Berkovich nanoindentation study of monocrystalline tungsten: a crystal plasticity study of surface pile-up deformation

References

• S.R. Kalidindi and S. Pathak, Determination of the effective zero-point and the extraction of spherical nanoindentation stress-strain curves, Acta Mater. 56 (2008), pp. 3523–3532.10.1016/j.actamat.2008.03.036
   Web of Science ®Google Scholar
• X. Li and B. Bhushan, A review of nanoindentation continuous stiffness measurement technique and its applications, Mater. Charact. 48 (2002), pp. 11–36.10.1016/S1044-5803(02)00192-4
   Web of Science ®Google Scholar
• Y.J. Park and G.M. Pharr, Nanoindentation with spherical indenters: Finite element studies of deformation in the elastic-plastic transition regime, Thin Solid Films 447–448 (2004), pp. 246–250.10.1016/S0040-6090(03)01102-7
   Web of Science ®Google Scholar
• R. Saha and W.D. Nix, Effects of the substrate on the determination of thin film mechanical properties by nanoindentation, Acta Mater. 50 (2002), pp. 23–38.10.1016/S1359-6454(01)00328-7
   Web of Science ®Google Scholar
• H. Bei, Z.P. Lu, and E.P. George, Theoretical strength and the onset of plasticity in bulk metallic glasses investigated by nanoindentation with a spherical indenter, Phys. Rev. Lett. 93 (2004), pp. 125504-1–125504-4.
   Web of Science ®Google Scholar
• M.A. Lodes, A. Hartmaier, M. Göken, and K. Durst, Influence of dislocation density on the pop-in behavior and indentation size effect in CaF2 single crystals: Experiments and molecular dynamics simulations, Acta Mater. 59 (2011), pp. 4264–4273.10.1016/j.actamat.2011.03.050
   Web of Science ®Google Scholar
• W.W. Gerberich, D.E. Kramer, N.I. Tymiak, A.A. Volinsky, D.F. Bahr, and M.D. Kriese, Nanoindentation-induced defect–interface interactions: Phenomena, methods and limitations, Acta Mater. 47 (1999), pp. 4115–4123.10.1016/S1359-6454(99)00270-0
   Web of Science ®Google Scholar
• M. Liu, C. Lu, and A.K. Tieu, Crystal plasticity finite element method modelling of indentation size effect, Int. J. Solids Struct. 54 (2015), pp. 42–49.10.1016/j.ijsolstr.2014.11.008
   Web of Science ®Google Scholar
• D. Esqué-de los Ojos, J. Očenášek, and J. Alcalá, Sharp indentation crystal plasticity finite element simulations: Assessment of crystallographic anisotropy effects on the mechanical response of thin fcc single crystalline films, Comput. Mater. Sci. 86 (2014), pp. 186–192.10.1016/j.commatsci.2014.01.064
   Web of Science ®Google Scholar
• M. Mata, O. Casals, and J. Alcalá, The plastic zone size in indentation experiments: The analogy with the expansion of a spherical cavity, Int. J. Solids Struct. 43 (2006), pp. 5994–6013.10.1016/j.ijsolstr.2005.07.002
   Web of Science ®Google Scholar
• J. Rodríguez and M.A.G. Maneiro, A procedure to prevent pile up effects on the analysis of spherical indentation data in elastic-plastic materials, Mech. Mater. 39 (2007), pp. 987–997.10.1016/j.mechmat.2007.04.003
   Web of Science ®Google Scholar
• B. Eidel, Crystal plasticity finite-element analysis versus experimental results of pyramidal indentation into (001) fcc single crystal, Acta Mater. 59 (2011), pp. 1761–1771.10.1016/j.actamat.2010.11.042
   Web of Science ®Google Scholar
• W.Z. Yao, C.E. Krill III, B. Albinski, H.C. Schneider, and J.H. You, Plastic material parameters and plastic anisotropy of tungsten single crystal: A spherical micro-indentation study, J. Mater. Sci. 49 (2014), pp. 3705–3715.10.1007/s10853-014-8080-z
