2015-Sustainable Industrial Processing Summit
SIPS 2015 Volume 1: Aifantis Intl. Symp. / Multiscale Material Mechanics
| Editors: | Kongoli F, Bordas S, Estrin Y |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2015 |
| Pages: | 300 pages |
| ISBN: | 978-1-987820-24-9 |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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Fracture in Strain Gradient Plasticity
Emilio Martinez Paneda1;1UNIVERSITY OF OVIEDO, Gijon, Spain;
Type of Paper: Invited
Id Paper: 306
Topic: 1
Abstract:
Experiments have shown that metallic materials display strong size effects at the micron and sub-micron scales, with smaller being stronger. Such size effects have been attributed to geometrically necessary dislocations (GNDs) associated with inhomogeneous plastic flow and, since the earlier seminal works of Aifantis, several continuum strain gradient plasticity (SGP) theories have been developed in order to incorporate some length-scale parameters in the constitutive equations.
These size effects are especially significant in fracture problems as the plastic zone adjacent to the crack tip is physically small and contains strong spatial gradients of deformation. Finite element (FE) simulations have shown that GNDs near the crack tip promote strain-hardening, leading to a much higher stress level in the vicinity of the crack than that predicted by classical plasticity. Moreover, recent numerical studies revealed that the domain ahead of the crack where strain gradients significantly influence crack tip fields could be one order of magnitude higher when finite strains are taken into account.
In this work, the influence of the plastic strain gradient on the fracture process of metallic materials is evaluated within the finite deformation theory by means of both mechanism-based and phenomenological SGP theories. The relation between material parameters and the physical length over which gradient effects prominently enhance crack-tip stresses is identified and quantified. Physical implications of the results are discussed and the relevance of accounting for size effects in the modelization of damage is thoroughly examined. Several numerical tools are evaluated with the aim of integrating SGP modeling in a robust numerical framework.
Keywords:
Materials; Mechanics; Multiscale; Plasticity; Solids;References:
[1] E.C. Aifantis, Some thoughts on degrading materials, Georgia Tech., Atlanta, 1982. In: Atluri, S.N., Fitzerald, J.E., (Eds.), NSF Workshop on Mechanics of Damage and Fracture, pp. 1-12[2] E.C. Aifantis: On the microstructural origin of certain inelastic models, Journal of Engineering Materials and Technology, 106 (1984), 326-330.
[3] E.C. Aifantis: On the role of gradients in the localization of deformation and fracture, International Journal of Engineering Science., 30 (1992), 1279-1299.
[4] N.A. Fleck and J.W. Hutchinson: A phenomenological theory for strain-gradient effects in plasticity, Journal of the Mechanics and Physics of Solids, 41 (1993), 1825-1857.
[5] N.A. Fleck and J.W. Hutchinson: Strain gradient plasticity, Advances in Applied Mechanics, 33 (1997), 295-361.
