Strengthening and mechanisms; finite elements; nickel; size e ffects; LIMARC
Abstract :
[en] The miniaturization of metallic samples has been proved to deeply affect their mechanical properties leading to a softening or a hardening effect depending on the order of the dimension reduction. The objective of this work is to provide new numerical results which explain the softening mechanisms on the mechanical behavior for nickel polycrystals which have been experimentally characterized by the authors in a previous published paper (Keller et al., 2011). Based on a strain gradient crystalline plasticity model identified for nickel, simulations of tensile tests were performed for samples with different thicknesses and grain sizes. The simulations correctly reproduce the softening effect linked to a decrease in the thickness and in the number of grains across the thickness. The analysis of the plasticity mechanisms shows that the softening is due to surface effects which are discussed in terms of grain orientations, dislocation mean free path and long-range back-stress. The model also predicts a hardening mechanism for further dimension reduction if the samples have only grain boundaries perpendicular to the tensile direction. In this case, the modification of the mechanical behavior is due to strain gradients formation.
Disciplines :
Materials science & engineering
Author, co-author :
Keller, Clément ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Département Argenco : Secteur MS2F
Hug, eric
Habraken, Anne ; Université de Liège - ULiège > Département ArGEnCo > Département ArGEnCo
Duchene, Laurent ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Département Argenco : Secteur MS2F
Language :
English
Title :
Finite element analysis of the free surface effects on the mechanical behavior of thin nickel polycrystals
Publication date :
2012
Journal title :
International Journal of Plasticity
ISSN :
0749-6419
Publisher :
Pergamon Press - An Imprint of Elsevier Science, Oxford, United Kingdom
S. Akarapu, H.M. Zbib, and D.F. Bahr Analysis of heterogeneous deformation and dislocations dynamics in single crystals micropillars under compression International Journal of Plasticity 26 2010 239 257
A. Arsenlis, and D.M. Parks Modeling the evolution of crystallographic dislocation density in crystal plasticity Journal of the Mechanics and Physics of Solids 50 9 2002 1979 2009 (Pubitemid 34660553)
M. Ashby The deformation of plastically non-homogeneous materials Philosophical Magazine 21 1970 399 424
W. Ashmawi, and M. Zikry Effects on grain boundaries and dislocation density evolution on large strain deformation modes in fcc crystalline materials Journal of Computer-Aided Material Journal 7 2000 55 62 (Pubitemid 30589443)
C. Bayley, W. Brekelmans, and M. Geers A comparison of dislocation induced back stress formulations in strain gradient crystal plasticity International Journal of Solids and Structures 43 24 2006 7268 7286 (Pubitemid 44486177)
E. Bonifaz, and N. Richards The plastic deformation of non-homogeneous polycrystals International Journal of Plasticity 24 2 2008 289 301 (Pubitemid 350080970)
Y. Cao, Z. Xue, X. Chen, and D. Raabe Correlation between the flow stress and the nominal indentation hardness of soft metals Scripta Materialia 59 10 2008 518 521
B. Devincre, L. Kubin, and T. Hoc Physical analyses of crystal plasticity by DD simulations Scripta Materialia 54 5 2006 741 746 (Pubitemid 43038784)
B. Devincre, L. Kubin, and T. Hoc Collinear superjogs and the low-stress response of fcc crystals Scripta Materialia 57 10 2007 905 908 (Pubitemid 47321894)
D. Dimiduk, M. Uchic, and T. Parthasarathy Size-affected single slip behaviour of pure nickel microcrystals Acta Materialia 53 2005 4065 4077 (Pubitemid 41172385)
Dumoulin, S., 2001. De l'utilisation d'une loi monocristalline en vue de la caractrisation du comportemment plastique du multicristal d'aluminium. Ph.D. Thesis, Universite de Savoie, France.
H. Espinosa, B. Prorok, and B. Peng Plasticity size effect in free-standing submicron polycrystalline fcc films subjected to pure tension Journal of the mechanics and physics of solids 52 2004 667 689
H.D. Espinosa, M. Panico, S. Berbenni, and K.W. Schwarz Discrete dislocation dynamics simulation to interpret plasticity size and surface effects in freestanding FCC thin films International Journal of Plasticity 22 2006 2091 2117 (Pubitemid 44051840)
U. Essmann, and H. Mughrabi Annihilation of dislocations during tensile, cyclic deformation, limits of dislocation densities Philosophical Magazine A 40 1979 731 756 (Pubitemid 10445998)
L.P. Evers, W.A.M. Brekelmans, and M.G.D. Geers Non-local crystal plasticity model with intrinsic SSD and GND effects Journal of the Mechanics and Physics of Solids 52 2004 2001 2379
L.P. Evers, W.A.M. Brekelmans, and M.G.D. Geers Scale dependent crystal plasticity framework with dislocation density and grain boundary effects International journal of solids and structures 41 2004 5209 5230
FEAP, 2010. Feap: A finite element analysis program. University of California, Berkeley. URL .
