Abstract
The simplest, yet robust, gradient elasticity theory (GRADELA) as first introduced by the last author is used to deduce nonsingular expressions for the stress and strain fields near dislocation lines and crack tips. These expressions are particularly useful for small volumes where the details of the deformation field need to be known for interpreting related experimental observations. Various implications are discussed in relation to the determination of the size of dislocation cores, the size of maximum stress or maximum strain in crack tips, and the interpretation of X-ray line profile measurements in determining internal stresses.
Similar content being viewed by others
References
Aifantis EC (1992) On the role of gradients in the localization of deformation and fracture. Int J Eng Sci 30:1279–1299. doi:10.1016/0020-7225(92)90141-3
Aifantis EC (1999) Strain gradient interpretation of size effects. Int J Fract 95:299–314. doi:10.1023/A:1018625006804
Aifantis EC (2003) Update on a class of gradient theories. Mech Mater 35:259–280
Altan BS, Aifantis EC (1997) On some aspects in the special theory of gradient elasticity. J Mechan Behav Mats 8:231–282
Askes H, Aifantis EC (2008) Discussion of “A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir)relevance for nanotechnologies” (preprint)
Exadaktylos GE, Vardoulakis I (2001) Microstructure in linear elasticity and scale effects: a reconsideration of basic rock mechanics and rock fracture mechanics. Tectonophysics 335:81–109. doi:10.1016/S0040-1951(01)00047-6
Georgiadis HG, Anagnostou DS (2008) Problems of the Flamant-Boussinesq and Kelvin type in dipolar gradient elasticity. J Elast 90:71–98. doi:10.1007/s10659-007-9129-x
Georgiadis HG, Vardoulakis I, Velgaki EG (2004) Dispersive Rayleigh-wave propagation in microstructured solids characterized by dipolar gradient elasticity. J Elast 74:17–45. doi:10.1023/B:ELAS.0000026094.95688.c5
Georgiadis HG (2003) The Mode III crack problem in microstructured solids governed by dipolar gradient elasticity: static and dynamic analysis. J Appl Mechan Trans ASME 70:517–530
Gutkin MY, Aifantis EC (1999a) Dislocations in the theory of gradient elasticity. Scr Mater 40:559–566. doi:10.1016/S1359-6462(98)00424-2
Gutkin MYu, Aifantis EC (1999b) Dislocations and disclinations in gradient elasticity. Phys Stat Sol 214B:245–284
Gutkin MY, Aifantis EC (1997) Edge dislocation in gradient elasticity. Scr Mater 36:129–135. doi:10.1016/S1359-6462(96)00352-1
Gutkin MY, Aifantis EC (1996) Screw dislocation in gradient elasticity. Scr Mater 35:1353–1358. doi:10.1016/1359-6462(96)00295-3
Kioseoglou J, Dimitrakopulos GP, Komninou P, Karakostas T, Aifantis EC (2008) Dislocation core investigation by geometric phase analysis and the dislocation density tensor. J Phys D Appl Phys 41:035408. doi:10.1088/0022-3727/41/3/035408
Kioseoglou J, Dimitrakopulos GP, Komninou P, Karakostas T, Konstantopoulos I, Avlonitis M et al (2006) Analysis of partial dislocations in wurtzite GaN using gradient elasticity. Phys Status Solidi, A Appl Mater Sci 203:2161–2166. doi:10.1002/pssa.200566018
Lazar M, Maugin GA, Aifantis EC (2006) Dislocations in second strain gradient elasticity. Int J Solids Struct 43:1787–1817. doi:10.1016/j.ijsolstr.2005.07.005
Lazar M, Maugin GA (2005) Nonsingular stress and strain fields of dislocations and disclinations in first strain gradient elasticity. Int J Eng Sci 43:1157–1184. doi:10.1016/j.ijengsci.2005.01.006
Maranganti R, Sharma P (2007) A novel atomistic approach to determine strain-gradient elasticity constants: Tabulation and comparison for various metals, semiconductors, silica, polymers and the (ir)relevance for nanotechnologies. J Mech Phys Solids 55:1823–1852. doi:10.1016/j.jmps.2007.02.011
Polizzotto C (2003) Gradient elasticity and nonstandard boundary conditions. Int J Solids Struct 40:7399–7423. doi:10.1016/j.ijsolstr.2003.06.001
Ribarik G, Ungar T, Aifantis EC (2008) X-ray line profile analysis using the theory of gradient elasticity (work in progress)
Ru CQ, Aifantis EC (1993) A simple approach to solve boundary value problems in gradient elasticity. Acta Mech 101:59–68. doi:10.1007/BF01175597
Triantafyllidis N, Aifantis EC (1986) A gradient approach to localization of deformation—I: hyperelastic materials. J Elast 16:225–237. doi:10.1007/BF00040814
Acknowledgments
The support by NSF under NIRT Grant DMI-0532320 and by the Greek Government Programs PENED and PYTHAGORAS is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Additional information
An erratum to this article can be found at http://dx.doi.org/10.1007/s00542-009-0919-x
Rights and permissions
About this article
Cite this article
Kioseoglou, J., Konstantopoulos, I., Ribarik, G. et al. Nonsingular dislocation and crack fields: implications to small volumes. Microsyst Technol 15, 117–121 (2009). https://doi.org/10.1007/s00542-008-0700-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00542-008-0700-6