The indentation size effect of single-crystalline tungsten revisited
Source abstract
Abstract
Abstract In this study, we have investigated the indentation size effect (ISE) of single crystalline tungsten with low defect density. As expected, the hardness shows a pronounced increase with decreasing indentation depth as well as a strong strain rate dependence. For penetration depths greater than about 300 nm, the ISE is well captured by the Nix–Gao model in the context of geometrically necessary dislocations. However, clear deviations from the model are observed in the low depth regime resulting in a bilinear effect. The hardness behavior in the low depth regime can be modeled assuming a non-uniform spacing of the geometrically necessary dislocations. We propose that the bilinear indentation size effect observed reflects the evolution of the geometrically necessary dislocation density. With increasing strain rate, the bilinear effect becomes less pronounced. This observation can be rationalized by the activation of different slip systems. Graphic abstract
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Metal and Thin Film Mechanics · Advanced materials and composites · Microstructure and mechanical properties
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (44)
Show source-provided references
1. G.M. Pharr, E.G. Herbert, Y. Gao, The indentation size effect: a critical examination of experimental observations and mechanistic interpretations. Annu. Rev. Mater. Res. 40, 271–292 (2010)10.1146/annurev-matsci-070909-104456 ↗
2. K. McElhaney, J.J. Vlassak, W.D. Nix, Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J. Mater. Res. 13, 1300–1306 (1998)10.1557/JMR.1998.0185 ↗
3. Y. Liu, A.W. Ngan, Depth dependence of hardness in copper single crystals measured by nanoindentation. Scripta Mater. 44, 237–241 (2001)10.1016/S1359-6462(00)00598-4 ↗
4. K. Durst, B. Backes, M. Göken, Indentation size effect in metallic materials: correcting for the size of the plastic zone. Scripta Mater. 52, 1093–1097 (2005)10.1016/j.scriptamat.2005.02.009 ↗
5. Q. Ma, D.R. Clarke, Size dependent hardness of silver single crystals. J. Mater. Res. 10, 853–863 (1995)10.1557/JMR.1995.0853 ↗
6. G. Feng, W.D. Nix, Indentation size effect in MgO. Scripta Mater. 51, 599–603 (2004)10.1016/j.scriptamat.2004.05.034 ↗
7. J. Swadener, E. George, G. Pharr, The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50, 681–694 (2002)10.1016/S0022-5096(01)00103-X ↗
8. V. Maier, C. Schunk, M. Göken, K. Durst, Microstructure-dependent deformation behaviour of bcc-metals-indentation size effect and strain rate sensitivity. Philos. Mag. 95, 1766–1779 (2015)10.1080/14786435.2014.982741 ↗
9. K. Durst, B. Backes, O. Franke, M. Göken, Indentation size effect in metallic materials: modeling strength from pop-in to macroscopic hardness using geometrically necessary dislocations. Acta Mater. 54, 2547–2555 (2006)10.1016/j.actamat.2006.01.036 ↗
10. D.F. Bahr, D. Kramer, W. Gerberich, Non-linear deformation mechanisms during nanoindentation. Acta Mater. 46, 3605–3617 (1998)10.1016/S1359-6454(98)00024-X ↗
11. W.D. Nix, H. Gao, Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46, 411–425 (1998)10.1016/S0022-5096(97)00086-0 ↗
12. Y. Huang, F. Zhang, K. Hwang, W. Nix, G. Pharr, G. Feng, A model of size effects in nano-indentation. J. Mech. Phys. Solids 54, 1668–1686 (2006)10.1016/j.jmps.2006.02.002 ↗
13. X. Qiu, Y. Huang, W. Nix, K. Hwang, H. Gao, Effect of intrinsic lattice resistance in strain gradient plasticity. Acta Mater. 49, 3949–3958 (2001)10.1016/S1359-6454(01)00299-3 ↗
14. N. Fleck, G. Muller, M.F. Ashby, J.W. Hutchinson, Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42, 475–487 (1994)10.1016/0956-7151(94)90502-9 ↗
15. J. Hutchinson, N. Fleck, Strain gradient plasticity. Adv. Appl. Mech. 33, 295–361 (1997)10.1016/S0065-2156(08)70388-0 ↗
16. G.I. Taylor, The mechanism of plastic deformation of crystals. Part I - theoretical. Proc. R. Soc. Lond. A 145, 362–387 (1934)10.1098/rspa.1934.0106 ↗
17. N. Stelmashenko, M. Walls, L. Brown, Y.V. Milman, Microindentations on W and Mo oriented single crystals: an SEM study. Acta Metall. Mater. 41, 2855–2865 (1993)10.1016/0956-7151(93)90100-7 ↗
18. J.R. Stephens, Review of deformation behavior of tungsten at temperature less than 0.2 absolute melting temperature, NASA Technical Memorandum TM X-2482 (1972)
19. E. Lassner, W.-D. Schubert, Tungsten: Properties, Chemistry, Technology of the Element, Alloys, and Chemical Compounds (Springer, Boston, 1999).10.1007/978-1-4615-4907-9 ↗
20. P. Gumbsch, J. Riedle, A. Hartmaier, H.F. Fischmeister, Controlling factors for the brittle-to-ductile transition in tungsten single crystals. Science 282, 1293–1295 (1998)10.1126/science.282.5392.1293 ↗
21. P. Gumbsch, Brittle fracture and the brittle-to-ductile transition of tungsten. J. Nucl. Mater. 323, 304–312 (2003)10.1016/j.jnucmat.2003.08.009 ↗
22. A.S. Argon, S.R. Maloof, Plastic deformation of tungsten single crystals at low temperatures. Acta Metall. 14, 1449–1462 (1966)10.1016/0001-6160(66)90165-9 ↗
23. P. Beardmore, D. Hull, Deformation and fracture of tungsten single crystals. J. Less Common Metals 9, 168–180 (1965)10.1016/0022-5088(65)90094-9 ↗
24. R.M. Rose, D.P. Ferriss, J. Wulff, Yielding and plastic flow in single crystals of tungsten. Trans. Met. Soc. AIME 224, 981–990 (1962)
25. J. Riedle, P. Gumbsch, H. Fischmeister, Cleavage anisotropy in tungsten single crystals. Phys. Rev. Lett. 76, 3594–3597 (1996)10.1103/PhysRevLett.76.3594 ↗
26. D. Rupp, S.M. Weygand, Anisotropic fracture behaviour and brittle-to-ductile transition of polycrystalline tungsten’’. Philos. Mag. 90, 4055–4069 (2010)10.1080/14786435.2010.504198 ↗
27. J. Reiser, M. Rieth, A. Möslang, B. Dafferner, A. Hoffmann, X. Yi, D. Armstrong, Tungsten foil laminate for structural divertor applications: tensile test properties of tungsten foil. J. Nucl. Mater. 434, 357–366 (2013)10.1016/j.jnucmat.2012.12.003 ↗
28. D. Rupp, Bruch Und Spröd-Duktil-Übergang in Polykristallinem Wolfram: Einfluss von Mikrostruktur Und Lastrate (Shaker Verlag, Dueren, 2010).
