Slip Transmission Matlab toolbox

Figure 1 Slip transmission analysis for an EBSD map of near alpha phase Ti alloy.

The Matlab toolbox STABiX provides a unique and simple way to analyse slip transmission in a bicrystal. Graphical User Interfaces (GUIs) are implemented in order to import EBSD results, and to represent and quantify grain boundary slip resistance. Key parameters, such as the number of phases, crystal structure (fcc, bcc, or hcp), and slip families for calculations, are set by the user. With this information, grain boundaries are plotted and color coded according to the \(m'\) factor [1] that quantifies the geometrical compatibility of the slip planes normals and Burgers vectors of incoming and outgoing slip systems. Other potential functions that could assess the potential to develop damage are implemented (e.g. residual Burgers vector [2] and [3], \(N\) factor [4], resolved shear stress [5], misorientation…).

Furthermore, the toolbox provides the possibility to plot and analyze the case of a bicrystal, and to model sphero-conical indentation performed in a single crystal or close to grain boundaries (i.e. quasi bicrystal deformation). All of the data linked to the bicrystal indentation (indenter properties, indentation settings, grain boundary inclination, etc.) are collected through the GUI. A Python^TM file can be then exported in order to carry out a fully automatic 3D crystal plasticity finite element simulations of the indentation process using one of the constitutive models available in DAMASK [6] and [7]. The plasticity of single crystals is quantified by a combination of crystal lattice orientation mapping, instrumented sphero-conical indentation, and measurement of the resulting surface topography [8] and [9]. In this way the stress and strain fields close to the grain boundary can be rapidly assessed. Activation and transmission of slip are interpreted based on these simulations and the mechanical resistance of grain boundaries can be quantified.

How to get STABiX code ?

First of all, download the source code of the Matlab toolbox.

Source code is hosted at Github.

Download source code as a .zip file.

How to cite STABiX in your papers ?

“STABiX v1.6” = https://doi.org/10.5281/zenodo.14854

“STABiX v2.0” = https://dx.doi.org/10.13140/RG.2.2.25845.83687/2

Reference paper

“STABiX documentation.”

“A Matlab toolbox to analyze slip transfer through grain boundaries” D. Mercier, C. Zambaldi, T. R. Bieler, 17th International Conference on Textures of Materials (ICOTOM17), at Dresden, Germany (2014). IOP Conference Series: Materials Science and Engineering Volume 82 conference 1. https://doi.org//10.1088/1757-899X/82/1/012090

“Spherical indentation and crystal plasticity modeling near grain boundaries in alpha-Ti.” D. Mercier, C. Zambaldi, P. Eisenlohr, Y. Su, M. A. Crimp, T. R. Bieler, Poster presented at “Indentation 2014” Conference in Strasbourg (France) (December 2014). https://doi.org//10.13140/RG.2.1.3044.8486

“Study of Bi-Crystal Grain Boundary Deformation in Commercially Pure Tantalum.” B. Dunlap et al., CHEMS Forum (2015).

“Grain Boundaries and Plasticity.” D. Mercier, C. Zambaldi, P. Eisenlohr, M. A. Crimp, T. R. Bieler, R. Sánchez Martín. Invited talk at “MTEX Workshop 2016” Conference in Chemnitz (Germany) (February 2016). https://doi.org//10.13140/RG.2.2.27427.66084

“Quantifying deformation processes near grain boundaries in α titanium using nanoindentation and crystal plasticity modeling.” Y. Su, C. Zambaldi, D. Mercier, P. Eisenlohr, T.R. Bieler, M.A. Crimp, International Journal of Plasticity, (2016). https://doi.org//10.1016/j.ijplas.2016.08.007

“Evaluation of an inverse methodology for estimating constitutive parameters in face-centered cubic materials from single crystal indentations.” A. Chakraborty, P. Eisenlohr, European Journal of Mechanics - A/Solids, (2017). https://doi.org//10.1016/j.euromechsol.2017.06.012

“Micromechanics of magnesium and its alloys studied by nanoindentation.” R. Sánchez Martín, PhD thesis, Universidad Carlos III de Madrid (2017).

“Investigation of single crystal and bi-crystal deformation in body-centered cubic tantalum using indentation.” B. Dunlap, PhD thesis, Michigan State University (2018).

