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I.

INTRODUCTION

SINCE 1900 many hardness tests have been proposed which have in common the definition of hardness itself. 1,2,3 This definition apparently originated with Brinell4 and is of the form L H = -A

[1]

where H, the hardness number, is equal to the applied load divided by the projected area. Some tests use the actual indented area while others use the projected area. In either case, the area is typically computed after measuring a characteristic distance, d, (diameter, diagonal, depth, etc.). Equation [1] then takes the form L H-

cd 2

[2]

where c is a constant depending on the chosen indenter geometry. To the author's knowledge, there is no fundamental reason for defining hardness in this fashion except to obtain units of stress. This definition has served quite well for hardness tests performed using loads of 200 g and higher. However, hardness tests performed at lower loads, called microhardness tests, have lost significance because it has been repeatedly shown that microhardness numbers depend on applied load. Therefore, it is necessary to state this load along with the hardness number. This situation is obviously no better than quoting both L and A. Hardness tests in the load range 0 to tOO g generally produce curves resembling those shown in Figure 1. The abscissa could have been applied load, indented area, diagonal length, etc. with little change in the character of the plot. At large indentation depths, load or area, the hardness curve approaches a finite limit. The vertical lines are intended to show that scatter in hardness values increases significantly as load is decreased. It is this scatter and the above mentioned dependence of hardness on load that has caused investigators to proceed with deserved caution or to ignore the test altogether. If it were not for these problems, the microhardness test would still be useful, especially for the many surface modified materials emerging today. Reported here is a

Monte Carlo simulation of microhardness testing which explains the aforementioned behavior for very small loads or shallow indentations. In addition, a new definition of hardness is suggested which has no load dependence and which does not suffer as badly from experimental error at low applied loads. Finally, a discussion of the utility of this new approach to microhardness testing is provided.

II.

CRITIQUE OF CONVENTIONAL DEFINITION OF HARDNESS

Meyer~ was the first to suggest that the load is related to d by the equation [3]

L = ad"

At loads below 100 g it has been found6 that n is typically less than 2.0. Consequently, the general trend to increasing hardness numbers as load or d is decreased should come as

IJIll l,,,,,,

-r

cd

CO ~J z rr

|

0 E G. YOST is Member, Technical Staff, Sandia National Laboratories, Albuquerque, NM 87185. Manuscript submitted June 14, 1982. METALLURGICALTRANSACTIONS A

i,,,,.._

"INDENTATION

DEPTH

Fig. 1--Microhardness test results plotted v s indentation depth showing an increase in hardness and scatter near the specimen surface. VOLUME 14A, MA