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Comptes Rendus. Physique
Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations
Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 267-293.

Part of the special issue: Plasticity and Solid State Physics

With decreasing system sizes, the mechanical properties and dominant deformation mechanisms of metals change. For larger scales, bulk behavior is observed that is characterized by a preservation and significant increase of dislocation content during deformation whereas at the submicron scale very localized dislocation activity as well as dislocation starvation is observed. In the transition regime it is not clear how the dislocation content is built up. This dislocation storage regime and its underlying physical mechanisms are still an open field of research. In this paper, the microstructure evolution of single crystalline copper micropillars with a 110 crystal orientation and varying sizes between 1 and 10 μm is analysed under compression loading. Experimental in situ HR-EBSD measurements as well as 3d continuum dislocation dynamics simulations are presented. The experimental results provide insights into the material deformation and evolution of dislocation structures during continuous loading. This is complemented by the simulation of the dislocation density evolution considering dislocation dynamics, interactions, and reactions of the individual slip systems providing direct access to these quantities. Results are presented that show, how the plastic deformation of the material takes place and how the different slip systems are involved. A central finding is, that an increasing amount of GND density is stored in the system during loading that is located dominantly on the slip systems that are not mainly responsible for the production of plastic slip. This might be a characteristic feature of the considered size regime that has direct impact on further dislocation network formation and the corresponding contribution to plastic hardening.

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DOI: 10.5802/crphys.55
Keywords: Micropillar compression, Size effect, Dislocation based plasticity, HR-EBSD, Continuum dislocation dynamics
Kolja Zoller 1; Szilvia Kalácska 2; Péter Dusán Ispánovity 3; Katrin Schulz 4, 5

1 Karlsruhe Institute of Technology, Institute for Applied Materials - Computational Materials Science (IAM-CMS), Kaiserstr. 12, 76131 Karlsruhe, Germany
2 Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory of Mechanics of Materials and Nanostructures, CH-3602 Thun, Feuerwerkerstrasse 39. Switzerland
3 Eötvös Loránd University, Department of Materials Physics, Pázmány P. stny. 1/A, 1117 Budapest, Hungary
4 Karlsruhe Institute of Technology (KIT), Institute for Applied Materials - Computational Materials Science (IAM-CMS), Kaiserstr. 12, 76131 Karlsruhe, Germany
5 Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany
     author = {Kolja Zoller and Szilvia Kal\'acska and P\'eter Dus\'an Isp\'anovity and Katrin Schulz},
     title = {Microstructure evolution of compressed micropillars investigated by in situ {HR-EBSD} analysis and dislocation density simulations},
     journal = {Comptes Rendus. Physique},
     pages = {267--293},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {22},
     number = {S3},
     year = {2021},
     doi = {10.5802/crphys.55},
     language = {en},
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Kolja Zoller; Szilvia Kalácska; Péter Dusán Ispánovity; Katrin Schulz. Microstructure evolution of compressed micropillars investigated by in situ HR-EBSD analysis and dislocation density simulations. Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 267-293. doi : 10.5802/crphys.55. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.55/

[1] D. Dimiduk; M. Uchic; T. Parthasarathy Size-affected single-slip behavior of pure nickel microcrystals, Acta Mater., Volume 53 (2005) no. 15, pp. 4065-4077 | Article

[2] D. M. Dimiduk; C. Woodward; R. Lesar; M. D. Uchic Scale-free intermittent flow in crystal plasticity, Science, Volume 312 (2006) no. 5777, pp. 1188-1190 | Article

[3] C. A. Volkert; E. T. Lilleodden Size effects in the deformation of sub-micron Au columns, Philos. Mag., Volume 86 (2006) no. 33–35, pp. 5567-5579 | Article

[4] J. R. Greer; W. C. Oliver; W. D. Nix Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients, Acta Mater., Volume 53 (2005) no. 6, pp. 1821-1830 | Article

[5] Z. Shan; R. K. Mishra; S. S. Asif; O. L. Warren; A. M. Minor Mechanical annealing and source-limited deformation in submicrometre-diameter Ni crystals, Nat. Mater., Volume 7 (2008) no. 2, pp. 115-119 | Article

