# MDDP Supplemental Notes

1. The first portion of the MDDP section aims at introducing the basic procedure to run a dislocation dynamics simulation using the code MDDP and its supporting routine, FCCdata. This will be done in the context of an elementary problem involving dislocation multiplication from a dislocation segment pinned at both ends, commonly referred to as Frank Read source (FRS).
2. The second part of the homework is an exercise of multiscale modeling; more specifically, upscale bridging of dislocation mobility from the nanoscale to the microscale. The validity of the results of dislocation dynamics simulations hinges on the validity of the mobility law used. The mobility describes the lattice resistance to dislocation glide which is a complex phenomenon involving different mechanisms like phonon and electron drag and is very dependent on the details of core structure as well as temperature and pressure. Because of that, molecular dynamics is the framework most suited to capture mobility, which can then be passed on as one of the centerpieces of the dislocation dynamics calculations.

## Part 1. Frank read source operation

### Description of the simulation

The simulation box for our example is 12000b x 12000b x 12000b (in units of the magnitude of the Burgers vector, b, with the origin in the center of the box. The crystal is oriented so that the normal to the (111) plane is along the global z-axis, the [-211] crystallographic direction along the x-axis and the [0-11] along the y-direction. The initial dislocation structure consists of a dislocation line of length 2000b extending along the x-axis with its line sense in the negative x-direction. Its Burgers vector points in the negative y-direction. This makes the character of this dislocation pure edge. Shear stress yz is applied with constant shear strain rate of 10 s-1. The two end points of the dislocation are pinned. The boundary condition is rigid walls in all directions, which means that the dislocations cannot penetrate the walls and would pile-up against it. Under the effect of the shear stress, the dislocation bows out, forms a loop and continuous operating in this mode generating increased number of loops. This process becomes harder as more dislocations pile up against the walls and induce back stress on the source, ultimately shutting it down.

### Running the simulation

This simulation is performed using MDDP and requires two input files DDinput and data. DDinput features the details of the initial dislocation structure (coordinates, global Burgers’ vector components, slip plane, node constrains, and connectivity of the dislocation nodes), the loading parameters and the mesh size and the time step. The data file includes the material parameters and additional numerical and output control parameter. Please refer to the manual for more details.
1. Create a directory and include in it the executable version of MDDP08 (you can use either the Windows MDDP08 executable or the Linux executable) as well as the two input files DDinput and data. The file’s name should be precisely DDinput and data.
2. From the command line, execute the program by typing MDDP08.exe (Windows) or ./MDDP08 (Linux) and hit Return
3. Respond by y to start the calculations
4. The screen output , in order is:
Step number, current number of node, total strain, stress, dislocation density, current time step, and load stepping time increment
5. The calculations will run until the maximum step numbers is met. In our case you can stop the run when sufficient dislocation activity occurs to demonstrate the operation of the FRS and the hardening effect.

### Post processing - visualization of the dislocation structure

TecPlot is a general postprocessor which offers enhanced capabilities and can read output data from different software. The output files from MDDP are configured to be ready used with TecPlot. The information describing the dislocation structure is dumped into a chain of files starting with “tech” followed by a series number of the file (tech002, tech004, etc.). Each file has the dislocation structure data for 500 time steps. The first 500 steps are written to tech002, the next 500 steps are written to tech004, and so on. This is done in order to keep the files’ size reasonable. A video tutorial can be found here. To visualize the dislocation structure, open TecPlot and follow these steps:

• From File-->Load Data Files ‐‐ change Files of type: to TecPlot Data Loader and browse for the directory in which you ran the executable
• In the File name: box type te* and hit enter
• The folder should populate with files from tech002 to techIJK (where IJK is the final number of tech files generated)
• Select all of the files you wish to load, and click Open
• Under Plot change XY Line to 3D Cartesian
• From the Plot drop menu, select Axis and from the Axis Details box, check the Show Axis box to show all axes; uncheck Preserve length when changing range, and change the Min: and Max: values for each axis to -6000 and 6000, respectively; click Close
• Under Plot go to Vectorvariableschoose V1, V2, and V3 for U, V, and W respectively. Then go to VectorLength and make sure that the Relative Grid Units/Magnitudes set to 1.0 by going to and click Close
• Click Zone Style... select all of the zones and uncheck Show Zone; Click on Zone 001 and check Show Zone
• On the left hand side of the screen, check the box next to Vector. You should be able to see the initial dislocation lines and use the typical controls to rotate, zoom, etc. to help you visualize the structure
• To visualize the structure at different time steps, under DataEdit Time Strands... Select Constant Delta and ensure that Delta: is set to 1; Click Apply (For a large amount of zones this will take somewhere between 10 minutes and 1 hour to animate)
• An area for animation playback should appear with play, step forward, and go to end blue- colored buttons; you should now be able to play the animation\
• You can modify the speed of playback by clicking Details... next to Solution time:

### Post processing- XY plot of time histories and stress-strain curves

￼The main file that contains this information is DDtimeResults.out, which plots the history of multiple variables including the dislocation density, stress, strain, etc. Each plot is referred to as a map in TecPlot. Open TecPlot and follow these steps:

• From File-->Load Data Files ‐‐ change Files of type: to TecPlot Data Loader and browse for the directory in which you ran the executable
• In the File name: box type DD* and hit enter
• Choose DDtimeResults.out and click Open
• The initial XY plot will be a disDensity vs. timenow; you can change this by clicking Mapping Style...
• In the Mapping Style window you will have several map numbers with corresponding names and the variables they are plotted against
• To create the stress-strain curve for your DDtimeResults.out uncheck Show Map for disDens... and check Stress; Right-click on 1:timenow to change the x-axis variable to 4:Strain
• From the Plot drop menu, select Axis and from the Axis Details box, click Reset Range and select Reset to Nice Values; select Y1 at the top and repeat the previous procedure; click Close
• You can now repeat the entire process to produce other curves such as dislocation density vs. stress or strain

## Part 2: Bridging mobility from molecular dynamics to dislocation dynamics

### Description of the simulation

The data and DDinput files provided in the MFRS folder represent a simulation box of size 2000b x 2000b x 10000b along the x-, y-, and z-direction, respectively, and containing an initial dislocation structure consisting of 12 Frank Read sources distributed randomly on all slip systems.

### Simulation information

• Follow the same process as instructed in Part 1 for running the simulation and visualizing the data output.
• For the axis sizes you should change them to match the simulation box size generated by the MFRS DDinput file (2000 x 2000 x 10000).
• Note that since there are 12 FRS the simulation may need to run for more steps than in Part 1, and the output will be larger.

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