Fluctuations in crystalline plasticity

Jérôme Weiss; Peng Zhang; Oğuz Umut Salman; Gang Liu; Lev Truskinovsky

doi:10.5802/crphys.51

Fluctuations in crystalline plasticity
[Fluctuations plastiques dans les matériaux cristallins]

Jérôme Weiss ¹ ; Peng Zhang ² ; Oğuz Umut Salman ³ ; Gang Liu ² ; Lev Truskinovsky ⁴

¹ ISTerre, CNRS/Université Grenoble-Alpes, 38041 Grenoble, France
² State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, 710049, China
³ CNRS, LSPM UPR3407, Sorbonne Université Paris Nord, 93430, Villetaneuse, France
⁴ PMMH, CNRS UMR 7636, ESPCI ParsiTech, 10 Rue Vauquelin, 75005, Paris, France

Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 163-199.

Résumé
Abstract

Malgré une étude précurseur de Becker et Orowan en 1932 sur le Zinc, l’analyse des fluctuations dans la dynamique de la déformation plastique des matériaux cristallins a été pendant longtemps négligée, probablement du fait que dans la plupart des matériaux métalliques d’intérêt industriel ces fluctuations sont indétectables en termes de comportement mécanique aux échelles macroscopiques. La situation a changé drastiquement il y a une vingtaine d’années lorsque, d’une part, l’enregistrement des signatures acoustiques des avalanches de dislocations dans certains matériaux hexagonaux a montré que ces dernières pouvaient être distribuées en loi de puissance, suggérant une dynamique critique, et d’autre part il a été observé que la plasticité des systèmes de taille micro- et nano-métrique devenait intermittente pour la plupart des matériaux non-alliés. Dans cet article, nous discutons, sur la base de récents travaux et dans le cadre de la physique statistique, de la nature et des propriétés statistiques et d’échelle de ces fluctuations plastiques en fonction de la symétrie cristalline, de la taille du système considéré, ainsi que du désordre interne, qu’il soit émergent (structures de dislocations) ou ajusté par des techniques d’alliage. On met ainsi en lumière des effets de taille très prononcés sur la stochasticité de la déformation plastique, un rapport d’échelle $R = L / l$ entre la taille finie du système $L$ et une échelle interne $l$ jouant un rôle majeur pour expliquer ces transitions de comportement. On discute également le lien avec d’autres effets d’échelle, sur le seuil d’écoulement plastique ou la nature des mécanismes de durcissement, et on montre comment les techniques d’alliage peuvent réduire ces instabilités plastiques. Ceci ouvre la voie vers une métallurgie et des pratiques d’ingénierie aux échelles sous-microniques tenant compte du caractère stochastique intrinsèque de la plasticité à ces échelles, et tentant de le supprimer ou de l’atténuer.

Recently acoustic signature of dislocation avalanches in HCP materials was found to be long tailed in size and energy, suggesting critical dynamics. Moreover, the intermittent plastic response was found to be generic for micro- and nano-sized systems independently of their crystallographic symmetry. These rather remarkable discoveries are reviewed in this paper in the perspective of the recent studies performed in our group. We discuss the physical origin and the scaling properties of plastic fluctuations and address the nature of their dependence on crystalline symmetry, system size, and disorder content. A particular emphasis is placed on the formation of dislocation structures, and on our ability to temper plastic fluctuations by alloying. We also discuss the “smaller is wilder” size effect that culminates in a paradoxical crack-free brittle behavior of very small, initially dislocation free crystals. We argue that the implied transition between different rheological behaviors is regulated by the ratio of length scales $R = L / l$ , where $L$ is the system size and $l$ is the internal length. We link this size effect with size dependence of strength (“smaller is stronger”) and the size-induced switch between different hardening mechanisms. We show that the task of taming the intermittency of plastic flow at ultra-small scales can be accomplished by generating tailored quenched disorder which allows one to control micro- and nano-forming and opens new perspectives in micro-metallurgy and structural engineering of miniature load-carrying elements. These insights were beyond the reach of conventional theoretical approaches that do not explicitly account for the stochastic nature of collective dislocation dynamics.

