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Research Papers: Contact Mechanics

Multiple Normal Loading-Unloading Cycles of a Spherical Contact Under Stick Contact Condition

[+] Author and Article Information
Y. Zait, V. Zolotarevsky, Y. Kligerman

Department of Mechanical Engineering, Technion, Haifa 32000, Israel

I. Etsion1

Department of Mechanical Engineering, Technion, Haifa 32000, Israeletsion@technion.ac.il

1

Corresponding author.

J. Tribol 132(4), 041401 (Sep 13, 2010) (7 pages) doi:10.1115/1.4002103 History: Received April 06, 2010; Revised June 29, 2010; Published September 13, 2010; Online September 13, 2010

The multiple normal loading-unloading process of an elastic-plastic sphere by a rigid flat is analyzed using finite element method for stick contact condition and both kinematic and isotropic hardening models. The behavior of the global contact parameters as well as the stress field within the sphere tip is presented for several loading cycles. It was found that under stick contact condition, secondary plastification occurs even after the second loading cycle and that the hardening model used has little effect on the loading-unloading process. The cyclic loading process gradually converges into elastic shakedown.

FIGURES IN THIS ARTICLE
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Copyright © 2010 by American Society of Mechanical Engineers
Topics: Stress , Hardening , Cycles
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Figures

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Figure 1

A deformable sphere in contact with a rigid flat: just before loading (dashed lines), (a) during loading, and (b) after unloading shown in solid lines

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Figure 2

The (a) kinematic and (b) isotropic hardening models for a 2D stress field

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Figure 3

The finite element model

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Figure 4

The load-interference hysteretic loop during seven loading-unloading cycles following maximum loading to a dimensionless interference of ωmax∗=60

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Figure 5

Von Mises stress contours σe=Y at the end of the first four loading-unloading cycles with dimensionless maximum contact load Pmax∗=245: (a) loading and (b) unloading

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Figure 6

The evolution of the stress components σrr and σθθ at the point r/amax=1.15 located on the free sphere surface during the first unloading and the second loading phases for a maximum loading Pmax∗=245

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Figure 7

The radial location of the outer boundary of the secondary plastification annulus versus the number of loading-unloading cycles for maximum loading Pmax∗=245

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Figure 8

The evolution of the dimensionless von Mises stress σe/Y during seven loading-unloading cycles as a function of the contact load P∗ and the dimensionless equivalent strain εe/εY at three radial locations: r1=1.15amax (a, d), r2=1.35amax (b, e), and r3=1.55amax (c, f). The numbers shown in parts (d)–(f) indicate loading cycles.

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Figure 9

The dimensionless maximum contact area A/A0 as a function of loading cycles for maximum loading Pmax∗=40

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Figure 10

Stress-load hysteretic loops on the sphere surface just outside the maximum contact area during the (a) second to fourth, (b) fifth to seventh, and (c) eighth to tenth loading-partial unloading cycles between P∗=50 and P∗=180

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