×

The equivalent axisymmetric model for Berkovich indenters in power-law hardening materials. (English) Zbl 1421.74079

Summary: W. D. Nix and H.-J. Gao [J. Mech. Phys. Solids 46, No. 3, 411–425 (1998; Zbl 0977.74557)] established an important relation between the micro-indentation hardness and indentation depth for axisymmetric indenters. For the Berkovich indenter, however, this relation requires an equivalent cone angle. J. Qin et al. [“The equivalence of axisymmetric indentation model for three-dimensional indentation hardness”, J. Mater. Res. 24, No. 3, 776–783 (2009; doi:10.1557/jmr.2009.0095)] showed that the widely used equivalent cone angle from the criterion of equal base area leads to significant errors in micro-indentation, and proposed a new equivalence of equal cone angle for iridium. It is shown in this paper that this new equivalence holds for a wide range of plastic work hardening materials. In addition, the prior equal-base-area criterion does not hold because the Berkovich indenter gives much higher density of geometrically necessary dislocations than axisymmetric indenter. The equivalence of equal cone angle, however, does not hold for the Vickers indenter.

MSC:

74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
74C05 Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials)

Citations:

Zbl 0977.74557
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Al-Rub, R. K. Abu; Voyiadjis, G. Z.: Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments, International journal of plasticity 20, 1139-1182 (2004)
[2] Arsenlis, A.; Parks, D. M.: Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density, Acta materialia 47, 1597-1611 (1999)
[3] Ashby, M. F.: Deformation of plastically non-homogeneous materials, Philosophical magazine 21, 399-424 (1970)
[4] Begley, M. R.; Hutchinson, J. W.: The mechanics of size-dependent indentation, Journal of the mechanics and physics of solids 46, 2049-2068 (1998) · Zbl 0967.74043 · doi:10.1016/S0022-5096(98)00018-0
[5] Bishop, J. F. W.; Hill, R.: A theory of plastic distortion of a polycrystalline aggregate under combined stresses, Philosophical magazine 42, 414-427 (1951) · Zbl 0042.22705
[6] Bishop, J. F. W.; Hill, R.: A theoretical derivation of the plastic properties of a polycrystalline face-centred metal, Philosophical magazine 42, 1298-1307 (1951) · Zbl 0044.45002
[7] Cottrell, A. H.: The mechanical properties of materials, (1964) · Zbl 0127.23901
[8] Chen, J. Y.; Wei, Y.; Huang, Y.; Hutchinson, J. W.; Hwang, K. C.: The crack tip fields in strain gradient plasticity: the asymptotic and numerical analyses, Engineering fracture mechanics 64, 625-648 (1999)
[9] Fleck, N. A.; Hutchinson, J. W.: A phenomenological theory for strain gradient effects in plasticity, Journal of the mechanics and physics of solids 41, 1825-1857 (1993) · Zbl 0791.73029 · doi:10.1016/0022-5096(93)90072-N
[10] Fleck, N. A.; Hutchinson, J. W.: Stain gradient plasticity, Advances in applied mechanics 33, 295-361 (1997) · Zbl 0894.73031
[11] Gao, H.; Huang, Y.; Nix, W. D.; Hutchinson, J. W.: Mechanism-based strain gradient plasticity – I. Theory, Journal of the mechanics and physics of solids 47, 1239-1263 (1999) · Zbl 0982.74013 · doi:10.1016/S0022-5096(98)00103-3
[12] Huang, Y.; Chen, J. Y.; Guo, T. F.; Zhang, L.; Hwang, K. C.: Analytic and numerical studies on mode I and mode II fracture in elastic – plastic materials with strain gradient effects, International journal of fracture 100, 1-27 (1999)
[13] Huang, Y.; Gao, H.; Nix, W. D.; Hutchinson, J. W.: Mechanism-based strain gradient plasticity – II. Analysis, Journal of the mechanics and physics of solids 48, 99-128 (2000) · Zbl 0990.74016 · doi:10.1016/S0022-5096(99)00022-8
[14] Huang, Y.; Qu, S.; Hwang, K. C.; Li, M.; Gao, H.: A conventional theory of mechanism-based strain gradient plasticity, International journal of plasticity 20, 753-782 (2004) · Zbl 1254.74019
