In crystalline materials plastic deformation observed on the microscopic level is a stohastic process, opposed to what one can observe in case of bulk samples. This process can be described by the motion of dislocations. The most simple 2D models have the capability to reproduce this stohastic behavior. In this case the motion of the dislocations are deterministically governed by the equation of motion for each dislocation which kind of suggest a deterministic end state regardless of the underlying non linear dynamics.
In this project you will examine different ML models to try to predict the critical external stress, based on the initial relaxed configuration. For this end, you need to utilise a prewritten 2D dislocation simulation tool (SDDDST) to create a dataset of relaxed dislocation simulations and the corresponfing loaded systems.
The simulator with a short description about basic usage can be found here: SDDDST While deatiled informations can be found in this publication: https://iopscience.iop.org/article/10.1088/1361-651X/ab76b2/meta
You can use any tools based on your preferences. E.g.: python, bash, gnuplot, tensorflow, etc... Do not be afraid to modify the actual source of the simulation tool, but keep in mind if you modify something, the functionality has to stay intact most of the time, otherwise you are going to get invalid results!
- Download and build the source of sdddst onto your computer. Study the available documentation and the help menu. Play around with it ;) Create a configuration with two dislocations in non equilibrium state (with same and different Burgers-vectors) and relax the system. Analyse the results and the log file! Make a script to be able to generate random dislocation configurations with the given number of dislocations, while the net Burgers vector sum is zero. Repeat the evaluation from the two dislocation case for a more complex system.
- Create a small script which is able to extract how the internal stress field, generated by dislocation looks like. Plot it for different configurations! Determine the GND as well. Visualize it!
- Run simulations for dislocations with system size 256, 400, 800. Analyize the stress-strain curves. Plot the average curve along with the individual ones.
- Build an ANN which tries to predict the stress value where an avalanche occurs! Pro tip: Use the provided reading materials.
- Try a different ML model!
- Measure the accuracy of the models for different system sizes.
- Try to identify additional features.
- Dislocations - Wikipedia
- Gábor Péterffy and Péter Dusán Ispánovity: An efficient implicit time integration method for discrete dislocation dynamics
- Henri Salmenjoki, Mikko J. Alava & Lasse Laurson: Machine learning plastic deformation of crystals
- Hirth & Lotte: Theory of dislocations
- Péter Dusán Ispánovity, István Groma, Géza Györgyi, Ferenc F. Csikor and Daniel Weygand: Submicron Plasticity: Yield Stress, Dislocation Avalanches, and Velocity Distribution
- Péter Dusán Ispánovity, István Groma, Géza Györgyi, Péter Szabó and Wolfgang Hoffelner: Criticality of Relaxation in Dislocation Systems
- H H. M. Cleveringa, E. Van Der Gissen & A. Needleman: Comparison of discrete dislocation and continuum plasticity predictions for a composite material