SIMLab Crystal Mechanics model - Hypoelastic formulation (SCMM-Hypo)

These crystal plasticity subroutines uses either a rate-dependent formulation or a Combined Constraints Crystal Plasticity (CCCP) framework. The rate-dependent crystal plasticity model with coupled damage and ductile failure as described in Frodal et al. (2021) is implemented into a user defined material model for Abaqus/Standard and Abaqus/Explicit (UMAT & VUMAT). The Combined Constraints Crystal Plasticity (CCCP) framework by Zamiri & Pourboghrat (2010) is used toghether either with coupled damage and ductile failure as described in Frodal et al. (2021) or with the Crystal Porous Plasticity (CP²) model by Han et al. (2013), implemented using the numerical framework of Khadyko et al. (2021) into a user defined material model for Abaqus/Standard and Abaqus/Explicit (UMAT & VUMAT). Note that the model used is decided at compile time based on compiler directives, the models can also be compiled without a damage model.

Cite

Please cite the articles listed below if you use this model

@article{Frodal.et.al.2019,
title = {Modelling and simulation of ductile failure in textured aluminium alloys subjected to compression-tension loading},
journal = {International Journal of Plasticity},
volume = {118},
pages = {36-69},
year = {2019},
issn = {0749-6419},
doi = {https://doi.org/10.1016/j.ijplas.2019.01.008},
url = {https://www.sciencedirect.com/science/article/pii/S0749641918305904},
author = {Bjørn Håkon Frodal and Lars Edvard Blystad Dæhli and Tore Børvik and Odd Sture Hopperstad}
}

@article{Frodal.et.al.2021,
title = {On the coupling of damage and single crystal plasticity for ductile polycrystalline materials},
journal = {International Journal of Plasticity},
volume = {142},
pages = {102996},
year = {2021},
issn = {0749-6419},
doi = {https://doi.org/10.1016/j.ijplas.2021.102996},
url = {https://www.sciencedirect.com/science/article/pii/S0749641921000711},
author = {Bjørn Håkon Frodal and Susanne Thomesen and Tore Børvik and Odd Sture Hopperstad}
}

@article{Khadyko.et.al.2021,
title = {Finite element simulation of ductile fracture in polycrystalline materials using a regularized porous crystal plasticity model},
journal = {International Journal of Fracture},
volume = {228},
pages = {15-31},
year = {2021},
doi = {https://doi.org/10.1007/s10704-020-00503-w},
author = {Mikhail Khadyko and Bjørn Håkon Frodal and Odd Sture Hopperstad}
}

Subroutine input

Property number	Material input
1	Elastic constant c11
2	Elastic constant c12
3	Elastic constant c44
4	Reference slip rate, γ0 or Regularization parameter, m
5	Instantaneous strain rate sensitivity, m or Regularization parameter, ρ
6	Initial critical resolved shear stress, τc0
7	Latent hardening coefficient, q
8	Texture flag (1=Euler angles from material card, 2=Euler angles from history card, 3=Euler angles are generated from a random texture, i.e., a uniform ODF)
9	Initial Euler angle, ϕ1 in degree
10	Initial Euler angle, Φ in degree
11	Initial Euler angle, ϕ2 in degree
12	Hardening flag (1 for Voce or 2 for Kalidindi et al. (1992))
13	Hardening parameter, h0 or θ1 depending on hflag
14	Hardening parameter, τs or τ1 depending on hflag
15	Hardening parameter, a or θ2 depending on hflag
16	Hardening parameter, 0.0 or τ2
17	Tangent operator flag (1=Elastic tangent operator, 2=Consistent tangent operator)
18	Initial damage, f0
19	Critical damage, fc
20	Damage/yield surface evolution parameter, q1
21	Damage/yield surface evolution parameter, q2
22	Damage/yield surface evolution parameter, a

Warning: Do not use a local coordinate system (CSYS) or a material orientation with this subroutine in Abaqus Standard. This will break the co-rotational formulation.

Warning: Texture flag = 3 should only be used for elements with 1 integration point. Otherwise integration points within the same element will have different crystallographic orientations.

Note that the Tangent operator flag, property number 17, is only used for Abaqus Standard, and the Quasi-Newton solution technique should be used when the Elastic tangent operator is selected. The Quasi-Newton solution technique is located under the step settings in the Abaqus CAE.

