DYNAMIC HARDNESS DURING DIFFERENT PHASES OF INDENTATION. Vytautas Vasauskas Kaunas University of Technology, Lithuania.

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1 DYNAMIC HARDNESS DURING DIFFERENT PHASES OF INDENTATION ytuts susks Kuns University of Technology, Lithuni. Abstrct. The pper reports on the underlying concept for securing the mesuring bsis used in the method of dynmic hrdness which employes one of the stndrd indenttion methods nd vrious shpes of indenter. The complete dynmic indenttion cycle cn be divided into the three following phses: strting phse, indenttion phse nd rebound phse. The vlue for severl engineering metls obtined dynmic hrdness in vrious phses of indenttion ws higher thn the sttic hrdness. 1. Introduction There is fundmentl difference between sttic nd dynmic hrdness testing: in sttic tests the effective force cting on the penetrtion indenter is clerly nd comprehensively determined throughout the entire process of indenttion into the specimen [1]. In the cse of dynmic indenttion, however, the lod (F) cting on the indenter chnges during the vrious phses of the impct cycle [, ]. The depth of penetrtion together with the known geometry of the indenter provides n indirect mesure of the re (volume) of contct t full lod, from which the men contct pressure, nd thus hrdness, my be estimted [4]. The present work reviews these two most commonly used methods of nlysis of dynmic indenttion test dt nd their ssocited corrections. A mesurement for determining the dynmic hrdness tht prllels the method for sttic hrdness determintion pertinent to moderte velocity impct ws obtined.. Bckground Conventionl dynmic hrdness test methods re bsed lmost exclusively on the mesurement of the potentil residul energy [1]. It is disdvntge for ll test methods developed in recent yers tht for prcticl ppliction, reference to the stndrdized procedures is lwys required. In very mny cses the difference between clibrtion mchine nd series-procedures hrdness tester seems not to be entirely understood []. Striker h 0 S0 strt Strik contct stge non-contct stge rb h Sreb Indenter Specimen Indent Specim h=0 h mx A h reb Strting Indenttion Rebou Rebound d Fig. 1. Dynmic hrdness indenttion test phses for triple striker indenter specimen system: strting, indenttion nd rebound phses. Contct or non contct stges for indenter specimen system re evident The dynmic hrdness vlue during impct is equl to the energy expended in producing the indenttion fter rebound hs occurred (=energy of impct minus energy of rebound) divided by the volume of indenttion [1]. A different pproch ws dopted in testers clled Shore rebound R

