historical origins of indentation hardness testing_walley

SPECIAL ISSUE ARTICLE

Historical origins of indentation hardnesstesting

S. M. Walley*

Although it has been known for thousands of years that materials differ in hardness, quantitative

methods of measuring hardness by performing careful indentation experiments only began to be

developed during the nineteenth century. At the beginning of the twentieth century, hardness

testing machines began to be commercially available. The methods that have persisted to this

day may be divided into two broad categories: (1) those where a hardened steel ball or cone is

pressed into a surface under a known load; and (2) those where sharp diamonds of various

shapes are pressed into a surface also under a known load. An issue that has long been of

interest is the relation of hardness to simpler measures of material strength, particularly the tensile

strength. The review will cover the development of the various static and dynamic techniques and

their subsequent application to a wide range of materials.

Keywords: Hardness testing, Reviews, Historical development, Indentation, Brinell, Knoop, Vickers, Berkovich, Hertz, Martens, de Reaumur, Shorescleroscope, Rockwell, Meyer

Deep historyIt has long been known that some substances are harderthan others in that one substance may scratch or cutanother but not the reverse. The earliest references tothis phenomenon I have been able to find so far is fromthe Hebrew prophets (quotations from the EnglishStandard Version):

The sin of Judah is written with a pen of iron; with apoint of diamond it is engraved on the tablet of theirheart. Jeremiah 17: 1 (seventh century BC)

Like emery harder than flint have I made yourforehead. Ezekiel 3: 9 (seventh century BC)

They made their hearts diamond-hard lest theyshould hear the law and the words that the LORD ofhosts had sent by his Spirit through the formerprophets. Zechariah 7: 12 (sixth century BC)

As in any history, there has to be a cutoff. This I choseto be the 1950s, the decade in which David Taborpublished his famous book The Hardness of Metals1 aswell as a number of influential journal papers.2–5 Thewriting of this present historical account would havebeen much more difficult, and probably impossible,without the excellent bibliography put together byWilliams in 1942.6 I also acknowledge the excellenthistorical overviews of all forms of hardness investiga-tions published by Kohn in 19527 and O’Neill in 1934(second edition 1967).8,9

According to Todhunter10 writing in the 1890s, theearliest reported study of the hardness of materials was

by Huygens in his Traite de la Lumiere (Leyden, 1690) inwhich he describes differences in the scratching ofIceland Spar by a knife held at two different angles tothe sliding direction.11,12 Huygens interpreted the doublerefraction of light in this crystalline material in terms ofit consisting of flattened spheroids. His mechanicalexperiments with the knife were performed with a viewto confirming this hypothesis. Todhunter also helpfullysurveys other studies on hardness up to around 1860and found that they were mostly concerned withminerals, one exception being a Dutch investigator(Musschenbroek) who reported in 1729 that he had useda chisel attached to a pendulum to study the dynamichardnesses of various woods and metals.

After the invention of the telescope and microscope, itbecame necessary to polish glass lenses to high precision.As a result of doing this, Isaac Newton noticed andwrote in his Opticks that ‘…metal is more difficult topolish than glass…’,13,14 but as Newton himself realisedthere were a number of reasons why this is so (if thedifference were simply due to hardness, the oppositewould be true). Detailed descriptions of how to polishmetallic mirrors for telescopes were given later in theeighteenth century by Mudge15 and also early in thenineteenth century by Cecil.16 The use of diamondsin machining was described by Wollaston in 1816.17

The anisotropy of diamond was reported by CharlesBabbage in 183218 as follows: ‘An experienced work-man, on whose judgement I can rely, informed me thathe had seen a diamond ground with diamond powder ona cast-iron mill for three hours without it being at allworn, but that, changing its direction with reference tothe grinding surface, the same edge was ground down’.

Mohs19 is widely credited with the idea of a relativeand graded scale for the abrasive hardness of minerals.However, Todhunter10 pointed out that at least two

Fracture and Shock Physics Group, Cavendish Laboratory, J.J. ThomsonAvenue, Cambridge CB3 0HE, UK

*Corresponding author, email [email protected]

� 2012 Institute of Materials, Minerals and MiningPublished by Maney on behalf of the InstituteReceived 23 August 2011; accepted 23 December 2011DOI 10.1179/1743284711Y.0000000127 Materials Science and Technology 2012 VOL 0 NO 0 1

suta wijaya

Text Box

http://www.smf.phy.cam.ac.uk/Publications/Strength%20papers/717StrWalleyMST28.pdf

other researchers, Werner (in Germany) and Hauy (inFrance) had previously published the idea of a scale ofhardness defined by mutual scratchability. By 1848,Dana20 had arranged 10 minerals (ranging from talc todiamond) in sequence.

Hodgkinson21 published in 1835 the results of a studyof the dynamic hardness of a wide range of materialsusing the Newton’s Cradle arrangement (Fig. 1).

First indentation techniquesProbably the first machines for performing indentationmeasurements were reported by Wade in 185622 (Fig. 2)and Calvert and Johnson in 185923 (Fig. 3). Wadewrote: ‘The comparative softness, or hardness of metals,is determined by the bulk of the cavities, or indentations,made by equal pressures; the softness being as a bulkdirectly, and the hardness, as the bulk inversely’. Thatthese are likely to be the first such investigations isattested by the first sentence of the paper by Calvert andJohnson: ‘The process at present adopted for determin-ing the comparative degree of hardness of bodies,consists in rubbing one body against another, and thatwhich indents or scratches the other is admitted to be theharder of the two bodies experimented upon’. Calvertand Johnson then rank eight substances in decreasingorder of hardness, namely, diamond, topaz, quartz,

steel, iron, copper, tin and lead. They continue: ‘Thismethod is not only very unsatisfactory in its results, butit is also inapplicable for determining with precision thevarious degrees of hardness of the different metals andtheir alloys. We therefore thought that is would beuseful and interesting if we were to adopt a processwhich would enable us to represent by numbers thecomparative degrees of hardness of various metals andtheir alloys’.

Unwin (in 1896)24 and Jaggar (in 1897)25 confirm thathardness previous to the 1850s was determined byvarious scratch tests. Why were people at the end of thenineteenth century dissatisfied with the long establishedscratch methods of determining hardness? One reasonwas given by Auerbach who was of the opinion thatscratch hardness was too complicated a conceptcompared to indentation26 (see also page 143 ofWilliams’ book6).

Calvert and Johnson used the machine shown inFig. 3 in a different manner to the indentation machinesdeveloped in the late nineteenth and early twentiethcenturies in that: ‘When we wished to determine thedegree of hardness of a substance, we …gradually addedweights on the end of the lever, C, until the steel point,

1 Schematic diagram of Newton’s cradle arrangement

used by Hodgkinson in the 1830s21 to investigate rela-

tive dynamic hardness of range of materials

2 Wade’s indenting tool for testing of cannon in early 1850s22

3 Indentation machine developed by Calvert and Johnson

in 1850s23

Walley Historical origins of indentation hardness testing

2 Materials Science and Technology 2012 VOL 0 NO 0

F, entered 3?5 mm (or 0?128 of an inch) during half anhour, and then read off the weight’. An example of oneof the tables of results they obtained is given in Table 1.They gave the following reasons for their choice ofmetals thus: ‘We specially confined our researches to thisclass, wishing the results to be practically useful toengineers and others who have to employ metals, andoften require to know the comparative hardness ofmetals and alloys’.

Middelberg in 1886 wrote in a short letter27 that hehad used a knife indentation technique for some years todetermine the relative hardness of railway tyres (Fig. 4).

Unwin in 1896 reported an indentation technique thatused a short square section tool steel bar pressed into abar of the test material (Fig. 5). His measure of hardnesswas the depth of the indentation produced by a givenload when the bar had stopped penetrating. An exampleof his results is presented in Fig. 6.

A method that has been returned to from time to time,which its protagonists say is useful in giving anindication of the relative hardness of two materialsand which is claimed to be relevant to machining orcutting, is the crossed cylinders method28–30 (see alsoFig. 7).

Figure 7 is from Cowdery’s 1930 paper.30 In it he saysthe first reported use of the mutual indentationtechnique was by de Reaumur in 1722.31 However,having read what de Reaumur wrote (or at least its 1922

reprint), I have come to the conclusion that Cowderymisinterpreted the French text (unless the 1922 reprintleft some text out). The tract was about converting ironinto steel and techniques then employed to harden andsoften the steel. He discusses the hardness of steel in anumber of places, but (as far as I can judge) only twicediscusses ways of actually measuring it (in his tenthmemoir on ‘The Art of Converting Forged Iron intoSteel’). Both these techniques were proposed as thoughtexperiments: for as you can see from the footnote toQuote 2, he was pessimistic about putting his ideas intopractice as skilled workmen were not very well paid orwell regarded in French society at the time!

