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Rolling contact deformation of 1100 aluminum disks

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Abstract

The plastic deformation produced by pure, two dimensional, rolling contacts has been studied by subjecting 1100 aluminum disks to repeated contacts with well-defined relative peak contact pressures in the range 2 ≤P 0/k c ≤ 6.8. Two microstructural conditions are examined: as-received (warm worked) and annealed, displaying cyclic softening and cyclic hardening, respectively. Measurements of the distortion of wire markers imbedded in the rims, microhardness values of the plastically deformed layer, and changes in disk radius and width are reported. These are used to evaluate the plastic circumferential, radial, and axial displacements of the rim surface and the depth of the plastically deformed layer. These features are compared with the classical, elastic-quasi plastic analysis of rolling, and with recent elastic-plastic finite element calculations. The results show that the rim deformation state approaches plane strain when the disk width-to-Hertzian half contact width-ratioB/w ≥ 200. The presence of a solid lubricant has no detectable influence on the character of the plane strain deformation. The measurements of the per cycle forward (circumferential) displacements for the two conditions are self-consistent and agree with the finite element calculations when the resistance to plastic deformation is attributed to the instantaneous cyclic yield stress, but not when the resistance is identified with the initial monotonie yield stress. At the same time, the extent of the plastic zone is 5× greater than predicted by the analyses. These and other results can be rationalized by drawing on the special features of the resistance to cyclic deformation. They support the view that the deformation produced by theN th rolling contact is governed by the shape of the stress-strain hysteresis loop after the corresponding number of stress-strain cycles which depends on the cycle strain amplitude, degree of reversibility, and the strain path imposed by the contact loading at different depths.

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Abbreviations

B :

Disk width.

δ x , δy, δz :

The accumulated, plastic, circumferential, radial, and axial displacements at the rim surface; note: S, is also referred to as the forward displacement.

δy/yo:

A measure of the accumulated radial compression strain of the plastic zone.

2δ z /B :

A measure of the accumulated axial extension strain of the plastic zone.

dδ x :

The instantaneous, net, per cycle, circumferential displacement at the rim surface. Estimates derived from the measurements were obtained by fitting a curve _ to the δx, -N data and differentiating.

\(d\overline \delta _x \) :

The average, net, per cycle, circumferential displacement at the rim surface.

d′δ x :

The relaive, net, per cycle, circumferential displacement at the rim surface defined by Hamilton:11 dδ x = (dδ x /w)(G/p o).

d′δ x :

The relative, net, per cycle, circumferential displacement at the rim surface employed here:dδ x = (dδx/w)(G/kc) = d°x(p0/k).

d′δ x MJ:

The d′δx-values derived from the analysis of Merwin and Johnson.8

d′δxBHR:

The d′δx-values derived from the finite element calculations of Bhargava, Hahn, and Rubin.9

E :

Young's Modulus.

G :

Elastic shear modulus.

k :

Plastic shear yield strength under monotonic loading;k c = σc/√3.

v :

Poisson's ratio.

P :

Contact load per unit length.

p :

Contact pressure;p =p o[l−x2/w2]0.5.

p o :

Peak Hertzian contact pressure,p o =2P/πw.

p :

Average pressure during flow in plane strain compression.

R 1 :

Radius of the plastically deforming rim.

R 2 :

Radius of the contacting rolling element.

σ o :

The 0.2 pct-offset or 0.02 pct offset tension or compression yield strength for monotonie loading.

σ c :

The 0.2 pet-offset or 0.02 pct offset tension or compression yield strength for repeated cyclic loading.

μ :

Coefficient of friction.

x,y,z :

Coordinates of a point in the rim relative to position of the contact (see Figure 2(a)).

y o :

Extent of the active plastic zone below the rim surface (see Figure 2(a)).

2w :

The Hertzian contact width (see Figure 2(a)).w = {4P/π}[(l -v 2 1]/E) + (1 -v 2 2/E)/ l/R1 + l/R2)1/2 where the subscripts 1 and 2 refer to the rim and contacting rolling element, respectively.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, Vanderbilt University, 37235, Nashville, TN

    G. T. Hahn (Professor)

  2. New Departure Hyatt Division, General Motors Corporation, 44870, Sandusky, OH

    Q. Huang (Engineer)

Authors
  1. G. T. Hahn
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  2. Q. Huang
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Hahn, G.T., Huang, Q. Rolling contact deformation of 1100 aluminum disks. Metall Trans A 17, 1561–1572 (1986). https://doi.org/10.1007/BF02650092

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