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Surface treatment and tribology

Which statement correctly describes the empirical law of friction (the Amontons–Coulomb law) that often holds for dry sliding friction between metals?

  1. AFriction force is proportional to the apparent contact area, so doubling the contact area at the same load roughly doubles the friction force
  2. BFriction force is roughly proportional to the normal load and hardly depends on the apparent contact area
  3. CFriction force increases in proportion to the sliding speed, and static friction is smaller than kinetic friction
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Answer: B. Friction force is roughly proportional to the normal load and hardly depends on the apparent contact area

Under the Amontons–Coulomb law, the friction force F is proportional to the normal load W (F = μW) and depends little on the apparent contact area or the sliding speed. A surface carries tiny asperities, and only their tips actually touch. Because the asperities deform plastically to support the load, the real area of contact equals the load divided by the hardness and is proportional to the load regardless of the apparent area. The friction force is proportional to this real area of contact, so it ends up proportional to the load. The idea that friction scales with the apparent area confuses the real area of contact with the apparent area. Proportionality to speed is a property of viscous resistance in fluids, and in dry friction the static friction coefficient is generally larger than the kinetic one.

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  1. A flat steel block (indentation hardness H = 2.0 GPa) rests on a plate of the same steel, and a normal load of 1.0 kN is applied over an apparent contact area of 10 cm². Assuming every contacting asperity deforms plastically and estimating the real area of contact as Ar = W/H, which is closest to its fraction of the apparent contact area?
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