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Technical Brief

Plastic Zone Size at Sharp Indentation of Classical Elastic–Plastic Materials: Behavior at Ideally Plastic Hardening

[+] Author and Article Information
Per-Lennart Larsson

Department of Solid Mechanics,
Royal Institute of Technology,
Stockholm SE-10044, Sweden
e-mail: pelle@hallf.kth.se

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received June 8, 2015; final manuscript received September 17, 2015; published online October 12, 2015. Assoc. Editor: Peter W. Chung.

J. Eng. Mater. Technol 138(1), 014502 (Oct 12, 2015) (3 pages) Paper No: MATS-15-1131; doi: 10.1115/1.4031736 History: Received June 08, 2015; Revised September 17, 2015

Sharp indentation problems are examined based on finite element methods (FEMs) and self-similarity considerations. The analysis concerns classical elastic–plastic materials with low, or no, strain-hardening and especially the details of the behavior of the size of the plastic zone are at issue. The results are correlated using a single parameter, comprising both geometrical and mechanical properties, and compared with previously presented semi-analytical findings. The numerical analysis is restricted to cone indentation of elastic-ideally plastic materials.

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References

Johnson, K. L. , 1970, “ The Correlation of Indentation Experiments,” J. Mech. Phys. Solids, 18(2), pp. 115–126. [CrossRef]
Johnson, K. L. , 1985, Contact Mechanics, Cambridge University Press, Cambridge, UK.
Tabor, D. , 1951, Hardness of Metals, Cambridge University Press, Cambridge, UK.
Atkins, A. G. , and Tabor, D. , 1965, “ Plastic Indentation in Metals With Cones,” J. Mech. Phys. Solids, 13(3), pp. 149–164. [CrossRef]
Bhattachharya, A. K. , and Nix, W. D. , 1988, “ Finite Element Simulation of Indentation Experiments,” Int. J. Solids Struct., 24(9), pp. 881–891. [CrossRef]
Bhattachharya, A. K. , and Nix, W. D. , 1988, “ Analysis of Elastic and Plastic Deformation Associated With Indentation Testing of Thin Films on Substrates,” Int. J. Solids Struct., 24(12), pp. 1287–1298. [CrossRef]
Laursen, T. A. , and Simo, J. C. , 1992, “ A Study of the Mechanics of Microindentation Using Finite Elements,” J. Mater. Res., 7(3), pp. 618–626. [CrossRef]
Giannakopoulos, A. E. , Larsson, P.-L. , and Vestergaard, R. , 1994, “ Analysis of Vickers Indentation,” Int. J. Solids Struct., 31(19), pp. 2679–2708. [CrossRef]
Mesarovic, S. D. , and Fleck, N. A. , 2000, “ Spherical Indentation of Elastic–Plastic Solids,” Int. J. Solids Struct., 37, pp. 7071–7091. [CrossRef]
Mesarovic, S. D. , and Fleck, N. A. , 1999, “ Frictionless Indentation of Dissimilar Elastic–Plastic Spheres,” Proc. R. Soc. London, Ser. A, 455(1987), pp. 2707–2728. [CrossRef]
Larsson, P.-L. , 2001, “ Investigation of Sharp Contact at Rigid Plastic Conditions,” Int. J. Mech. Sci., 43(4), pp. 895–920. [CrossRef]
Larsson, P.-L. , 2004, “ On the Mechanical Behavior of Global Parameters in Material Characterization by Sharp Indentation Testing,” J. Test. Eval., 32(4), pp. 310–321.
Mata, M. , Casals, O. , and Alcala, J. , 2006, “ The Plastic Zone Size in Indentation Experiments: The Analogy With the Expansion of a Spherical Cavity,” Int. J. Solids Struct., 43(20), pp. 5994–6013. [CrossRef]
ABAQUS, 2008, ABAQUS Manual v.6.7, Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, RI.
Larsson, P.-L. , 2006, “ Modelling of Sharp Indentation Experiments: Some Fundamental Issues,” Philos. Mag., 86(33–35), pp. 5155–5177. [CrossRef]
Rydin, A. , and Larsson, P.-L. , 2012, “ On the Correlation Between Residual Stresses and Global Indentation Quantities: Equi-Biaxial Stress Field,” Tribol. Lett., 47(1), pp. 31–42. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Schematics of the cone indentation test, top and side views, with Cartesian coordinates Xi. The indentation depth h is shown.

Grahic Jump Location
Fig. 2

Definition of the two plastic zone radius parameters (ra and rh)

Grahic Jump Location
Fig. 3

Cone indentation of elastic-ideally plastic materials. Nondimensionalized plastic zone radius parameters, r¯a = ra/a and r¯h = rh/a, as function of the parameter Λ in Eq. (1). (o) r¯a derived from finite element simulations. (•) r¯h derived from finite element simulations. (—) r¯a determined from Eqs. (9) and (10). (- - - -) r¯h determined from Eqs. (9) and (10).

Grahic Jump Location
Fig. 4

Cone indentation of elastic-ideally plastic materials. Nondimensionalized plastic zone radius parameters, r¯a = ra/a, r¯h = rh/a, and r¯p = rp/a, as function of the parameter Λ in Eq. (1). (—) r¯a determined from Eq. (9). (- - - -) r¯h determined from Eq.(9). (o) r¯p as defined by Johnson [1,2] and determined from Eq. (11) with ν = 0.3.

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