[6] N.A. Fleck and J.W. Hutchinson: A reformulation of strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49 (2001), 2245-2271
[7] H. Gao, Y. Huang, W.D. Nix and J.W. Hutchinson: Mechanism-based strain gradient plasticity I. Theory, Journal of the Mechanics and Physics of Solids, 47 (1999), 1239-1263
[8] Y. Huang, H. Gao, W.D. Nix and J.W. Hutchinson: Mechanism-based strain gradient plasticity II. Analysis, Journal of the Mechanics and Physics of Solids, 48 (2000), 99-128
[9] G. Elssner, D. Korn and M. Rühle: The influence of interface impurities on fracture energy of UHV diffusion-bonded metal ceramic bicrystals, Scripta Metallurgica et Materialia, 31 (1994), 1037-1042
[10] D. Korn, G. Elssner, R.M. Cannon and M. Rühle: Fracture properties of intefacially doped Nb-Al2O3 bicrystals: I, fracture characteristics, Acta Materialia, 50 (2002), 3881-3901
[11] Y. Wei and J.W. Hutchinson: Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 45 (1997), 1253-1273
[12] J.Y. Chen, Y. Wei, Y. Huang, J.W. Hutchinson and K.C. Hwang: The crack-tip fields in strain-gradient plasticity: the asymptotic and numerical analyses, Engineering Fracture Mechanics, 64 (1999), 625-648
[13] H. Jiang, Y. Huang, Z. Zhuang and K.C. Hwang: Fracture in mechanism-based strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 49 (2001), 979-993
[14] K.C., Hwang, H. Jiang, Y. Huang and H. Gao: Finite deformation analysis of mechanism-based strain gradient plasticity: torsion and crack tip field, International Journal of Plasticity, 19 (2003), 235-251
[15] X. Pan and H. Yuan: Computational assessment of cracks under strain-gradient plasticity, International Journal of Fracture, 167 (2011), 235-248
[16] H. Yuan and J. Chen: Analysis of size effects based on lower-order gradient plasticity model, Computational Materials Science, 19 (2000), 143-157
[17] V. Tvergaard and C.F. Niordson: Size effects at a crack-tip interacting with a number of voids, Philosophical Magazine, 88 (2008), 3827-3840
[18] L.P. Mikkelsen and S. Goutianos: Suppressed plastic deformation at blunt crack-tips due to strain gradient effects, International Journal of Solids and Structures, 46 (2009), 4430-4436
[19] E. Martínez-Pañeda and C. Betegón: Modeling damage and fracture within strain-gradient plasticity, International Journal of Solids and Structures, 59 (2015), 208-215
[20] R.P. Gangloff. Hydrogen-assisted cracking in high-strength alloys. Comprehensive Structural Integrity. Environmentally-Assisted Fracture, vol. 6, 2003. Elsevier, Oxford.
[21] G.I. Taylor: Plastic strain in metals, Journal of the Institute of Metals, 62 (1938), 307-324.
[22] C.F. Niordson and P. Redanz: Size-effects in plane strain sheet-necking, Journal of the Mechanics and Physics of Solids, 52 (2004), 2431-2454.
[23] Y. Huang, S. Qu, K.C. Hwang, M. Li and H. Gao: A conventional theory of mechanism-based strain gradient plasticity, International Journal of Plasticity, 20 (2004), 753-782.
[24] C.F. Niordson and J.W. Hutchinson: On lower order strain gradient plasticity theories, European Journal of Mechanics – A/Solids, 22 (2003), 771-778.
[25] V. Olden, C. Thaulow, R. Johnsen, E. Ostby and T. Berstad: Influence of hydrogen from cathodic protection on the fracture susceptibility of 25%Cr duplex stainless steel – Constant load SENT testing and FE-modelling using hydrogen influenced cohesive zone elements, Engineering Fracture Mechanics, 76 (2009), 827-844.
[26] R.M. McMeeking: Finite deformation analysis of crack-tip opening in elastic-plastic materials and implications for fracture, Journal of the Mechanics and Physics of Solids, 25 (1977), 357-381.
[27] R.L.S. Thomas, J.R. Scully and R.P. Gangloff: Internal hydrogen embrittlement of ultrahigh-strength AERMET 100 steel, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 34 (2003), 327-344.
[28] Y. Lee and R.P. Gangloff: Measurement an modeling of hydrogen environment-assisted cracking of ultra-high-strength steel, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 38 (2007), 2174-2190.
[29] R.P. Gangloff, H.M. Ha, J.T. Burns and J.R. Scully: Measurement an modeling of hydrogen environment-assisted cracking in Monel K-500, Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science, 45 (2014), 3814-3834.
[30] W.D. Nix and H. Gao: Indentation size effects in crystalline materials: a law for strain gradient plasticity, Journal of the Mechanics and Physics of Solids, 46 (1998), 411-425.
[31] N.A. Fleck, G.M. Muller, M.F. Ashby and J.W. Hutchinson: Strain gradient plasticity: theory and experiment, Acta Metallurgica et Materialia, 42 (1994), 475-487.
[32] R.K. Abu Al-Rub and G.Z. Voyiadjis: Determination of the material intrinsic length scale of gradient plasticity theory, Journal of the Mechanics and Physics of Solids, 49 (2001), 979-993