Quote 1

Au point de vue durete, on pourra se proposer deuxbuts differents: ou bien chercher la meilleuretemperature de trempe, c’est-a-dire le meilleur graind’un acier, en etudiant sa durete tout le long d’unebarre chauffee a un bout et trempee; ou biencomparer les duretes de deux aciers sur deux barressemblablement traitees, en etablissant la correspon-dence entre duretes et grosseurs de grain.

Les eprouvettes utilisees pour examen de la cassureserviront donc encore ici; on fait un essai a la limesur une surface plane, en bordure de la cassure. On aemploye pour cela un certain nombre de limes enmatieres de duretes croissants: verre, cristal deroche tender, cailloux transparents et durs, agathe,jaspe, topaze ou saphir, diamant.

My translation of quote 1

In considering hardness, one could propose twodifferent objectives: either look for the best quench-ing temperature (that is to say the one that producesthe best grain for a steel) by studying hardnessalong the length of a bar that has been heated at oneend and then quenched, or compare the hardness oftwo steels on two bars similarly treated, byestablishing the correspondence between hardnessand grain size.

The specimens used to examine fracture will thusserve well here; one makes a test with a file on aplane surface, near the break. One would use filesfor this purpose made of materials of increasinghardness: glass, soft rock crystals, hard transparentstones, agate, jasper, topaz or sapphire, diamond.

Quote 2

Pour essayer en meme temps la durete et le corps,certains ouvriers forgent un ciseau dans le metal a

Table 1 Example of one of tables of results from Calvertand Johnson’s studies:23 authors normalised theirdata with respect to cast iron

Names of metals

Weightemployed Calculated cast

iron51000lbs.

Staffordshire cold blastcast iron: grey, no. 3

4800 1000

Steel 4600 958?Wrought iron 4550 948Platinum 1800 375Copper: pure 1445 301Aluminium 1300 271Silver: pure 1000 208Zinc do 880 183Gold do 800 167Cadmium do 520 108Bismuth do 250 52Tin do 130 27Lead do 75 16

4 Schematic diagram of Middelberg’s knife indentation

technique for studying hardness of railway tyres275 Indentation hardness machine reported by Unwin in

189624


Materials Science and Technology 2012 VOL 0 NO 0 3

etudier, le trempent a un certain degre de chaleur etessayent de lui faire couper du fer a froid; si latentative n’aboutit pas, ils le trempent a une autretemperature, et ainsi de suite jusqu’a reussite. Si onattaque le fer obliquement, l’aspect des copeauxdonne des indications sur la durete du ciseau. Ceprocede tres rudimentaire peut etre perfectionne; ilsuffit de tremper une barre d’acier par un bout et dela graduer; l’essai du ciseau sur les differentesparties de la barre continue une mesure de la duretedu ciseau. On pourrait egalement, au lieu de frappersur le ciseau a l’aide d’un marteau, utiliser un poidstombant d’une certain hauteur, la variable de l’essaietant le nombre de coups (1).

(1) De Reaumur n’a d’ailleurs pas grand espoir devoir pratiquer ses methods d’essais; «Dans l’etatou sont les arts, tant qu’on ne cherchera pas aentretenir une noble emulation entre les ouvriers,tant qu’on negligera de recompenser ceux qui sedistinguent dans leur profession, il ne faut pas sepromettre qu’ils s’attacheront a de pareillesrecherches et qu’ils feront quelque chose avecprecision… »

My translation of quote 2

In order to measure hardness and malleability at thesame time, some workmen forge a chisel out of themetal of interest, quenching it at a certaintemperature. They then try to cut iron with it whencold. If this is not successful, they quench it atanother temperature, and so on until they aresuccessful. If the chisel is used to attack ironobliquely, the form of the chips produced gives anindication of the chisel’s hardness. This veryrudimentary procedure could be perfected byquenching a steel bar from one end in a graduatedmanner. Testing the chisel at different places alongthe bar would give a value for the chisel’s hardness.Equally one could, instead of hitting the chisel witha hammer, drop a weight on it from a knownheight, the test variable being the number of blowsrequired (1).

(1) de Reaumur did not, however, have great hopesof seeing his testing methods being put into practice:‘In the present state of the mechanical arts, in so faras improvement to technique is not sought amongworkmen and those who distinguish themselves in

6 Hardness results from machine shown in Fig. 524

7 Four different crossed cylinders method for measuring mutual hardness of metals30



their trades are not rewarded, one must not kidoneself that they will pay any attention to researchessuch as mine nor that they will make such thingswith the necessary precision…’.

Both static and dynamic machines for quantifyingindentation hardness became commercially availablearound 1900.32–34 Why then? Shore commented in 191133

that: ‘Hardness testing instruments have during the pastfew years come into practically universal use, both in thiscountry [the United States] and abroad. The apparentsuddenness of this popular movement may be due to morethan one cause. One is surely the development of theautomobile, and another perhaps the appearance, at whatmay be said to have been the psychological moment, of acheap and rapid method of performing the test itself’.Lysaght34 later reckoned that the reason indentationhardness testing took off so quickly after around 1900was the transition to mass production of items in theautomotive, aeronautic, machine tool and similar indus-tries requiring every item produced to be quality tested.Turner in 1886 (and later, more comprehensively in1909)35,36 gave a number of reasons why people wereinterested in the hardness of metals, particularly iron andsteel: efficacy of machine tools, wear resistance (includingerosion by water and sand) and brittleness after tempering.He published a comparison of the various methodsavailable showing that one tempering technique wouldimply that the material is suitable for a given applicationwhereas another would not (Fig. 8).

According to Clamer in 1908,37 the most widely usedhardness measuring technique in the early 1900s wasthe Brinell Ball Test. This technique was published byBrinell in 1900.38 The technique originally consisted ofpressing a hard steel ball under a known load into thematerial of interest. The Brinell hardness H was thencalculated by dividing the load P by the surface areaof the indentation (a spherical cap),39 a method alsosuggested by Martens in 1898,32,40 i.e.

H~P

pDd(1)

where D is the diameter of the ball indenter and d is thedepth of the indentation. Meyer later found41 that theload is a function of the diameter of the indentation di i.e.

P~adni (2)

where a and n are numbers which both depend on thematerial being tested. a also depends on the size of the ball.Meyer also suggested that the hardness be defined as theload divided by the projected area of the indentation, i.e.

H~P

pD=2ð Þ D{ D2{d2i

� �1=2h i (3)

This is a formula that is relatively easy to implement in aworkshop or a factory. The validity of Meyer’s formulahas been investigated by a number of authors sincethen.2,42–47

One problem with the Brinell test is that the hard-ness number increases with increasing load due to acombination of workhardening and increase in thediameter of the indentation.

As mentioned above, one very important reason whyindentation hardness testing took off so quickly was thatit was believed that it would give a more sensitiveindication of the wear resistance of materials (particularlysteels) used in friction bearings than the previously widelyused file or scratch test.48,49 However, as Unwin showedin 1916,50 the relation between Brinell hardness andresistance to abrasion is not straightforward (Fig. 9).

8 Plot of percentage loss of hardness for steel used for

wood working measured as function of tempering tem-

perature using four different hardness methods36

9 Does hardness give measure of wear resistance?50



Nevertheless, in 1937 Tonn51 established an empiricalrelation between Brinell hardness and abrasive wear

Abrasive wear~1

0:0205|Brinell hardnessz1:32(4)

Some wear processes (such as solid particle erosion) areso complex that people are still looking for simplerelations between wear resistance and indentation hard-ness to this day.52–54

The Brinell hardness is a ‘static’ measurement. Butaround the same time, dynamic methods were also beinginvestigated.55 Vincent in 1900 measured the diameter ofdents produced by dropping steel balls on variousmaterials.56 Shore in 190757 observed that measuringabrasion hardness using a file (which he said had beenstandard workshop practice for many years previous)was not able to distinguish the differing machinabilitiesof the new alloy steels being developed at that time. Hethus devised the ‘scleroscope’ (from the Greek forhardness), a device that measured the rebound of a steelball or pointed cylinder dropped down a graduated glasstube onto the material of interest.58 He observed thatdynamic hardness was proportional to elasticity.Another dynamic method of measuring hardness waspatented by Ballentine also in 1907.59 This method(along with a few others, including the static techniquedue to Brinell) was assessed by Clamer et al. in 1908.37

One amusing and ingenious way dynamic hardnesshas been used on a production line was to sort out(unwanted) soft steel balls from those of the desiredhardness by bouncing the mixture obliquely off a hardanvil: the soft balls rebounded less high and were caughtin a lower bin (Fig. 10).

