Abstract
A theoretical model is established to describe the effect of cooperative grain boundary (GB) sliding and migration on dislocation emission from the tip of branched crack in deformed nanocrystalline solids. The explicit solutions of complex potentials are obtained by means of complex variable method and conformal mapping technique. The critical stress intensity factors (SIFs) for the first lattice dislocation emission from the tip of branched crack are calculated. The effects of the lengths of branched crack and main crack, and the angle between their planes on the critical SIFs for dislocation emission are evaluated in detail. The results indicate that the emission of lattice dislocations from the tip of branched crack is strongly influenced by cooperative GB sliding and migration. When main crack approaches the branched crack, dislocation emission from the tip of branched crack will be suppressed. The main crack tends to propagate while shorter branched crack is prone to be blunted by emitting lattice dislocations from its tip. As a special case, when the planes of main crack and the branched crack are flattened out into one, the present results are in good agreement with previously known results.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aifantis EC (2011) Gradient nanomechanics: Applications to deformation, fracture, and diffusion in nanopolycrystals. Metall Mater Trans A 42:2985–2998. doi:10.1007/s11661-011-0725-9
Barai P, Weng GJ (2009) Mechanics of very fine-grained nanocrystalline materials with contributions from grain interior, grain boundary zone, and grain-boundary sliding. Int J Plast 25:2410–2434. doi:10.1016/j.ijplas.2009.04.001
Bhaduri S, Bhaduri SB (1997) Enhanced low temperature toughness of \({\text{ Al }}_{2}{\text{ O }}_{3}\). Nanostruct Mater 8:755–763. doi:10.1016/S0965-9773(97)00215-8
Bobylev SV, Mukherjee AK, Ovid’Ko IA (2009) Emission of partial dislocations from amorphous intergranular boundaries in deformed nanocrystalline ceramics. Scr Mater 60:36–39. doi:10.1016/j.scriptamat.2008.08.025
Bobylev S, Morozov N, Ovid’ko I (2010) Cooperative grain boundary sliding and migration process in nanocrystalline solids. Phys Rev Lett 105:055504. doi:10.1103/PhysRevLett.105.055504
Bobylev S, Morozov N, Ovid’ko I (2011) Cooperative grain boundary sliding and nanograin nucleation process in nanocrystalline, ultrafine-grained, and polycrystalline solids. Phys Rev B Condens Matter 84:094103. doi:10.1103/PhysRevB.84.094103
Cheng S, Zhao Y, Wang Y, Li Y, Wang X-L, Liaw PK, Lavernia EJ (2010) Structure modulation driven by cyclic deformation in nanocrystalline NiFe. Phys Rev Lett 104:255501. doi:10.1103/PhysRevLett.104.255501
Dao M, Lu L, Asaro R, De Hosson JTM, Ma E (2007) Toward a quantitative understanding of mechanical behavior of nanocrystalline metals. Acta Mater 55:4041–4065. doi:10.1016/j.actamat.2007.01.038
Fang Q, Liu Y (2006) Size-dependent interaction between an edge dislocation and a nanoscale inhomogeneity with interface effects. Acta Mater 54:4213–4220. doi:10.1016/j.actamat.2006.05.012
Fang Q, Liu Y, Jin B, Wen P (2009) Effect of interface stresses on the image force and stability of an edge dislocation inside a nanoscale cylindrical inclusion. Int J Solids Struct 46:1413–1422. doi:10.1016/j.ijsolstr.2008.11.013
