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Manual for Code
VISCO-PLASTIC SELF-CONSISTENT (VPSC)
Version 7d
(last updated: April 01, 2012)
C.N. Tomé
(Los Alamos National Laboratory - USA) tome@lanl.gov
and
R.A. Lebensohn
(Los Alamos National Laboratory - USA) lebenso@lanl.gov
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INDEX
Copyright / Disclosure ……………………………………………………. 1
General Description / Recommendation …………..……..………………. 2
What’s new in VPSC7………………………………..…………..……..… 3
SECTION 1: Theory and Models
1-1 Introduction ………………………..……………………………. 4
1-2 Kinematics …………………………….………………………… 4
1-3 Updating crystal orientation and grain shape …………………… 6
1-3-1 Crystallographic & morphologic texture rotation
1-3-2 Grain co-rotation
1-5 Self-consistent polycrystal formalism……………………………. 8
1-5-1 Local behavior and homogenization
1-5-2 Green function and Fourier transform
1-5-3 Viscoplastic inclusion and Eshelby tensors
1-5-4 Interaction and localization equations
1-5-5 Self-consistent equations
1-5-6 Algorithm
1-5-7 Secant, affine, tangent and intermediate linearizations
1-6 Hardening of slip and twinning systems………………………… 21
1-6-1 Voce hardening
1-6-2 MTS hardening
1-6-3 Dislocation density model of Beyerlein et al (placeholder)
1-6-4 Dislocation density model of Rauch et al (placeholder)
1-7 Twinning model ………………………………………………… 26
1-8- Second order formulation ……………………………………..… 27
1-8-1 Second order moments
1-8-2 Second order procedure
1-8-3 Numerical implementation
1-9 References……………………………………………………….. 33
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SECTION 2: Description of VPSC code
2-1 Numerical algorithm……………………………………………… 35
2-2 Simulation of deformation: Input/Output options………………… 36
2-3-1 Grain shape evolution option
2-3-2 Variable velocity gradient option
2-4 Code architecture ………………………………………………. 41
2-5 Units, reference system and conventions ..…………………….. 42
2-6 Description of Input files……………………………………….. 44
2-7 Description of Output files……………………………………… 55
2-8 Interfacing VPSC with FE codes (VPSC7FE) ….……………… 62
SECTION 3: Examples and applications of VPSC code
Example 1: Tension and Compression of FCC ………………..…… 66
Example 2: Rolling of FCC ………………………………………… 70
Example 3: Rolling of BCC ………………………………………… 74
Example 4: Rolling of a 2-phase FCC+BCC aggregate ……….…… 77
Example 5: Torsion of FCC …..…………………………………….. 79
Example 6: Application of MTS model to rolled aluminum ……….. 82
Example 7: Twinning and anisotropy of HCP zirconium …………… 85
Example 8: Compression of (orthorhombic) olivine ………………… 91
Example 9: Compression of ice (constant rate and creep)…………… 94
Example 10: Equal Channel Angular Extrusion of FCC…………… 98
Examples of VPSC7FE ……………………………………………… 100
SECTION 4: Appendices
Appendix A: Taylor factor ………………..……………………… 102
Appendix B: Von Mises equivalent stress & strain ………………..… 105
Appendix C: Voce hardening and algorithm ………………..…… 107
Appendix D: Crystal rotation and misorientation ………………..…… 109
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Code Visco-Plastic Self-Consistent (VPSC)
Version 7d – February 2012 (under developement)
C.N. Tomé, Los Alamos National Laboratory, USA, tome@lanl.gov
R.A. Lebensohn, Los Alamos National Laboratory, USA, lebenso@lanl.gov
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COPYRIGHT NOTICE
Portions of this program were prepared by the Regents of the University of California at
Los Alamos National Laboratory (the University) under Contract No. W-7405-ENG-36
with the U.S. Department of Energy (DOE). This software can be identified by the code
LA-CC-99-72 issued by the Classification Office of Los Alamos National Laboratory.
The University has certain rights in the program pursuant to the contract and the program
should not be copied or distributed outside your organization. All rights in the program
are reserved by the DOE and the University. Neither the U.S. Government nor the
University makes any warranty, express or implied, or assumes any liability or
responsibility for the use of this software.
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DISCLOSURE
We distribute this code free of charge on a personal basis and ask you not to make it
available to other users. We would appreciate if you acknowledge its use when reporting
your results.
These notes contain a description of the theory, the capabilities of the VPSC code, and
several examples. The code itself is in a permanent state of change and new options, bug-
fixes and changes are incorporated as required by new developments, new applications,
or as suggested by interactions with the users. In addition, not every possible combination
of running conditions is tested when the code is modified. As a consequence use it at
your own risk and let us know if you find bugs or run into trouble while using it. We
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appreciate comments and suggestions that may improve the interface with the users. We
strongly recommend running the benchmark cases included in the examples and make
sure that you can reproduce the same results.
GENERAL DESCRIPTION
VPSC is a computer code written in FORTRAN 77 which simulates the plastic
deformation of polycrystalline aggregates. VPSC stands for Visco Plastic Self Consistent
and refers to the particular mechanical regime addressed (VP) and to the approach used
(SC). VPSC was developed for application to low-symmetry materials (hexagonal,
trigonal, orthorhombic, trigonal), although it also performs well on cubic materials.
VPSC accounts for full anisotropy in properties and response of the single crystals and
the aggregate. It simulates the plastic deformation of aggregates subjected to external
strains and stresses. VPSC is based on the physical shear mechanisms of slip and
twinning, and accounts for grain interaction effects. In addition to providing the
macroscopic stress-strain response, it accounts for hardening, reorientation and shape
change of individual grains. As a consequence, it predicts the evolution of hardening and
texture associated with plastic forming. The simulation procedure can be applied to
deformation of metals, intermetallics and geologic aggregates.
RECOMMENDATION
The VPSC7 manual includes a thorough description of the related theory. Most of
Section 1 can be skipped if you are only interested in running the code. However,
Subsections 1-6 and 1-7, dealing with hardening and twinning models, should be read. In
addition, most of Section 2, describing input and output files, should be read. The user is
advised to become familiar with the examples in Section 3, because they highlight
different capabilities of the code. Reproducing the numerical results of the examples is
highly recommended both, to become familiar with the input/output files and procedures,
and to make sure that the code was properly installed in the user’s computer.
When compiling VPSC, always use the double precision option.
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