Première publication : 2021-03-26
Publié le : 2021-12-16

DOI : 10.5802/crphys.51

Keywords: Plasticity, Dislocations, Statistical physics, Avalanches, Critical phenomena
Mot clés : Plasticité, Dislocations, Physique statistique, Avalanches, Phénomènes critiques

Affiliations des auteurs :

Jérôme Weiss ¹ ; Peng Zhang ² ; Oğuz Umut Salman ³ ; Gang Liu ² ; Lev Truskinovsky ⁴

¹ ISTerre, CNRS/Université Grenoble-Alpes, 38041 Grenoble, France
² State Key Laboratory for Mechanical Behavior of Materials, Xi’an Jiaotong University, Xi’an, 710049, China
³ CNRS, LSPM UPR3407, Sorbonne Université Paris Nord, 93430, Villetaneuse, France
⁴ PMMH, CNRS UMR 7636, ESPCI ParsiTech, 10 Rue Vauquelin, 75005, Paris, France

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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Jérôme Weiss; Peng Zhang; Oğuz Umut Salman; Gang Liu; Lev Truskinovsky. Fluctuations in crystalline plasticity. Comptes Rendus. Physique, Volume 22 (2021) no. S3, pp. 163-199. doi : 10.5802/crphys.51. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.51/

Bibliographie
Cité par

[1] R. Becker; E. Orowan Sudden expansion of zinc crystals, Z. Phys., Volume 79 (1932), pp. 566-572

[2] J. Weiss; J.-R. Grasso Acoustic emission in single crystals of ice, J. Phys. Chem. B, Volume 101 (1997) no. 32, pp. 6113-6117 | DOI

[3] M.-C. Miguel; A. Vespignani; S. Zapperi; J. Weiss; J.-R. Grasso Intermittent dislocation flow in viscoplastic deformation, Nature, Volume 410 (2001) no. 6829, pp. 667-671 | DOI

[4] 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 | DOI

[5] N. Friedman; A. T. Jennings; G. Tsekenis; J.-Y. Kim; M. Tao; J. T. Uhl; J. R. Greer; K. A. Dahmen Statistics of dislocation slip avalanches in nanosized single crystals show tuned critical behavior predicted by a simple mean field model, Phys. Rev. Lett., Volume 109 (2012) no. 9, 095507 | DOI

[6] E. Orowan Zur kristallplastizität. I, Z. Phys., Volume 89 (1934) no. 9–10, pp. 605-613

[7] E. Orowan Zur kristallplastizität. II, Z. Phys., Volume 89 (1934) no. 9–10, pp. 614-633

[8] E. Orowan Zur kristallplastizität. III, Z. Phys., Volume 89 (1934) no. 9–10, pp. 634-659

[9] M. Polanyi Über eine Art Gitterstörung, die einen Kristall plastisch machen könnte, Z. Phys., Volume 89 (1934) no. 9–10, pp. 660-664

[10] G. I. Taylor The mechanism of plastic deformation of crystals. Part I.—Theoretical, Proc. R. Soc. Lond. A, Volume 145 (1934) no. 855, pp. 362-387

[11] A. Timpe Probleme der Spannungsverteilung in ebenen Systemen einfach gelöst mit Hilfe der Airyschen Function, Z. Math. Phys., Volume 52 (1905), pp. 348-383

[12] V. Volterra Sur l’équilibre des corps élastiques multiplement connexes, Ann. Sci. Éc. Norm. Supér., Volume 24 (1907), pp. 401-517 | DOI

[13] J. Hirth A brief history of dislocation theory, Metall. Trans. A, Volume 16 (1985) no. 12, pp. 2085-2090 | DOI

[14] J. Savage Dislocations in seismology, Dislocations Solids, Volume 3 (1980), pp. 251-339

[15] A. Garroni; S. Müller $Γ$ -limit of a phase-field model of dislocations, SIAM J. Math. Anal., Volume 36 (2005) no. 6, pp. 1943-1964 | DOI

[16] M. Ariza; M. Ortiz Discrete crystal elasticity and discrete dislocations in crystals, Arch. Ration. Mech. Anal., Volume 178 (2005) no. 2, pp. 149-226 | DOI

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

[18] E. Kröner Allgemeine kontinuumstheorie der versetzungen und eigenspannungen, Arch. Ration. Mech. Anal., Volume 4 (1959) no. 1, 273 | DOI

[19] J. Hutchinson; N. Fleck Strain gradient plasticity, Adv. Appl. Mech., Volume 33 (1997), pp. 295-361

[20] A. Acharya; J. Bassani Lattice incompatibility and a gradient theory of crystal plasticity, J. Mech. Phys. Solids, Volume 48 (2000) no. 8, pp. 1565-1595 | DOI

[21] A. Acharya A model of crystal plasticity based on the theory of continuously distributed dislocations, J. Mech. Phys. Solids, Volume 49 (2001) no. 4, pp. 761-784 | DOI

[22] C. Fressengeas; V. Taupin; L. Capolungo An elasto-plastic theory of dislocation and disclination fields, Int. J. Solids Struct., Volume 48 (2011) no. 25–26, pp. 3499-3509 | DOI