Farrokh B, Khan AS (2009) Grain size, strain rate, and temperature dependence of flow stress in ultra-fine grained and nanocrystalline Cu and Al: Synthesis, experiment, and constitutive modeling. Int J Plast 25:715–732. doi:10.1016/j.ijplas.2008.08.001
Feng H, Fang QH, Zhang LC, Liu YW (2013a) Special rotational deformation and grain size effect on fracture toughness of nanocrystalline materials. Int J Plast 42:50–64. doi:10.1016/j.ijplas.2012.09.015
Feng H, Fang QH, Zhang LC, Liu YW (2013b) Effect of cooperative grain boundary sliding and migration on emission of dislocations from a crack tip in nanocrystalline materials. Mech Mater 61:39–48. doi:10.1016/j.mechmat.2013.02.006
Gianola D, Van Petegem S, Legros M, Brandstetter S, Van Swygenhoven H, Hemker K (2006) Stress-assisted discontinuous grain growth and its effect on the deformation behavior of nanocrystalline aluminum thin films. Acta Mater 54:2253–2263. doi:10.1016/j.actamat.2006.01.023
Gutkin MY, Ovid’Ko IA (2005) grain boundary migration as rotational deformation mode in nanocrystalline materials. Appl Phys Lett 87:251916–251916–251913. doi:10.1063/1.2147721
Hirth JP, Lothe J (1982) Theory of dislocations. Wiley, New York
Huang M, Li Z (2004) Dislocation emission criterion from a blunt crack tip. J Mech Phys Solids 52:1991–2003. doi:10.1016/j.jmps.2004.03.003
Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–364
Juan PA, Berbenni S, Capolungo L (2012) Prediction of internal stresses during growth of first- and second-generation twins in Mg and Mg alloys. Acta Mater 60:476–486. doi:10.1016/j.actamat.2011.10.018
Meyers MA, Mishra A, Benson DJ (2006) Mechanical properties of nanocrystalline materials. Prog Mater Sci 51:427–556. doi:10.1016/j.pmatsci.2005.08.003
Morozov N, Ovid’ko I, Sheinerman A, Aifantis E (2010) Special rotational deformation as a toughening mechanism in nanocrystalline solids. J Mech Phys Solids 58:1088–1099. doi:10.1016/j.jmps.2010.04.003
Mukhopadhyay A, Basu B (2007) Consolidation-microstructure-property relationships in bulk nanoceramics and ceramic nanocomposites: a review. Int Mater Rev 52:257–288. doi:10.1179/174328007X160281
Muskhelishvili NI (1977) Some basic problems of the mathematical theory of elasticity. Springer, Berlin. doi:10.1007/978-94-017-3034-1
Neuber H (1946) Theory of notch stresses. JW Edwards, Denver
Ovid’ko IA, Sheinerman AG (2007) Special strain hardening mechanism and nanocrack generation in nanocrystalline materials. Appl Phys Lett 90:171927–171927–171923. doi:10.1063/1.2734393
Ovid’Ko IA, Sheinerman AG (2010) Ductile vs. brittle behavior of pre-cracked nanocrystalline and ultrafine-grained materials. Acta Mater 58:5286–5294. doi:10.1016/j.actamat.2010.05.058
Ovid’Ko IA, Sheinerman AG (2012) Nanoscale rotational deformation near crack tips in nanocrystalline solids. J Phys D Appl Phys 45:335301. doi:10.1088/0022-3727/45/33/335301
Ovid’Ko IA, Sheinerman AG, Aifantis EC (2008) Stress-driven migration of grain boundaries and fracture processes in nanocrystalline ceramics and metals. Acta Mater 56:2718–2727. doi:10.1016/j.actamat.2008.02.004
Ovid’Ko I, Sheinerman A, Aifantis E (2011) Effect of cooperative grain boundary sliding and migration on crack growth in nanocrystalline solids. Acta Mater 59:5023–5031. doi:10.1016/j.actamat.2011.04.056
Rice JR, Thomson R (1974) Ductile versus brittle behaviour of crystals. Philos Mag 29:73–97. doi:10.1080/14786437408213555
Romanov AE, Vladimirov VI (1992) Disclinations in crystalline solids. In: Nabarro FRN (ed) Dislocations in solids, vol 9. North-Holland, Amsterdam, pp 191–402