29. A. Leitner, V. Maier-Kiener, D. Kiener, Dynamic nanoindentation testing: is there an influence on a material’s hardness? Mater. Res. Lett. 5, 486–493 (2017)10.1080/21663831.2017.1331384 ↗
30. D.E. Stegall, M.A. Mamun, B. Crawford, A. Elmustafa, Indentation size effect in fcc metals: an examination of experimental techniques and the bilinear behavior. J. Mater. Res. 27, 1543 (2012)10.1557/jmr.2012.91 ↗
31. G.M. Pharr, J.H. Strader, W. Oliver, Critical issues in making small-depth mechanical property measurements by nanoindentation with continuous stiffness measurement. J. Mater. Res. 24, 653–666 (2009)10.1557/jmr.2009.0096 ↗
32. B. Merle, V. Maier-Kiener, G.M. Pharr, Influence of modulus-to-hardness ratio and harmonic parameters on continuous stiffness measurement during nanoindentation. Acta Mater. 134, 167–176 (2017)10.1016/j.actamat.2017.05.036 ↗
33. M. Rester, C. Motz, R. Pippan, The deformation-induced zone below large and shallow nanoindentations: a comparative study using EBSD and TEM. Phil. Magn. Lett. 88, 879–887 (2008)10.1080/09500830802498978 ↗
34. M. Rester, C. Motz, R. Pippan, Indentation across size scales-a survey of indentation-induced plastic zones in copper {1 1 1} single crystals. Scripta Mater. 59, 742–745 (2008)10.1016/j.scriptamat.2008.06.003 ↗
35. M. Rester, C. Motz, R. Pippan, Where are the geometrically necessary dislocations accommodating small imprints? J. Mater. Res. 24, 647–651 (2009)10.1557/jmr.2009.0131 ↗
36. M. Rester, C. Motz, R. Pippan, Microstructural investigation of the volume beneath nanoindentations in copper. Acta Mater. 55, 6427–6435 (2007)10.1016/j.actamat.2007.08.001 ↗
37. E. Demir, D. Raabe, N. Zaafarani, S. Zaefferer, Investigation of the indentation size effect through the measurement of the geometrically necessary dislocations beneath small indents of different depths using EBSD tomography. Acta Mater. 57, 559–569 (2009)10.1016/j.actamat.2008.09.039 ↗
38. F. Javaid, Y. Xu, E. Bruder, K. Durst, Indentation size effect in tungsten: quantification of geometrically necessary dislocations underneath the indentations using HR-EBSD. Mater. Charact. 142, 39–42 (2018)10.1016/j.matchar.2018.05.016 ↗
39. J. Wang, L. Luan, T. Volz, S.M. Weygand, R. Schwaiger, Size-dependent geometrically necessary dislocation structures in single-crystalline tungsten. Submitted (2021)10.1557/s43578-022-00733-9 ↗
40. J. Hirth, J. Lothe, Theory of Dislocations, 2nd edn. (Wiley, New York, 1982).
41. A. Argon, Strengthening mechanisms in crystal plasticity. Oxford University Press on Demand (2008)10.1093/acprof:oso/9780198516002.001.0001 ↗
42. N.J.V. Schmitt, Experimentelle Untersuchung des Verformungs- und Bruchverhaltens von Ein-, Bi- und Polykristallinem Wolfram auf der Mikroskala (Karlsruhe Institute of Technology, 2016), http://digbib.ubka.uni-karlsruhe.de/volltexte/1000062471
43. M. Cordill, N. Moody, W. Gerberich, Effects of dynamic indentation on the mechanical response of materials. J. Mater. Res. 23, 1604–1613 (2008)10.1557/JMR.2008.0205 ↗
44. B. Lucas, W. Oliver, Indentation power-law creep of high-purity indium. Metall. Mater. Trans. A 30, 601–610 (1999)10.1007/s11661-999-0051-7 ↗