Interaction of dislocation pile-up with a low-angle tilt boundary: a discrete dislocation dynamics study

Abstract

The pile-up of dislocations between two low-angle tilt boundaries (LATB) in an fcc crystal was simulated using three-dimensional discrete dislocation dynamics. The LATB was constructed using glissile edge dislocations stacked on each other. The dislocations in the pile-up were chosen such that their reactions with the dislocations in the LATB resulted in glissile junctions. Parallel pairs of dislocations were inserted to a maximum allowable value estimated from theoretical expressions. A resolved shear stress was applied and increased in steps so as to move the dislocations in the pile-up towards the boundaries. The shear stress required to break the lead dislocation from the wall was determined for varying spacings between the two boundaries. The shear stress and boundary spacing followed the Hall–Petch type relation. Dislocation pile-ups without a LATB were also simulated. The spacing of the dislocations in the pile-up with LATB was found to be closer (ie higher dislocation density) than that without LATB. It was shown through analytical expressions that LATB exerts an attractive force on the dislocations in the pile-up thereby creating a denser pile-up.

Keywords:

• Dislocation dynamics
• dislocation interactions
• grain boundaries
• dislocation pile-up
• Hall–Petch effect

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Attractive configurations lead to the formation of junctions thereby pinning the dislocation. A repulsive LATB would not result in any junction formation and hence the strength of a repulsive configuration would be lower than that of the attractive one. Repulsive configurations were not studied here.

2. In the present case as the incoming dislocations cut the wall at an angle, y values would also need to be considered to accurately calculate the force of attraction. Force distribution for a non-zero y is seen to be similar to that for y = 0. The general conclusion that the boundary exerts a force of attraction on a pile-up does not change.