2 scleroscopes, where the height of the rebound itself is used s mesure of the dynmic scleroscope hrdness. If the height of the fll is constnt, the height of the rebound is roughly proportionl to the sttic hrdness of the mteril concerned. The second is the energy quotient return (EQUOTIP) method where the energy loss in the elstic-plstic contct is evluted electroniclly from the rtio of the velocities of the indenter before nd fter impct []. During the process, the impct velocity A nd the rebound velocity R of the indenter re mesured when it is bout 1 mm from the test surfce. These two mesurements re used to determine the EQUOTIP hrdness vlue L by mens of the eqution L=1000 R / A. To llow comprison between the kinetic energies t impct in vrious types of test the concept of the equivlent impct energy ws introduced [4]. The complete test procedure for dynmic hrdness mesurement my be divided into the following stges: strting (striking) phse; indenttion phse nd rebound phse (Fig. 1). During the strting (striking) phse the potentil energy of the testing work-piece is converted into kinetic energy either by free fll or by spring mechnism. Thus for given contct geometry the intrinsic coefficient of restitution is uniquely determined by the degree of recovery nd useful mesure of the degree of reversibility of contct deformtion. At the end of the indenttion process, where the plstic flow of the metl hs come to the end nd regime of purely elstic stresses hs been reched, the pressure involved in the formtion of indenttion of the sme size under sttic conditions. Therefore, possible clssifiction of the dynmic hrdness mesurements must reviewed only for two questions, which dels with the dynmic hrdness mesurements contct or non-contct? This method is bsed on n nlysis of the energy tht for the residul energy remining in the impct indenter of spring cs mvk ctivted device nd present prior to impct + mgs + W f =, where cs / - potentil energy of the spring system; mgs potentil grvittionl energy; W f the energy consumed due to frictionl effects long the pth s, m-mss of impcting indenter, v k -incident velocity. In greement with the introductory sttements bove the efficiency of the indenttion process is defined s η = W1 / W0, where W 1 = Fdh is the work performed on the smple s result of single representtive impct, nd W 0 is the totl kinetic energy of the striker. The impct process cn be modelled most esily if we ssume tht contct dynmic yield pressure p d (i.e. dynmic hrdness, H d ) opposes the indenter. In relity p d chnges continuously during the impct process (Fig. ). It is converient, initilly, to consider the indenttion between the indenter nd specimen s hving two phses, of which the second my be further divided into two stges. Thus the ssumed constnt p d will correspond to some men vlue. In such cse, simple energy blnce between the kinetic energy of the impcting indenter nd the energy required to form the resulting impression volume gives n expression for dynmic hrdness, H d. For exmple (Fig. 1), if m is the mss of the impcting indenter, v its incident velocity, v r is rebound velocity nd the finl 0, 5m( v vreb ) volume of the impression formed, then p d = = H dv. Invrince of the indenttion pressure in hrdness mesurements requires tht the plstic zone volume be governed exclusively by the indenttion volume. It follows from this tht the indenttion volume be compensted by 1/ the misfit induced in the totl plstic zone. It hs been shown tht the reltion β = ( / ) = b / [ ] is n importnt prmeter nd found the following reltion = 1+ ln( β ), where b is the plstic zone dimension, is the core rdius. Method of energy mesurement is bsed on the mesurement of both kinetic energy components, i.e. the impct energy nd rebound energy. Deformtion model, ssume tht the volume of impression produced by the impct indenter, is proportionl to the kinetic energy, W, of the indenter but is independent of its shpe or tip ngle, θ. Since the volume of rigid cone with n pex ngle of θ is = π / 4cotθ d, where d is the dimeter of the bottom of the right cone W = W = π W0 / 4 cotθd W kd, where W o is the H σ y o = o 1

The lod cn be derived by tking the hrdness H = αf / h, where α is constnt depending on the geometry of the indenter pex ngle nd h the depth of the surfce impression.

3 ssumedly constnt kinetic energy bsorbed per unit volume of deformed metl, nd k=π cot θ / 4, is constnt. F c 1 Fig.. Indenttion volumes for cross-section: model for indenttion, b zone of plstic flow in the mteril underneth the indenttion in the test specimen The lod reches its mximum vlue t mximum penetrtion. The lod cn be derived by tking the hrdness H = αf / h, where α is constnt depending on the geometry of the indenter pex ngle nd h the depth of the surfce impression. The mximum penetrtion during impct cn be obtined by equting the frction of the kinetic energy tht is lost during the impct of the indenter on the specimen with the plstic work (W pl ) b W pl h mx = 0 F( z )dz 1 = mv ( 1 e ) (1) where v is the impct velocity, h mx the mximum penetrtion, m the mss of the indenter, nd e the coefficient of restitution. Integrtion of Eq.(1) leds to n expression for h mx which depends on H -1/.. Experimentl Dynmic indenttion experiments were produced in the specimen by impct in the velocity rnge 1 to 40 ms -1. As ws shown by D.Tbor [1] dynmic effects become significnt for impct velocities 100 ms -1. The conformity of the dt to this line indictes tht ny vrition of hrdness over the velocity rnge 5 to 40 ms -1 is smll. The mesurement system consists of n impct device nd n electronic indictor device (Fig. ). Fig.. Schemtic of the experimentl set-up for dynmic indenttion The impct device fires the impct body ginst the mteril to be tested in system striker indenter specimen [4]. The detected signls re smpled nd processed by the computer, which monitors s well the trnsducer moves. A piezoelectric trnsducer sensed lods, while displcements were determined from the indenter trvel recorded by mens of the photocell. The

