##
**The mechanics of size-dependent indentation.**
*(English)*
Zbl 0967.74043

Summary: Indentation tests at scales of the order of one micron have shown that measured hardness increases significantly with decreasing indent size, a trend at odds with the size-independence implied by conventional plasticity theory. In this paper, strain gradient plasticity theory is used to model materials undergoing small-scale indentations. Finite element implementation of the theory as it pertains to indentation modeling is briefly reviewed. Results are presented for frictionless conical indentations. A strong effect of including strain gradients in the constitutive description is found with hardness increasing by a factor of two or more over the relevant range of behavior. The results are used to investigate the role of the two primary constitutive length parameters in the strain gradient theory. The study indicates that indentation may be the most effective test for measuring one of the length parameters.

### 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) |

### Keywords:

small strains; small rotations; size-dependent indentation; hardness; elastic-plastic material; strain gradient plasticity; small-scale indentations; frictionless conical indentations
PDF
BibTeX
XML
Cite

\textit{M. R. Begley} and \textit{J. W. Hutchinson}, J. Mech. Phys. Solids 46, No. 10, 2049--2068 (1998; Zbl 0967.74043)

Full Text:
DOI

### References:

[1] | Acharya, A. and Bassani, J. L. (1996) On non-local flow theories that preserve the classical structure of incremental boundary value problems. In IUTAM Symposium on Micromechanics of Plasticity and Damage, ed. A. Pineau and A. Zaoui, pp. 3-10. Kluwer Academic Publishers. |

[2] | Acharya, A. and Bassani, J. L. (1997) Incompatibility and crystal plasticity. To be published. · Zbl 0963.74010 |

[3] | Atkinson, M., J.mater. res, 10, 2908-2915, (1995) |

[4] | Atkins, A.G.; Tabor, D., Journal of the mechanics and physics of solids, 13, 149-164, (1965) |

[5] | Bhattacharya, A.K.; Nix, W.D., International journal of solids and structures, 27, 1047-1058, (1991) |

[6] | Brown, L. M. (1997) Transition from laminar to irrotational motion in plasticity. To be published. · Zbl 0907.73025 |

[7] | De Guzman, M.S.; Neubauer, G.; Flinn, P.; Nix, W.D., Mater. res. symp. proc, 308, 613-618, (1993) |

[8] | Doerner, M.F.; Nix, W.D., J. mater. res, 1, 601-609, (1986) |

[9] | Fleck, N.A.; Hutchinson, J.W., Journal of the mechanics and physics of solids, 41, 1825-1857, (1993) |

[10] | Fleck, N. A. and Hutchinson, J. W. (1997) Strain gradient plasticity. In Advances in Applied Mechanics, ed. J. W. Hutchinson and T. Y. Wu, Vol. 33. Academic Press, New York. · Zbl 0894.73031 |

[11] | Fleck, N.A.; Muller, G.M.; Ashby, M.F.; Hutchinson, J.W., Acta metallica materiala, 42, 475-487, (1994) |

[12] | Gane, N.; Cox, J.M., Philos. mag, 22, 881-891, (1970) |

[13] | Giannakopoulos, A.E.; Larsson, P.-L., Mech. matls, 25, 1-35, (1997) |

[14] | Johnson, K.L., Journal of the mechanics and physics of solids, 18, 115-126, (1970) |

[15] | Ma, Q.; Clarke, D.R., J. mater. res, 10, 853-863, (1995) |

[16] | McElhaney, K. W., Vlassak, J. J. and Nix, W. D. (1997) J. Mater. Res., to be published. |

[17] | Mindlin, R.D., Arch. ration. mech. anal, 16, 51-78, (1965) |

[18] | Nix, W.D., Mat. sci. and engr. A, 236, 37-44, (1997) |

[19] | Pethica, J.B.; Hutchings, R.; Oliver, W.C., Philos.mag, 48, 593-606, (1983) |

[20] | Poole, W.J.; Ashby, M.F.; Fleck, N.A., Scriptametall. mater, 34, 559-564, (1996) |

[21] | Rubenstein, C., Journal of applied mechanics, 48, 796, (1981) |

[22] | Samuels, L. E. (1986) Microindentation Techniques in Materials Science and Engineering, ed. P. J. Blau and B. R. Law, pp. 5-24. ASTM STP 880, American Society for Testing and Materials, Philadelphia, PA. |

[23] | Shu, J. and Fleck, N. A. (1996) The prediction of a size effect in micro-indentation. InternationalJournal of Solids and Structures, submitted. |

[24] | Shu, J. Y., King, W. E. and Fleck, N. A. (1997) Finite elements for materials with strain gradient effects. International Journal of Numerical Methods in Engineering, submitted. · Zbl 0943.74072 |

[25] | Smyshlaev, V.P.; Fleck, N.A., Journal of the mechanics and physics of solids, 44, 465-496, (1996) |

[26] | Specht, B., International journal of numerical methods in engineering, 26, 705-715, (1988) |

[27] | Stelmashenko, N.A.; Walls, M.G.; Brown, L.M.; Miman, Y.V., Acta metallica materiala, 41, 2855-2865, (1993) |

[28] | Toupin, R.A., Arch. ration. mech. anal, 11, 385-414, (1962) |

[29] | Xia, Z.C.; Hutchinson, J.W., Journal of the mechanics and physics of solids, 44, 1621-1648, (1996) |

[30] | Zienkiewicz, O. C. and Taylor, R. L. (1989) The Finite Element Method : Volumes I and II, 4th edn. McGraw-Hill, London. |

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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.