Howe and Levy61 investigated the effect of repeatingShore scleroscope tests on the same spot. They foundthat the hardness increased with the number of tests.This was attributed to workhardening. However, theresults from experiments where the frequency of the testswas varied (from once every 6 s, 5 min, 30 min and60 min) were not as expected. They thought that thehigh frequency tests (repetition every 6 seconds) wouldlead to an accumulation of heat so that the rate ofworkhardening would be decreased. However, they didnot find this to be true ‘[reminding] us of the profundityof our ignorance of the nature and habits of plasticdeformation’ (Fig. 11).

Hardness was also used early on as a laboratory researchtool to study, for example, internal friction of metals byseeing how hardness varied with temperature62,63 (Figs. 12and 13).

It can be seen from Fig. 13 that duration of loading hasan effect on the measured hardness even for classically‘plastic’ materials such as metals. It seems that recordingindentation load as a function of time only widely began inthe early 1950s,64,65 although Martens built a machinethat was capable of doing this in 1898!32,66 Such measure-ments are of particular importance for viscoelastic ma-terials such as polymers (see, for example, Fig. 14) but arenow standard in all academic studies of indentationhardness.67

Comparison of techniquesThe reasons that indentation methods were preferred inindustry to tensile testing are the following: indentationis non-destructive, cheap and can be applied directly toall items of a factory’s output.68 However, the varioushardness tests give different results. So there were quite anumber of detailed studies performed comparing thedifferent techniques in order to derive conversion tablesand formulae.34,68–74 Some results of these investigationsare presented graphically in Figs. 15–17.

One important issue is that, as Turner36 and Auchy78

pointed out, the Brinell test is static, whereas the Shoretest is dynamic (it had been known for several decadesthat the static and dynamic mechanical properties ofmaterials differ79). To address this issue, Shore andHadfield performed a large number of experiments69

(see also Fig. 18). One major source of inaccuracy in theBrinell test that they found was the ball flattens whenmaterials above a certain hardness are tested. Toovercome this, they performed some experiments with

10 Method of separating out unwanted soft steel balls:6

originally published in Ref. 60

11 Effect of interval between Shore scleroscope tests on

hardness values for steel61



a spherical diamond, but they thought that this wouldnot generally be possible in routine laboratory orindustrial testing. By 1939, Scott and Gray recom-mended that materials harder than 450 BHN should nothave their hardness measured using a standard Brinellsteel ball.80 However, since the Brinell method was awidely trusted technique, by 1943 hard steel balls,tungsten carbide balls, and even hemispherical dia-monds were available for testing very hard materials.81

The main problem Shore and Hadfield identified wasthat the scleroscope gave results closer to the elastic limit ofthe material whereas Brinell hardness machines producedsubstantial plastic deformation and hence measuredproperties closer to ultimate strength. Thus direct compar-ison was only possible if low loads (less than 1000 kgf) wereused in the Brinell test. The issue of comparing the differentmethods of indentation testing continues to be studied(occasionally) right up to the present day.82,83

Rockwell and Rockwell patented in 191984,85 a methodof hardness testing that has the effect of subtracting offthe elastic response of the material, i.e. measuring theplastic hardness only. This is done by first applying aninitial small load to the indenter (10 kgf), then adding a

12 Plot of hardness (as measured by Brinell himself) of two steels as function of temperature62

13 Effect of temperature on hardness of two elements:

times given are duration of loading; data from Ref. 63,

replotted in Ref. 6; purpose of this study was investi-

gation of internal friction

14 Indentation load as function of time for PMMA indented initially using load of 25 gf and secondly by load of 0?5 gf64



much larger load (10 times larger for a ball or 15 timeslarger for a cone), and then removing the smaller load.The measure of hardness is the depth of the indentationafter this has been done. The Rockwell C test (which usesa diamond cone) in particular met the need for hardnesstesting of materials harder than those which the Brinelltest could accurately measure.80 Petrenko68 recommendedthat balls be used with soft materials and cones for hardmaterials when using the Rockwell method.

In order to preserve geometrical similarity during anindentation, the Vickers test was developed in which theindenter is a square section diamond pyramid.86–88 Oneimportant advance on previous methods was that it canbe used to test very hard materials. It also has no lowerlimit, so is very versatile. Cone indenters also exhibitgeometrical similarity41,89,90 so that ideally the hardnessmeasured will be independent of load.81 However, Fig. 19presents evidence that using a pyramid does not entirelyremove the load dependence of hardness. Scott and

Gray80 also reckoned that the Vickers method was not aspractical to use in a factory as the Rockwell technique.The change in hardness for small loads became increas-ingly important when obtaining hardness from very smallindentations (microhardness) became both desirable andrequired.91,92

The Knoop test94 uses a diamond indenter whosediagonals differ from each other by a factor of 7. Thismeans that elastic recovery has the largest effect along theshorter diagonal (BB in Fig. 20) so that it is possible (bymeasuring the two diagonals after the load has beenremoved and also knowing the dimensions of the indenter)to determine both the recovered and the unrecovereddimensions of the indentation. A direct comparison ofKnoop, Vickers and Brinell indentations made on a single

15 Early comparison (1911) of hardness methods for a

range of materials75

16 Graph of two Rockwell methods (ball and diamond) against Brinell hardness for wide range of materials76

17 Relationships between Brinell and Rockwell numbers

given by different investigators: Figure from Ref. 68

containing data from Refs. 70, 76 and 77



block of metal is given in Fig. 21 (the author does not statewhat metal these tests were performed on).

A problem with the Vickers and Knoop diamondindenters was identified by Berkovich at a time when itwas desired to perform very small (micro) hardness tests.The problem was that it is difficult to ensure that all foursides of a four-sided pyramid meet at a point.65 Mostindenters instead had a ridge about 0?5 mm long. Thisdoes not matter very much if the indenter is large, butbecomes increasingly important for small indenters. To

overcome this problem Berkovich introduced thetriangular cross-section (or three-faceted) pyramidalindenter.95

It is clear from Fig. 21 that even at the surface theflow of material around an indentation is complicated.In cross-section (Fig. 22), it can be seen that ameasurement of the width (or diameter) of an indenta-tion in top view will overestimate the value in the planeof the original surface due to ‘pile-up’ around theindentation.90 Also the load will be partly supported bythis ridge of material, although Devries75 reckoned thatthe resistance of the material remaining underneath theindenter would be decreased by the flow of materialaway. Since the change in flow stress of both the piled-up material and the material underneath the indenter areboth unknown (and the change will not be the same for

18 Comparison between Brinell ball and Shore scleroscope hardness numbers69

19 Relation of hardness number to load for two different

diamond pyramid methods and two materials93

20 Schematic drawing of Knoop indentation6

21 Comparison of Knoop (leftmost), Vickers (middle) and

Brinell (rightmost) indentations6



different materials), it called into question how accu-rately such measurements can discriminate between, say,the machinability of closely related alloys (one of thereasons indentation testing was originally introduced onthe shop floor).

In 1922, Foss and Brumfield published a detailedstudy96 of the effect on the Brinell hardness numberof three different ways of measuring the size of the

indentation (see Fig. 23 where it is apparent that the sizeof the indent could be assessed by the chords A–A, B–Bor C–C). They found that for low Brinell hardnessnumbers (less than 150), there was very little differencebetween the three methods, but as the depth of theindentation decreased, the hardness number computedfrom the depth of the indentation increased very muchmore rapidly than the hardness number computed fromthe true area of the indentation. They also found that theamount of ‘swell’ (pile-up or sink-in) depended on thematerial being tested (Fig. 24) and for extruded brass rod,the ‘swell’ was markedly anisotropic (see inset to Fig. 24).

22 Schematic diagram showing pile-up around cone

indentation90

23 Three different ways (A–A, B–B or C–C) size of Brinell

indentation could be measured for indentation where

pile-up occurs96

24 Comparison of amount of ‘swell’ (pile-up or sink-in) expressed as percentage of depth of indentation for various

metals:96 inset shows anisotropy in swell for extruded brass rod



However, Norbury and Samuel97 published a detailedstudy of both piling-up and sinking-in for Brinell and anumber of other tests and found that although it was alarge effect, it had ‘a constant value for a given material,irrespective of the size of the impression, if expressed asa percentage of the measured depth of impression’.

Ideas why materials differ in propertiesThe main drivers for investigating the mechanicalproperties of metals in the nineteenth century, particu-larly steel, were the development of pressure vessels forsteam engines, rails for the railways, guns and ironships.22,98,99 One of the pioneers of these studies wasKirkaldy in London.100,101 The machine that Kirkaldydeveloped was so large it was never moved and is nowpreserved in situ in a museum.