Contents

• Motivation of this Work
  • Strategy
• Getting started
  • Source Code
  • READ ME
  • Path management
  • The GUIs
  • The YAML configuration files
  • MTEX toolbox
  • OpenGL
• Bicrystal Definition
  • Crystallographic properties of a bicrystal
• Strain Transfer Across Grain Boundaries
  • Geometrical Criteria
  • Stress Criteria
  • Combination of Criteria
  • Relationships between slip transmission criteria
  • Slip transmission parameters implemented in the STABiX toolbox
  • Slip and twin systems implemented in the STABiX toolbox
  • Effects of number of slip systems on slip transmission
  • References
• Experimental data
  • EBSD map GUI
    • TSL-OIM data preparation
    • Reconstructed Boundaries File (RB)
    • Grain File Type 2 (GF2)
    • Loading other type of EBSD data files…
    • How to generate a .ang file with TSL-OIM software?
    • Possible errors introduced during files exportation from TSL-OIM
    • Issues with plot of EBSD maps
  • Bicrystal GUI
  • Convention for bicrystal EBSD/indentation experiments
• EBSD map GUI
  • Loading EBSD data
  • Smoothing GBs segments
  • Misorientation angle
  • m’ parameter
  • Residual Burgers vector
  • Schmid factor and slip trace analysis
  • Plot options
• Bicrystal GUI
  • Loading Bicrystal data
  • Plotting and analyzing a bicrystal
  • Distribution of all slip transmission parameters
• CPFE simulation preprocessing GUIs
  • How to load crystallographic properties of the SX or of the BX?
  • Single crystal (SX) indentation
    • Convention for the single crystal mesh
  • Bicrystal (BX) indentation
    • Convention for the bicrystal mesh
  • Scratch test on SX and BX
  • Indenter’s geometry
    • AFM topography
  • Contact definition
  • Mesh definition
  • Python setup
  • Adjusting the configuration settings
  • Installing DAMASK
  • Writing the CPFE input files
  • Input files
  • Using the CPFE input files
  • Running a job with DAMASK
  • See also
• Analysis of literature data
  • Residual Burgers vector
    • Kacher and Robertson (2012)
    • Patriarca et al. (2013)
    • Kacher and Robertson (2014)
    • Cui et al. (2014)
  • m’ factor
    • Guo et al. (2014)
• A Matlab toolbox to analyze grain boundary inclination from SEM images
  • How to use the toolbox ?
  • See also
  • Links
  • Authors
  • Acknowledgements
  • Keywords
• References
  • Related Projects
  • Institutions

References

[1]

J. Luster and M.A. Morris, “Compatibility of deformation in two-phase Ti-Al alloys: Dependence on microstructure and orientation relationships.”, Metal. and Mat. Trans. A (1995), 26(7), pp. 1745-1756.

[2]

M.J. Marcinkowski and W.F. Tseng, “Dislocation behavior at tilt boundaries of infinite extent.”, Metal. Trans. (1970), 1(12), pp. 3397-3401.

[3]

W. Bollmann, “Crystal Defects and Crystalline Interfaces”, Springer-Verlag (1970).

[4]

J.D. Livingston and B. Chalmers, “Multiple slip in bicrystal deformation.”, Acta Metallurgica (1957), 5(6), pp. 322-327.

[5]

T.R. Bieler et al., “The role of heterogeneous deformation on damage nucleation at grain boundaries in single phase metals.”, Int. J. of Plast. (2009), 25(9), pp. 1655–1683.

[6]

F. Roters et al., “Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications.”, Acta Materialia (2010), 58(4), pp. 1152-1211.

[7]

DAMASK — the Düsseldorf Advanced Material Simulation Kit.

[8]

C. Zambaldi et al., “Orientation informed nanoindentation of α-titanium: Indentation pileup in hexagonal metals deforming by prismatic slip”, J. Mater. Res. (2012), 27(01), pp. 356-367.

[9]

C. Zambaldi, “Anisotropic indentation pile-up in single crystals”.

Contact

Author:

David Mercier [1] and C. Zambaldi [1], based on previous work of T. R. Bieler [2] and C. Zambaldi [1].

[1] Max-Planck-Institut für Eisenforschung, 40237 Düsseldorf, Germany

[2] Chemical Engineering and Materials Science, Michigan State University, East Lansing 48824 MI, USA

Contributors

• Raúl Sánchez Martín (IMDEA, Madrid, Spain) contributed Python code to generate Abaqus indentation models.

• Adrien Berger (LML, Lille, France) contributed slip transmission models.

Acknowledgements

This work was supported by the DFG/NSF Materials World Network grant references (DFG ZA 523/3-1 and NSF-DMR-1108211).

The authors are grateful to Philip Eisenlohr, Martin Crimp and Yang Su of Michigan State University, and the Max-Planck-Institut für Eisenforschung for support.

Keywords

Matlab toolbox ; Graphical User Interface (GUI) ; Grain Boundary (GB) ; Polycrystalline Metals ; Slip Transmission ; Bi-Crystal (BX) ; Electron backscatter diffraction (EBSD) ; Instrumented indentation ; Crystal Plasticity Finite Element Method (CPFEM) ; python^TM toolbox ; DAMASK.