4 piezoelectric trnsducer (140 khz resonnt) is pplied to the indenter, thus ensuring tht impct signls cn be received even when process is elstic. After further mplifiction, the signls re nlysed for member of counts nd intensity (ADS 10 bits). Function F(t) nd h(t) re ccounted for dots. Choosing striker brs of vrious lengths cn vry the durtion of the input pulse nd the mplitude of the incident compression stress pulse (or the incident lod). Fig.4 shows the indenttion depth under lod. This represents condition where the indentor under lod is exerting force tht is in equilibrium nd pposed by mteril- depended force. Evlutions of the dynmic force re summrized in Fig.4, which shows the force t three stges of indenttionrebound stge for metls of vrious hrdness HRC. An exmintion of the energy blnce during the impct indictes tht t lest 70-80% of the initil kinetic energy of the indenter is dissipted only in plstic deformtion in the specimen. The kinetic energy of the rebounding is estimted from mesured coefficients of restitution depending on indenttion geometry, impct velocity nd specimen mteril. Thus, Wo = W 1 ηo, where W 1 is ll ccumulted initil kinetic energy of striker, η o is totl efficiency for the striker-indenter-specimen set is η o =η 1 η, where η 1 = , η is loss of energy t the indenter-specimen impct for non-liner plstic deformtion of cone indenter. Indenttion lod F mx Indenttion depth h mx Fmx F 1 (inerti term) t 1, 1, F~U=f(t) F F h h h T 1 (initil indenttion) (rebound t Elstic recovery Residul plstic depth Specimen hrdness HRC h~u=f(t) Fig. 4. Typicl continuous indenttion force displcement curves. Indenttion phse corresponds to three wves of deformtion F 1, t 1., ms F, F, m1 According to Fig. we hve η = ( 1 eθ ), where e θ is restitution fctor s function of indenter m1 + m pex ngle θ, m 1 is striker mss, m is indenter mss; for m 1 /m =0.5 nd cone ngles θ=90 o 160 o η = The coefficient of restitution e is, of course not mteril property, but useful mesure of the degree of reversibility of the contct deformtion processes. ( 1 eθ ) gives the frction of the kinetic energy input expended in indenttion cycle. It my be seen tht the dissipted system energy will be distributed between the striker nd indenter in inverse proportion to their reltive stiffness. Then totl efficiency of the dynmic system in our experiments ws for vrious indenttion ngles in the rnges Results nd Discussion The existence of residul indenttion nd tht the penetrtion vries with pplied contct lod F through the indenttion cycle (Fig. 4) mens tht the F(h) curve must show some hysteresis on unloding nd indenttion volume relxes elsticlly. It is pprent from the experimentl curves (Fig. 4) tht in generl the coefficient of restitution of impcting solids cpble of undergoing plstic deformtion will not be constnt. At the end of the impct where the elstic compression nd recovery tke plce, the plstic flow of the mteril hs come to n end. There is no further bulk displcement of metl round the indenter, nd no energy is expended in pushing the metl wy from the indenttion. All the deformtion round the indenter is now of n elstic nture, nd ny

