at the School of Mechanical Engineering with Thomas H Siegmund.

A Dislocation Density based Strain Gradient Plasticity Theory

Strain gradient models incorporate a length scale to account for size effects that are for example observed in nano-indentation and nano-torsion experiments, and also are relevant in crack tip fields. The evolving dislocation density provides a natural length scale through its inverse square root. We identify two sets of dislocation densities. The first is related to plastic strain and it introduces a material length, i.e. the average distance of dislocation motion. The second dislocation density is related to plastic strain gradients and commonly referred to as Geometrical Necessary Dislocations. In the absence of a strain gradient the model leads to a uni-axial hardening close to that of a power-law hardening. In the presence of a strain gradient, the material hardens substantially. The plasticity model is employed together with a cohesive surface model to study the evolution of material damage, which leads to fatigue crack propagation. (see image below)

A Dislocation Density based Cohesive Surface Model

Dislocations play a central role in fatigue crack growth of metals. On the one hand, they shield the crack tip through plastic deformation, reducing the stress level at the crack tip and by increasing the crack growth resistance through energy dissipation. The shielding effect of dislocations is well captured by continuum models of fatigue which include plasticity. On the other hand, dislocations possess their own singular elastic stress field, and in the vicinity of the crack tip elevate the stress level. If sufficient dislocations are found in the proximity of the crack tip, the stress at the crack tip is elevated sufficiently to overcome the strength. Thus a crack can advance. The dislocation density based cohesive surface model combines both effects to establish a novel and comprehensive cohesive surface model.

The work is supported by the Air Force Office for Scientific Research.

Papers