Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-25T05:14:24.621Z Has data issue: false hasContentIssue false
  • English
  • Français

Crystal plasticity FEM study of nanoindentation behaviors of Cu bicrystals and Cu–Al bicrystals

Published online by Cambridge University Press:  17 August 2015

Mao Liu ,
Cheng Lu ,
Kiet Anh Tieu  and
Kun Zhou
Mao Liu*
Affiliation:
School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, Wollongong, New South Wales 2522, Australia
Cheng Lu
Affiliation:
School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, Wollongong, New South Wales 2522, Australia
Kiet Anh Tieu
Affiliation:
School of Mechanical, Materials and Mechatronic Engineering, University of Wollongong, Wollongong, New South Wales 2522, Australia
Kun Zhou*
Affiliation:
School of Mechanical & Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore
*
a)Address all correspondence to these authors. e-mail: [email protected]
b)e-mail: [email protected]
Get access

Abstract

A crystal plasticity finite element constitutive model combined with Bassani and Wu hardening law has been developed to investigate the effects of grain/phase boundary (GB/PB) on mechanical properties and microtexture evolution of Cu bicrystals and Cu–Al bicrystals during nanoindentation process. The simulated load–displacement curve for the Cu single crystal with Goss initial orientation has been analyzed and compared with the result from the experiment to validate the parameters. The numerical results indicate that the effects of GB/PB on load–displacement curves, indentation Young's moduli, Mises stresses, pile-up patterns are insignificant for Cu bicrystals while they are significant for Cu–Al bicrystals. The main reason is that PB works as a very effective barrier to resist the plastic slip propagation of the deformed material. The effects from different misorientations of GBs/PBs are insignificant for both Cu bicrystals and Cu–Al bicrystals. The effects of GB/PB on lattice rotation angles for both Cu bicrystals and Cu–Al bicrystals are significant.

