The hardness of abrasives is defined in terms of the static indentation hardness as determined by Knoop or Vickers hardness test [MALK08]. Chip formation needs a high degree of grit hardness and toughness [KLOC05a]. Moreover, cutting edge sharpness over a longer period is affected by the grit hardness and wear resistance. There is no direct physical relation between hardness and toughness, but commonly harder abrasive grains are more friable [MALK08].
Jackson gives the rule of thumb that a grit has to be at least 20 % harder than the workpiece to be suitable as abrasive [JACK11, p. 9]. He regards hardness as the key factor in controlling attritious grit wear (see Sect. 6.4.2 “Grit Surface Wear”). In addition, hardness can change with the temperature, meaning temperature hardness has to be also considered in tool use [JACK11, p. 9].