[6] T. A. Parthasarathy; S. I. Rao; D. M. Dimiduk; M. D. Uchic; D. R. Trinkle Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples, Scr. Mater., Volume 56 (2007) no. 4, pp. 313-316 | Article

[7] H. Tang; K. Schwarz; H. Espinosa Dislocation-source shutdown and the plastic behavior of single-crystal micropillars, Phys. Rev. Lett., Volume 100 (2008) no. 18, 185503 | Article

[8] S. I. Rao; D. Dimiduk; T. A. Parthasarathy; M. Uchic; M. Tang; C. Woodward Athermal mechanisms of size-dependent crystal flow gleaned from three-dimensional discrete dislocation simulations, Acta Mater., Volume 56 (2008) no. 13, pp. 3245-3259 | Article

[9] J. A. El-Awady; M. Wen; N. M. Ghoniem The role of the weakest-link mechanism in controlling the plasticity of micropillars, J. Mech. Phys. Solids, Volume 57 (2009) no. 1, pp. 32-50 | Article | Zbl: 1421.74108

[10] P. D. Ispánovity; Á. Hegyi; I. Groma; G. Györgyi; K. Ratter; D. Weygand Average yielding and weakest link statistics in micron-scale plasticity, Acta Mater., Volume 61 (2013) no. 16, pp. 6234-6245 | Article

[11] P. M. Derlet; R. Maass A probabilistic explanation for the size-effect in crystal plasticity, Philos. Mag., Volume 95 (2015) no. 16–18, pp. 1829-1844 | Article

[12] M. Staker; D. Holt The dislocation cell size and dislocation density in copper deformed at temperatures between 25 and 700 C, Acta Metall., Volume 20 (1972) no. 4, pp. 569-579 | Article

[13] F. Prinz; A. Argon Dislocation cell formation during plastic deformation of copper single crystals, Phys. Status Solidi (a), Volume 57 (1980) no. 2, pp. 741-753 | Article

[14] H. Mughrabi; T. Ungar; W. Kienle; M. Wilkens Long-range internal stresses and asymmetric X-ray line-broadening in tensile-deformed [001]-orientated copper single crystals, Philos. Mag. A, Volume 53 (1986) no. 6, pp. 793-813 | Article

[15] P. Hähner; K. Bay; M. Zaiser Fractal dislocation patterning during plastic deformation, Phys. Rev. Lett., Volume 81 (1998) no. 12, pp. 2470-2473 | Article

[16] M. Zaiser; K. Bay; P. Hähner Fractal analysis of deformation-induced dislocation patterns, Acta Mater., Volume 47 (1999) no. 8, pp. 2463-2476 | Article

[17] X. Zhao; J. Wu; Y. Chiu; I. Jones; R. Gu; A. Ngan Critical dimension for the dislocation structure in deformed copper micropillars, Scr. Mater., Volume 163 (2019), pp. 137-141 | Article

[18] D. Norfleet; D. Dimiduk; S. Polasik; M. Uchic; M. Mills Dislocation structures and their relationship to strength in deformed nickel microcrystals, Acta Mater., Volume 56 (2008) no. 13, pp. 2988-3001 | Article

[19] D. Kiener; P. Guruprasad; S. M. Keralavarma; G. Dehm; A. A. Benzerga Work hardening in micropillar compression: In situ experiments and modeling, Acta Mater., Volume 59 (2011) no. 10, pp. 3825-3840 | Article

[20] R. Maaß; S. Van Petegem; D. Grolimund; H. Van Swygenhoven; D. Kiener; G. Dehm Crystal rotation in Cu single crystal micropillars: In situ Laue and electron backscatter diffraction, Appl. Phys. Lett., Volume 92 (2008) no. 7, 071905 | Article

[21] C. Kirchlechner et al. Dislocation storage in single slip-oriented Cu micro-tensile samples: new insights via X-ray microdiffraction, Philos. Mag., Volume 91 (2011) no. 7–9, pp. 1256-1264 | Article

[22] A. Arsenlis; D. Parks Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density, Acta Mater., Volume 47 (1999) no. 5, pp. 1597-1611 | Article

[23] A. J. Wilkinson; D. Randman Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction, Philos. Mag., Volume 90 (2010) no. 9, pp. 1159-1177 | Article