[23] P.-L. Valdenaire; Y. Le Bouar; B. Appolaire; A. Finel Density-based crystal plasticity: From the discrete to the continuum, Phys. Rev. B, Volume 93 (2016) no. 21, 214111

[24] 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. Publ., 1992, pp. 455-472 | DOI

[25] L. Kubin Dislocations, Mesoscale Simulations and Plastic Flow, 5, Oxford University Press, 2013 | DOI

[26] D. Rodney Molecular dynamics simulation of screw dislocations interacting with interstitial frank loops in a model FCC crystal, Acta Mater., Volume 52 (2004) no. 3, pp. 607-614 | DOI

[27] L. A. Zepeda-Ruiz; A. Stukowski; T. Oppelstrup; V. V. Bulatov Probing the limits of metal plasticity with molecular dynamics simulations, Nature, Volume 550 (2017) no. 7677, pp. 492-495 | DOI

[28] R. Madec; B. Devincre; L. Kubin Simulation of dislocation patterns in multislip, Scr. Mater., Volume 47 (2002) no. 10, pp. 689-695 | DOI

[29] L. Kubin; C. Fressengeas; G. Ananthakrishna Collective behaviour of dislocations in plasticity, Dislocations in Solids, Volume 11 (2002), pp. 101-192 | DOI

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

[31] C. Laird; P. Charsley; H. Mughrabi Low energy dislocation structures produced by cyclic deformation, Mater. Sci. Eng., Volume 81 (1986), pp. 433-450 | DOI

[32] M. Sauzay; L. P. Kubin Scaling laws for dislocation microstructures in monotonic and cyclic deformation of fcc metals, Prog. Mater. Sci., Volume 56 (2011) no. 6, pp. 725-784 | DOI

[33] J. Weiss Ice: The paradigm of wild plasticity, Philos. Trans. R. Soc. Lond. A, Volume 377 (2019) no. 2146, 20180260

[34] S. Brinckmann; J.-Y. Kim; J. R. Greer Fundamental differences in mechanical behavior between two types of crystals at the nanoscale, Phys. Rev. Lett., Volume 100 (2008) no. 15, 155502 | DOI

[35] K. Ng; A. Ngan Stochastic nature of plasticity of aluminum micro-pillars, Acta Mater., Volume 56 (2008) no. 8, pp. 1712-1720 | DOI

[36] 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 | DOI

[37] T. Hu; L. Jiang; A. K. Mukherjee; J. M. Schoenung; E. J. Lavernia Strategies to approach stabilized plasticity in metals with diminutive volume: A brief review, Crystals, Volume 6 (2016) no. 8, 92

[38] M. Zaiser; P. Moretti Fluctuation phenomena in crystal plasticity—a continuum model, J. Stat. Mech.: Therory Exp., Volume 2005 (2005) no. 08, P08004

[39] M. Zaiser Statistical aspects of microplasticity: Experiments, discrete dislocation simulations and stochastic continuum models, J. Mech. Behav. Mater., Volume 22 (2013) no. 3–4, pp. 89-100 | DOI

[40] S. Xia; A. El-Azab Computational modelling of mesoscale dislocation patterning and plastic deformation of single crystals, Modell. Simul. Mater. Sci. Eng., Volume 23 (2015) no. 5, 055009

[41] M. Monavari; M. Zaiser Annihilation and sources in continuum dislocation dynamics, Mater. Theory, Volume 2 (2018) no. 1, 3 | DOI

[42] M. Lebyodkin; Y. Brechet; Y. Estrin; L. Kubin Statistics of the catastrophic slip events in the Portevin–Le Châtelier effect, Phys. Rev. Lett., Volume 74 (1995) no. 23, p. 4758 | DOI

[43] G. Ananthakrishna; S. Noronha; C. Fressengeas; L. Kubin Crossover from chaotic to self-organized critical dynamics in jerky flow of single crystals, Phys. Rev. E, Volume 60 (1999) no. 5, pp. 5455-5462

[44] M. Bharathi; M. Lebyodkin; G. Ananthakrishna; C. Fressengeas; L. Kubin The hidden order behind jerky flow, Acta Mater., Volume 50 (2002) no. 11, pp. 2813-2824 | DOI

[45] G. Ananthakrishna Current theoretical approaches to collective behavior of dislocations, Phys. Rep., Volume 440 (2007) no. 4–6, pp. 113-259 | DOI

[46] Y. R. Efendiev; L. Truskinovsky Thermalization of a driven bi-stable FPU chain, Contin. Mech. Thermodyn., Volume 22 (2010) no. 6, pp. 679-698 | DOI

