This paper presents an overview of the hardness differential required for abrasion. Empirically, the abrasive must be at least 1.2 times harder than the worn surface if it is to produce a scratch. This value has been determined theoretically using slip-line field modeling, which assumes rigid-plastic mechanical behavior, an assumption that is inadequate for most abrasive particles. Two approaches using elastic-plastic models and three tribological pairs with similar ratios of abrasive hardness to worn material hardness were tested to gain an understanding of the hardness differential required for abrasion. The analysis showed that the ratios of the property of the abrasive to the property of the worn surface did not change with the model used when the mechanical behavior of the materials was similar. However, when the behavior of the materials was very dissimilar—as is often the case in abrasive processes—the ratios varied greatly depending on the model used, showing that there is a need for models to describe the hardness differential required for abrasion.
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