A great deal of empirical data was obtained in the latterpart of the nineteenth century, but it was not at all clearthen why some materials were hard and brittle, others softand ductile, and yet others hard and ductile.24,102–104 Fullunderstanding of these matters would not come aboutuntil the development of quantum mechanics105,106 (andits subsequent application to chemical bonding107–111)and dislocation112–116 and fracture117,118 mechanics.

Before this time, a number of ideas were exploredincluding: atomic weight,119 electrical and magneticproperties,120–130 cohesion,131–134 crystal structure,135–139

amorphous component,140–143 thermal properties144–146

and density147 (at least for alloys of varying composition).

One characteristic of metals that began to be studiedintensively in the 1880s148,149 and which has since provedvery fruitful was grain size.150–153 Papers relating grainsize to indentation hardness began to appear after theFirst World War154–159 (although de Reaumur hadspeculated that there might be a relation between grainsize and hardness in 1722:31 see the quote earlier in thispaper). Bassett and Davis154 made the qualitativeobservation that when rolled cartridge brass wasannealed the grain size increased and the hardnessdecreased (Fig. 25).

Matthewson160 derived the following relation fromBassett and Davis’s154 data

Brinell hardness !

number of grains per square millimetreð Þ1=2(5)

Note that Matthewson mistakenly published this as areciprocal relationship, whereas Bassett and Davis’sdata clearly show the hardness increasing with thenumber of grains per square millimetre.

25 Plot of Brinell hardness number and grain size against

annealing temperature for rolled cartridge brass154

26 Plot of inverse square of grain size against Brinell

hardness number for various steels161

27 Comparison of various hardness tests with tensile

elastic limit and ultimate strength166

28 Plot of relation between maximum stress and Brinell

hardness for number of carbon steels subjected to

various heat treatments168



However, Rawdon and Jimeno-Gil’s observations onsteel157 were not as clear cut. Wood in 1930161 foundthat hardness was inversely proportional to the squareof the grain size (determined using an X-ray method) ofvarious steels (Fig. 26).

Relation to other mechanical propertiesFor many applications. the measurement that is reallyneeded is the tensile strength. So ideally one wouldperform tensile tests, but these are much more expensiveto perform than hardness indentations. Tensile tests arealso destructive. whereas indentation tests are not162,163

(at least for large objects). So the obvious question soonarose as to the relation of hardness measurements totensile measurements164–167 (see also Fig. 27).

The earliest papers I have found comparing indenta-tion hardness and tensile measurements were published in1915.168,169 Abbott performed a very thorough study onabout 300 types of steel subjected to a number of differentheat treatments. Each steel in each condition wassubjected to a tensile test as well as Brinell (quasistatic)and scleroscope (dynamic) indentation testing. Some ideaof the number of tests he performed is given in Fig. 28,the first of 18 such figures in his paper!

It is clear from Fig. 28 that there is a linear relation-ship between tensile strength and hardness and this wasstated explicitly by Unwin in 1918101 as

T~0:2Hz6 (6)

Y~0:23H{13:5 (7)

where T is the tensile strength, Y is the yield point (both intons per square inch) and H is the Brinell hardness (inkilograms per square millimetre). McWilliam and Barnesalso studied a large number of steels (though not as manyas Abbott) and found that the ratio of maximum tensilestress to Brinell hardness lay in the range 0?23–0?26. Oneof the authors (McWilliam) performed many of thecalculations in India and commented about his experiencethus: ‘All the above calculations were made in the midstof an Indian jungle to the accompaniment of thethreatening note of the mosquito and the wild howls ofjackals, so suggestive of hostile criticism, that all thefigures were doubly checked’.

A number of other studies into the relationshipbetween tensile strength and hardness were publishedbetween then and 1947170–179 (see, for example, Fig. 29)when Tabor published his famous paper2 which, amongmany other things, explained the relationship betweenhardness and yield stress (see also Refs. 1, 180 and 181).

Even for purely elastic deformation, the stress fieldsare complicated. Hertz famously derived expressions forthe stresses at the surface of an elastic half-space againstwhich an elastic sphere is pressed.182,183 He did not giveexpressions for the stresses within the half-space, for hestates ‘the formulae are far too complicated to allow ofour doing this directly. But by considering the stressesnear the z-axis and near the surface we can form a roughnotion of this distribution’. He then gives a figure(reproduced here as Fig. 30) for which he states that‘arrow-heads pointing towards each other denote atension, those pointing away from each other apressure’. Huber gave the solution to the problem ofthe bulk stresses beneath an elastic indentation in apaper published in 1904.184

Coker in 1921185 applied the photoelastic technique(which he had recently developed)186 to the problem ofdeformation beneath a cylindrical flat ended punch(Fig. 31).

Timoshenko and Goodier give a more understandablederivation of the Hertz surface stress field in theirtextbook on elasticity.187 The formula for the radius ofcontact a was written by Frank and Lawn in 1967 in the

29 Plots of a Brinell hardness and b tensile strength against magnetic hysteresis area for nickel steel156

30 Hertz’s schematic diagram of stresses produced by

loading rigid flat by elastic sphere183



form given in equation (8) using Hertz’s theory188

(ignoring friction)

a3~3

4kPR (8)

where k~ 1{n21

� �=E1z 1{n2

2

� �=E2, E1,2 and n1,2 are the

Young’s moduli and Poisson’s ratios of the twomaterials, P is the normal load and R is the radius ofthe indenting sphere. The effect of friction on theHertzian surface stresses was investigated by Johnsonand co-workers.189 It should be emphasised that Hertz’sanalysis is not for plastic indentation as he assumed anelastic response only. However, his analysis is a goodapproximation for both the static and dynamic interac-tions of hard metal, ceramic or glass balls with silicaglasses and ceramics.188,190–193

Detailed analyses of the plastic flow of materialaround indentations of various shapes were performedby Hencky,194 Prandtl,195 Ishlinsky196 and Shield.197

They all assumed the indented material was rigidperfectly plastic, i.e. no elasticity, no workhardening.Ishlinsky performed a slip line field analysis for both aflat cylindrical punch and a ball indenter. For the flatindenter, he found that the hardness was 2?84Y where Yis the yield stress in compression. This is close to whatlater became known as the Tabor factor relating

hardness H to yield stress (H53Y). Note that Taboronly ever said this was an approximate relation. Manyassumptions were made in deriving this factor, e.g.which yield function the material obeys (whether Trescaor von Mises) interfacial friction, etc. Shield197 laterredid Ishlinsky’s calculation using a more accuratemethod (Fig. 32).

Absolute hardnessA major problem with all hardness testing methods isthat they alter the material whose properties you aretrying to measure. This was realised in the early 1890s byAuerbach who published a number of papers on theproblem of ‘absolute hardness’.26,198,199 This issue washelpfully reviewed by Mahin and Foss in 1939.200

Honda132 suggested that intrinsic hardness be definedas ‘the intensity of maximum pressure which justproduces yielding’. The main problem with this defini-tion is that elastic contact between a ball and a flatsurface initially produces infinite stresses. In practice, ofcourse, the indenter flattens and the surface plasticallyindents.182,183 Mahin and Foss200 favoured the followingdefinition of absolute hardness as ‘the maximum unitstress which a material will support without permanentindentation’. The way they achieved this measurementwas to drill a number of holes of different depth using adrill with a spherical cutting surface whose diameter wasthe same as the Brinell ball indenter they used (5 mm).They then loaded each hole with the indenter until theyfound the one that did not increase the size of the hole.Apart from this being normally impractical to do, Heyerand Kenyon commented in the discussion section of thepaper that ‘[Hardness tests] were never designed tomeasure ‘absolute’ properties and practically all effortsto eliminate the complicating variables and reduce themto such fundamentals have proved fruitless. When suchproperties are to be measured, it seems to be much betterto design special tests than to try and adapt old ones’.

Concluding remarksTowards the end of the nineteenth century, it became clearthe scratch method used in workshops since timeimmemorial was no longer adequate for distinguishingbetween the new types of steels being developed, particu-larly in regard to their wear resistance. Thus during the firstdecade of the twentieth century, indentation techniques(which had first been described around 50 years before)

31 Photoelastic fringes showing stress in large rectangu-

lar block loaded over small part of its upper surface

by cylindrical flat ended punch185

32 Slip line field solution for body occupying space z>0 indented by flat ended cylindrical punch centred on r50 and

contacting surface out as far as A197



began to be widely used in factories as a non-destructivemethod of assessing the tensile strength of metalsincorporated into finished products. This was needed asin some manufactures, testing of every item produced wasrequired. Understanding of why materials differed inhardness, and indeed what ‘hardness’ actually is, laggedseveral decades behind the widespread adoption ofindentation methods in industry. In the meantime, severaldifferent machines for measuring hardness were developedand sold commercially. The measurements these machinesgenerated were found to be difficult to relate to oneanother for a variety of reasons. For example, some weredynamic (e.g. Shore scleroscope), others quasistatic (e.g.Brinell) techniques. Also the Shore scleroscope measuredhardness close to the elastic limit, whereas Brinellindentations produced a large amount of permanentdeformation (plasticity). They also gave conflicting resultsabout, for example, the effect of temperature on mechan-ical properties. The problem may be simply stated thatmany different properties of a material contribute to thevalues obtained in indentation testing. Thus, techniquesthat in some respects started life as ‘rough and ready’ testson production lines, designed primarily for quality control,have in later years been interpreted to reveal manyfundamental features of plastic flow: flow stress, work-hardening and fracture toughness. It is well to remember,however, that it remains widely useful in the machine shopand the production line, and is most useful as astandardised discriminator of materials.