[47] V. Berdichevsky Beyond classical thermodynamics: Dislocation-mediated plasticity, J. Mech. Phys. Solids, Volume 129 (2019), pp. 83-118 | DOI

[48] J. Langer; E. Bouchbinder; T. Lookman Thermodynamic theory of dislocation-mediated plasticity, Acta Mater., Volume 58 (2010) no. 10, pp. 3718-3732 | DOI

[49] J. Langer Statistical thermodynamics of dislocations in solids (2020) (https://arxiv.org/abs/2003.03209)

[50] P. D. Ispánovity; L. Laurson; M. Zaiser; I. Groma; S. Zapperi; M. J. Alava Avalanches in 2D dislocation systems: Plastic yielding is not depinning, Phys. Rev. Lett., Volume 112 (2014) no. 23, 235501 | DOI

[51] H. Song; D. Dimiduk; S. Papanikolaou Universality class of nanocrystal plasticity: Localization and self-organization in discrete dislocation dynamics, Phys. Rev. Lett., Volume 122 (2019) no. 17, 178001 | DOI

[52] M. Zaiser Scale invariance in plastic flow of crystalline solids, Adv. Phys., Volume 55 (2006) no. 1–2, pp. 185-245 | DOI

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

[54] J. R. Greer; J. T. M. De Hosson Plasticity in small-sized metallic systems: Intrinsic versus extrinsic size effect, Prog. Mater. Sci., Volume 56 (2011) no. 6, pp. 654-724 | DOI

[55] S. Papanikolaou; Y. Cui; N. Ghoniem Avalanches and plastic flow in crystal plasticity: An overview, Model. Simul. Mat. Sci. Eng., Volume 26 (2017) no. 1, 013001 | DOI

[56] R. Maass; P. Derlet Micro-plasticity and recent insights from intermittent and small-scale plasticity, Acta Mater., Volume 143 (2018), pp. 338-363 | DOI

[57] Y. Cui; N. Ghoniem Spatio-temporal plastic instabilities at the nano/micro scale, J. Micromech. Mol. Phys., Volume 3 (2018) no. 03n04, 1840006

[58] J. P. Sethna; M. K. Bierbaum; K. A. Dahmen; C. P. Goodrich; J. R. Greer; L. X. Hayden; J. P. Kent-Dobias; E. D. Lee; D. B. Liarte; X. Ni et al. Deformation of crystals: Connections with statistical physics, Annu. Rev. Mater. Res., Volume 47 (2017), pp. 217-246 | DOI

[59] I. Ovid’Ko; R. Valiev; Y. Zhu Review on superior strength and enhanced ductility of metallic nanomaterials, Prog. Mater. Sci., Volume 94 (2018), pp. 462-540 | DOI

[60] G. Dehm; B. N. Jaya; R. Raghavan; C. Kirchlechner Overview on micro-and nanomechanical testing: New insights in interface plasticity and fracture at small length scales, Acta Mater., Volume 142 (2018), pp. 248-282 | DOI

[61] I. Groma Statistical theory of dislocation, Mesoscale Models (S. Mesarovic; S. Forest; H. Zbib, eds.) (CISM International Centre for Mechanical Sciences (Courses and Lectures)), Volume 587, Springer, 2019, pp. 87-139 | DOI

[62] J. Weiss; W. B. Rhouma; T. Richeton; S. Dechanel; F. Louchet; L. Truskinovsky From mild to wild fluctuations in crystal plasticity, Phys. Rev. Lett., Volume 114 (2015) no. 10, 105504 | DOI

[63] S. Papanikolaou; D. M. Dimiduk; W. Choi; J. P. Sethna; M. D. Uchic; C. F. Woodward; S. Zapperi Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator, Nature, Volume 490 (2012) no. 7421, pp. 517-521 | DOI

[64] P. Zhang; O. U. Salman; J.-Y. Zhang; G. Liu; J. Weiss; L. Truskinovsky; J. Sun Taming intermittent plasticity at small scales, Acta Mater., Volume 128 (2017), pp. 351-364 | DOI

[65] M. Zaiser; N. Nikitas Slip avalanches in crystal plasticity: Scaling of the avalanche cut-off, J. Stat. Mech.: Theory Exp., Volume 2007 (2007) no. 04, P04013

[66] J. Weiss; W. B. Rhouma; S. Deschanel; L. Truskinovsky Plastic intermittency during cyclic loading: From dislocation patterning to microcrack initiation, Phys. Rev. Mater., Volume 3 (2019) no. 2, 023603