[24] S. Kalácska; J. Ast; P. D. Ispánovity; J. Michler; X. Maeder 3D HR-EBSD characterization of the plastic zone around crack tips in tungsten single crystals at the micron scale, Acta Mater., Volume 200 (2020), pp. 211-222 | Article

[25] N. M. Della Ventura; S. Kalácska; D. Casari; T. E. Edwards; A. Sharma; J. Michler; R. Logé; X. Maeder {101 ¯2} twinning mechanism during in situ micro-tensile loading of pure mg: Role of basal slip and twin-twin interactions, Mater. Des., Volume 197 (2020), 109206

[26] S. Kalácska; Z. Dankházi; G. Zilahi; X. Maeder; J. Michler; P. D. Ispánovity; I. Groma Investigation of geometrically necessary dislocation structures in compressed Cu micropillars by 3-dimensional HR-EBSD, Mater. Sci. Eng. A, Volume 770 (2020), 138499 | Article

[27] C. R. Weinberger; W. Cai Surface-controlled dislocation multiplication in metal micropillars, Proc. Natl Acad. Sci. USA, Volume 105 (2008) no. 38, pp. 14304-14307 | Article

[28] A. Cao; E. Ma Sample shape and temperature strongly influence the yield strength of metallic nanopillars, Acta Mater., Volume 56 (2008) no. 17, pp. 4816-4828 | Article

[29] S. Xu; Y. Guo; A. Ngan A molecular dynamics study on the orientation, size, and dislocation confinement effects on the plastic deformation of Al nanopillars, Int. J. Plast., Volume 43 (2013), pp. 116-127 | Article

[30] F. F. Csikor; C. Motz; D. Weygand; M. Zaiser; S. Zapperi Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale, Science, Volume 318 (2007) no. 5848, pp. 251-254 | Article

[31] J. Senger; D. Weygand; P. Gumbsch; O. Kraft Discrete dislocation simulations of the plasticity of micro-pillars under uniaxial loading, Scr. Mater., Volume 58 (2008) no. 7, pp. 587-590 | Article

[32] I. Ryu; W. D. Nix; W. Cai Plasticity of bcc micropillars controlled by competition between dislocation multiplication and depletion, Acta Mater., Volume 61 (2013) no. 9, pp. 3233-3241 | Article

[33] J. A. El-Awady Unravelling the physics of size-dependent dislocation-mediated plasticity, Nat. Commun., Volume 6 (2015) no. 1, pp. 1-9

[34] M. Stricker; M. Sudmanns; K. Schulz; T. Hochrainer; D. Weygand Dislocation multiplication in stage II deformation of fcc multi-slip single crystals, J. Mech. Phys. Solids, Volume 119 (2018), pp. 319-333 | Article

[35] J. Senger; D. Weygand; O. Kraft; P. Gumbsch Dislocation microstructure evolution in cyclically twisted microsamples: a discrete dislocation dynamics simulation, Model. Simul. Mater. Sci. Eng., Volume 19 (2011) no. 7, 074004 | Article

[36] I. Groma; F. Csikor; M. Zaiser Spatial correlations and higher-order gradient terms in a continuum description of dislocation dynamics, Acta Mater., Volume 51 (2003) no. 5, pp. 1271-1281 | Article

[37] I. Groma; Z. Vandrus; P. D. Ispánovity Scale-free phase field theory of dislocations, Phys. Rev. Lett., Volume 114 (2015) no. 1, 015503 | Article

[38] I. Groma; M. Zaiser; P. D. Ispánovity Dislocation patterning in a two-dimensional continuum theory of dislocations, Phys. Rev. B, Volume 93 (2016) no. 21, 214110 | Article

[39] P. D. Ispánovity; S. Papanikolaou; I. Groma Emergence and role of dipolar dislocation patterns in discrete and continuum formulations of plasticity, Phys. Rev. B, Volume 101 (2020) no. 2, 024105 | Article

[40] T. Hochrainer; S. Sandfeld; M. Zaiser; P. Gumbsch Continuum dislocation dynamics: towards a physical theory of crystal plasticity, J. Mech. Phys. Solids, Volume 63 (2014), pp. 167-178 | Article