Acknowledgements

I would like to thank Professor R. W. Armstrong,Professor L. M. Brown, Dr M. M. Chaudhri, ProfessorJ. E. Field and Professor M. A. Meyers for their commentson this paper. I would also like to thank Dr A. C. A.Woode for advice and help in translating de Reaumur’sFrench. I also thank the referees for their suggestions forimproving the paper and informing me about publicationsI would not otherwise have known about.

References1. D. Tabor: ‘The hardness of metals’; 1951, Oxford, Clarendon

Press.

2. D. Tabor: ‘A simple theory of static and dynamic hardness’, Proc.

R. Soc. Lond. A, 1947, 192A, 247–274.

3. D. Tabor: ‘Mohs’ hardness scale: a physical interpretation’, Proc.

Phys. Soc. Lond. B, 1954, 67B, 249–257.

4. D. Tabor: ‘The physical meaning of indentation hardness’, Sheet

Met. Ind., 1954, 31, 749–763.

5. D. Tabor: ‘The physical meaning of indentation and scratch

hardness’, Br. J. Appl. Phys., 1956, 7, 159–166.

6. S. R. Williams: ‘Hardness and hardness measurements’; 1942,

Cleveland, OH, ASM Internaitonal.

7. J. A. Kohn: ‘Survey of the study of hardness’, Ind. Diamond Rev.,

1952, 12, (Suppl. 1), 1–16.

8. H. O’Neill: ‘The hardness of metals and its measurement’; 1934,

London, Chapman & Hall.

9. H. O’Neill: ‘Hardness measurement of metals and alloys’; 1967,

London, Chapman & Hall.

10. I. Todhunter: ‘Hardness and elasticity’, in ‘A history of the theory

of elasticity and of the strength of materials’, (ed. K. Pearson),

Vol. 2, Part 1, ‘Saint-Venant to Lord Kelvin’, 582–592; 1893,

Cambridge, Cambridge University Press.

11. C. Huygens: ‘Traite de la Lumiere. Ou sont expliquees les causes

de ce qui luy arrive dans la reflexion, & dans la refraction; et

particulierement dans l’etrange refraction du cristal d’Islande’,

95–96; 1690, Leiden, Pierre vander Aa.

12. C. Huygens: ‘Treatise on light: in which are explained the causes

of that which occurs in reflexion, & in refraction, and particularly

in the strange refraction of Iceland crystal’, 99; 1912, London,

Macmillan.

13. I. Newton: ‘Opticks: or a treatise of the reflections, refractions,

inflections and colours of light’, 4th edn, Proposition 7, Theorem

6; 1730, London, William Innys.

14. I. Newton: ‘Opticks: or a treatise of the reflections, refractions,

inflections and colours of light’, 4th edn, 104–107; 1931, London,

G. Bell and Sons Ltd (republ. Dover, 1952).

15. J. Mudge: ‘Directions for making the best composition for the

metals of reflecting telescopes; together with a description for the

process for grinding, polishing, and giving the great speculum

the true parabolic curve’, Philos. Trans. R. Soc. Lond., 1777, 67,

296–349.

16. W. Cecil: ‘On an apparatus for grinding telescopic mirrors and

object lenses’, Trans. Camb. Philos. Soc., 1827, 2, 85–103.

17. W. H. Wollaston: ‘On the cutting diamond’, Philos. Trans. R. Soc.

Lond., 1816, 106, 265–269.

18. C. Babbage: ‘On the economy of machinery and manufactures’,

10–11; 1832, London, C. Knight.

19. F. Mohs and A. Haidinger: ‘Hardness’, in‘Treatise on mineralogy

or the natural history of the mineral kingdom’, Vol. 1, 300–307;

1825, Edinburgh, A. Constable and Co.

20. J. D. Dana: ‘Hardness’, in ‘Manual of mineralogy, including

observations on mines, rocks, reduction of ores, and the

applications of the science to the arts, 64–65; 1848, New Haven,

CT, Durrie & Peck.

21. E. Hodgkinson: ‘On the collision of imperfectly elastic bodies’,

Rep. Br. Assoc. Adv. Sci., 1835, 4, 534–543.

22. W. Wade: ‘Hardness of metals’, in ‘Reports on experiments on the

strength and other properties of metals for cannon with a

description of the machines for testing metals, and of the

classification of cannon in service’, (ed. H. K. Craig), 259–275,

313–314, plate XVI; 1856, Philadelphia, PA, Henry Carey Baird.

23. F. C. Calvert and R. Johnson: ‘On the hardness of metals and

alloys’, Philos. Mag., 1859, 17, 114–121.

24. W. C. Unwin: ‘A new indentation test for determining the

hardness of metals’, Min. Proc. Inst. Civil Eng., 1896, 129, 334–

349.

25. T. A. Jaggar: ‘A microsclerometer for determining the hardness of

minerals’, Am. J. Sci., 1897, 4, 399–412.

26. F. Auerbach: ‘Absolute Hartemessung’, Ann. Phys. Chem., 1891,

43, 61–100.

27. G. A. A. Middelberg: ‘The hardness of metals’, Engineering, 1886,

42, 481.

28. A. Foppl: ‘Uber die mechanische Harte der Metalle, besonders des

Stahls’, Ann. Phys. Chem., 1897, 63, 103–108.

29. B. P. Haigh: ‘Prism hardness: a new method of testing hardness in

materials yielding a scale that is equally applicable to the hardest

and softest metals and expresses the values in units of stress’, Proc.

Inst. Mech. Eng., 1920, 99, 891–913.

30. I. H. Cowdery: ‘Hardness by mutual indentation’, Proc. ASTM,

1930, 30, (2), 559–570.

31. M. de Reaumur: ‘L’Art de Convertir le Fer Forge en Acier et l’Art

d’Adoucir le Fer Fondu’; 1722, Paris, Michel Brunet (republ. in

Rev. Metall. Memoires, 1922, 19, 441–468).

32. A. Martens: ‘Handbuch der Materialenkunde’; 1898, Berlin,

Springer.

33. A. F. Shore: ‘The property of hardness in metals and materials’,

Proc. ASTM, 1911, 11, 733–743.

34. V. E. Lysaght: ‘Indentation hardness testing. Definition of

hardness. Commonly used hardness testers. Conversion of

hardness numbers’, Can. Chem. Metall., 1936, 20, 380–384.

35. T. Turner: ‘The hardness of metals’, Proc. Birmingham Philos.

Soc., 1886, 5, 282–312.

36. T. Turner: ‘Notes on tests for hardness’, J. Iron Steel Inst., 1909,

79, 426–443.

37. G. H. Clamer, A. E. Outerbridge, Jr, A. W. Allen and W. H.

Wahl: ‘Ballentine’s process of testing the hardness and density of

metals’, J. Franklin Inst., 1908, 166, 447–451.

38. J. A. Brinell: ‘Ein Verfahren zur Hartebestimmung nebst einigen

Anwendungen desselben’, Baumaterialienkunde, 1900, 5, 276–280,

294–297, 317–320, 364–367, 392–394, 412–416.

39. J. F. Springer: ‘Methods of testing materials for hardness’,

Cassier’s Mag., 1908, 34, 387–401.

40. H.-R. Wilde and A. Wehrstedt: ‘Introduction of Martens

hardness HM’, Materialprufung, 2001, 42, 468–470.

41. E. Meyer: ‘Untersuchungen uber Harteprufung und Harte’, Phys.

Z., 1908, 9, 66–74.

42. R. F. Bishop, R. Hill and N. F. Mott: ‘The theory of indentation

and hardness tests’, Proc. Phys. Soc. Lond., 1945, 57, 147–159.



43. H. M. Finniston, E. R. W. Jones and P. E. Madsen: ‘Meyer

analysis of metals’, Nature, 1949, 164, 1128–1129.

44. M. A. Meyer and K. J. B. van Laer: ‘Plastic deformation and the

Meyer constants of metals’, Nature, 1952, 169, 237–238.

