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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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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