This article describes investigations into the existence of correlation between experimentally determined cyclic parameters and hardness of quenched and tempered representative low-alloy steel 42CrMo4. A good correlation was found to exist between cyclic strength coefficient K’ and Brinell hardness HB, but not between cyclic strain hardening exponent n‘ and hardness HB. Nevertheless, good agreement between calculated and experimental cyclic stress-strain curves shows that cyclic parameters i.e. cyclic stress-strain curves of the investigated steel can be successfully estimated from its hardness.U radu je istraženo postojanje korelacije između eksperimentalnih vrijednosti cikličkih parametara i tvrdoće poboljšanog niskolegiranog čelika 42CrMo4. Ustanovljena je dobra koreliranost koeficijenta cikličke čvrstoće K’ i Brinellove tvrdoće HB, ali ne i eksponenta cikličkog deformacijskog očvršćivanja n’ i tvrdoću HB. Usprkos tome, dobivenim cikličkim krivuljama naprezanje-deformacija pokazano je da se ciklički parametri i njima definirane cikličke krivulje naprezanje-deformacija ispitivanog čelika sa zadovoljavajućom točnošću mogu procjenjivati već i samo na osnovi njegove tvrdoće

M. Franulović

R. Basan

S. Smokvina Hanza

English

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R. BASAN, M. FRANULOVI], S. SMOKVINA HANZAESTIMATION OF CYCLIC STRESS-STRAINCURVES FOR LOW-ALLOY STEEL FROM HARDNESSReceived – Prispjelo: 2009-05-14Accepted – Prihva}eno: 2009-08-20Original Scientific Paper – Izvorni znanstveni radINTRODUCTIONIn order to shorten product development time and cutdown expenses, simulations and virtual testing of prod-uct models are increasingly being performed duringearly stages of product development cycle, while differ-ent versions are still being considered. One of the mostimportant design decisions which must be made at thatpoint is the proper choice of material. For modelling andsimulation of response of dynamically loaded structuresand components, cyclic and fatigue properties which de-scribe material behaviour must be known. The experi-ment-based determination of their values is certainly themost accurate one. However, due to complexities andhigh costs of cyclic experiments, especially if more ma-terials are taken into consideration, it quickly becomesprohibitive. Since monotonic experiments are simple,inexpensive and usually readily available, advantages ofusing simple tensile data and hardness for estimation ofcyclic and fatigue properties is obvious. For estimationof strain-based approach fatigue properties frommonotonic material properties, number of methods weresuggested 1-5 and reviewed 5-7.This points to the fact that the need for such solutionsexists. Although no suggestions were given for directestimation of cyclic properties i.e. cyclic material be-haviour from monotonic properties, such possibilitywould certainly contribute to improve product design,especially in early stages of development. This work de-scribes investigations of correlations between experi-mentally determined cyclic parameters and hardness oflow-alloy steel 42CrMo4.CYCLIC STRESS-STRAIN CURVESStress-strain response of cyclically loaded materialcan be quite different from the one when it is loadedmonotonically. During loading, material can exhibitstrain hardening, strain softening, its response can bestable and in some cases it can even behave differentlyin various loading phases. The well accepted and widelyused method of describing stress-strain response of mostcyclically loaded metal materials is stabilized ormid-life true stress - true strain curve. It can be deter-mined from strain-controlled cyclic experiments per-formed on a number of standard material specimens [8].The set of representative hysteresis curves, resulting cy-clic stress-strain curve and monotonic stress-straincurve are shown in Figure 1.General methodology and exact procedure for deter-mination of material stress-strain response to com-pletely reversed, cyclic, uniaxial, tensile-compressiveMETALURGIJA 49 (2010) 2, 83-86 83This article describes investigations into the existence of correlation between experimentally determined cyclicparameters and hardness of quenched and tempered representative low-alloy steel 42CrMo4. A good correla-tion was found to exist between cyclic strength coefficient K’ and Brinell hardness HB, but not between cyclicstrain hardening exponent n‘ and hardness HB. Nevertheless, good agreement between calculated and experi-mental cyclic stress-strain curves shows that cyclic parameters i.e. cyclic stress-strain curves of the investigatedsteel can be successfully estimated from its hardness.Key words: cyclic loading, stress-strain curves, hardness, estimationProcjena cikli~kih krivulja naprezanje-deformacija niskolegiranog ~elika na osnovi