X. Feaugas On the origin of the tensile flow stress in the stainless steel AISI 316L at 300 K: back stress, effective stress Acta Materialia 47 13 1999 3617 3632 (Pubitemid 30503023)
X. Feaugas, and H. Haddou Grain-size effects on tensile behaviour of nickel, AISI 316L stainless steel Metallurgical Transactions 34A 2003 2329 2340
Fivel, M., 1997. Etudes numriques diffrentes chelles de la dformation plastique des monocristaux de structure cfc. Ph.D. Thesis, Institut National de Polytechnique de Grenoble, France.
N. Fleck, G. Muller, M. Ashby, and J. Hutchinson Strain gradient plasticity: theory and experiment Acta Metallurgica et Materialia 42 2 1994 475 487
J. Flinn, D. Field, G. Korth, T. Lillo, and J. Macheret The flow stress behaviour of OFHC polycrystalline copper Acta Materialia 49 2001 2065 2074 (Pubitemid 32528987)
J. Fourie The flow stress gradient between the surface, centre of deformed copper single crystals Philosophical Magazine 17 1967 735 756
J. Fourie Sub-surface dislocation structure of deformed copper Philosophical Magazine 21 1970 977 985
P. Franciosi, M. Berveiller, and A. Zaoui Latent hardening in copper and aluminium single crystals Acta Metallurgica 28 3 1980 273 283 (Pubitemid 10465920)
H. Fu, D. Benson, and M. Meyers Analytical and computational description of effect of grain size on yield stress of metals Acta Materialia 49 2001 2567 2582 (Pubitemid 32621528)
J. Gau, C. Principe, and J. Wang An experimental study on size effects on flow stress and formability of aluminium and brass microforming Journal of Material Processing Technology 184 2007 42 46 (Pubitemid 46205233)
M. Geers, W. Brekelmans, and P. Janssen Size effects in miniaturized polycrystalline fcc samples: strengthening versus weakening International Journal of Solids and Structures 43 24 2006 7304 7321 (Pubitemid 44488679)
M. Geiger, M. Kleiner, R. Eckstein, R. Tiesler, and U. Engel Microforming Annals of the CIRP 5 50 2001 445 462 (Pubitemid 34012686)
J.R. Greer, W.C. Oliver, and W.D. Nix Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients Acta Materialia 53 6 2005 1821 1830 (Pubitemid 40245699)
M.E. Gurtin A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocations Journal of the Mechanics and Physics of Solids 50 1 2002 5 32 (Pubitemid 33089064)
Hamelin, C., Diak, B., Pilkey, A., in press. Multiscale modelling of the induced plastic anisotropy in bcc metals. International Journal of Plasticity. doi:10.1016/j.ijplas.2011.01.003.
M. Henning, and H. Vehoff Local mechanical behaviour, slip band formation within grains of thin sheets Acta Materialia 53 2005 1285 1292 (Pubitemid 40200570)
P. Janssen, T. de Keijser, and M. Geers An experimental assessment of grain size effect in the uniaxial straining of thin Al sheet with a few grains across the thickness Material Science and Engineering A419 2006 238 248
T. Kals, and R. Eckstein Miniaturization in sheet metal working Journal of Material Processing Technology 103 2000 95 101
Keller, C., 2009. Etude experimentale des transitions volume/surface des proprietes mecaniques du nickel polycristallin de haute purete. Ph.D. Thesis, Universite de Caen/Basse-Normandie.
C. Keller, and E. Hug Hall-petch behaviour of Ni polycrystals with a few grains per thickness Materials Letters 62 10-11 2008 1718 1720 (Pubitemid 351192107)
C. Keller, E. Hug, and D. Chateigner On the origin of the stress decrease for nickel polycrystals with few grains across the thickness Materials Science and Engineering: A 500 1-2 2009 207 215
C. Keller, E. Hug, and X. Feaugas Microstructural size effects on mechanical properties of high purity nickel International Journal of Plasticity 27 4 2011 637 654
C. Keller, E. Hug, R. Retoux, and X. Feaugas TEM study of dislocation patterns in near-surface and core regions of deformed nickel polycrystals with few grains across the cross section Mechanics of Materials 42 1 2010 44 54
D. Kiener, W. Grosinger, G. Dehm, and R. Pippan A further step towards an understanding of size-dependant crystal plasticity: in situ tension experiments of miniaturized single-crystal copper samples Acta Materialia 56 2008 580 592
U. Kocks, and H. Mecking Physics, phenomenology of strain hardening: the fcc case Progress in Materials Science 48 2003 171 273
D. Kuhlmann-Wilsdorf Theory of plastic deformation: properties of low energy dislocation structures Material Science and Engineering A 113 1989 1 41
B. Landolt Landolt-Bornstein tables vol. III 1966 Springer-Verlag p. 6
M. Lederer, V. Groger, G. Khatibi, and B. Weiss Size dependency of mechanical properties of high purity aluminium foils Materials Science and Engineering A 527 3 2010 590 599
Mecking, H., 1977. Description of hardening curves of fcc single, polycrystals. In: Work Hardening in Tension, Fatigue. American Institute of Mining, Metallurgical, Petroleum Engineers, pp. 66-88.
