The determination of yield strength from hardness measurements
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HARDNESStests have always appeared attractive as a means for estimating other mechanical properties of metals. Tabor' has shown that the ultimate strength of a material, ~u, is given by* *Units of yield strength and hardnessare kg per sq mm.
(ru : ~.9
[i-(m-2>] [I '5- (m-2) I -211J
[1]
where H is the Diamond pyramid hardness and m is the Meyer's hardness coefficient. It has been shown theoretically and confirmed experimentally' that = m - 2
[2]
where n is the strain hardening coefficient. Also, the true stress-strain c u r v e in t h e p l a s t i c r e g i o n c a n b e approximated by a = KEn
[3]
where (r is the stress, c the true strain and K is a constant. Using Eqs. [2] and [3] and the additional information that H/2.9 is approximately equivalent to the stress at a strain of 8 pct during a tensile test, Tabor I derived Eq. [I]. Since H and m - 2 can be obtained from hardness measurements, an indication of ultimate tensile strength may also be obtained. However, there appear to have been no attempts to obtain a general expression relating the 0.2 pct offset yield strengths of metals to hardness. Atkins and Tabor 9 derived compressive stress strain curves for steel and copper from hardness measurements but could not extend the curves below 4 pct strain. Devenpeck and Weinstein ~~indicated the possibility of obtaining a proportional limit from hardness measurements but did not derive a specific relationship. A good correlation between the 0.2 pct offset yield strength and hardness for many different steels in the quenched and tempered condition has been established2 but the reasons for the correlation were not investigated, nor was the treatment extended to other metals. It has also been showns that the yield stress of a severely cold worked material should be given by % -- H / 3
[4]
J. R. CAHOON is Associate Professor, Metallurgical Science Laboratory, Department of Mechanical Engineering, University of Manitoba, Winnepeg, Manitoba. W. H. BROUGHTON and A. R. KUTZAK, formerly Students at the University of Manitobe, are now with Fisher Controls Company, Woodstock, Ontario, and Mobile Oil Company, Calgary, Alberta, respectively. Manuscript submitted June 22, 1970. METALLURGICAL TRANSACTIONS
and this relation has been verified experimentally to some degree, but for this derivation it is assumed that the strain hardening coefficient, n, equals zero. However, Marcinkowski et al. 4 showed for annealed Fe-Cr alloys which exhibited some strain hardening that ay ~ H / 5 . Speich and Warlimonts found that ay ~ H/4 for some low carbon martensites and Fe-Ni alloys. The present investigation was initiated in an attempt to derive a general expression which correlates the 0.2 pct offset yield strength with hardness for various materials and which would include the strain hardening coefficient since it seems reasonable that this coefficient would affect the yield strength versus hardness correlation. Also, it is possible that the strengthening mechanism could affect the correlation and therefore it was decided to stud
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