tvrdo}e. Uradu je istra`eno postojanje korelacije izme|u eksperimentalnih vrijednosti cikli~kih parametara i tvrdo}e po-bolj{anog niskolegiranog ~elika 42CrMo4. Ustanovljena je dobra koreliranost koeficijenta cikli~ke ~vrsto}e K’ iBrinellove tvrdo}e HB, ali ne i eksponenta cikli~kog deformacijskog o~vr{}ivanja n’ i tvrdo}u HB. Usprkos tome,dobivenim cikli~kim krivuljama naprezanje-deformacija pokazano je da se cikli~ki parametri i njima definiranecikli~ke krivulje naprezanje-deformacija ispitivanog ~elika sa zadovoljavaju}om to~no{}u mogu procjenjivative} i samo na osnovi njegove tvrdo}e.Klju~ne rije~i: cikli~ko optere}enje, krivulje naprezanje-deformacija, tvrdo}a, procjenaISSN 0543-5846METABK 49(2) 83-86 (2010)UDC – UDK 669.15-194.2:539.37:620.172.2=111R. Basan, M. Franulovi}, S. Smokvina Hanza, Faculty of Engineering,University of Rijeka, Rijeka, Croatialoading are given in 9. Cyclic stress-strain curves ofmost metals can be successfully represented withRamberg-Osgood equation 8:        2 2 2 2 21   	e pE Kn(1)where: - true total strain range, e - true elastic strainrange, p - true plastic strain range,  - stress range,E - modulus of elasticity,  	 Kn  2 2p- cyclicstrength coefficient, n - cyclic strain hardening expo-nent.MATERIAL DATAThe chosen material is high-strength low-alloy steel42CrMo4 (ISO 683/1; AISI4140; W.Nr. 1.7225) whichis typically used for production of various highly-loadedmachine components and elements such as gears, roll-ing bearings, shafts and cams. Its chemical compositionis given in Table 1.Table 1. Chemical composition of steel 42CrMo4 / wt. %C Si Mn P S Cr0,43 0,26 0,65 0,015 0,021 1,07Ni Mo Cu Al Sn0,19 0,16 0,16 0,021 0,006Required data i.e. hardness, monotonic and cyclicproperties, determined from results of own experiments10 were supplemented with those acquired from avail-able literature 11-15. In total, necessary data weregathered for 40 normalized and quenched and tempered42CrMo4 steels.Values of Brinell hardness HB cover rather widerange, starting from 186 HB and ending with 670 HB.Hardness HB, ultimate strength Rm, cyclic strength coef-ficient K and cyclic strain hardening exponent n aregiven in Table 2.RESULTSThe approach in which direct relationship betweenmaterial parameters of interest is characterized, iswidely used 1-4. Due to its practicality, this approachwas chosen for estimation of cyclic stress-strain curves84 METALURGIJA 49 (2010) 2, 83-86R. BASAN et al.: ESTIMATION OF CYCLIC STRESS-STRAIN CURVES FOR LOW-ALLOY STEEL FROM HARDNESSFigure 1. Stress-strain curvesTable 2. Hardness, monotonic and cyclic parametersof steel 42CrMo4HB E/MPa Rm/MPA K’/MPa n’/-186 205000 665 957 0,1808220 190500 740 673 0,115220 190500 740 637 0,097199 190500 735 807 0,087276 206000 925 1448 0,16282 197000 900 1062 0,0866290 190500 940 1086 0,079290 190500 940 789 0,054293 207000 848 1084 0,082332 190500 1120 1234 0,065332 190500 1120 1097 0,067332 211400 1111 1367 0,104332 211400 1111 2400 0,206332 211400 1111 1146 0,084343 206000 1100 1420 0,12359 206000 1102 1670 0,16381 206842 1410 1974 0,14381 207000 1413 2266 0,124400 200000 1551 1756 0,098400 199000 1550 1556 0,07430 206000 1402 2243 0,17450 206842 1760 2251 0,12450 207000 1758 1997 0,088450 200000 1929 1910 0,088450 206000 1757 2359 0,11450 199000 1929 2000 0,1475 206842 1930 3208 0,14475 200000 1929 2399 0,094475 206000 1929 2713 0,11475 199000 2032 2073 0,08475 200000 2033 1974 0,081505 197000 1750 2483 0,1128526 212000 1890 3599 0,1283526 201000 1789 2708 0,12560 199948 2240 3413 0,11560 206000 2239 4222 0,13568 196000 1900 2412 0,09670 200000 2248 7119 0,179670 199000 2446 3484 0,07670 199000 2447 2821 0,05parameters K and n from Brinell hardness HB in thiswork as well.Two separate nonlinear regressions without weightfactors have been performed on two data sets consistingof Brinell hardnesses HB, as independent variables andcorresponding values of cyclic strength coefficient Kand cyclic strain hardening exponent n as dependentvariables. The relationship which was found to exist be-tween HB and K can be described rather well with asimple expression:K = 0,009(HB)2+0,1173(HB)+376,75 (2)for which the square of correlation coefficient wasfound to be R2 = 0,703. No such correlation could befound between HB and n so that strain hardening expo-nent was approximated with constant value n = 0,1087.This was calculated middle value of n for all materialsconsidered.Experimental values of K and n with superimposedcorresponding calculated values are shown in diagramsin Figures 2 and 3.Using both experiment-based and hardness-basedvalues of K and n and “plastic” part of expression (1),values of  were calculated for following values ofp/2: 0,1 %, 0,2 %, 1 % and 2 %. Results obtained for0,2 % and 2 % are given in form of diagrams in Figures 4and 5.To