[15] Huang, Y.; Zhang, F.; Hwang, K. C.; Nix, W. D.; Pharr, G. M.; Feng, G.: A model of size effects in nano-indentation, Journal of the mechanics and physics of solids 54, 1668-1686 (2006) · Zbl 1120.74658 · doi:10.1016/j.jmps.2006.02.002
[16] Huang, Y.; Zhang, F.; Saha, R.; Nix, W. D.; Hwang, K. C.; Qu, S.; Li, M.: Indentation of a hard film on a soft substrate: strain gradient hardening effects, International journal of plasticity 23, 25-43 (2007) · Zbl 1266.74032
[17] Li, M.; Chen, W. M.; Liang, N. G.; Wang, L. D.: A numerical study of indentation using indenters of different geometry, Journal of materials research 19, 73-78 (2004)
[18] Ma, Q.; Clarke, D. R.: Size-dependent hardness of silver single-crystals, Journal of materials research 10, 853-863 (1995)
[19] Mcelhaney, K. W.; Vlassak, J. J.; Nix, W. D.: Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments, Journal of materials research 13, 1300-1306 (1998)
[20] Niordson, C. F.; Hutchinson, J. W.: Non-uniform plastic deformation of micron scale objects, International journal for numerical methods in engineering 56, 961-975 (2003) · Zbl 1046.74013 · doi:10.1002/nme.593
[21] Nix, W. D.; Gao, H. J.: Indentation size effects in crystalline materials: a law for strain gradient plasticity, Journal of the mechanics and physics of solids 46, 411-425 (1998) · Zbl 0977.74557 · doi:10.1016/S0022-5096(97)00086-0
[22] Nye, J. F.: Some geometrical relations in dislocated crystals, Acta metallurgica 1, 153-162 (1953)
[23] Qin, J.; Huang, Y.; Hwang, K. C.; Song, J.; Pharr, G. M.: The effect of indenter angle on the microindentation hardness, Acta materialia 55, 6127-6132 (2007)
[24] Qin, J.; Huang, Y.; Xiao, J.; Hwang, K. C.: The equivalence of axisymmetric indentation model for three-dimensional indentation hardness, Journal of materials research 24, 776-783 (2009)
[25] Qiu, X.; Huang, Y.; Nix, W. D.; Hwang, K. C.; Gao, H.: Effect of intrinsic lattice resistance in strain gradient plasticity, Acta materialia 49, 3949-3958 (2001)
[26] Qu, S.; Huang, Y.; Nix, W. D.; Jiang, H.; Zhang, F.; Hwang, K. C.: Indenter tip radius effect on the nix – Gao relation in micro- and nanoindentation hardness experiments, Journal of materials research 19, 3423-3434 (2004)
[27] Qu, S.; Huang, Y.; Pharr, G. M.; Hwang, K. C.: The indentation size effect in the spherical indentation of iridium: a study via the conventional theory of mechanism-based strain gradient plasticity, International journal of plasticity 22, 1265-1286 (2006) · Zbl 1161.74342 · doi:10.1016/j.ijplas.2005.07.008
[28] Saha, R.; Xue, Z. Y.; Huang, Y.; Nix, W. D.: Indentation of a soft metal film on a hard substrate: strain gradient hardening effects, Journal of the mechanics and physics of solids 49, 1997-2014 (2001) · Zbl 1093.74501 · doi:10.1016/S0022-5096(01)00035-7
[29] Shi, M. X.; Huang, Y.; Gao, H.: The J-integral and geometrically necessary dislocations in nonuniform plastic deformation, International journal of plasticity 20, 1739-1762 (2004) · Zbl 1066.74511 · doi:10.1016/j.ijplas.2003.11.013
[30] Swadener, J. G.; George, E. P.; Pharr, G. M.: The correlation of the indentation size effect measured with indenters of various shapes, Journal of the mechanics and physics of solids 50, 681-694 (2002) · Zbl 1116.74300 · doi:10.1016/S0022-5096(01)00103-X
[31] Taylor, G. I.: The mechanism of plastic deformation of crystals. Part I. – theoretical, Proceedings of the royal society of London A 145, 362-387 (1934) · JFM 60.0712.02 · doi:10.1098/rspa.1934.0106
[32] Taylor, G. I.: Plastic strain in metal, Journal of the institute of metals 62, 307-324 (1938)
[33] Xue, Z.; Huang, Y.; Hwang, K. C.; Li, M.: The influence of indenter tip radius on the micro-indentation hardness, Journal of engineering materials and technology – transactions of the ASME 124, 371-379 (2002)
[34] Zhang, F.; Saha, R.; Huang, Y.; Nix, W. D.; Hwang, K. C.; Qu, S.; Li, M.: Indentation of a hard film on a soft substrate: strain gradient hardening effects, International journal of plasticity 23, 25-43 (2007) · Zbl 1266.74032
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.