Technical Notes - Hardness of Metals and Alloys

HARDNESS is one of the most common properties of metals and alloys but is one of the most difficult to define or express in terms of the fundamental units. In the Brinell or Vicker's hardness test, the hardness number N is defined as N = L/A where L is the load in kilograms and A is the area in mm'. This does not necessarily imply that a pressure of N kilograms per mm2 actually acts on the specimen.' It is essential that for a true comparison of hardness values the angle of indentation be kept constant,' a which is not done in the Brinell test. For this and other reasons, the Brinell hardness value is not based on a satisfactory physical concept.' The concept of hardness based on the work done per unit volume of indentation3-6 offers a simple and scientific definition. An attempt has been made here to develop this concept (at constant angle) and to compare the values so obtained with the Bhn for different metals and alloys. In Fig. 1 a vertical load L is applied to a compara- tively hard ball of diameter D creating an indentation of diameter 6 and depth h on the specimen S. The work done, W, is then given by W = So Ldh. [I] Since L is not independent of h, Honda and Takahasip and Matsumura" assumed different functions leading to equations which do not apply equallye to a wide variety of metals and alloys. A better relation is obtained from Meyer's Law L = ad" [2] where A and n are constants depending on the nature of the material but independent of the ball diameter D. From Fig. 1 it is obvious that h = R(l — cosq) and d = 2R sin 8.