and (2) crystal plasticity material models, which
include the development and determination of
micro-mechanics material models and the imple-
mentation of the models in commercial FE codes.
Thus significant eff orts should be made on these
two aspects of research for micro-forming appli-
cations.
REFERENCES
[1] M. Geiger, M. Kleiner, R. Eckstein, N. Tiesler,
U. Engel, Microforming, CIRP Ann. 50 (2) (2001)
445–462.
[2] U. Engel, R. Eckstein, Micro-forming – from basic
research to its realization, J. Mater. Process. Technol.
125–126 (2002) 35–44.
[3] G.I. Taylor, Plastic strain in metals, J. Inst. Met. 62
307–325.
[4] R. Hill, Generalized constitutive relations for incre-
mental deformation of metal crystals by multislip, J.
Mech. Phys. Solids 14 (2) (1966) 95–102.
[5] J.R. Rice, Inelastic constitutive relations for solids: an
internal-variable theory and its application to metal
plasticity, J. Mech. Phys. Solids 19 (6) (1971)
433–455.
[6] R. Hill, J.R. Rice, Constitutive analysis of elastic-
plastic crystals at arbitrary strain, J. Mech. Phys.
Solids 20(6) (1972) 401–413.
[7] R.J. Asaro, J.R. Rice, Strain localization in ductile
single crystals, J. Mech. Phys. Solids 25 (1977)
309–338.
[8] R.J. Asaro, Micromechanics of crystals and polycrys-
tals, Adv. Appl. Mech 23 (1983) 1–115.
[9] D. Peirce, R.J. Asaro, A. Needleman, An analysis of
nonuniform and localized deformation in ductile sin-
gle crystals, Acta Metall 30 (1982) 1087–1119.
[10] Y. Huang, A user-material subroutine incorporating
single crystal plasticity in the ABAQUS finite element
program, Harvard University Report, MECH 178
(1991).
[11] F.J. Harewood, P.E. McHugh, Comparison of the
implicit and explicit finite element methods using
crystal plasticity, Comput. Mater. Sci 39 (2007)
481–494.
[12] L.M. Kutt, A.B. Pifko, J.A. Nardiello, J.M. Papazian,
Slow-dynamic finite element simulation of manufactur-
ing processes, Comput. Struct 66 (1) (1998) 1–17.
[13] W.J. Chung, J.W. Cho, T. Belytschko, On the
dynamic effects of explicit FEM in sheet metal form-
ing analysis, Eng. Computations 15 (6) (1998)
750–776.
[14] H.-H. Choi, S.-M. Hwang, Y.H. Kang, J. Kim,
B.S. Kang, Comparison of implicit and explicit finite
element methods for the hydroforming process of an
automobile lower arm, Int. J. Adv. Manuf. Technol
20(6) (2002) 407–413.
[15] H. Riesch-Oppermann, VorTess Generation of 2-D
random Poisson-Voronoi mosaics as framework for
the micro-mechanical modelling of polycrystalline
materials, Report FZKA 6325, Forschungszentrum
Karlsruhe, Karlsruhe, Germany (1999).
[16] K. Kobayashi, K. Sugihara, Crystal Voronoi diagram
and its applications, Future Gener. Comp. Sy 18 (5)
(2002) 681–692.
[17] U.F. Kocks, C.N. Tom
e, H.-R. Wenk, Texture and
Anisotropy, Cambridge University Press, Cam-
bridge, UK (1998).
[18] K.S. Zhang, M.S. Wu, R. Feng, Simulation of micro-
plasticity-induced deformation in uniaxially strained
ceramics by 3-D Voronoi polycrystal modelling, Int.
J. Plast. 21 (4) (2005) 801–834.
[19] J. Cao, W. Zhuang, S. Wang, K. Ho, N. Zhang,
J. Lin, T.A. Dean, An integrated crystal plasticity
FE system for micro-forming simulation, To appear
in Int. J. of Multiscale Modelling (2008).
[20] H.X. Zhu, S.M. Thorpe, A.H. Windle, The geomet-
rical properties of irregular two-dimensional Voro-
noi tessellations, Philos. Mag. A 81 (12) (2001)
2765–2783.
[21] A. Okabe, B. Boots, K. Sugihara, Spatial Tessella-
tions: Concepts and Applications of Voronoi Dia-
grams, Wiley, New York (1992).
[22] D. Stoyan, W.S. Kendall, J. Mecke, Stochastic Geom-
etry and its Application, Wiley, New York (1987).
[23] M. F
atima Vaz, M.A. Fortes, Grain size distribution:
the lognormal and the gamma distribution functions,
Scripta Metallurgica 22 (1988) 35–40.
[24] B. Zhu, R.J. Asaro, P. Krysl, K. Zhang, J.R.
Weertman, Effects of grain size distribution on the
mechanical response of nanocrystalline metals: Part
A, Acta Mater. 54 (2006) 3307–3320.
[25] C. Wang, G. Liu, G. Wang, W. Xue, On the quasi-
stationary grain size distribution from two Gamma
size distributions in three-dimensional grain growth,
Mater. Lett 61 (2007) 4262–4266.
[26] K.C. Ho, N. Zhang, J. Lin, T.A. Dean, An integrated
approach for virtual microstructure generation and
micromechanics modelling for micro-forming simu-
lation, Proceedings of ASME, MNC2007, MicroNa-
noChina07, Sanya, Hainan, China, (Jan. 10–13,
2007) 1–9.
[27] J. Cao, N. Krishnan, Z. Wang, H. Lu, K. Wing, A.
Swanson, Micro-forming: experimental investiga-
tion of the extrusion process for micropins and its
numerical simulation using RKEM, Trans. ASEM
126 (2004) 642–652.
[28] K. Krishnan, J. Cao, K. Dohda, Study of the size
effect on friction conditions in micro-extrusion: Part
1: Micro-extrusion experiments and analysis, J.
Manuf. Sci. E. -ASME 129 (2007) 669–676.
376 CHAPTER 23 Micro-Mechanics Modeling for Micro-Forming Processes