45. A. A. Lankov: ‘The Meyer law and strain hardening of

elastoplastic materials’, J. Frict. Wear, 1993, 14, (6), 18–27.

46. G. Berg and P. Grau: ‘Meyer’s hardness law and its relation to

other measures of ball hardness tests’, Cryst. Res. Technol., 1997,

32, 149–154.

47. M. Sakai: ‘The Meyer hardness: a measure for plasticity?’,

J. Mater. Res., 1999, 14, 3630–3639.

48. C. A. M. Smith and H. J. Humphries: ‘Some tests on white anti-

friction bearing metals’, J. Inst. Met., 1911, 5, 194–211.

49. R. A. Hadfield and S. A. Main: ‘Note on Brinell and scratch tests

for hardened steel’, Proc. Inst. Mech. Eng., 1919, 97, 581–586.

50. W. C. Unwin: ‘Report of the hardness test research committee’,

Proc. Inst. Mech. Eng., 1916, 91, 677–778.

51. W. Tonn: ‘Beitrag zur Kenntnis des Verschleißvorganges beim

Kurzversuch am Beispiel der reinen Metalle’, Z. Metallkd, 1937,

29, 196–198.

52. S. G. Sapate and A. V. R. Rao: ‘Effect of material hardness on

erosive wear behavior of some weld-deposited alloys’, Mater.

Manuf. Processes, 2002, 17, 187–198.

53. M. Divikar, V. K. Agarwal and S. N. Singh: ‘Effect of the

material surface hardness on the erosion of AISI 316 steel’, Wear,

2005, 259, 110–117.

54. G. Pintaude, F. G. Bernardes, M. M. Santos, A. Sinatora and E.

Albertin: ‘Mild and severe wear of steels and cast irons in sliding

abrasion’, Wear, 2009, 267, 19–25.

55. M. Martel: ‘Sur la mesure de la durete des metaux a la

penetration, au moyen d’empreintes obtenues par choc avec un

couteau pyramidal’, in ‘Commission des Methodes d’Essai des

Materiaux de Construction’, Vol. III, Section A (Metaux),

Rapports Particuliers (Deuxieme Serie), 261–277; 1895, Paris,

Ministere des Travaux Publics.

56. J. H. Vincent: ‘Experiments on impact’, Proc. Camb. Philos. Soc.,

1900, 10, 332–357.

57. A. F. Shore: ‘An instrument for testing hardness’, Am. Mach.,

1907, 30, 747–751.

58. A. F. Shore: ‘The scleroscope’, Proc. ASTM, 1910, 10, 490–517.

59. W. I. Ballentine: ‘Processing of testing the hardness and density of

metals and other materials’, US Patent 855,923, 1907.

60. E. K. Hammond: ‘Manufacture of steel balls’, Machinery, 1917,

23, 753–760.

61. H. M. Howe and A. G. Levy: ‘Notes on the Shore scleroscope

test’, Proc. ASTM, 1916, 16, (2), 36–52.

62. J. A. Brinell: ‘Researches on the comparative hardness of acid and

basic open-hearth steel at various temperatures by means of ball-

testing’, Iron Steel Mag., 1905, 9, 16–19.

63. P. Ludwik: ‘Uber die Anderung der inneren Reibung der Metalle

mit der Temperatur’, Z. Phys. Chem., 1916, 91, 232–247.

64. P. Grodzinski: ‘Hardness testing of plastics’, Plastics, 1953, 18,

312–314.

65. D. Newey, M. A. Wilkins and H. M. Pollock: ‘An ultra-low-load

penetration hardness tester’, J. Phys. E: Sci. Instrum., 1982, 15E,

119–122.

66. A. Martens: ‘Die Festigkeitsiegenschaften und die Harte’, in

‘Handbuch der Materialenkunde’, (ed. E. Heyn), 2nd edn, 248–

418; 1912, Berlin, Springer.

67. M. R. VanLandingham: ‘Review of instrumented indentation’,

J. Res. Natl. Inst. Stand. Technol., 2003, 108, 249–265.

68. S. N. Petrenko: ‘Relationships between Rockwell and Brinell

numbers’, Bur. Stand. J. Res., 1930, 5, 19–50.

69. A. F. Shore and R. Hadfield: ‘Report on hardness testing:

Relation between ball hardness and scleroscope hardness’, J. Iron

Steel Inst., 1918, 98, 59–88.

70. E. C. Brumfield: ‘Some comparisons between Rockwell and

Brinell hardness’, Trans. Am. Soc. Steel Treat., 1926, 9, 841–856.

71. R. R. Moore: ‘Relationships between Rockwell, Brinell and

Scleroscope numbers’, Trans. Am. Soc. Steel Treat., 1927, 12, 968–

975.

72. T. N. Holden: ‘New conversion tables show relations among

hardness tests’, Iron Age, 1930, 126, (80–81), 932.

73. W. E. J. Beeching: ‘Relationships of hardness numbers’, Met. Ind.,

1934, 44, 188.

74. R. H. Heyer: ‘Hardness conversion relationships’, Proc. ASTM,

1942, 42, 708–726.

75. R. P. Devries: ‘A comparison of five methods of hardness

measurement’, Proc. ASTM, 1911, 11, 709–725.

76. J. H. Cowdery: ‘Relation between Rockwell and Brinell hardness

scales’, Trans. Am. Soc. Steel Treat., 1925, 7, 244–260.

77. S. C. Spalding: ‘Comparison of Brinell annd Rockwell hardness of

hardened high speed steel’, Trans. Am. Soc. Steel Treat., 1924, 6,

499–504.

78. G. Auchy: ‘The hardness of steel. It is both static and dynamic:

the Brinell and Shore tests differentiated’, Iron Age, 1910, 85,

1398–1399.

79. W. K. Hatt and E. Marburg: ‘Bibliography on impact tests and

impact testing machines’, Proc. ASTM, 1902, 2, 283–297.

80. H. Scott and T. H. Gray: ‘Relation between the Rockwell ‘‘C’’

and diamond pyramid hardness scales’, Trans. ASM, 1939, 27,

363–381.

81. S. R. Williams: ‘Present types of hardness tests’, Proc. ASTM,

1943, 43, 815–834.

82. V. E. Lysaght: ‘Hardness conversion tables for copper’, J. Mater.,

1971, 6, 503–513.

83. N. A. Sakharova, J. V. Fernandes, J. M. Antunes and M. C.

Oliveira: ‘Comparison between Berkovich, Vickers and conical

indentation tests: a three-dimensional numerical simulation

study’, Int. J. Solids Struct., 2009, 46, 1095–1104.

84. H. M. Rockwell and S. P. Rockwell: ‘Hardness tester’, US Patent

1,294,171, 1919.

85. S. P. Rockwell: ‘Hardness testing machine’, US Patent 1,516,207,

1924.

86. R. L. Smith: ‘Apparatus for determining the hardness of a body’,

UK Patent 11,936, 1916.

87. R. Smith and G. Sandland: ‘An accurate method of determining

the hardness of metals, with particular reference to those of a high

degree of hardness’, Proc. Inst. Mech. Eng., 1922, 102, 623–641.

88. R. L. Smith and G. E. Sandland: ‘Some notes on the use of a

diamond pyramid for hardness testing’, J. Iron Steel Inst., 1925,

111, 285–304.

89. P. Ludwik: ‘Die Kugeldruckprobe, ein neues Verfahren zur

Hartebestimmung von Materialen’; 1908, Berlin, Springer.

90. E. Meyer: ‘Untersuchungen uber Harteprufung und Harte’,

Z. Ver. Dtsch Ing., 1908, 52, 645–654, 740–748, 835–844.

91. P. Grodzinski: ‘An automatic light-load Bergsman type hardness

tester’, J. Sci. Instrum., 1951, 28, 117–121.

92. W. Weiler: ‘Hardness testing: a new method for economical and

physically meaningful microhardness testing’, Br. J. Non-Destr.

Test., 1989, 31, 253–258.

93. D. R. Tate: ‘A comparison of microhardness indentation tests’,

Trans. ASM, 1945, 35, 374–389.

94. F. Knoop, C. G. Peters and W. B. Emerson: ‘A sensitive

pyramidal diamond tool for indentation measurements’, J. Res.

Natl Bur. Stand., 1939, 23, 39–61.

95. E. S. Berkovich: ‘Three-faceted diamond pyramid for microhard-

ness testing’, Ind. Diamond Rev., 1951, 11, 129–132.

96. F. E. Foss and R. C. Brumfield: ‘Some measurements on the

shape of Brinell ball indentation’, Proc. ASTM, 1922, 22, (2), 312–

334.