H. Mecking, and U. Kocks Kinetics flow, strain hardening Acta Metallurgica 29 1981 1865 1875
J. Michel, and P. Picart Size effects on the constitutive behaviour for brass in sheet metal forming Journal of Material Processing Technology 141 2003 439 446
S. Miyazaki, K. Shibata, and H. Fujita Effect of specimen thickness on mechanical properties of polycrystalline aggregates with various grain size Acta Metallurgica 27 1979 855 862 (Pubitemid 9453192)
H. Mughrabi Investigation of plastically deformed copper single crystal in the stress applied state Physical Status Solidii 39 1970 317 327
H. Mughrabi Some consequences of surface, size effects in plastically deformed copper single crystals Physical Status Solidii 44 1971 391 402
T. Narutani, and J. Takamura Grain-size strengthening in terms of dislocation density measured by resistivity Acta Materialia 39 8 1991 2037 2049 (Pubitemid 21680057)
N. Nicaise, S. Berbenni, F. Wagner, M. Berveiller, and X. Lemoine Coupled effects of grain size distributions and crystallographic textures on the plastic behaviour of if steels International Journal of Plasticity 27 2 2011 232 249
L. Nicola, E.V. der Giessen, and A. Needleman Size effects in polycrystalline thin films analyzed by discrete dislocation plasticity Thin Solid Films 479 1-2 2005 329 338 (Pubitemid 40391100)
T.A. Parthasarathy, S.I. Rao, D.M. Dimiduk, M.D. Uchic, and D.R. Trinkle Contribution to size effect of yield strength from the stochastics of dislocation source lengths in finite samples Scripta Materialia 56 4 2007 313 316 (Pubitemid 44834485)
L. Raulea, A. Goijaerts, L. Govaert, and F. Baaijens Size effects in the processing of thin metal sheets Journal of Material Processing Technology 115 2001 44 48 (Pubitemid 32698390)
J.G. Sevillano Flow stress, work hardening Material Science, Technology vol. 6 1993 VCH Publishersm, Inc. 18 88
M. Shiekhelsouk, V. Favier, K. Inal, and M. Cherkaoui Modelling the behaviour of polycrystalline austenitic steel with twinning-induced plasticity effect International Journal of Plasticity 25 1 2009 105 133
J.Y. Shu, and N.A. Fleck Strain gradient crystal plasticity: size-dependent deformation of bicrystals Journal of the Mechanics and Physics of Solids 47 1999 297 324
J.Y. Shu, N.A. Fleck, E.V. der Giessen, and A. Needleman Boundary layers in constrained plastic flow: comparison of nonlocal and discrete dislocation plasticity Journal of the Mechanics and Physics of Solids 49 6 2001 1361 1395 (Pubitemid 32421475)
Smallman, R.E., Ngan, A.H.W., 2007. Mechanical properties I. In: Physical Metallurgy and Advanced Materials. Butterworth-Heinemann, pp. 289-381.
J.S. Stolken, and A.G. Evans A microbend test method for measuring the plasticity length scale Acta Materialia 46 1998 5109 5115 (Pubitemid 128421651)
H. Suzuki, S. Ikeda, and S. Takeushi Deformation in thin copper crystals Journal of the Physical Society of Japan 11 1956 382 393
P. Swann The dislocation distribution near the surface of deformed copper Acta Metallurgica 14 1966 900 903
Tabourot, L., Fivel, M., Rauch, E., 1998. Use of mesoscopic simulation to model the dislocation densities evolution law. In: Cartensen, J.V., et al. (Ed.), Proceedings of the 19th Ris International Symposium on Material Science, Modelling of Structure and Mechanics of Materials from Macroscale to Product. Roskilde, Denmark, pp. 511-516.
B. Yang, C. Motz, W. Grosinger, and G. Dehm Cyclic loading behavior of micro-sized polycrystalline copper wires Procedia Engineering 2 1 2010 925 930 fatigue 2010
B. Yang, C. Motz, W. Grosinger, W. Kammrath, and G. Dehm Tensile behavior of micro-sized copper wires studied using a novel fibre tensile module International Journal of Material Research 99 1 2008 716 724