Abstract
A phase mixture model was used to study the plastic deformation behaviors in hardening stage of nanocrystalline materials. The material was considered as a composite of grain interior phase and grain boundary (GB) phase. The constitutive equations of the two phases were determined in term of their main deformation mechanisms. In softening stage, a shear band deformation mechanism was presented and the corresponding constitutive relation was established. Numerical simulations have shown that the predications fit well with experimental data. The investigation using the finite-element method (FEM) provided a direct insight into quantifying shear localization effect in nanocrystalline materials.
Similar content being viewed by others
References
Arroyo M, Belytschko T (2005) Meccanica 40:455–469
Wan H, Delale F (2010) Meccanica 45:43–51
Omidi M, Alaie S, Rousta A (2012) Meccanica 47:817–833
Zhou JQ, Li ZH, Zhu RT, Li YL, Zhang ZZ (2008) J Mater Process Technol 197:325–336
Meyers MA, Mishra A, Benson DJ (2006) Prog Mater Sci 51(4):427–556
Kim HS, Estrin Y, Bush MB (2000) Acta Mater 48(2):493–504
Kim HS, Estrin Y (2005) Acta Mater 53:765–772
Zhou JQ, Zhu RT, Zhang ZZ (2008) Mater Sci Eng A 480:419–427
Islamgaliev RK, Valiev RZ, Mishra RS, Mukherjee AK (2001) Mater Sci Eng A 304–306:206–210
Mukherjee AK (2002) Mater Sci Eng A 322:1–22
Gutkin YuM, Ovid_ko IA, Skiba NV (2004) Acta Mater 52:1711–1720
Joshi SP, Ramesh KT (2008) Acta Mater 56:282–291
Coble RL (1963) J Appl Phys 34:1679–1682
Conrad H, Narayan J (2000) Scr Mater 42:1025–1030
Nabarro FRN (1948) Report of a conference on the strength of solids Physical Society, London, pp 75–90
Herring C (1950) J Appl Phys 21:437–445
Estrin Y (1996) Dislocation-density-related constitutive modeling. In: Krausz AS, Krausz K (eds) Unified constitutive laws of plastic deformation. Academic Press, New York, pp 69–106
Jiang H, Zhou JQ, Zhu RT, Liu YG (2011) Mater Des 32:598–604
Soppa E, Schmauder S, Fischer G, Thesing J, Ritter R (1999) Comput Mater Sci 16:323–332
Berbenni S, Favier V, Berveiller M (2007) Comput Mater Sci 39:96–105
Gross D, Li M (2002) Appl Phys Lett 80:746–748
Li S, Zhou JQ, Ma L, Xu N, Zhu RT, He XH (2009) Comput Mater Sci 45:390–397
Zhou JQ, Li YL, Zhang ZZ (2007) Acta Mech Solida Sin 20:13–20
Ranganathan S, Divakarb R, Raghunathanb VS (2001) Scr Mater 44:1169–1174
ABAQUS (2002) Reference Manual. Hibbit, Karlson and Sorensen, Pawtucket
Zhu RT, Zhou JQ, Jiang H, Liu YG, Ling X (2010) Mater Sci Eng A 527:1751–1760
Zhu RT, Zhou JQ, Li XB, Jiang H, Ling X (2010) Mater Charact 61:396–401
Frost H, F AM (1982) Deformation-mechanism maps: the plasticity and creep of metals and ceramics. Pergamon Press, Oxford
Wei YJ, Gao HJ (2008) Mater Sci Eng A 478:16–25
Cheng S, Ma E, Wang YM, Kecskes LJ, Youssef KM, Koch CC, Trociewitz UP, Han K (2005) Acta Mater 53:1521–1533
Hasnaoui A, Van Swygenhoven H, Derlet PM (2002) Phys Rev B 66:184112
Sansoz F, Dupont V (2007) Mater Sci Eng C 27:1509–1513
Weng GJ (1983) J Mech Phys Solids 31:193–203
Li J, Weng GJ (2007) Int J Plast 23:2115–2133
Jiang B, Weng GJ (2003) Metall Mater Trans 34A:765–772
Jiang B, Weng GJ (2004) J Mech Phys Solids 52:1125–1149
Jiang B, Weng GJ (2004) Int J Plast 20:2007–2026
Acknowledgements
This work was supported by Research Innovation Program for College Graduates of Jiangsu Province (CXZZ11_0342), Natural Science Foundation of Hubei Province (Q20111501) and Key Project of Chinese Ministry of Education (211061).
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
About this article
Cite this article
Zhang, S., Wang, Y., Jiang, H. et al. Constitutive model for plastic deformation of nanocrystalline materials with shear band. Meccanica 48, 175–185 (2013). https://doi.org/10.1007/s11012-012-9592-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-012-9592-8