Browse > Article
http://dx.doi.org/10.12989/sem.2017.61.2.275

On elastic and plastic length scales in strain gradient plasticity  

Liu, Jinxing (Faculty of Civil Engineering and Mechanics, Jiangsu University)
Wang, Wen (Faculty of Civil Engineering and Mechanics, Jiangsu University)
Zhao, Ziyu (Faculty of Civil Engineering and Mechanics, Jiangsu University)
Soh, Ai Kah (School of Engineering, Monash University Malaysia)
Publication Information
Structural Engineering and Mechanics / v.61, no.2, 2017 , pp. 275-282 More about this Journal
Abstract
The Fleck-Hutchinson theory on strain gradient plasticity (SGP), proposed in Adv. Appl Mech 33 (1997) 295, has recently been reformulated by adopting the strategy of decomposing the second order strain presented by Lam et al. in J Mech Pays Solids 51 (2003) 1477. The newly built SGP satisfies the non negativity of plastic dissipation, which is still an outstanding issue in other SGP theories. Furthermore, it explicitly shows how elastic strain gradients and corresponding elastic characteristic length scales come into play in general elastic-plastic loading histories. In this study, the relation between elastic length scales and plastic length scales is investigated by taking wire torsion as an example. It is concluded that the size effects arising when two sets of length scales are of the same order are essentially elastic instead of plastic.
Keywords
strain gradient elasticity (SGE); strain gradient plasticity (SGP); plastic dissipation; length scale; size effect;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Aifantis, E. (1999), "Strain gradient interpretation of size effects", Int. J. Fract., 95(1), 299-314.   DOI
2 Anand, L., Gurtin, M., Lele, S. and Gething, C. (2005), "A onedimensional theory of strain-gradient plasticity: formulation, analysis, numerical results", J. Mech. Phys. Solid., 53(8), 1789-1826.   DOI
3 Bertram, A. and Forest, S. (2014), "The thermodynamics of gradient elastoplasticity", Continuum Mech. Thermodyn., 26(3), 269-286.   DOI
4 Dunstan, D., Ehrler, B., Bossis, R., Joly, S., P'ng, K. and Bushby, A. (2009), "Elastic limit and strain hardening of thin wires in torsion", Phys. Rev. Lett., 103(15), 155501.   DOI
5 Evans, A. and Hutchinson, J. (2009), "A critical assessment of theories of strain gradient plasticity", Acta Materialia, 57(5), 1675-1688.   DOI
6 Fleck, N. and Hutchinson, J. (1997), "Strain gradient plasticity", Adv. Appl. Mech., 33, 295-361.
7 Fleck, N. and Hutchinson, J. (2001), "A reformulation of strain gradient plasticity", J. Mech. Phys. Solid., 49(10), 2245-2271.   DOI
8 Fleck, N., Muller, G., Ashby, M. and Hutchinson, J. (1994), "Strain gradient plasticity: theory and experiment", Acta Metallurgica Et Materialia, 42(2), 475-487.   DOI
9 Fleck, N. and Willis, J. (2009), "A mathematical basis for straingradient plasticity theory. part ii: tensorial plastic multiplier", J. Mech. Phys. Solid., 57(7), 1045-1057.   DOI
10 Forest, S. and Sievert, R. (2003), "Elastoviscoplastic constitutive frameworks for generalized continua", Acta Mechanica, 160(1), 71-111.   DOI
11 Gao, H. and Huang, Y. (2001), "Taylor-based nonlocal theory of plasticity", Int. J. Solid. Struct., 38(15), 2615-2637.   DOI
12 Hutchinson, J. (2000), "Plasticity at the micron scale", Int. J. Solid. Struct., 37(1-2), 225-238.   DOI
13 Gao, H., Huang, Y., Nix, W. and Hutchinson, J. (1999), "Mechanism-based strain gradient plasticity-i. theory", J. Mech. Phys. Solid., 47(6), 1239-1263.   DOI
14 Gudmundson, P. (2004), "A unified treatment of strain gradient plasticity", J. Mech. Phys. Solid., 52(6), 1379-1406.   DOI
15 Huang, Y., Qu, S., Hwang, K., Li, M. and Gao, H. (2004), "A conventional theory of mechanism-based strain gradient plasticity", Int. J. Plast., 20(4-5), 753-782.   DOI
16 Hutchinson, J. (2012), "Generalizing j2 flow theory: fundamental issues in strain gradient plasticity", Acta Mechanica Sinica, 28(4), 1078-1086.   DOI
17 Kiener, D., Motz, C., Grosinger, W., Weygand, D. and Pippan, R. (2010), "Cyclic response of copper single crystal micro-beams", Scripta Materialia, 63(5), 500-503.   DOI
18 Fleck, N., Hutchinson, J. and Willis, J. (2014), "Strain gradient plasticity under non-proportional loading", Proc. Royal Soc.: A, 470(2170), 20140267-20140267.   DOI
19 Liu, J. and Soh, A. (2014), "Bridging strain gradient elasticity and plasticity toward general loading histories", Mech. Mater., 78(16), 11-21.   DOI
20 Liu, D., He, Y., Dunstan, D., Zhang, B., Gan, Z., Hu, P. and Ding, H. (2013), "Toward a further understanding of size effects in the torsion of thin metal wires: An experimental and theoretical assessment", Int. J. Plast., 41(1), 30-52.   DOI
21 Nix, W. and Gao, H. (1998), "Indentation size effects in crystalline materials: a law for strain gradient plasticity", J. Mech. Phys. Solid., 46(3), 411-425.   DOI
22 Stolken, J. and Evans, A. (1998), "A microbend test method for measuring the plasticity length scale", Acta Materialia, 46(14), 5109-5115.   DOI
23 Lam, D., Yang F., Chong, A., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solid., 51(8), 1477-1508.   DOI