C-'

1 ' -T)"' A ' uWADC TECHNICAL REPORT 55-114C-'3 ITHE RELATIONSHIP OF HARDNESS MEASUREMENTS TOTHE TENSILE AND COMPRESSION FLOW CURVESR. E. LENIIARTGENERAL ELECTRIC RESEAIRClH LABIORATORYJUNE 1955,AETWRIGHT AIR DEVELOPMENT CENTERrov-NOTICESWhen Government drawings, specifications, or other data are used for any purpose otherthan in connection with a definitely related Government procurement opcrattion, the United StatesGovernment thereby incurs no responsibility nor any obligation whatsoever; and the fact thatthe Government may have formulated, furnished, Or in any way supplied the saia drawings,.specifications, or other data, is not to be regarded by implication or otherwise as in any mannerlicensing the holder or any other person or , or conveying any rights or permissionfo manufacture, use, or sell any patented invention titht may in any way be related requesters may obtain copies of this report from the ASTIA Document ServiceCenter, Knott Building, Dayton 2, report has been released to the Office of Technical Services.

2 U. S. Department of Com-merce, Washington 25, D. C., for sale to 'the general of WADC Technical Reports and Technical Notes should not be returned to the WrightAir Development Center unless return is required by security considerations, contractual obliga-tions, or notice on a specific ' 1 WADC TECHNICAL REPORT 55-114 THE RELATIONSHIP OF HARDNESS MEASUREMENTS TOTHE TENSILE AND COMPRESSION FLOW CURVESR. E. LENHARTGENERAL 2 LECTRIC RESEARCH LABORATORYJUNE 1955 ,%. ,AERONAUTICAL RESEARCH LABORATORYCONTRACT No. AF 33(616)-2120 TASK No. 70527 PROJECT No. 7351 "METALLIC MATERIALS"WRIGHT AIR DEVELOPMENT CENTERAIR RESEARCH AND DEVELOPMENT COMMANDUNITED STATES AIR FORCE -WRIGHT.

3 ' 71 TTERSON AIR FORCE BASE, OHIOC arpenter Litho & Prtg. Co., springfield, 1956 -%.4*%- :N.,.' K T .;r '7.'e ''' ..e . - ,. '' ' " , ..' ''' ' ' "..,.."".'-\-'FOREIMRDThis report was prepared by the General Electric Company ResearchLaboratory under United States Air Force Contract No. AF 33(616) IAThis contract was initiated under Task 70627, "Deformation Mechanismsof Metals," a part of Project 7351, qMetallic Materials," and wasadministered under the direction of the Aeronautical Research Labor-story, Directorate of Research, Wright Air Development Center, withMajor A. A. Marston as Task Scientist. tt 'Y,,.- ,..WADC-TR-55-1149~~ *1 'oABSTRACT.

4 The approximation of a uniaxial tensile stress flow '..-curve from hardness measurements is possible by utilizingcertain empirical conversion constants. Agreement of thetensile and hardness testing methods is possible upon metalssuch as aluminum, copper, and steel. However, magnesium___ is not amenable to such a conversion of testing presence of profuse twinning at low stress levels isbelieved to be the reason for unfavorable results in magnesiumI .PUBLICATION REVIEWThis report has been reviewed and is THE COMMANDERt-M.;-.' .. LINGARDC olonel, USAFC hief, Aeronautical Research LaboratoryDirectorate of Research' -:I -rdI'.. WADC-TR-55-114 iiio.

5 '-. - ,--.',.- ,; .,'.."- .- ..-"- ,: -''.-'''''''.."" """'''L "''" "- . - ' . % .% % ' % ..' .% .% % ..~ .. % -' -..-i: .I* .- ..: ., , b , , :- : .. , .. -., , ..-" " S *-TABLE OF CONTENTSPageIntroduction ..Background ..Experimental Procedures and Results ..3 ,..6 Conclusions ..9 ..0 .. 10 LIL4- WADC-TR-55-114 iv-A. ;THE RELATIONSHIP OF HARDNESS MEASUREMENTS TO THETENSILE AND COMPRESSION FLOW CURVESR. E. Lenhart . ~ introduction -r-llVcHardness, in its most familiar connotation, is the resistanceof a material to local inaentation. When the size and depth of theindentation is measured, and the load that produced the indentation isspecified, the hardness can be define in a quantitative manner.

6 TheBrinell, Vickers, and Rockwell(1, 2, 3) hardness testing methods arethe three most common procedures for obtaining quantitative hardnessSvalues upon metals. These testing machines impress either a hardenedball, a diamond pyramid, or a diamond cone into the metal. The resultsare essentially a measure of the resistance to plastic deformation of themetal by external familiar uniaxial stress tensile test is also a measure ofthe resistance to plastic deformation of a metal by external relationship of the hardness to the tensile method of producing plasticdeformation has in general been ill-defined. The complex nature of thestress distribution during plastic flow in the hardness test precludes a --simply derived relationship to the tensile test.

7 However, Tabor(4, 5,6)has developed an empirical correlation that relates the two and enablesa conversion of one measurement to the other. The usefulness of thiscorrelation depends upon its exactitudes and its limitations. This report J6presents data intended to corroborate the work of Tabor and to specify"a major limitation of his empirical mean pressure between the surface of the indenter and theindented metal is equal to the ratio of the load to the projected area of* the indentation. Meyer, in 1908, was the first to propose this relation-ship, and it is now referred to as the Meyer hardness. Thus,Hn i~ -W- (1)ird2 WADC-TR-55-114* where, Hm is the Meyer hardness number, W is the applied load, and dis the diameter of the indention.

8 It is interesting to note that the Meyerhardness has the dimensions of stress.!t ",The relationship between the load W and the size of the indenta-tion d was also expressed by Meyer as, LEK;W kdn (2)Here, k and n are material constants. The value of n is generally than 2 and usually lies between 2 and It is found that forfully annealed metals, n has a value near 2. 5 while for fully work hard- *-. -ened materials it is close to 2."The true stress-strain curve for m als may be approximated4 Nover an appreciable range of deformation b7In1a =gem (3)where, g and m are constants and o and e are the stress and strain > ~respectively. The value of _m usually lies between zero and 0.

9 5 withannealed cubic materials being close to the upper value. This equationhas'been referred to as the "mechanical equation of state" and is ex-pounded in detail by Hollomon and Lubahn. (8) If Eq. (2) is substitutedinto Eq. (1) then4kdn n-Hm= -kd , (4)r-"?where k, = 4 Examination of Eqs. (3) and (4) reveals that both are .., .isuitable for defining the plastic properties of metals. Both equations :. :are of the exponential form with the exponents being nearly equal. How-ever, the relationship between a and Hm and between e and d being un-defined precludes free substitution of one equation into the other. Forexample, Eq. (3) has the limitation of constant strain rate which is notmaintained on a hardness test.

10 As previously mentioned, Tabor hasapproached this problem by obtaining empirical constants that relatethese variables. Readers are referred to his works for the details ofhis experiments that have produced the following equations. -aN ..WADC-TR-55-114 2-'." -! . -@ >, >> -. -,- , .1 .- ,,.-. -,.-. -., *..- ,..Hm = a (5)e = (6)Dwhere D is the diameter of the indenting conc-ot of tensile flow curves being derived from hardnessmeasurements is of interest from at least two viewpoints. First, thepreparatic! aR-d testing of a hardness specimen requires much less ex-pense and than the tensile specimen. This point is of particularbenefit to large alloy exploration programs.