[41] T. Hochrainer Multipole expansion of continuum dislocations dynamics in terms of alignment tensors, Philos. Mag., Volume 95 (2015) no. 12, pp. 1321-1367 | Article

[42] T. Hochrainer Thermodynamically consistent continuum dislocation dynamics, J. Mech. Phys. Solids, Volume 88 (2016), pp. 12-22 | Article | MR: 3453936

[43] K. Schulz; L. Wagner; C. Wieners A mesoscale continuum approach of dislocation dynamics and the approximation by a Runge–Kutta discontinuous Galerkin method, Int. J. Plast., Volume 120 (2019), pp. 248-261 | Article

[44] M. Sudmanns; M. Stricker; D. Weygand; T. Hochrainer; K. Schulz Dislocation multiplication by cross-slip and glissile reaction in a dislocation based continuum formulation of crystal plasticity, J. Mech. Phys. Solids, Volume 132 (2019), 103695 | Article | MR: 3998800

[45] S. Schmitt; M. Stricker; P. Gumbsch; K. Schulz A mechanism-based homogenization of a dislocation source model for bending, Acta Mater., Volume 164 (2019), pp. 663-672 | Article

[46] K. Zoller; K. Schulz Analysis of single crystalline microwires under torsion using a dislocation-based continuum formulation, Acta Mater., Volume 191 (2020), pp. 198-210 | Article

[47] E. Schmid; W. Boas Kristallplastizität : mit besonderer Berücksichtigung der Metalle, Struktur und Eigenschaften der Materie in Einzeldarstellungen, Volume 17, Springer, Berlin, 1935 | Article

[48] M. Uchic; P. Shade; D. Dimiduk Plasticity of micromoter-scale single crystals in compression, Annu. Rev. Mater. Res., Volume 39 (2009), pp. 361-386 | Article

[49] J. Wheeler; J. Michler Elevated temperature, nano-mechanical testing in situ in the scanning electron microscope, Rev. Sci. Instrum., Volume 84 (2013), 045103 | Article

[50] I. N. Sneddon Boussinesq’s problem for a flat-ended cylinder, Proc. Camb. Philos. Soc., Volume 42 (1946) no. 1, pp. 29-39 | Article | MR: 16039 | Zbl: 0060.42002

[51] J. Nye Some geometrical relations in dislocated crystals, Acta Metall., Volume 1 (1953) no. 2, pp. 153-162 | Article

[52] E. Kröner; G. Rieder Kontinuumstheorie der Versetzungen, Z. Phys., Volume 145 (1956) no. 4, pp. 424-429 | Article | Zbl: 0071.23801

[53] B. C. Larson; J. Z. Tischler; A. El-Azab; W. Liu Dislocation density tensor characterization of deformation using 3D X-Ray microscopy, J. Eng. Mater. Technol., Volume 130 (2008) no. 2, 021024 | Article

[54] T. Britton; J. Hickey Understanding deformation with high angular resolution electron backscatter diffraction (HR-EBSD), IOP Conf. Ser.: Mater. Sci. Eng., Volume 304 (2018), 012003 | Article

[55] D. Chen; J.-C. Kuo; W.-T. Wu Effect of microscopic parameters on EBSD spatial resolution, Ultramicroscopy, Volume 111 (2011) no. 9–10, pp. 1488-1494 | Article

[56] S. Das; F. Hofmann; E. Tarleton Consistent determination of geometrically necessary dislocation density from simulations and experiments, Int. J. Plast., Volume 109 (2018), pp. 18-42 | Article

[57] A. Wilkinson; D. Dingley; G. Meaden Strain mapping using electron backscatter diffraction, Electron Backscatter Diffraction in Materials Science (A. J. Schwatz; M. Kumar; B. L. Adams; D. P. Field, eds.), Springer Science+Business Media, Boston, MA, 2009, pp. 231-249 | Article

[58] A. Wilkinson; D. Randman Determination of elastic strain fields and geometrically necessary dislocation distributions near nanoindents using electron back scatter diffraction, Philos. Mag., Volume 90 (2010) no. 9, pp. 1159-1177 | Article

[59] M. Sudmanns; J. Bach; D. Weygand; K. Schulz Data-driven exploration and continuum modeling of dislocation networks, Model. Simul. Mater. Sci. Eng., Volume 28 (2020), 065001 | Article