[67] P. Zhang; O. Salman; J. Weiss; L. Truskinovsky Variety of scaling behaviors in nanocrystalline plasticity, Phys. Rev. E, Volume 102 (2020), 023006

[68] P. Zhang; J.-J. Bian; J.-Y. Zhang; G. Liu; J. Weiss; J. Sun Plate-like precipitate effects on plasticity of Al–Cu alloys at micrometer to sub-micrometer scales, Mater. Design, Volume 188 (2020), 108444

[69] G. l’Hôte; S. Cazottes; J. Lachambre; M. Montagnat; P. Courtois; J. Weiss; S. Deschanel Dislocation dynamics during cyclic loading in copper single crystal, Materialia, Volume 8 (2019), 100501

[70] O. U. Salman; L. Truskinovsky Minimal integer automaton behind crystal plasticity, Phys. Rev. Lett., Volume 106 (2011) no. 17, 175503 | DOI

[71] R. Tinder; J. Trzil Millimicroplastic burst phenomena in zinc monocrystals, Acta Metall., Volume 21 (1973) no. 7, pp. 975-989 | DOI

[72] R. Fisher; J. Lally Microplasticity detected by an acoustic technique, Can. J. Phys., Volume 45 (1967) no. 2, pp. 1147-1159 | DOI

[73] D. R. James; S. H. Carpenter Relationship between acoustic emission and dislocation kinetics in crystalline solids, J. Appl. Phys., Volume 42 (1971) no. 12, pp. 4685-4697 | DOI

[74] T. Imanaka; K. Sano; M. Shimizu Dislocation attenuation and acoustic emission during deformation in copper single crystals, Cryst. Lattice Defects, Volume 4 (1973) no. 1, pp. 57-64

[75] N. Kiesewetter; P. Schiller The acoustic emission from moving dislocations in aluminium, Phys. Status Solidi (a), Volume 38 (1976) no. 2, pp. 569-576 | DOI

[76] P. D. Rouby; P. Fleischmann; C. Duvergier Un modèle de sources ďémission acoustique pour l’analyse de l’émission continue et de l’émission par salves I. Analyse théorique, Philos. Mag. A, Volume 47 (1983) no. 5, pp. 671-687

[77] P. Duval; M. Ashby; I. Anderman Rate-controlling processes in the creep of polycrystalline ice, J. Phys. Chem., Volume 87 (1983) no. 21, pp. 4066-4074 | DOI

[78] J. T. Uhl; S. Pathak; D. Schorlemmer; X. Liu; R. Swindeman; B. A. Brinkman; M. LeBlanc; G. Tsekenis; N. Friedman; R. Behringer et al. Universal quake statistics: From compressed nanocrystals to earthquakes, Sci. Rep., Volume 5 (2015), 16493

[79] E. K. Salje; K. A. Dahmen Crackling noise in disordered materials, Annu. Rev. Condens. Matter Phys., Volume 5 (2014), pp. 233-254 | DOI

[80] J. Weiss; M. C. Miguel Dislocation avalanche correlations, Mater. Sci. Eng. A, Volume 387 (2004), pp. 292-296 | DOI

[81] J. Weiss; D. Marsan Three-dimensional mapping of dislocation avalanches: Clustering and space/time coupling, Science, Volume 299 (2003) no. 5603, pp. 89-92 | DOI

[82] T. Richeton; P. Dobron; F. Chmelik; J. Weiss; F. Louchet On the critical character of plasticity in metallic single crystals, Mater. Sci. Eng. A, Volume 424 (2006) no. 1-2, pp. 190-195 | DOI

[83] J. Weiss; T. Richeton; F. Louchet; F. Chmelik; P. Dobron; D. Entemeyer; M. Lebyodkin; T. Lebedkina; C. Fressengeas; R. J. McDonald Evidence for universal intermittent crystal plasticity from acoustic emission and high-resolution extensometry experiments, Phys. Rev. B, Volume 76 (2007) no. 22, 224110 | DOI

[84] Y. Chen; B. Gou; W. Fu; C. Chen; X. Ding; J. Sun; E. K. Salje Fine structures of acoustic emission spectra: How to separate dislocation movements and entanglements in 316L stainless steel, Appl. Phys. Lett., Volume 117 (2020) no. 26, 262901 | DOI

[85] T. Richeton; J. Weiss; F. Louchet Breakdown of avalanche critical behaviour in polycrystalline plasticity, Nat. Mater., Volume 4 (2005) no. 6, pp. 465-469 | DOI

[86] T. Niiyama; T. Shimokawa Barrier effect of grain boundaries on the avalanche propagation of polycrystalline plasticity, Phys. Rev. B, Volume 94 (2016) no. 14, 140102 | DOI

