Motivation of this Work
=======================

.. include:: includes.rst

The micromechanical behavior of grain boundaries is one of the key components in the understanding of heterogeneous deformation of metals [#Bieler_2014]_.
To investigate the nature of the strengthening effect of grain boundaries, slip transmission across interfaces has been investigated through
bicrystal deformation experiments during the sixty past decades [#Aust_1968]_, [#LivingstonChalmers_1957]_, [#Shen_1986]_, [#Shen_1988]_, [#LusterMorris_1995]_,
[#Marcinkowski_1970]_, [#Bollmann_1970]_, [#LimRaj_1985]_, [#Lee_1989]_, [#Lee_1990_2]_, [#Clark_1992]_, [#Abuzaid_2012]_, [#Seal_2012]_ and [#Kacher_2014]_.
Originally, interactions between dislocations and grain boundaries
have been observed in the transmission electron microscope (TEM) after strain test or in situ [#Shen_1986]_, [#Shen_1988]_ and [#Kacher_2014]_. Some authors observed as
well slip transmission during indentation tests performed close to grain boundaries [#WoNgan_2004]_, [#Soer_2005]_, [#Britton_2009]_, [#Pathak_2012]_ and [#Lawrence_2014]_.

To better understand the role played by the grain boundaries, we developed a |matlab| toolbox with Graphical User Interfaces (GUI),
to analyze and to quantify the micromechanics of grain boundaries.
This toolbox aims to link experimental results to crystal plasticity finite element (CPFE) simulations [#DAMASK]_.

Strategy
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Comparison of topographies of indentations at grain boundaries to simulated indentations as predicted by 3D CPFE modelling.

The goals of this research are:

1 - Carry out indentation within the interiors of large grains of alpha-titanium to effectively collect single crystal data coupled with extensive
(three-dimensional) characterization of the resulting plastic defect fields surrounding the indents [#Zambaldi_2012]_. By correlating with models of the indentation,
a precise constitutive description of the anisotropic plasticity of single-crystalline titanium shall be developed [#Roters_2010]_ and [#DAMASK]_.

2 - Extension of this methodology to indentations close to grain boundaries, i.e. quasi bi-crystal deformation.

3 - Comparison of the measured characteristics of indentations at grain boundaries to simulated indentations as predicted by a constitutive model
calibrated using the single crystal indentations.
 
4 - Based on this qualitative understanding, a grain boundary transmissivity description will be
developed validated against the collected indent characteristics.