[60] E. Orowan Zur Kristallplastizität, Z. Phys., Volume 89 (1934), pp. 605-659 | Article

[61] D. Rodney; R. Phillips Structure and strength of dislocation junctions: An atomic level analysis, Phys. Rev. Lett., Volume 82 (1999) no. 8, pp. 1704-1707 | Article

[62] C. Shin; M. Fivel; D. Rodney; R. Phillips; V. Shenoy; L. Dupuy Formation and strength of dislocation junctions in FCC metals: A study by dislocation dynamics and atomistic simulations, J. Phys. IV, Volume 11 (2001) no. PR5, p. Pr5-19–Pr5-26

[63] P. Franciosi; M. Berveiller; A. Zaoui Latent hardening in copper and aluminium single crystals, Acta Metall., Volume 28 (1980) no. 3, pp. 273-283 | Article

[64] R. Madec; B. Devincre; L. Kubin; T. Hoc; D. Rodney The role of collinear interaction in dislocation-induced hardening, Science, Volume 301 (2003) no. 5641, pp. 1879-1882 | Article

[65] K. Schulz; D. Dickel; S. Schmitt; S. Sandfeld; D. Weygand; P. Gumbsch Analysis of dislocation pile-ups using a dislocation-based continuum theory, Model Simul. Mater. Sci. Eng., Volume 22 (2014) no. 2, 025008 | Article

[66] S. Schmitt; P. Gumbsch; K. Schulz Internal stresses in a homogenized representation of dislocation microstructures, J. Mech. Phys. Solids, Volume 84 (2015), pp. 528-544 | Article | MR: 3413452

[67] C. Wieners A geometric data structure for parallel finite elements and the application to multigrid methods with block smoothing, Comput. Vis. Sci., Volume 13 (2010) no. 4, pp. 161-175 | Article | MR: 2645017 | Zbl: 1216.65164

[68] C. Wieners Distributed point objects. A new concept for parallel finite elements, Domain Decomposition Methods in Science and Engineering, Volume 2005, Springer, Berlin, Heidelberg, 2005, pp. 175-182 | Article | MR: 2235740 | Zbl: 1067.65134

[69] H. Ledbetter; E. Naimon Elastic properties of metals and alloys. II. Copper, J. Phys. Chem. Ref. Data, Volume 3 (1974) no. 4, pp. 897-935 | Article

[70] J. Rösler; H. Harders; M. Bäker Mechanisches Verhalten der Werkstoffe, Springer-Verlag, Wiesbaden, 2019 | Article

[71] E. Date; K. Andrews Anisotropic and composition effects in the elastic properties of polycrystalline metals, J. Phys. D, Volume 2 (1969) no. 10, pp. 1373-1381 | Article

[72] W. P. Davey Precision measurements of the lattice constants of twelve common metals, Phys. Rev., Volume 25 (1925) no. 6, pp. 753-761 | Article

[73] L. P. Kubin; G. Canova; M. Condat; B. Devincre; V. Pontikis; Y. Bréchet Dislocation microstructures and plastic flow: a 3D simulation, Solid State Phenomena, Volume 23, Trans Tech Publications, Switzerland, 1992, pp. 455-472 | Article

[74] L. Kubin; B. Devincre; T. Hoc Modeling dislocation storage rates and mean free paths in face-centered cubic crystals, Acta Mater., Volume 56 (2008) no. 20, pp. 6040-6049 | Article

[75] D. Weygand; L. Friedman; E. Van der Giessen; A. Needleman Aspects of boundary-value problem solutions with three-dimensional dislocation dynamics, Model. Simul. Mater. Sci. Eng., Volume 10 (2002) no. 4, pp. 437-468 | Article

[76] J. Bonneville; B. Escaig; J. Martin A study of cross-slip activation parameters in pure copper, Acta Metall., Volume 36 (1988) no. 8, pp. 1989-2002 | Article

[77] J. Wu; W. Tsai; J. Huang; C. Hsieh; G.-R. Huang Sample size and orientation effects of single crystal aluminum, Mater. Sci. Eng. A, Volume 662 (2016), pp. 296-302 | Article

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