The equation V = KWL/H, stating that wear volume V is proportional to the normal load W and sliding distance L and inversely proportional to hardness H. K is the wear coefficient, which varies widely with the wear mechanism.
Japanese name: アーチャードの摩耗式
Archard wear equation appears in 1 practice question across 1 topic, including Surface treatment and tribology.
Archard assumed that the real contact spots between two sliding surfaces produce wear debris with a certain probability during sliding. The real area of contact equals the load W divided by the hardness H, so the number of contact spots is proportional to W/H. The distance slid before a contact spot is replaced is about the size of the spot, so the number of opportunities to form wear debris over a sliding distance L is proportional to L. Putting these together, the wear volume can be written V = KWL/H. The dimensionless wear coefficient K has the meaning of the probability that a contact spot becomes wear debris.
K is large, about 10⁻⁴ to 10⁻², for unlubricated adhesive wear between metals of the same kind, and falls to about 10⁻⁶ to 10⁻⁵ for mild wear protected by oxide films and to about 10⁻⁸ to 10⁻⁶ under good lubrication. In practice, the specific wear rate k = V/(WL), which lumps K/H together without separating out the hardness, is often used, expressed in mm³/(N·m). Because the specific wear rate can also be used for polymers, composites and coatings, whose hardness is hard to define, it is widely used to compare wear resistance. When comparing values, it is important to match the test method and conditions.
The Archard equation is useful for life estimates and material comparisons in the mild-wear regime, where wear is proportional to load and sliding distance. However, above certain loads or speeds, frictional heat can break down oxide films or adhesion can spread, causing a transition to severe wear, with wear larger by orders of magnitude. The wear rate also changes during the initial running-in period. K should therefore be determined in tests close to the actual operating conditions, and the equation should be used after confirming where the wear regime changes.
Answer: B. About 2.5 mm³, and doubling the load roughly doubles it
V = KWL/H = 1.0×10⁻⁴×50×1000/(2.0×10⁹) = 2.5×10⁻⁹ m³ = 2.5 mm³. The Archard equation assumes that a number of contact spots proportional to the real area of contact W/H produce wear debris a number of times proportional to the sliding distance, so the wear volume is proportional to the load and the sliding distance and inversely proportional to the hardness. Doubling the load doubles the real area of contact even if the apparent contact area stays the same, so the wear volume also roughly doubles. About 2.5×10⁻³ mm³ is the value calculated with the sliding distance taken as 1 instead of 1000 m. K varies widely, from about 10⁻⁸ to 10⁻², with the wear mechanism and conditions, so it is determined by experiment.
In a harder material, the real area of contact needed to support the same load is smaller, so there are fewer contact spots producing wear debris. In abrasive wear too, a surface harder than sand grains and the like is hard to cut. Hard but brittle materials, however, can wear by cracking.
In the Archard equation, the wear volume does not depend on the apparent area. Enlarging the area lowers the pressure and temperature, however, making it easier to stay in the mild-wear regime, so in practice life can be extended. For the same volume, a larger area also means a shallower wear depth.
In a pin-on-disk or ball-on-disk test, the specimen is slid under a set load and sliding distance, and the wear volume is found from the mass loss or the shape of the wear track. Dividing that volume by the load and sliding distance gives the specific wear rate, and multiplying by the hardness gives the dimensionless wear coefficient.
The Archard equation assumes that a number of contact spots proportional to the real area of contact W/H produce wear debris a number of times proportional to the sliding distance, so the wear volume is proportional to the load and the sliding distance and inversely proportional to the hardness.
In a pin-on-disk test, a pin of hardness H = 2.0 GPa is loa…Real area of contact Abrasive wear Adhesive wear Carburizing Electroless nickel plating Nitriding Stribeck curve