evaluate predictive accuracy of the proposed esti-mation method, the error criterion 6 was used and frac-tions i.e. percentages of calculated values falling withinscatterband of specified width factor s, Ef (s) were deter-mined. Percentages of calculated stress amplitudes /2 which from experimental values deviate less than10 %, between 10 and 20 % between 20 and 30 % andmore than 30 % are given in diagram in Figure 6.To fully define the relationship between cyclic strainand stress amplitudes (1), apart from the values K andn, the value of modulus of elasticity E is also required.However, since its exact value can be easily obtainedfrom a simple test, “elastic” part of expression (1) wasnot included in the analysis. It can be noted from avail-METALURGIJA 49 (2010) 2, 83-86 85R. BASAN et al.: ESTIMATION OF CYCLIC STRESS-STRAIN CURVES FOR LOW-ALLOY STEEL FROM HARDNESSFigure 2. Experimental and calculated values of K’Figure 3. Experimental and calculated values of n’Figure 4. Values of /2 calculated for p/2 = 0,2 %Figure 5. Values of ∆ /2 calculated for ∆ p/2 = 2 %able material data (Table 2) that a number of steels withidentical hardness (for example, 400 HB and 450 HB)have somewhat different ultimate strength Rm. This,along with information presented in 16 indicates pos-sibility for improving accuracy of cyclic properties esti-mation by taking into account material microstructureand other material properties such as monotonic yieldstress Re, ultimate strength Rm or the difference betweenthem.CONCLUSIONThis work describes the investigation of correlationsbetween experimentally determined cyclic strength co-efficient K and Brinell hardness HB and between cyclicstrain hardening exponent n and hardness HB ofquenched and tempered low-alloy steel 42CrMo4. Arather good correlation was found to exist between K’and HB so that a simple expression characterizing theirrelationship was proposed. As no correlation could bedetermined between n and HB, n was approximatedwith a constant value. Calculated and experimental cy-clic stress-strain curves are in good agreement. Thisconfirms that cyclic parameters i.e. cyclic stress-straincurves can be successfully estimated from hardness onlyand that estimation procedure proposed for investigatedlow-alloy steel 42CrMo4 is valid.AcknowledgementThe authors thank to Ministry of Science, Education andSports of the Republic of Croatia for funding the scien-tific project Nr. 069-0692195-1796 ”Materials, durabil-ity and load capacity of modern gear transmissions”.REFERENCES1 S.S. Manson, Exp Mech SESA, 5, 7 (1965), 193-226.2 J.H. Ong, International Journal of Fatigue, 15 (1993),213-219.3 M.L. Roessle, A. Fatemi, International Journal of Fatigue,22 (2000), 495-511.4 M.A. Meggiolaro, J.T.P. Castro, International Journal ofFatigue, 26 (2004), 463-476.5 R. Basan, Zamor i o{te}enje materijala boka zuba zup~ani-ka, Disertacija, Tehni~ki fakultet - Sveu~ili{te u Rijeci, Ri-jeka, 20096 J.H. Park, J.H. Song, International Journal of Fatigue, 15(1995), 365-373.7 K.S. Lee, J.H. Song, International Journal of Fatigue, 28(2006), 386-400.8 N.E. Dowling, Mechanical Behavior of Materials: Enginee-ring Methods for Deformation, Fracture and Fatigue. Prenti-ce Hall International, New Jersey, 2006.9 ASTM Standard E606, 1992 (1998)10 R. Basan, M. Franulovi}, R. Kunc, Engineering Review, 28(2008) 2, 23-30.11 R.W. Landgraf, Cyclic deformation and fatigue behavior ofhardened steels, T.&A.M. Report No. 320, University ofIllinois, Urbana, 196812 P.N. Thielen, Fatigue studies on 4140 quenched and tempe-red steel, Dissertation, Northwestern University, Evanston,197513 SAE Standard J1099, 199814 L. Reis, B. Li, M. Freitas, Fatigue & Fracture of Enginee-ring Materials & Structures, 27 (2004), 775-784.15 R. Kunc, I. Prebil, J. Korelc, T. Rodi~, M. Torkar, Materialsand Technology, 35 (2001), 107-112.16 B. Smoljan, S. Smokvina Hanza, D. Iljki}, G.E. Totten, I.Felde, Computer simulation of mechanical properties of ste-el dies, 2nd International Conference on Heat Treatmentand Surface Engineering of Tools and Dies: Extended ab-stracts in Materials and Technology (ISSN 1580-2949); 42(2008) (Special issue) / Leskov{ek, V.; Smoljan, B.; Jager,H.; Jenko, M. (ur.). Ljubljana : Institute of Metals and Tec-hnology, (2008), 154-155.Note: Linguistic advisor for English language is Ksenija Mance, Facultyof Engineering, Rijeka.86 METALURGIJA 49 (2010) 2, 83-86R. BASAN et al.: ESTIMATION OF CYCLIC STRESS-STRAIN CURVES FOR LOW-ALLOY STEEL FROM HARDNESSFigure 6. Percentage of estimated values of stress ampli-tude /2 which from experiment-based valuesdeviate up to 10 %, 10 to 20 %, 20 to 30 % andmore than 30 %

Procjena cikličkih krivulja naprezanje-deformacija niskolegiranog čelika na osnovi tvrdoće

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