Theory of Hardness and Measurements Applicable to Contact Problems

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Abstract
The theory of the hardness is reviewed and measurements are made with respect to the application of hardness data to contact problems, particularly for the determination of the real contact area. The ball indentation method is recommended, with hardness H defined as the ratio P/Sm between the contact load P and the mouth area Sm of the indentation. This hardness is not a single valued material constant but is a function of the specific depth D of the indentation, where D is the ratio between the actual depth and the radius of curvature of the indentation. The variation of H with geometric and metallurgical conditions is discussed together with some empirical formulae to describe the experimental results. The relation between the hardness and the yield point is discussed. A comparison with Brinell and Rockwell hardness numbers is also made. The indentation which two crossed cylindrical rods produce in each other is found to give nearly the same hardness as the ball indentation tests if D exceeds a certain value.

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