DDD-FEA modelling of Micro-cantilevers

Ed Tarleton has successfully embedded discrete dislocation dynamics simulations of plasticity within a finite element analysis framework that handles complex displacement and traction boundary conditions. The work has been a collaboration with Dan Balint (Imperial) and has provided an important tool for analysis of small scale mechanical testing experiments. The first application has been to simulate micro-cantilever bend tests on hexagonal Ti and Zr crystals conducted by Jicheng Gong. The concave domain shape causes some additional challenges in tracking dislocations slipping out of the micro-cantilevers. The marked size effect, stochastic flow behaviour, and slip band spacing evident in the experiments are all well captured by the simulations.


The animation above shows the response of a 5 micron deep cantilever to a point load deflecting the free end on the right. The green dots indicate the position of dislocation sources. The dislocations move through the material on by glide on three (prism) slip planes. Dislocations pile-up near the soft barrier formed by the neutral axis, or exit the upper and lower surfaces leaving steps. The plot (lower right) shows how the max stress - max strain varies as dislocation bursts pass through the sample.

cantilever slip steps
Slip bands and the corresponding surface slip steps are captured by the model and their spacing matches well to the experimental observations.

cantilever stress field

Analytic expressions for the stress field for dislocations in an infinite capture the very local effects while the boundary conditions (and image stress corrections) are handled by the finite element analysis. The positions of dislocations and their combined stress field are tracked in the simulations.

Related References

A Discrete Dislocation Plasticity Study of the Micro-cantilever Size Effect
E. Tarleton, D. S. Ballint, J. C. Gong, and A. J. Wilkinson
Acta Materialia, (2015), in press

Contact: Angus Wilkinson
Ed Tarleton