97. A. L. Norbury and T. Samuel: ‘The recovery and sinking-in or

piling-up of material in the Brinell test and the effects of these

factors on the correlation of the Brinell with certain other

hardness tests’, J. Iron Steel Inst., 1928, 117, 673–687.

98. M. Merriman: ‘The work of the International Association for

Testing Materials’, Proc. ASTM, 1899, 1, 17–25.

99. W. K. Hatt and E. Marburg: ‘Preliminary report on the present

state of knowledge concerning impact tests’, Proc. ASTM, 1899,

1, 27–50.

100. D. Kirkaldy: ‘Results of an experimental enquiry into the

comparative tensile strength and other properties of various kinds

of wrought iron and steel etc.’; 1862, Glasgow, Bell & Bain.

101. W. C. Unwin: ‘The experimental study of the mechanical

properties of materials’, Proc. Inst. Mech. Eng., 1918, 95, 405–439.

102. R. A. Hadfield: ‘Memorandum on hardness’, Proc. Inst. Mech.

Eng., 1916, 91, 707–711.

103. H. E. Degler: ‘A comparison of methods for testing hardness’,

Am. Mach., 1925, 63, 381–384.

104. E. C. Bingham: ‘Some fundamental definitions of rheology’, Proc.

ASTM, 1929, 29, (2), 909–923.

105. M. Planck: ‘Uber das Gesetz der Energieverteilung im

Normalspectrum’, Ann. Phys., 1901, 4, 553–563.

106. M. Planck: ‘Uber die Elementarquanta der Materie und der

Elektricitat’, Ann. Phys., 1901, 4, 564–566.

107. P. P. Ewald: ‘The mechanical structure of solids from the atomic

viewpoint’, in ‘The physics of solids and fluids with recent

developments’, (ed. J. Dougall and W. M. Deans), 81–152; 1930,

Glasgow, Blackie & Son Ltd.



108. L. Pauling: ‘Quantum mechanics and the chemical bond’, Phys.

Rev., 1931, 37, 1185–1186.

109. L. Pauling: ‘The nature of the interatomic forces in metals’, Phys.

Rev., 1938, 54, 899–904.

110. L. Pauling: ‘The nature of the chemical bond’; 1939, New York,

Cornell University Press.

111. N. F. Mott and H. Jones: ‘The theory of the properties of metals

and alloys’; 1936, Oxford, Oxford University Press.

112. G. I. Taylor: ‘Faults in a material with yields to shear stress while

retaining its volume elasticity’, Proc. R. Soc. Lond. A, 1934, 145A,

1–18.

113. G. I. Taylor: ‘The mechanism of plastic deformation of crystals. 1:

Theoretical’, Proc. R. Soc. Lond. A, 1934, 145A, 362–387.

114. G. I. Taylor: ‘The mechanism of plastic deformation of crystals. 2:

Comparison with observations’, Proc. R. Soc. Lond. A, 1934,

145A, 388–404.

115. E. Orowan: ‘Zur Kristallplastizitat’, Z. Phys., 1934, 89, 605–659.

116. M. Polanyi: ‘Uber eine Art gitterstorung, die einen Kristall

plastisch machen konnte’, Z. Phys., 1934, 89, 660–664.

117. A. A. Griffith: ‘The theory of rupture’, Proc. 1st Int. Cong. on

‘Applied mechanics’, 55–63; 1925, Delft, Technische Boekhandel

en Drukkerij J. Waltman Jr.

118. J. J. Gilman: ‘Commentary on Griffith’s crack theory ‘‘The

phenomena of rupture and flow in solids’’’, Trans. ASM, 1968, 61,

861–907.

119. S. Bottone: ‘On a relation subsisting between the atomic weights,

specific gravities, and hardness of the metallic elements’, Chem.

News, 1873, 27, 215–216.

120. C. Barus: ‘On the relation between the thermoelectric properties,

the specific resistance, and the hardness of steel’, Philos. Mag.,

1879, 8, 341–368.

121. L. M. Cheesman: ‘Uber den Einfluss der mechanischen Harte aur

die magnetischen Eigenschaften des Stahles und des Eisens’, Ann.

Phys. Chem., 1882, 15, 204–224.

122. L. M. Cheesman: ‘Erratum: Uber den Einfluss der mechanischen

Harte aur die magnetischen Eigenschaften des Stahles und des

Eisens’, Ann. Phys. Chem., 1883, 16, 712.

123. C. Barus: ‘On the probability of an inherent relation of the

electrical resistance and the hardness of steel’, Phys. Rev. (Ser. I),

1910, 30, 347–349.

124. C. W. Burrows: ‘Magnetic criteria of the mechanical properties of

a 1% carbon-steel’, Proc. ASTM, 1913, 13, 570–581.

125. J. A. Mathews: ‘Magnetic habits of alloy steels’, Proc. ASTM,

1914, 14, (2), 50–71.

126. C. W. Burrows: ‘Correlation of the magnetic and mechanical

properties of steel’, Bull. Bur. Stand., 1916, 13, 173–210.

127. C. Nusbaum: ‘Certain aspects of magnetic analysis’, Proc. ASTM,

1919, 19, (2), 96–116.

128. K. Heindlhofer: ‘Mechanical and magnetic hardness. Studies in

practical magnetic inspection of ball bearing races heat-treated in

quantity: correlation of hardness’, Iron Age, 1925, 116, 606–608.

129. H. Styri: ‘Relation between magnetic properties, impact strength,

and hardness’, Proc. ASTM, 1931, 31, (2), 94–106.

130. J. V. Emmons and R. L. Sanford: ‘A correlation of some

mechanical and magnetic properties of 1?21% carbon tool steel’,

Proc. ASTM, 1932, 32, (2), 380–397.

131. G. H. Gulliver: ‘Cohesion of steel and relation between tension

and compression yield points’, Proc. R. Soc. Edinburgh, 1908, 28,

374–381.

132. K. Honda: ‘On a mechanical theory of the hardness of metals’,

Sci. Rep. Tohoku Imp. Univ., 1917, 6, 95–99.

133. T. W. Richards: ‘A brief review of a study of cohesion and

chemical attraction’, Trans. Faraday Soc., 1928, 24, 111–120.

134. S. Dushman: ‘Cohesion and atomic structure’, Proc. ASTM, 1929,

29, (2), 7–64.

135. J. A. Ewing and W. Rosenhain: ‘The crystalline structure of

metals’, Philos. Trans. R. Soc. Lond. A, 1900, 193A, 353–375.

136. J. A. Ewing and W. Rosenhain: ‘The crystalline structure of

metals. 2’, Philos. Trans. R. Soc. Lond. A, 1900, 195A, 279–301.

137. F. Osmond and G. Cartaud: ‘The crystallography of iron’, J. Iron

Steel Inst., 1906, 71, 444–492.

138. F. Osmond and G. Cartaud: ‘The crystallography of iron’, Trans.

AIME, 1906, 37, 813–859.

139. J. E. Lennard-Jones and P. A. Taylor: ‘Some theoretical

calculations of the physical properties of certain crystals’, Proc.

R. Soc. Lond. A, 1925, 109A, 476–508.

140. G. T. Beilby: ‘The hardening of metals: introductory paper’,

Trans. Faraday Soc., 1915, 10, 212–215.

141. J. C. W. Humfrey: ‘The part played by the amorphous phase in

the hardening of steels’, Trans. Faraday Soc., 1915, 10, 240–247.

142. A. McCance: ‘The interstrain theory of hardness’, Trans. Faraday

Soc., 1915, 10, 257–264.

143. T. Turner: ‘Hardness and hardening’, J. Inst. Met., 1917, 18, 87–

114.

144. A. H. Stuart: ‘The modulus of elasticity and its relation to other

physical quantities’, Proc. Inst. Mech. Eng., 1912, 83, 1155–1159.

145. J. Innes: ‘The mechanics of solidity’, Nature, 1920, 106, 377.

146. R. G. Durrant: ‘Comment on ‘‘The mechanics of solidity’’’,

Nature, 1920, 106, 440–441.

147. H. Heape: ‘The density and the hardness of the cast alloys of

copper with tin’, J. Inst. Met., 1923, 29, 467–489.

148. H. C. Sorby: ‘On the application of very high powers to the study

of the microscopical structure of steel’, J. Iron Steel Inst., 1886, 29,

140–147.

149. H. C. Sorby: ‘On the microscopical structure of iron and steel’,

J. Iron Steel Inst., 1887, 31, 255–288.

150. E. O. Hall: ‘The deformation and ageing of mild steel. 3:

Discussion of results’, Proc. Phys. Soc. Lond. B, 1951, 64B,

747–753.

151. N. J. Petch: ‘The cleavage strength of polycrystals’, J. Iron Steel

Inst., 1953, 174, 25–28.