Keywords

finite element crystal plasticitynanoindentationgrain/phase boundaryCu–Al bicrystalsmicrotexture
Type
Articles
Information
Journal of Materials Research , Volume 30 , Issue 16 , 28 August 2015 , pp. 2485 - 2499
Copyright
Copyright © Materials Research Society 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7(6), 1564 (1992).CrossRefGoogle Scholar
Gane, N. and Cox, J.M.: Micro-hardness of metals at very low loads. Philos. Mag. 22(179), 881 (1970).CrossRefGoogle Scholar
Swadener, J.G., George, E.P., and Pharr, G.M.: The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50(4), 681 (2002).CrossRefGoogle Scholar
Lloyd, S.J., Castellero, A., Giuliani, F., Long, Y., McLaughlin, K.K., Molina-Aldareguia, J.M., Stelmashenko, N.A., Vandeperre, L.J., and Clegg, W.J.: Observations of nanoindents via cross-sectional transmission electron microscopy: A survey of deformation mechanisms. Proc. R. Soc. A 461(2060), 2521 (2005).CrossRefGoogle Scholar
Rester, M., Motz, C., and Pippan, R.: Indentation across size scales - A survey of indentation-induced plastic zones in copper {111} single crystals. Scr. Mater. 59(7), 742 (2008).CrossRefGoogle Scholar
Haghighi, S.E., Lu, H.B., Jian, G.Y., Cao, G.H., Habibi, D., and Zhang, L.C.: Effect of alpha″ martensite on the microstructure and mechanical properties of beta-type Ti-Fe-Ta alloys. Mater. Des. 76, 47 (2015).CrossRefGoogle Scholar
Mayeur, J.R., Beyerlein, I.J., Bronkhorst, C.A., and Mourad, H.M.: Incorporating interface affected zones into crystal plasticity. Int. J. Plasticity 65, 206 (2015).CrossRefGoogle Scholar
Britton, T.B., Randman, D., and Wilkinson, A.J.: Nanoindentation study of slip transfer phenomenon at grain boundaries. J. Mater. Res. 24(03), 607 (2009).CrossRefGoogle Scholar
Ohmura, T., Minor, A.M., Stach, E.A., and Morris, J.W.: Dislocation-grain boundary interactions in martensitic steel observed through in situ nanoindentation in a transmission electron microscope. J. Mater. Res. 19(12), 3626 (2004).CrossRefGoogle Scholar
Wang, M.G. and Ngan, A.H.W.: Indentation strain burst phenomenon induced by grain boundaries in niobium. J. Mater. Res. 19(8), 2478 (2004).CrossRefGoogle Scholar
Wo, P.C. and Ngan, A.H.W.: Investigation of slip transmission behavior across grain boundaries in polycrystalline Ni3Al using nanoindentation. J. Mater. Res. 19(1), 189 (2004).CrossRefGoogle Scholar
Ohmura, T., Tsuzaki, K., and Yin, F.X.: Nanoindentation-induced deformation behavior in the vicinity of single grain boundary of interstitial-free steel. Mater. Trans. 46(9), 2026 (2005).CrossRefGoogle Scholar
Lee, C.S., Han, G.W., Smallman, R.E., Feng, D., and Lai, J.K.L.: The influence of boron-doping on the effectiveness of grain boundary hardening in Ni3Al. Acta Mater. 47(6), 1823 (1999).CrossRefGoogle Scholar
Soifer, Y.M., Verdyan, A., Kazakevich, M., and Rabkin, E.: Nanohardness of copper in the vicinity of grain boundaries. Scr. Mater. 47(12), 799 (2002).CrossRefGoogle Scholar
Ohmura, T. and Tsuzaki, K.: Analysis of grain boundary effect of bulk polycrystalline materials through nanomechanical characterization. J. Phys. D: Appl. Phys. 41(7), 074015 (2008).CrossRefGoogle Scholar
Goken, M., Kempf, M., Bordenet, M., and Vehoff, H.: Nanomechanical characterizations of metals and thin films. Surf. Interface Anal. 27(5–6), 302 (1999).3.0.CO;2-D>CrossRefGoogle Scholar
Soer, W.A., Aifantis, K.E., and De Hosson, J.T.M.: Incipient plasticity during nanoindentation at grain boundaries in body-centered cubic metals. Acta Mater. 53(17), 4665 (2005).CrossRefGoogle Scholar
Eliash, T., Kazakevich, M., Semenov, V.N., and Rabkin, E.: Nanohardness of molybdenum in the vicinity of grain boundaries and triple junctions. Acta Mater. 56(19), 5640 (2008).CrossRefGoogle Scholar
