Khruschov's rule and the abrasive wear resistance of multiphase solids

Khruschov has pointed out that the abrasive wear resistance of composites can often be expressed as ∑_iυ_i?_i where υ_i and ?_i are the volume fraction and wear resistance of the ith phase. This expression accurately predicts the wear resistance of metal composites but not of composites of metals and ceramic materials. While the volume abrasive wear rates of metals are believed to be proportional to the applied load, there is evidence that the volume wear rates of ceramic materials can be non-linear functions of both the applied load and the area of the abraded surface. The abrasive wear resistance of a model composite system is considered for steady state wear. For this system it can be shown that the relationship suggested by Khruschov is realized if the volume wear rates of the phases constituting the composite are proportional to the load. However, the relationship does not hold if the volume wear rates of the individual phases depend on the area or are non-linearly related to the load.