152. R. W. Armstrong, I. Codd, R. M. Douthwaite and N. J. Petch:

‘The plastic deformation of polycrystalline aggregates’, Philos.

Mag., 1962, 7, 45–58.

153. P. C. Jindal and R. W. Armstrong: ‘The dependence of the

hardness of cartridge brass on grain size’, Trans. Metall. Soc.

AIME, 1967, 239, 1856–1857.

154. W. H. Bassett and C. H. Davis: ‘Comparison of grain size

measurements and Brinell hardness of cartridge brass’, Trans.

AIME, 1919, 60, 428–457.

155. Z. Jeffries: ‘Effect of temperature, deformation and grain size on

the mechanical properties of metals’, Trans. AIME, 1919, 60, 474–

576.

156. N. J. Gebert: ‘A systematic investigation of the correlation of the

magnetic and mechanical properties of steel’, Proc. ASTM, 1919,

19, (2), 117–129.

157. H. S. Rawdon and E. Jimeno-Gil: ‘A study of the relation between

the Brinell hardness and the grain size of annealed carbon steels’,

Sci. Pap. Bur. Stand., 1920, 16, 557–593.

158. Z. Jeffries and R. S. Archer: ‘Mechanical properties as affected by

grain size’, Chem. Metall. Eng., 1922, 27, 789–792.

159. L. B. Pfeil: ‘The effect of cold work on the structure and hardness

of single iron crystals and the changes produced by subsequent

annealing’, Carnegie Scholarship Mem. Iron Steel Inst., 1927, 16,

153–210.

160. C. H. Matthewson: ‘Discussion on ‘‘Effect of temperature,

deformation and grain size on the mechanical properties of

metals’’’, Trans. AIME, 1919, 60, 562–569.

161. W. A. Wood: ‘X-ray study of grain size in steels of different

hardness values’, Philos. Mag., 1930, 10, 1073–1081.

162. G. R. Gohn: ‘A hardness conversion table for copper–beryllium

alloy strip’, Proc. ASTM, 1955, 55, 230–245.

163. J. T. Richards and E. M. Smith: ‘Problems associated with

hardness conversion of several copper alloys’, Proc. ASTM, 1957,

57, 161–169.

164. A. Wahlberg: ‘Brinell’s method of determining hardness and other

properties of iron and steel’, J. Iron Steel Inst., 1901, 59, 243–298.

165. A. Wahlberg: ‘Brinell’s method of determining hardness and other

properties of iron and steel. 2’, J. Iron Steel Inst., 1901, 60, 234–

271.

166. R. P. DeVries: ‘Hardness in its relation to other physical

properties’, Proc. ASTM, 1911, 11, 726–732.

167. G. L. Norris: ‘Resistance of steels to wear in relation to their

hardness and tensile properties’, Proc. ASTM, 1913, 13, 562–569.

168. R. R. Abbott: ‘The relation between maximum strength, Brinell

hardness and scleroscope hardness in treated and untreated alloys

and plain steels’, Proc. ASTM, 1915, 15, (2), 42–61.

169. A. McWilliam and E. J. Barnes: ‘Brinell hardness and tenacity

factors of a series of heat-treated special steels’, J. Iron Steel Inst.,

1915, 91, 125–139.

170. A. L. Norbury and T. Samuel: ‘Experiments on the Brinell-tensile

relationship’, J. Iron Steel Inst., 1924, 109, 479–491.

171. H. P. Hollnagel: ‘Hardness numbers and their relation: stress–

strain curve in practice and its interpretation in the light of

hardness’, Iron Age, 1925, 115, 770–773.

172. R. H. Greaves and J. A. Jones: ‘The ratio of the tensile strength of

steel to the Brinell hardness number’, J. Iron Steel Inst., 1926, 113,

335–353.



173. H. P. Hollnagel: ‘Stress–strain curves and physical properties of

metal with particular reference to hardness’, Trans. Am. Soc. Steel

Treat. 1926, 10, 87–108.

174. H. Bohner: ‘Uber den Zusammenhang zwischen Brinellharte und

Zugfestigkeit bei Reinaluminium und vergutbaren Aluminium-

legierungen’, Z. Metallkd, 1927, 19, 211–214.

175. S. Kokado: ‘Hardness and hardness measurements’, Tech. Rep.

Tohoku Imp. Univ., 1927, 6, 201–260.

176. C. H. Davis and E. L. Munson: ‘Hardness relationships and

physical properties of some copper alloys’, Proc. ASTM, 1929, 29,

(2), 422–437.

177. W. Rosenhain: ‘Brinell hardness and tensile strength’,

Metallurgist, 1931, 7, 83–85.

178. R. H. Heyer: ‘Factors affecting hardness relationships in the range

50 to 250 Brinell’, Proc. ASTM, 1944, 44, 1027–1050.

179. J. T. MacKenzie: ‘The Brinell hardness of gray cast iron and its

relation to some other properties’, Proc. ASTM, 1946, 46, 1025–

1038.

180. A. Krupkowski and W. Truszkowski: ‘On the relation between the

hardness number and coefficients of the tensile test’, Arch. Mech.

Stos., 1950, 2, 235–259.

181. D. Tabor: ‘The hardness and strength of metals’, J. Inst. Met.,

1951, 79, 1–18.

182. H. Hertz: ‘On the contact of elastic solids’, in ‘Miscellaneous

papers by Heinrich Hertz’, (ed. D. E. Jones and G. A. Schott),

146–162; 1896, London, Macmillan.

183. H. Hertz: ‘On the contact of rigid elastic solids and on hardness’,

in ‘Miscellaneous papers by Heinrich Hertz’, (ed. D. E. Jones and

G. A. Schott), 163–183; 1896, London, Macmillan.

184. M. T. Huber: ‘Zur Theorie der Beruhrung fester elastischer

Korper’, Ann. Phys., 1904, 14, 153–163.

185. E. G. Coker, K. C. Chakko and M. S. Ahmed: ‘Contact pressures

and stresses’, Proc. Inst. Mech. Eng., 1921, 100, 365–467.

186. E. G. Coker and H. F. Donaldson: ‘The applications of polarized

light to mechanical engineering problems of stress distribution’,

Proc. Inst. Mech. Eng., 1913, 84, 83–102.

187. S. P. Timoshenko and J. N. Goodier: ‘Theory of elasticity’, 3rd

edn, 398–422; 1970, Tokyo, McGraw-Hill Kogakusha.

188. F. C. Frank and B. R. Lawn: ‘On the theory of Hertzian fracture’,

Proc. R. Soc. Lond. A, 1967, 299A, 291–306.

189. K. L. Johnson, T. J. O’Connor and A. C. Woodward: ‘The effect

of the indenter elasticity on the Hertzian fracture of brittle

materials’, Proc. R. Soc. Lond. A, 1973, 334A, 95–117.

190. T. R. Wilshaw: ‘The Hertzian fracture test’, J. Phys. D: Appl.

Phys., 1971, 4D, 1567–1581.

191. M. M. Chaudhri and S. M. Walley: ‘Damage to glass surfaces by

the impact of small glass and steel spheres’, Philos. Mag. A, 1978,

37A, 153–165.

192. M. M. Chaudhri and L. Chen: ‘The orientation of the Hertzian

cone crack in soda-lime glass formed by oblique dynamic and

quasi-static loading with a hard sphere’, J. Mater. Sci., 1989, 24,

3441–3448.

193. B. R. Lawn: ‘Indentation of ceramics with spheres: a century after

Hertz’, J. Am. Ceram. Soc., 1998, 81, 1977–1994.

194. H. Hencky: ‘Uber einige statisch bestimmte Falle des

Gleichgewichts in plastischen Korpern’, Z. Angew. Math.

Mech., 1923, 3, 241–251.

195. L. Prandtl: ‘Uber die Eindringungsfestigkeit (Harte) plastischer

Baustoffe und die Festigkeit von Schneiden’, Z. Angew. Math.

Mech., 1921, 1, 15–20.

196. A. J. Ishlinsky: ‘The axial-symmetrical problem in plasticity and

the Brinell test (in Russian)’, Prikl. Matem. Mekh., 1944, 8, 201–

224.

197. R. T. Shield: ‘On the plastic flow of metals under conditions of

axial symmetry’, Proc. R. Soc. Lond. A, 1955, 233A, 267–287.

198. F. Auerbach and C. Barus: ‘Absolute hardness measurements’,

Misc. Doc. House Represent., 1891, 43, 207–236.

199. F. Auerbach: ‘Die Hartescala in absolutem Maasse’, Ann. Phys.

Chem., 1896, 58, 357–380.

200. E. G. Mahin and G. J. Foss, Jr: ‘Absolute hardness’, Trans. ASM,

1939, 27, 337–362.



historical origins of indentation hardness testing_walley

Documents