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Leakage of Metallic Seals: Role of Plastic Deformations

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Abstract

I study the influence of plastic deformations on the leakage of metallic seals. The solids are assumed to deform elastically as long as the stress is below the penetration hardness of the material, and yield plastically when the local stress reaches the penetration hardness. The metal surfaces are assumed to exhibit self-affine fractal surface roughness. We use the Persson contact mechanics theory and the Bruggeman effective medium theory to estimate the leak rate of the plastically deformed interface.

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Notes

  1. It is assumed that the critical constriction can be approximated by a rectangular pore with a quadratic cross section (side w) in the xy plane, and the height \(u_{\mathrm{c}}\) (in the z-direction), which is much smaller than w. The condition \(u_{\mathrm{c}}\) ≪  w is predicted by contact mechanics theory and also found in exact numerical simulations. However, the assumption of a quadratic pore cross section in the xy plane is never exact and this introduces another correction factor \(\alpha \) in (1), determined by the exact shape of the critical constriction. Thus, very close to the percolation threshold, as observed with increasing pressure when all the surface roughness is included in the study, Dapp and Müser have shown in Ref. [17] that the width of the critical junction scales as \(\sim (1-p/p_{\mathrm{c}})^{0.60}\), while the length scales with \(\sim (1-p/p_{\mathrm{c}})^{0.45}\), where p is the nominal contact pressure and \(p_{\mathrm{c}}\) the pressure at percolation (see also [18]). However, in our theory one is usually not close to the percolation threshold where the fluid leakage would vanish. When the contact is studied (at any given nominal contact pressure p) at the magnification where the non-contact area percolate, i.e., for \(A(\zeta )/A_{0} \approx 0.42\), there is usually still roughness at shorter length scales, and when this is included the pore will “open up”, and we will in general no longer be close to percolation threshold. Thus the strong elongation of the critical constriction which is expected close to the true percolation threshold (which is observed with an increase in the nominal contact pressure when all the roughness is included in the study) will not exist in most practical cases. In the Bruggeman theory which I actually use in the calculations the problem of the shape of the critical constriction does not enter!

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Acknowledgments

This work was performed within a Reinhart–Koselleck project funded by the Deutsche Forschungsgemeinschaft (DFG). We would like to thank DFG for the project support under the reference German Research Foundation DFG-Grant: MU 1225/36-1. The research work was also supported by the DFG-Grant: PE 807/10-1. This work is supported in part by COST Action MP1303.

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  1. PGI-1, FZ Jülich, Jülich, Germany

    B. N. J. Persson

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Persson, B.N.J. Leakage of Metallic Seals: Role of Plastic Deformations. Tribol Lett 63, 42 (2016). https://doi.org/10.1007/s11249-016-0728-1

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