.. [#Bieler_2014] `T.R. Bieler et al., "Grain boundaries and interfaces in slip transfer.", Current Opinion in Solid State and Materials Science (2014), 18(4), pp. 212-226. <https://doi.org/10.1016/j.cossms.2014.05.003>`_
.. [#Aust_1968] `K.T. Aust et al., "Solute induced hardening near grain boundaries in zone refined metals.", Acta Metallurgica (1968), 16(3), pp. 291-302. <https://doi.org/10.1016/0001-6160(68)90014-X>`_
.. [#LivingstonChalmers_1957] `J.D. Livingston and B. Chalmers, "Multiple slip in bicrystal deformation.", Acta Metallurgica (1957), 5(6), pp. 322-327. <https://doi.org/10.1016/0001-6160(57)90044-5>`_
.. [#Shen_1986] `Z. Shen et al., "Dislocation pile-up and grain boundary interactions in 304 stainless steel.", Scripta Metallurgica (1986), 20(6), pp. 921–926. <https://doi.org/10.1016/0036-9748(86)90467-9>`_
.. [#Shen_1988] `Z. Shen et al., "Dislocation and grain boundary interactions in metals.", Acta Metallurgica (1988), 36(12), pp. 3231–3242. <https://doi.org/10.1016/0001-6160(88)90058-2>`_
.. [#LusterMorris_1995] `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. <https://doi.org/10.1007/BF02670762>`_
.. [#Marcinkowski_1970] `M.J. Marcinkowski and W.F. Tseng, "Dislocation behavior at tilt boundaries of infinite extent.", Metal. Trans. (1970), 1(12), pp. 3397-3401. <https://link.springer.com/article/10.1007/BF03037870>`_
.. [#Bollmann_1970] `W. Bollmann, "Crystal Defects and Crystalline Interfaces", Springer-Verlag (1970) <https://doi.org/10.1007/978-3-642-49173-3>`_
.. [#LimRaj_1985] `L.C. Lim and R. Raj, "Continuity of slip screw and mixed crystal dislocations across bicrystals of nickel at 573K.", Acta Metallurgica (1985), 33, pp. 1577. <https://doi.org/10.1016/0001-6160(85)90057-4>`_
.. [#Lee_1989] `T.C. Lee et al., "Prediction of slip transfer mechanisms across grain boundaries.", Scripta Metallurgica, (1989), 23(5), pp. 799–803. <https://doi.org/10.1016/0036-9748(89)90534-6>`_
.. [#Lee_1990_2] `T.C. Lee et al., "An In Situ transmission electron microscope deformation study of the slip transfer mechanisms in metals", Metallurgical Transactions A (1990), 21(9), pp. 2437-2447. <https://doi.org/10.1007/BF02646988>`_
.. [#Clark_1992] `W.A.T. Clark et al., "On the criteria for slip transmission across interfaces in polycrystals.", Scripta Metallurgica et Materialia (1992), 26(2), pp. 203–206. <https://doi.org/10.1016/0956-716X(92)90173-C>`_
.. [#Abuzaid_2012] `W.Z. Abuzaid et al., "Slip transfer and plastic strain accumulation across grain boundaries in Hastelloy X.", J. of the Mech. and Phys. of Sol. (2012), 60(6) ,pp. 1201–1220. <https://doi.org/10.1016/j.jmps.2012.02.001>`_
.. [#Seal_2012] `J.R. Seal et al., "Analysis of slip transfer and deformation behavior across the α/β interface in Ti–5Al–2.5Sn (wt.%) with an equiaxed microstructure.", Mater. Sc. and Eng.: A (2012), 552, pp. 61-68. <https://doi.org/10.1016/j.msea.2012.04.114>`_
.. [#Kacher_2014] `J. Kacher et al., "Dislocation interactions with grain boundaries.", Current Opinion in Solid State and Materials Science (2014), in press. <https://doi.org/10.1016/j.cossms.2014.05.004>`_
.. [#WoNgan_2004] `P.C. Wo and A.H.W. Ngan, "Investigation of slip transmission behavior across grain boundaries in polycrystalline Ni3Al using nanoindentation.", J. Mater. Res. (2004), 19(1), pp. 189-201. <https://doi.org/10.1557/jmr.2004.19.1.189>`_
.. [#Soer_2005] `W.A. Soer et al. ,"Incipient plasticity during nanoindentation at grain boundaries in body-centered cubic metals.", Acta Materialia (2005), 53, pp. 4665–4676. <https://doi.org/10.1016/j.actamat.2005.07.001>`_
.. [#Britton_2009] `T.B. Britton et al., "Nanoindentation study of slip transfer phenomenon at grain boundaries.", J. Mater. Res., 2009, 24(3), pp. 607-615. <https://doi.org/10.1557/jmr.2009.0088>`_
.. [#Pathak_2012] `S. Patthak et al., "Studying grain boundary regions in polycrystalline materials using spherical nano-indentation and orientation imaging microscopy.", J. Mater. Sci. (2012), 47, pp. 815–823. <https://doi.org/10.1007/s10853-011-5859-z>`_
.. [#Lawrence_2014] `S.K. Lawrence et al., "Grain Boundary Contributions to Hydrogen-Affected Plasticity in Ni-201.", The Journal of The Minerals, Metals & Materials Society (2014), 66(8), pp. 1383-1389. <https://doi.org/10.1007/s11837-014-1062-4>`_
.. [#Zambaldi_2012] `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. <https://doi.org/10.1557/jmr.2011.334>`_
.. [#Roters_2010] `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. <https://doi.org/10.1016/j.actamat.2009.10.058>`_
.. [#DAMASK] `DAMASK — the Düsseldorf Advanced Material Simulation Kit <http://damask.mpie.de/>`_