5 kinetic energy imported to the mteril under these conditions should be reversible. As result the pressure t this stge my be expected to be essentilly the sme s the men pressure p m required to produce plstic yielding nd corresponds to the Meyer sttic hrdness number. As the indenttion ngle decreses, there will be corresponding decrese in the coefficient of restitution. The constitutive eqution describing the mechnicl behviour of elstic-plstic mteril is generlly given by the power-lw eqution σ=k ε n, where σ is the flow stress nd ε is the true strin. K nd n re the mteril prmeters, where K is the strength coefficient, nd n is the strinrte sensitivity fctor. We hve derived [4] the following eqution to describe the plstic deformtion of recovered indenttion volume in terms of the indenttion dimeter (depth): A Ao 1 1 ε 1 1 ln Ao sin θ = = =, where ε - verge contct deformtion, A1 = πd / 4 sinθ is surfce sin θ of indenttion, A o = πd / 4 projection re indenttion, θ is indenttion (cone) ngle, d is dimeter of indenttion. Estimtes of the strin beneth conicl indenters, bsed on simple geometry, indicte vlues rnging from to 0.5 for nd 90 0 cones respectively. Indenttion lod Indenttion depth U, HRC F~U=f(t) 0. 0 t, s.e E E-04 U, 0.6 HRC I II III Г~U=f(t) Fig. 5. Typicl dynmic indenttion force displcement curves (cone indenter θ =90 0 ) for vrious steel specimens (hrdness HRC = 67) The flow stresses t room temperture chnge significntly over this rnge nd therefore the hrdness depends on cone ngle nd metls show norml work-hrdening properties under these conditions. These chrcteristics re reflected in the results presented in Fig. 6. Thus ll the experiments reported here re bsed on cone tungsten crbide indenters of ngles 60 0 <θ<180 0 t the tip. The sttic hrdness is observed to increse s the deformtion size increses, indicting tht certin mount of strin hrdening hs occurred. In dynmic conclusion we hve, t first, tht when deformtion size increses hrdness (Fig. 6,, curve 1) decreses. The dynmic nd sttic hrdness mesurements obtined from indenttion digrms in contct indenttion phse for severl metls re shown in Fig. 6, b. The percentge hrdness increse in dynmic hrdness mximum over the sttic mximum vlue, i.e. (H d H s )/H s x100%, is lso indicted on the right side of Fig. 6, b. For steels this increse is between 10 0% nd for mterils like luminum nd copper vries from 1 10%. All the deformtion round indenter is now of n elstic nture, nd ny kinetic energy imprted to the mteril under these conditions should be reversible.

6 Hrdness, (10, Mp) Indenttion contct ngle, θ Mteril Ti6Al14 Tool steel Steel Gry iron Al Cu Dynmic: rebound H dr volume H dv Sttic H st b % Hrdness increse Fig. 6, - stress-strin curves for sttic nd dynmic indenttion hrdness: 1, -contct friction unccounted,, 4-contct friction nd efficiency of dynmic system striker-indenter-specimen set ccounted; b - summry of sttic nd dynmic indenttion hrdness mesurements for severl commercil metls As result the pressure t this stge my be expected to be essentilly the sme s H dv. As shown in fig.5 for the hrder metls the vlue H dr re less thn 10% higher thn H st,.whilst the vlues H dv.re 0 to 0% higher. With the soft metls the difference between H dv.nd H dr.becomes very mrked indeed. The dynmic yield pressure H dv.is now very much higher thn the sttic pressure H st.wheres H dr.remins reltively close to the sttic vlues. Dynmic hrdness is 1,1-1,40 times higher the sttic hrdness, becuse of the effect of strin rte on the deformtion of mteril. Also we see tht vlue of the friction ffects the mgnitude of the men pressures necessry to form the indenttions nd position of the mximum. 5. Conclusions The technique prllels the method for sttic indenttion hrdness determintion nd llows direct comprisons between sttic nd dynmic hrdness mesurements. The dynmic hrdness ws evluted from mesurements of prmeters for vrious phses of indenttion cycle. The dynmic hrdness ws found higher thn hrdness determined by sttic indenttion, lthough the morphology of the dmge surrounding the contct site is similr in sttic loding nd impct. It is obviously cler tht the bove dynmic hrdness testing methods does not mintin the simplicity nd the low cost of sttic hrdness testing. 6. References [1] Tbor D. The Hrdness of Metls, Oxford Univ.Press, London, [] Tiruptih, Y. nd Sundrjn, G. A Dynmic Indenttion Technique for the Chrcteriztion of the High Strin Rte Plstic Flow Behviour of Ductile Metls nd Alloys, J. Mech. Phys. Solids, v.9 (), 1991, p.p [] Leeb, D. Definition of the Hrdness lue L in the EQUOTIP Dynmic Mesuring Method, in: Hrdness testing in theory nd prctice, (DI-Berichte, 58).-Düsseldorf, 1986, p.p [4] susks,. Geometry effect of indenters on dynmic hrdness,-proc. of the XI IMEKO World Congress IMEKO 000, v. III.-Austrin Society for Mesurement nd Automtion, Austri, ien, 000, p.p

Lesson 8. Thermomechanical Measurements for Energy Systems (MENR) Measurements for Mechanical Systems and Production (MMER)

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