Nilsen, C.F. and Subramanian, K.N.: Indentation studies on 2-phase bicrystals of alpha-beta brass with various phase-boundary geometries. J. Mater. Sci. 20(10), 3790 (1985).CrossRefGoogle Scholar
Liu, Y., Varghese, S., Ma, J., Yoshino, M., Lu, H., and Komanduri, R.: Orientation effects in nanoindentation of single crystal copper. Int. J. Plast. 24(11), 1990 (2008).CrossRefGoogle Scholar
Kalidindi, S.R., Bronkhorst, C.A., and Anand, L.: Crystallographic texture evolution in bulk deformation processing of fcc metals. J. Mech. Phys. Solids 40(3), 537 (1992).CrossRefGoogle Scholar
Fivel, M.C., Robertson, C.F., Canova, G.R., and Boulanger, L.: Three-dimensional modeling of indent-induced plastic zone at a mesoscale. Acta Mater. 46(17), 6183 (1998).CrossRefGoogle Scholar
Liu, Y., Wang, B., Yoshino, M., Roy, S., Lu, H., and Komanduri, R.: Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale. J. Mech. Phys. Solids 53(12), 2718 (2005).CrossRefGoogle Scholar
Zaafarani, N., Raabe, D., Singh, R.N., Roters, F., and Zaefferer, S.: Three-dimensional investigation of the texture and microstructure below a nanoindent in a Cu single crystal using 3D EBSD and crystal plasticity finite element simulations. Acta Mater. 54(7), 1863 (2006).CrossRefGoogle Scholar
Zaafarani, N., Raabe, D., Roters, F., and Zaefferer, S.: On the origin of deformation-induced rotation patterns below nanoindents. Acta Mater. 56(1), 31 (2008).CrossRefGoogle Scholar
Lee, W.B. and Chen, Y.P.: Simulation of micro-indentation hardness of FCC single crystals by mechanism-based strain gradient crystal plasticity. Int. J. Plasticity 26(10), 1527 (2010).CrossRefGoogle Scholar
Eidel, B.: Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (001) fcc single crystal. Acta Mater. 59(4), 1761 (2011).CrossRefGoogle Scholar
Li, L., Shen, L.M., Proust, G., Moy, C.K.S., and Ranzi, G.: Three-dimensional crystal plasticity finite element simulation of nanoindentation on aluminium alloy 2024. Mater. Sci. Eng., A 579, 41 (2013).CrossRefGoogle Scholar
Taylor, G.I.: Plastic strain in metals. J. Inst. Met. 62, 307 (1938).Google Scholar
Hill, R.: Generalized constitutive relations for incremental deformation of metal crystals by multislip. J. Mech. Phys. Solids 14(2), 95 (1966).CrossRefGoogle Scholar
Asaro, R.J.: Crystal plasticity. J. Appl. Mech.-Trans. Asme. 50(4B), 921 (1983).CrossRefGoogle Scholar
Asaro, R.J. and Rice, J.R.: Strain localization in ductile single crystals. J. Mech. Phys. Solids 25(5), 309 (1977).CrossRefGoogle Scholar
Si, L.Y., Lu, C., Huynh, N.N., Tieu, A.K., and Liu, X.H.: Simulation of rolling behaviour of cubic oriented al single crystal with crystal plasticity FEM. J. Mater Process Technol. 201(1–3), 79 (2008).CrossRefGoogle Scholar
Huynh, N.N.: A modelling of microstructure evolution and crack opening in FCC materials under tension. Ph.D. Dissertation, University of Wollongong, Australia, 2009.Google Scholar
Liu, M., Lu, C., Tieu, K., and Yu, H.: Numerical comparison between Berkovich and conical nano-indentations: Mechanical behaviour and micro-texture evolution. Mater. Sci. Eng., A 619, 57 (2014).CrossRefGoogle Scholar
Peirce, D., Asaro, R.J., and Needleman, A.: An analysis of nonuniform and localized deformation in ductile single-crystals. Acta Metall. Mater. 30(6), 1087 (1982).CrossRefGoogle Scholar
Asaro, R.J. and Needleman, A.: Overview 42. Texture development and strain-hardening in rate dependent polycrystals. Acta Metall. Mater. 33(6), 923 (1985).CrossRefGoogle Scholar
Huang, Y.G.: A User-Material Subroutine Incorporating Single Crystal Plasticity in the ABAQUS Finite Element Program (Harvard University, Cambridge, MA, 1991).Google Scholar
Bassani, J.L. and Wu, T.Y.: Latent hardening in single-crystals 2. Analytical characterization and predictions. Proc. R. Soc. London, Ser. A 435(1893), 21 (1991).Google Scholar
