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Technical Brief

A Solution of Rigid Perfectly Plastic Cylindrical Indentation in Plane Strain and Comparison to Elastic-Plastic Finite Element Predictions With Hardening

[+] Author and Article Information
Robert L. Jackson

Department of Mechanical Engineering,
Auburn University,
Auburn, AL 36849
e-mail: jacksr7@auburn.edu

Manuscript received June 6, 2017; final manuscript received November 15, 2017; published online December 6, 2017. Editor: Yonggang Huang.

J. Appl. Mech 85(2), 024501 (Dec 06, 2017) (6 pages) Paper No: JAM-17-1300; doi: 10.1115/1.4038495 History: Received June 06, 2017; Revised November 15, 2017

The indentation of flat surfaces deforming in the plastic regime by various geometries has been well studied. However, there is relatively little work investigating cylinders indenting plastically deforming surfaces. This work presents a simple solution to a cylindrical rigid frictionless punch indenting a half-space considering only perfectly plastic deformation. This is achieved using an adjusted slip line theory. In addition, volume conservation, pileup and sink-in are neglected, but the model can be corrected to account for it. The results agree very well with elastic-plastic finite element predictions for an example using typical steel properties. The agreement does diminish for very large deformations but is still within 5% at a contact radius to cylinder radius ratio of 0.78. A method to account for strain hardening is also proposed by using an effective yield strength.

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References

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Figures

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Fig. 1

Schematic of the contact area between a rigid cylinder indenting a flat surface

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Fig. 2

A stress–strain curve of a uniaxial tension test of a rigid-perfectly plastic material

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Fig. 3

A general schematic of slip-lines in a plane

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Fig. 4

Schematic of a cylindrical rigid indenter penetrating a rigid-perfectly plastic half-space (note that the slip lines are drawn approximately and are not exact representations)

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Fig. 5

The finite element mesh and the rigid cylinder surface (lower left)

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Fig. 6

An enlarged view of the finite element mesh near the contact region

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Fig. 7

Comparison of the FEM predicted average contact pressure and the analytical derived equation based on slip-line theory

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Fig. 8

Error between the FEM and Eq. (18) predictions as a function of normalized indentation depth

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Fig. 9

Enlarged view of the error between the FEM and Eq. (18) predictions as a function of normalized indentation depth

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Fig. 10

The error between the FEM predictions and Eq. (18) as a function of b/R, highlighting the influence of pileup

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Fig. 11

The FEM predicted von Mises stress distribution for a small indentation depth: (a) δ/R = 0.002, and a large one and (b) δ/R = 0.26. Note that these are for the Sy = 200 MPa case.

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Fig. 12

Comparison of the FEM predicted average contact pressure and the analytical derived equation when bilinear strain hardening is considered

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