[87] T. Richeton; J. Weiss; F. Louchet Dislocation avalanches: Role of temperature, grain size and strain hardening, Acta Mater., Volume 53 (2005) no. 16, pp. 4463-4471 | DOI

[88] J. Schiøtz; K. W. Jacobsen A maximum in the strength of nanocrystalline copper, Science, Volume 301 (2003) no. 5638, pp. 1357-1359 | DOI

[89] F. Louchet; J. Weiss; T. Richeton Hall–Petch law revisited in terms of collective dislocation dynamics, Phys. Rev. Lett., Volume 97 (2006) no. 7, 075504 | DOI

[90] M. D. Uchic; D. M. Dimiduk; J. N. Florando; W. D. Nix Sample dimensions influence strength and crystal plasticity, Science, Volume 305 (2004) no. 5686, pp. 986-989 | DOI

[91] G. Richter; K. Hillerich; D. S. Gianola; R. Monig; O. Kraft; C. A. Volkert Ultrahigh strength single crystalline nanowhiskers grown by physical vapor deposition, Nano Lett., Volume 9 (2009) no. 8, pp. 3048-3052 | DOI

[92] A. Sharma; J. Hickman; N. Gazit; E. Rabkin; Y. Mishin Nickel nanoparticles set a new record of strength, Nat. Commun., Volume 9 (2018) no. 1, 4102

[93] D. Mordehai; O. David; R. Kositski Nucleation-controlled plasticity of metallic nanowires and nanoparticles, Adv. Mater., Volume 30 (2018) no. 41, 1706710

[94] D. Dunstan; A. Bushby The scaling exponent in the size effect of small scale plastic deformation, Int. J. Plast., Volume 40 (2013), pp. 152-162 | DOI

[95] A. Schneider; D. Kaufmann; B. Clark; C. Frick; P. Gruber; R. Mönig; O. Kraft; E. Arzt Correlation between critical temperature and strength of small-scale bcc pillars, Phys. Rev. Lett., Volume 103 (2009) no. 10, 105501 | DOI

[96] 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 | DOI

[97] J. R. Greer; W. D. Nix Nanoscale gold pillars strengthened through dislocation starvation, Phys. Rev. B, Volume 73 (2006) no. 24, 245410 | DOI

[98] M. Zaiser; J. Schwerdtfeger; A. Schneider; C. Frick; B. G. Clark; P. Gruber; E. Arzt Strain bursts in plastically deforming molybdenum micro- and nanopillars, Philos. Mag. A, Volume 88 (2008) no. 30–32, pp. 3861-3874 | DOI

[99] A. Lehtinen; G. Costantini; M. J. Alava; S. Zapperi; L. Laurson Glassy features of crystal plasticity, Phys. Rev. B, Volume 94 (2016) no. 6, 064101 | DOI

[100] R. Maaß; P. M. Derlet; J. R. Greer Small-scale plasticity: Insights into dislocation avalanche velocities, Scr. Mater., Volume 69 (2013) no. 8, pp. 586-589 | DOI

[101] A. Clauset; C. R. Shalizi; M. E. Newman Power-law distributions in empirical data, SIAM Rev., Volume 51 (2009) no. 4, pp. 661-703

[102] D. Sornette; G. Ouillon Dragon-kings: Mechanisms, statistical methods and empirical evidence, Eur. Phys. J.: Spec. Top., Volume 205 (2012) no. 1 | DOI

[103] D. Mordehai; S.-W. Lee; B. Backes; D. J. Srolovitz; W. D. Nix; E. Rabkin Size effect in compression of single-crystal gold microparticles, Acta Mater., Volume 59 (2011) no. 13, pp. 5202-5215 | DOI

[104] J. R. Rice; R. Thomson Ductile versus brittle behaviour of crystals, Philos. Mag. A, Volume 29 (1974) no. 1, pp. 73-97 | DOI

[105] P. Gumbsch; J. Riedle; A. Hartmaier; H. F. Fischmeister Controlling factors for the brittle-to-ductile transition in tungsten single crystals, Science, Volume 282 (1998) no. 5392, pp. 1293-1295 | DOI

[106] B. D. Wirth How does radiation damage materials?, Science, Volume 318 (2007) no. 5852, pp. 923-924 | DOI

[107] D. Kiener; C. Motz; M. Rester; M. Jenko; G. Dehm FIB damage of Cu and possible consequences for miniaturized mechanical tests, Mater. Sci. Eng. A, Volume 459 (2007) no. 1–2, pp. 262-272 | DOI