   Web of Science ®Google Scholar
• Y. Liu, S. Varghese, J. Ma, M. Yoshino, H. Lu, and R. Komanduri, Orientation effects in nanoindentation of single crystal copper, Int. J. Plast 24 (2008), pp. 1990–2015.10.1016/j.ijplas.2008.02.009
   Web of Science ®Google Scholar
• C. Zambaldi and D. Raabe, Plastic anisotropy of γ-TiAl revealed by axisymmetric indentation, Acta Mater. 58 (2010), pp. 3516–3530.10.1016/j.actamat.2010.02.025
   Web of Science ®Google Scholar
• N. Zaafarani, D. Raabe, F. Roters, and S. Zaefferer, On the origin of deformation-induced rotation patterns below nanoindents, Acta Mater. 56 (2008), pp. 31–42.10.1016/j.actamat.2007.09.001
   Web of Science ®Google Scholar
• C.A. Brookes, J.B. O’Neill, and B.A.W. Redfern, Anisotropy in the hardness of single crystals, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 322 (1971), pp. 73–88.10.1098/rspa.1971.0055
   Web of Science ®Google Scholar
• J. Alcala, O. Casals, and J. Ocenasek, Micromechanics of pyramidal indentation in fcc metals: Single crystal plasticity finite element analysis, J. Mech. Phys. Solids 56 (2008), pp. 3277–3303.10.1016/j.jmps.2008.07.004
   Web of Science ®Google Scholar
• O. Casals, J. Ocenasek, and J. Alcala, Crystal plasticity finite element simulations of pyramidal indentation in copper single crystals, Acta Mater. 55 (2007), pp. 55–68.10.1016/j.actamat.2006.07.018
   Web of Science ®Google Scholar
• A. Barnoush, Correlation between dislocation density and nanomechanical response during nanoindentation, Acta Mater. 60 (2012), pp. 1268–1277.10.1016/j.actamat.2011.11.034
   Web of Science ®Google Scholar
• S. Shim, H. Bei, M.K. Miller, G.M. Pharr, and E.P. George, Effects of focused ion beam milling on the compressive behavior of directionally solidified micropillars and the nanoindentation response of an electropolished surface, Acta Mater. 57 (2009), pp. 503–510.10.1016/j.actamat.2008.09.033
   Web of Science ®Google Scholar
• W. Wang, C.B. Jiang, and K. Lu, Deformation behavior of Ni3Al single crystals during nanoindentation, Acta Mater. 51 (2003), pp. 6169–6180.10.1016/S1359-6454(03)00436-1
   Web of Science ®Google Scholar
• W.Z. Yao, P. Wang, A. Manhard, C.E. Krill, and J.H. You, Effect of hydrogen on the slip resistance of tungsten single crystals, Mater. Sci. Eng. A 559 (2013), pp. 467–473.10.1016/j.msea.2012.08.127
   Web of Science ®Google Scholar
• P. Peralta, R. Ledoux, M. Hakik, R. Dickerson, and P. Dickerson, Characterization of surface deformation around vickers indents in monocrystalline materials, Metall. Mater. Trans. A 35 (2004), pp. 2247–2255.10.1007/s11661-006-0204-x
   Web of Science ®Google Scholar
• N.A. Stelmashenko and L.M. Brown, Deformation structure of microindentations in W(1 0 0): A transmission electron microscopy study, Philos. Mag. A 74 (1996), pp. 1195–1206.10.1080/01418619608239719
   Web of Science ®Google Scholar
• W.C. Oliver and G.M. Pharr, An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments, J. Mater. Res. 7 (1992), pp. 1564–1583.10.1557/JMR.1992.1564
   Web of Science ®Google Scholar
• H.J. Chang, M. Fivel, and M. Verdier, Indentation crystal plasticity: Experiments and multiscale simulations, Mater. Res. Soc. Symp. Proc. 1224 (2009), 1224-GG02-05.
