ICME 2017 HW3
In this homework, we will bridge information from the microscale to the mesoscale. You will dislocation dynamics simulations with multiple Frank Read sources to determine parameters for a hardening rule which will be used in a crystal plasticity code (CPFEM). Thus, there are two parts to this assignment:
- Dislocation Dynamics (DD) using Multiscale Dislocation Dynamics Plasticity (MDDP)
- Crystal Plasticity (CPFEM) implemented as a user material routine in ABAQUS or Calculix
This exercise uses the hardening law parameters obtained from DD calculations. The hardening law for slip systems is a critical aspect of crystal plasticity models and contains material related parameters which are difficult to obtain from experiments. Thus, DD serves as a "virtual experiment" from which the hardening parameters can be determined.
All necessary input files and scripts are available through the website. Save these files to your own directory (and make a backup copy) before trying to perform any simulations.
Use /scratch/"Your Directory" for best results.
Write a full report that follows a journal article manuscript format (include figures and tables in the text). Please double-space your document
Upon completion, submit via email a .pdf and .doc(x) file of your report. Be sure to also include the requested files and plots from each section of the homework.
Part 1 - Dislocation Dynamics Virtual Experiment
This exercise uses dislocation dynamics calculations to determine the parameters of the hardening law used in crystal plasticity. The hardening law for the slip systems is a critical aspect of crystal plasticity models and contains material related parameters that are hard to obtain from experiments. Dislocation dynamics can serve as a “virtual experiment” from which the hardening parameters can be determine using a fitting procedure.
The setup for MDDP is the same as in the previous homework.
Dislocation Forest Hardening
The steps to run and post-process the results from MDDP will be the same as in the previous homework. However, this time you need to create a DDinput file that includes multiple Frank-Read sources.
- 1. Using the three stress-strain curves from dislocation dynamics and by assuming a linear fit to the work hardening (post-yield portion of stress-strain curve), estimate the slope of the linear hardening regime. How does uncertainty affect the linear assumption? Is there a better assumption than linearity?
- 2. Fit dislocation density results to the Voce Hardening Law (Equation 9.9 in ICME textbook).
- 3. Report on your results
Part 2 - Upscale Dislocation Forest Hardening to Crystal Plasticity
- Run a one-element finite element simulation using the Voce hardening law with one crystal orientation.
- Plot a stress strain curve for each set of hardening constants.
- Report on your results.
For either software, you will need the input files for CPFEM in an aluminum material found here. If you are using a bcc material, you will also need the bcc slip system file here.
For Calculix, also download these two files: (umat_cpfem.f) & (calculix umat.f), and compile as described on the Calculix page (add link).
Single Crystal CPFEM Simulation
Create the input file.
(Hint: Calculix can take Abaqus input files, and an Abaqus student edition is available free of charge.)
- Create a cube
- Constrain the cube so that all rigid body displacements and rotations are constrained.
- Constrain one corner of the cube to be fixed in all directions
- Constrain two adjacent nodes to be fixed in the direction of loading. Make sure that these 3 nodes are all in a plane which is perpendicular to the direction of loading.
- Constrain one of these two adjacent nodes to be fixed in a second direction, such that this node cannot rotate about the fixed corner of the cube.
- Mesh the cube such that only a single element is created.
- Add a displacement to the face opposite of the constrained face, such that a large strain is applied to the cube.
- Add a user material to the cube (in Calculix, name it UMAT_XTAL), and set the number of dependent variables (*DEPVAR) equal to the number of grains times 70.
- For the single grain case a new material will need to be made that has a Depvar = 70 and a User Material with Mechanical Constants 1 = 1, 2 = 1
- For the multiple grain cases a new material will need to be made that has a Depvar = (70*# of grains) and a User Material with Mechanical Constants 1 = 1, 2 = 1
- Do not forget to apply this material to the Section
Set up the CPFEM input files.
- In the umat_xtal.f file, edit the line
data filePath & /'/cavs/cmd/data1/users/qma/abaqus_xtalplas/oneelement/'/to be the directory where your crystal plasticity inputs are stored.
- (FOR CALCULIX) Comment out the line
include ABAQUS ... somethingby adding a "c" to the beginning of the line.
- (FOR CALCULIX) Comment out the line
- Edit the texture. file to include only a single crystal.
- Change the first line to 1
- Leave the second line!
- Leave only one of the lines containing the Euler angles for the crystal orientations.
- In the test.xtali input file, change the second number on the first line to 1, for the number of grains.
- Make sure the line with
fcc.sx / single crystal input fileis updated to reflect the crystal structure of your material.
- Make sure the line with
Change the single crystal input file (fcc.sx or bcc.sx) to match that of your material
- The following lines need to be edited
108.2e3 61.3e3 28.5e3 / c11(c1), c12(c2), c44(c3) / # These numbers should match c11, c12, and c44 for your material . . 2.e-5 / bdrag / # This should match the drag coefficient obtained in Homework 2 35.5 39.5 1.85 0.0-4 5.0e10 / h0, tausi, taus0, xms, gamss0 / # The first three should match the values obtained in Part 1 . .
Run the simulation
The finite element simulation can be run locally, as it is a very small simulation.For Abaqus, run the job with
abaqus job=<YOUR_INPUTFILE_NAME> user=umat_xtal.fSimilarly, for Calculix, run the job with
For both, make sure to enter the job name without the ".inp" extension.
Access the results
- ABAQUS simulation output is stored in an output database file with extension ".odb". ODB files can be visualized and post processed in ABAQUS CAE or ABAQUS VIEWER.
- Calculix output can be viewed in Calulix's viewer, or in Paraview.
Room for Improvement
As with the previous homeworks, improve the tutorial(s) by adding/modifying the ICME website for:
- 1. Dislocation dynamics (MDDP)
- 2. Crystal Plasticity