Lu, C., Deng, G.Y., Tieu, A.K., Su, L.H., Zhu, H.T., and Liu, X.H.: Crystal plasticity modeling of texture evolution and heterogeneity in equal channel angular pressing of aluminum single crystal. Acta Mater. 59(9), 3581 (2011).CrossRefGoogle Scholar
Zhu, H.X., Thorpe, S.M., and Windle, A.H.: The geometrical properties of irregular two-dimensional Voronoi tessellations. Philos. Mag. A 81(12), 2765 (2001).CrossRefGoogle Scholar
Fischer-Cripps, A.C.: The IBIS Handbook of Nanoindentation (Fischer-Cripps Laboratories Pty Ltd, 2009).Google Scholar
Wu, T.Y., Bassani, J.L., and Laird, C.: Latent hardening in single-crystals 1. Theory and experiments. Proc. R. Soc. London, Ser. A 435(1893), 1 (1991).Google Scholar
Liu, M., Lu, C., and Tieu, K.A.: Crystal plasticity FEM study of the effects of BW hardening model parameters on nano-indentation deformation behaviour of copper single crystal. In TMS Annual Meeting, San Diego, CA, 2014; p. 317.Google Scholar
Franciosi, P., Berveiller, M., and Zaoui, A.: Latent hardening in copper and aluminum single-crystals. Acta Metall. Mater. 28(3), 273 (1980).CrossRefGoogle Scholar
Liu, Q., Maurice, C., Driver, J., and Hansen, N.: Heterogeneous microstructures and microtextures in cube-oriented Al crystals after channel die compression. Metall. Mater. Trans. A 29(9), 2333 (1998).CrossRefGoogle Scholar
Akef, A., Fortunier, R., Driver, J.H., and Watanabe, T.: Recrystallization of high symmetry aluminum single-crystals after plane-strain compression. Textures Microstruct. 14, 617 (1991).CrossRefGoogle Scholar
Casals, O., Ocenasek, J., and Alcala, J.: Crystal plasticity finite element simulations of pyramidal indentation in copper single crystals. Acta Mater. 55(1), 55 (2007).CrossRefGoogle Scholar
Alcala, J., Casals, O., and Ocenasek, J.: Micromechanics of pyramidal indentation in fcc metals: Single crystal plasticity finite element analysis. J. Mech. Phys. Solids 56(11), 3277 (2008).CrossRefGoogle Scholar
Huynh, N.N., Lu, C., Si, L., and Tieu, K.: A study of microstructural evolution around crack tip using crystal plasticity finite-element method. Proc. Inst. Mech. Eng., Part J 222(J3), 183 (2008).CrossRefGoogle Scholar
Liu, M., Tieu, A.K., Lu, C., Zhu, H.T., and Deng, G.Y.: A crystal plasticity study of the effect of friction on the evolution of texture and mechanical behaviour in the nano-indentation of an aluminium single crystal. Comp. Mater. Sci. 81, 30 (2014).CrossRefGoogle Scholar
Wei, Y.G., Wang, X.Z., and Zhao, M.H.: Size effect measurement and characterization in nanoindentation test. J. Mater. Res. 19(1), 208 (2004).CrossRefGoogle Scholar
Vlassak, J.J. and Nix, W.D.: Indentation modulus of elastically anisotropic half-spaces. Philos. Mag. A 67(5), 1045 (1993).CrossRefGoogle Scholar
Vlassak, J.J. and Nix, W.D.: Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42(8), 1223 (1994).CrossRefGoogle Scholar
Wang, W. and Lu, K.: Nanoindentation study on elastic and plastic anisotropies of Cu single crystals. Philos. Mag. 86(33–35), 5309 (2006).CrossRefGoogle Scholar
Soer, W.A. and De Hosson, J.T.M.: Detection of grain-boundary resistance to slip transfer using nanoindentation. Mater. Lett. 59(24–25), 3192 (2005).CrossRefGoogle Scholar
Wang, Y., Raabe, D., Kluber, C., and Roters, F.: Orientation dependence of nanoindentation pile-up patterns and of nanoindentation microtextures in copper single crystals. Acta Mater. 52(8), 2229 (2004).CrossRefGoogle Scholar
Hollatz, M., Bobeth, M., Pompe, W., and Marx, V.: Orientation dependent crack patterns in alumina films on NiAl single crystals due to spherical indentation. Acta Mater. 44(10), 4149 (1996).CrossRefGoogle Scholar
Wert, J.A., Liu, Q., and Hansen, N.: Dislocation boundary formation in a cold-rolled cube-oriented Al single crystal. Acta Mater. 45(6), 2565 (1997).CrossRefGoogle Scholar