[108] S. Lee; J. Jeong; Y. Kim; S. M. Han; D. Kiener; S. H. Oh FIB-induced dislocations in Al submicron pillars: Annihilation by thermal annealing and effects on deformation behavior, Acta Mater., Volume 110 (2016), pp. 283-294 | DOI

[109] J. Weiss; F. Louchet Seismology of plastic deformation, Scr. Mater., Volume 54 (2006) no. 5, pp. 747-751 | DOI

[110] D. Rodney; L. Ventelon; E. Clouet; L. Pizzagalli; F. Willaime Ab initio modeling of dislocation core properties in metals and semiconductors, Acta Mater., Volume 124 (2017), pp. 633-659 | DOI

[111] O. T. Abad; J. M. Wheeler; J. Michler; A. S. Schneider; E. Arzt Temperature-dependent size effects on the strength of Ta and W micropillars, Acta Mater., Volume 103 (2016), pp. 483-494 | DOI

[112] Y. Cui; G. Po; P. Srivastava; K. Jiang; V. Gupta; N. Ghoniem The role of slow screw dislocations in controlling fast strain avalanche dynamics in body-centered cubic metals, Int. J. Plast., Volume 124 (2020), pp. 117-132 | DOI

[113] G. Sparks; Y. Cui; G. Po; Q. Rizzardi; J. Marian; R. Maaß Avalanche statistics and the intermittent-to-smooth transition in microplasticity, Phys. Rev. Mater., Volume 3 (2019) no. 8, 080601

[114] Y. Cui; G. Po; N. Ghoniem Temperature insensitivity of the flow stress in body-centered cubic micropillar crystals, Acta Mater., Volume 108 (2016), pp. 128-137 | DOI

[115] A. Keh; S. Weissmann Deformation substructure in body-centered cubic metals, Electron Microscopy and Strength of Crystals, Interscience, New York, 1963, pp. 231-300

[116] M. Zaiser; S. Sandfeld Scaling properties of dislocation simulations in the similitude regime, Model. Simul. Mat. Sci. Eng., Volume 22 (2014) no. 6, 065012 | DOI

[117] J. D. Verhoeven; A. Pendray; W. Dauksch The key role of impurities in ancient Damascus steel blades, JOM, Volume 50 (1998) no. 9, pp. 58-64 | DOI

[118] H. Gao; Y. Hu; Y. Xuan; J. Li; Y. Yang; R. V. Martinez; C. Li; J. Luo; M. Qi; G. J. Cheng Large-scale nanoshaping of ultrasmooth 3D crystalline metallic structures, Science, Volume 346 (2014) no. 6215, pp. 1352-1356 | DOI

[119] R. Gu; A. Ngan Size effect on the deformation behavior of duralumin micropillars, Scr. Mater., Volume 68 (2013) no. 11, pp. 861-864 | DOI

[120] B. Girault; A. S. Schneider; C. P. Frick; E. Arzt Strength effects in micropillars of a dispersion strengthened superalloy, Adv. Eng. Mater., Volume 12 (2010) no. 5, pp. 385-388 | DOI

[121] Y. Pan; H. Wu; X. Wang; Q. Sun; L. Xiao; X. Ding; J. Sun; E. K. Salje Rotatable precipitates change the scale-free to scale dependent statistics in compressed Ti nano-pillars, Sci. Rep., Volume 9 (2019) no. 1, 3778

[122] D. Bacon; V. Vitek Atomic-scale modeling of dislocations and related properties in the hexagonal-close-packed metals, Metall. Mater. Trans. A, Volume 33 (2002) no. 3, pp. 721-733 | DOI

[123] E. Clouet; D. Caillard; N. Chaari; F. Onimus; D. Rodney Dislocation locking versus easy glide in titanium and zirconium, Nat. Mater., Volume 14 (2015) no. 9, pp. 931-936 | DOI

[124] J. A. El-Awady Unravelling the physics of size-dependent dislocation-mediated plasticity, Nat. Commun., Volume 6 (2015) no. 1, 5926

[125] J. Alcalá; J. Očenášek; K. Nowag; D. Esqué-de los Ojos; R. Ghisleni; J. Michler Strain hardening and dislocation avalanches in micrometer-sized dimensions, Acta Mater., Volume 91 (2015), pp. 255-266 | DOI

[126] T. J. Flanagan; O. Kovalenko; E. Rabkin; S.-W. Lee The effect of defects on strength of gold microparticles, Scr. Mater., Volume 171 (2019), pp. 83-86 | DOI

[127] O. U. Salman; L. Truskinovsky On the critical nature of plastic flow: One and two dimensional models, Int. J. Eng. Sci., Volume 59 (2012), pp. 219-254 | DOI

