Part 1

Part 1: Frank read source operation

Description of the simulation:

The simulation box for our example is 12000x12000x12000 (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.

2. From the command line, execute the program by typing MDDP08.exe 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.

Postprocessing- visualization of the dislocation structure

TecPlot is a general postprocessor which offers enhanced capabilities and can read output data from different softwares. 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. To visualize the dislocation structure, open TecPlot and follow these steps:

• From File -> Load Data Files -> TecPlot Data Loader and browse for the directory in which you ran the executable
• Choose tech002 and click on open
• From the Select Initial Plot box, Initial Plot type drop down menu choose3D Cartesian and check the Show First Zone Only box and then OK
• From the Plot drop menu, select Axis and from the Axis Details box, check the Show Axis box to show all axes
• From the Plot menu, go to Vector -> length -> choose V1, V2, and V3 for U, V, and W respectively. Then make sure that the Relative Grid Units/Magnitudes set to 1.0 and click Close.
• 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, you can use AnimateZones. Alternatively you can activate/deactivate specific zones (time steps) by clicking the Zone Style tab, selecting the desired zones and clicking on Zone Show and choosing the desired action.

Postprocessing- XY plot of time histories and stress-strain curves

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

• Choose tech002 and click on open
• From the Select Initial Plot box, Initial Plot type drop down menu choose XY Line and check the Show First Zone Only box and then OK
• To display different maps, click on Mapping Style tab and manipulate the different maps in the same way you manipulated the zones above. You might need to fix the x and y scale as you switch from one map to another. To do so, go to Plot -> Axis and click on the Reset Range -> Reset to Nice Values for each axis you want to adjust
• To plot the stress-strain curve, choose map number 2, Stress. Click on the X-axis Variable and from the drop down menu in the Select Variable box, choose strain.
• Using the Map Show choose to activate this map only (you will need to reset the range as described above)

Homework Requirement:

Go through the above procedure and

1. Obtain a plot of the dislocation density evolution as a function of time (you can used EditCopy to Clipboard and then paste in any document)

2. Obtain a plot of the stress vs time and verify the actual strain rate

3. Obtain the stress-strain curve

4. Using the same setup, modify the DDinput file so that the dislocation is of pure screw character. Repeat the same steps 1, 2, and 3 and compare the results