Sergueeva AV, Mara NA, Krasilnikov NA, Valiev RZ, Mukherjee AK (2006) Cooperative grain boundary sliding in nanocrystalline materials. Philos Mag 86:5797–5804. doi:10.1080/14786430600764906
Sergueeva AV, Mara NA, Mukherjee AK (2007) GB sliding in nanomaterials at elevated temperatures. J Mater Sci 42:1433–1438. doi:10.1007/s10853-006-0697-0
Sergueeva AV, Hulbert DM, Mara NA, Mukherjee AK (2009) Mechanical properties of nanocomposite materials. My Publ 1:127–172. doi:10.1016/B978-0-08-044965-4.50006-7
Sih G (1965) Stress distribution near internal crack tips for longitudinal shear problems. J Appl Mech 32:51–58. doi:10.1115/1.3625783
Wolf D, Yamakov V, Phillpot SR, Mukherjee A, Gleiter H (2005) Deformation of nanocrystalline materials by molecular-dynamics simulation: relationship to experiments? Acta Mater 53:1–40. doi:10.1016/j.actamat.2004.08.045
Wu MS, Zhou K, Nazarov AA (2007) Crack nucleation at disclinated triple junctions. Phys Rev B Condens Matter 76(13):134105
Xia SH, Wang JT (2010) A micromechanical model of toughening behavior in the dual-phase composite. Int J Plast 26:1442–1460. doi:10.1016/j.ijplas.2010.01.005
Xu J, Mao XZ, Xie ZH, Munroe P (2013) Connecting structural, mechanical and tribological characteristics of Al alloyed nanocrystalline molybdenum silicide coatings. J Phys D Appl Phys 46:65304. doi:10.1088/0022-3727/46/6/065304
Yinmin W, Mingwei C, Fenghua Z, En M (2002) High tensile ductility in a nanostructured metal. Nature 419:912–915. doi:10.1038/nature01133
Youssef KM, Scattergood RO, Murty KL, Horton JA (2005) Ultrahigh strength and high ductility of bulk nanocrystalline copper. Appl Phys Lett 87:091904. doi:10.1063/1.2034122
Youssef KM, Scattergood RO, Murty KL, Koch CC (2006) Nanocrystalline Al–Mg alloy with ultrahigh strength and good ductility. Scr Mater 54:251–256. doi:10.1016/j.scriptamat.2005.09.028
Yu M, Fang Q, Feng H, Liu Y (2014) Effect of cooperative grain boundary sliding and migration on dislocation emitting from a semi-elliptical blunt crack tip in nanocrystalline solids. Acta Mech 225:1–15. doi:10.1007/s00707-013-1039-3
Zhao Y, Qian J, Daemen LL, Pantea C, Zhang J, Voronin GA, Zerda TW (2004) Enhancement of fracture toughness in nanostructured diamond-SiC composites. Appl Phys Lett 84:1356–1358. doi:10.1063/1.1650556
Zhao Y, Fang Q, Liu Y (2014) Effect of cooperative nanograin boundary sliding and migration on dislocation emission from a blunt nanocrack tip in nanocrystalline materials. Philos Mag 94:700–730. doi:10.1080/14786435.2013.861091
Zhou K, Wu MS, Nazarov AA (2008) Relaxation of a disclinated tricrystalline nanowire. Acta Mater 56:5828–5836. doi:10.1016/j.actamat.2008.07.059
Zhu L, Zheng X (2010) Influence of interface energy and grain boundary on the elastic modulus of nanocrystalline materials. Acta Mech 213:223–234. doi:10.1007/s00707-009-0263-3
Zhu YT, Liao XZ, Wu XL (2012) Deformation twinning in nanocrystalline materials. J Mater Eng Perform 57:1–62. doi:10.1016/j.pmatsci.2011.05.001
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
He, T., Xiao, W., Zhang, Y. et al. Effect of cooperative grain boundary sliding and migration on dislocation emission from a branched crack tip in deformed nanocrystalline solids. Int J Fract 206, 1–10 (2017). https://doi.org/10.1007/s10704-017-0193-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10704-017-0193-3