[128] R. Baggio; E. Arbib; P. Biscari; S. Conti; L. Truskinovsky; G. Zanzotto; O. Salman Landau-type theory of planar crystal plasticity, Phys. Rev. Lett., Volume 123 (2019) no. 20, 205501 | DOI

[129] G. Puglisi; L. Truskinovsky Thermodynamics of rate-independent plasticity, J. Mech. Phys. Solids, Volume 53 (2005) no. 3, pp. 655-679 | DOI

[130] G. Picard; A. Ajdari; F. Lequeux; L. Bocquet Elastic consequences of a single plastic event: A step towards the microscopic modeling of the flow of yield stress fluids, Eur. Phys. J. E, Volume 15 (2004) no. 4, pp. 371-381

[131] B. Tyukodi; S. Patinet; S. Roux; D. Vandembroucq From depinning transition to plastic yielding of amorphous media: A soft-modes perspective, Phys. Rev. E, Volume 93 (2016) no. 6, 063005

[132] M. Ozawa; L. Berthier; G. Biroli; A. Rosso; G. Tarjus Random critical point separates brittle and ductile yielding transitions in amorphous materials, Proc. Natl Acad. Sci. USA, Volume 115 (2018) no. 26, pp. 6656-6661 | DOI

[133] S. Franz; S. Spigler Mean-field avalanches in jammed spheres, Phys. Rev. E, Volume 95 (2017) no. 2, 022139

[134] K. A. Dahmen; Y. Ben-Zion; J. T. Uhl Micromechanical model for deformation in solids with universal predictions for stress–strain curves and slip avalanches, Phys. Rev. Lett., Volume 102 (2009) no. 17, 175501 | DOI

[135] M. Popović; T. W. de Geus; M. Wyart Elastoplastic description of sudden failure in athermal amorphous materials during quasistatic loading, Phys. Rev. E, Volume 98 (2018) no. 4, 040901

[136] S. Suresh Fatigue of Materials, Cambridge University Press, 1998 | DOI

[137] K. Dahmen; J. P. Sethna Hysteresis, avalanches, and disorder-induced critical scaling: A renormalization-group approach, Phys. Rev. B, Volume 53 (1996) no. 22, pp. 14872-14905 | DOI

[138] H. B. da Rocha; L. Truskinovsky Rigidity-controlled crossover: From spinodal to critical failure, Phys. Rev. Lett., Volume 124 (2020) no. 1, 015501

[139] G. Durin; S. Zapperi The role of stationarity in magnetic crackling noise, J. Stat. Mech.: Theory Exp., Volume 2006 (2006) no. 01, P01002

[140] M. Ozawa; L. Berthier; G. Biroli; G. Tarjus Role of fluctuations in the yielding transition of two-dimensional glasses, Phys. Rev. Res., Volume 2 (2020) no. 2, 023203 | DOI

[141] H. Bhaumik; G. Foffi; S. Sastry The role of annealing in determining the yielding behavior of glasses under cyclic shear deformation (2019) (https://arxiv.org/abs/1911.12957)

[142] S. Franz; J. Rocchi Large deviations of glassy effective potentials, J. Phys. A: Math. Theor., Volume 53 (2020), 485002 | DOI

[143] A. Nicolas; K. Martens; J.-L. Barrat Rheology of athermal amorphous solids: Revisiting simplified scenarios and the concept of mechanical noise temperature, Europhys. Lett., Volume 107 (2014) no. 4, 44003 | DOI

[144] S. Papanikolaou; F. Bohn; R. L. Sommer; G. Durin; S. Zapperi; J. P. Sethna Universality beyond power laws and the average avalanche shape, Nat. Phys., Volume 7 (2011) no. 4, pp. 316-320 | DOI

[145] G. Sparks; R. Maass Shapes and velocity relaxation of dislocation avalanches in Au and Nb microcrystals, Acta Mater., Volume 152 (2018), pp. 86-95 | DOI

[146] A. Rinaldi; P. Peralta; C. Friesen; K. Sieradzki Sample-size effects in the yield behavior of nanocrystalline nickel, Acta Mater., Volume 56 (2008) no. 3, pp. 511-517 | DOI

[147] P. Derlet; R. Maass The stress statistics of the first pop-in or discrete plastic event in crystal plasticity, J. Appl. Phys., Volume 120 (2016) no. 22, 225101 | DOI

[148] J. Weiss; L. Girard; F. Gimbert; D. Amitrano; D. Vandembroucq (Finite) statistical size effects on compressive strength, Proc. Natl Acad. Sci. USA, Volume 111 (2014) no. 17, pp. 6231-6236 | DOI

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