   Google Scholar
• D. Peirce, R.J. Asaro, and A. Needleman, An analysis of nonuniform and localized deformation in ductile single crystals, Acta Metall. 30 (1982), pp. 1087–1119.10.1016/0001-6160(82)90005-0
   Google Scholar
• R.J. Asaro and J.R. Rice, Strain localization in ductile single crystals, J. Mech. Phys. Solids 25 (1977), pp. 309–338.10.1016/0022-5096(77)90001-1
   Web of Science ®Google Scholar
• R.J. Asaro and A. Needleman, Flow localization in strain hardening crystalline solids, Scr. Metall. 18 (1984), pp. 429–435.10.1016/0036-9748(84)90416-2
   Google Scholar
• R. Hill, The essential structure of constitutive laws for metal composites and polycrystals, J. Mech. Phys. Solids 15 (1967), pp. 79–95.10.1016/0022-5096(67)90018-X
   Web of Science ®Google Scholar
• R. Hill, Generalized constitutive relations for incremental deformation of metal crystals by multislip, J. Mech. Phys. Solids 14 (1966), pp. 95–102.10.1016/0022-5096(66)90040-8
   Web of Science ®Google Scholar
• R. Hill and J.R. Rice, Constitutive analysis of elastic-plastic crystals at arbitrary strain, J. Mech. Phys. Solids 20 (1972), pp. 401–413.10.1016/0022-5096(72)90017-8
   Web of Science ®Google Scholar
• Y. Huang, A user-material subroutine incorporating single crystal plasticity in the abaqus finite element program, Rep. MECH-178, Division of Applied Sciences, Harvard University, Cambridge, MA, 1991.
   Google Scholar
• J. Očenášek, M.R. Ripoll, S.M. Weygand, and H. Riedel, Multi-grain finite element model for studying the wire drawing process, Comput. Mater. Sci. 39 (2007), pp. 23–28.10.1016/j.commatsci.2006.01.024
   Web of Science ®Google Scholar
• C. Bohnert, N.J. Schmitt, S.M. Weygand, O. Kraft, and R. Schwaiger, Fracture toughness characterization of single-crystalline tungsten using notched micro-cantilever specimens, Int. J. Plast. 81 (2016), pp. 1–17.10.1016/j.ijplas.2016.01.014
   Web of Science ®Google Scholar
• W.D. Nix, Elastic and plastic properties of thin films on substrates: Nanoindentation techniques, Mater. Sci. Eng. A 234–236 (1997), pp. 37–44.10.1016/S0921-5093(97)00176-7
   Web of Science ®Google Scholar
• Y.B. Park, D.N. Lee, and G. Gottstein, The evolution of recrystallization textures in body centred cubic metals, Acta Mater. 46 (1998), pp. 3371–3379.10.1016/S1359-6454(98)00052-4
   Web of Science ®Google Scholar
• Y.-H. Lee and D. Kwon, Measurement of residual-stress effect by nanoindentation on elastically strained (1 0 0) W, Scr. Mater. 49 (2003), pp. 459–465.10.1016/S1359-6462(03)00290-2
   Web of Science ®Google Scholar
• G. Subhash, Y.J. Lee, and G. Ravichandran, Plastic deformation of CVD textured tungsten–I. Constitutive response, Acta Metall. Mater. 42 (1994), pp. 319–330.10.1016/0956-7151(94)90074-4
   Google Scholar
• M. Garfinkle, Room-temperature tensile behavior of <1 0 0> oriented tungsten single crystals with rehenium in ductile solid solution, Fourth Symposium on Refractory Metals, French Lick, IN, 1965.
   Google Scholar
• Y.J. Lee, G. Subhash, and G. Ravichandran, Constitutive modeling of textured body-centered-cubic (bcc) polycrystals, Int. J. Plast 15 (1999), pp. 625–645.10.1016/S0749-6419(99)00004-2
   Web of Science ®Google Scholar
• E. Lassner and W.-D. Schubert, Tungsten: Properties, chemistry, technology of the element, alloys, and chemical compounds, Springer, Berlin, 1999.10.1007/978-1-4615-4907-9
   Google Scholar
• W.Z. Yao, Crystal plasticity study of single crystal tungsten by indentation tests, Ph.D. diss., Ulm University, 2012.
   Google Scholar
• L. Kaun, A. Luft, J. Richter, and D. Schulze, Slip line pattern and active slip systems of tungsten and molybdenum single crystals weakly deformed in tension at room temperature, Phys. Status Solidi 26 (1968), pp. 485–499.10.1002/(ISSN)1521-3951
   Web of Science ®Google Scholar
• H.J. Chang, M. Fivel, D. Rodney, and M. Verdier, Multiscale modelling of indentation in FCC metals: From atomic to continuum, C. R. Phys. 11 (2010), pp. 285–292.10.1016/j.crhy.2010.07.007
   Web of Science ®Google Scholar
• N.A. Stelmashenko, M.G. Walls, L.M. Brown, and Y.V. Milman, Microindentations on W and Mo oriented single crystals: An STM study, Acta Metall. Mater. 41 (1993), pp. 2855–2865.10.1016/0956-7151(93)90100-7
   Google Scholar