Note also that the last Hardening parameter, property number 16, should be put to 0.0 when the Kalidindi et al. (1992) hardening model is used with Abaqus Standard.

Subroutine output

Variable number	Solution dependent variable
1-3	Euler angles, ϕ1, Φ, ϕ2
4-12	Components of the rotation tensor R
13-24	Critical resolved shear stresses τc(α)
25	Accumulated plastic shear strain Γ
26	Equivalent von Mises stress σeq
27	Equivalent von Mises plastic strain εpeq
28	Number of sub-steps in the current time step nsub
29	Damage variable, f
30	Status variable used for element deletion in Abaqus/Explicit

If the FC-Taylor homogenization approach is used in the subroutine, see compiler directives, then the 6 independent stress components are also stored in the solution dependent variables after the above given values (SDV's 31-36 if damage is included). The solution dependent variables are then repeated Ngrain number of times (By default Ngrain is 8, resulting in 36*8 = 288 solution dependent variables if damage is included).

Prerequisites

Before compiling the user material subroutine for the FEM code, install and check:

• A Fortran compiler compatible with the FE code (e.g. Intel Visual Fortran)
• Check the license of the FE solver, and the version of the FE solver

Compilation

Follow point 1 or 2 below to compile

1. First case, run a simulation with a local compiled library (the compilation will be done each time a simulation is run)
   • Clone the repository: SCMM-hypo from Github
   • Change the current directory to the SCMM-hypo folder
   • Copy the simulation input (e.g. MySim.inp) to the current directory
   • Run the simulation using the command: abaqus double job=MySim user=HypoImp int
   • Use the option user=HypoImp for the implicit solver (Abaqus/Standard)
   • Use the option user=HypoExp for the explicit solver (Abaqus/Explicit)
2. Second case, compile a library:
   • If needed, make a directory where to place the Abaqus library (e.g. library-dir = /home/username/abaqus-library for Linux or C:\\Users\\username\\abaqus-library for Windows)
   • Clone the repository: SCMM-hypo from Github
   • Change the current directory to the SCMM-hypo folder
   • Run the command: abaqus make library=HypoImp directory=library-dir
   • Use the option library=HypoImp for the implicit solver (Abaqus/Standard)
   • Use the option library=HypoExp for the explicit solver (Abaqus/Explicit)
   • Change the environment file to specify the path of the new library:
     • If needed, create an environment file, abaqus_v6.env, in your home directory and/or the current directory. Settings in the home directory file will be applied to all jobs that you run. Settings in the current directory file will be applied only to jobs run from the current directory
     • Add the entry: usub_lib_dir='library-dir'

Compiler directives

Note that the subroutines use preprocessor directives to determine if it is compiled for Abaqus/Standard, Abaqus/Explicit or neither. Specific choices can also be made at compile time instead of at runtime, e.g., the choice of which hardening model to use. For further information on the available preprocessor definitions see the Definitions.f file. These preprocessor directives can be used to minimize the computational time by including only necessary model features, and removing unecessary conditional statements.

If the subroutines are to be included in another file, use the preprocessor include directive (e.g., #include 'HypoImp.f') instead of the Fortran include statement (e.g., include 'HypoImp.f').

Tests

To run the tests:

1. Compile the subroutine using method nr. 2 above, for both Abaqus/Explicit and Abaqus/Standard, library-dir should point to the SCMM-hypo folder
2. Make sure that you have Abaqus and Python 3 installed with the necessary Python libraries (See ./Tests/Test.py)
3. Change the current directory to the SCMM-hypo folder
4. Run the command: python ./Tests/Test.py run to run the tests (If the subroutine has been compiled with the CCCP model append the flag --cccp. The flag --interactive can be appended this command to run all the Abaqus tests with the same flag)
5. When the Abaqus jobs have finished, run the command: python ./Tests/Test.py post to post-process the tests (If the tests has been run with the CCCP model append the flag --cccp. The flag --plot can be appended this command to plot the results)
6. To clean the test directory, run the command: python ./Tests/Test.py clean

Contributing

To contribute:

1. Fork the Project
2. Create your Feature Branch (git checkout -b feature/AmazingFeature)
3. Commit your Changes (git commit -m 'Add some AmazingFeature')
4. Push to the Branch (git push origin feature/AmazingFeature)
5. Open a Pull Request

Contact

Bjørn Håkon Frodal - @frodal - bjorn.h.frodal@ntnu.no