IOP Coferece Series: Materials Sciece ad Egieerig PAPER OPEN ACCESS Iformativeess Improvemet of ardess Test Methods for Metal Product Assessmet To cite this article: S Osipov et al 016 IOP Cof. Ser.: Mater. Sci. Eg. 13 0100 Related cotet - Research o a measuremet method for wheat hardess Chao Fa, Jig-bo Xu, Tie-ju Yag et al. - Traceability i hardess measuremets: from the defiitio to idustry Alessadro Germak, Korad errma ad Samuel Low View the article olie for updates ad ehacemets. This cotet was dowloaded from IP address 46.3.03.50 o 0/01/018 at 1:4
IV Iteratioal Coferece o Moder Techologies for No-Destructive Testig IOP Publishig IOP Cof. Series: Materials Sciece ad Egieerig 13 (016) 0100 doi:10.1088/1757-899x/13/1/0100 Iformativeess Improvemet of ardess Test Methods for Metal Product Assessmet S Osipov 1, I Podshivalov, O Osipov 3 ad A Zhatybaev 4 1 Leadig Researcher, Natioal Research Tomsk Polytechic Uiversity, Tomsk, Russia Associate Professor, Tomsk State Uiversity of Architecture ad Buildig, Tomsk, Russia 3 Egieer, Natioal Research Tomsk Polytechic Uiversity, Tomsk, Russia 4 Master Studet, Natioal Research Tomsk Polytechic Uiversity, Tomsk, Russia E-mail: osip1809@rambler.ru Abstract. The paper presets a combiatio of theoretical suggestios, results, ad observatios allowig to improve the iformativeess of hardess testig process i solvig problems of metal product assessmet while i operatio. The hardess value of metal surface obtaied by a sigle measuremet is cosidered to be radom. Various measures of locatio ad scatterig of the radom variable were eperimetally estimated for a umber of test samples usig the correlatio aalysis, ad their close iteractio was studied. It was stated that i metal assessmet, the mai iformative characteristics of hardess testig process are its average value ad mea-square deviatio for measures of locatio ad scatterig, respectively. 1. Itroductio The assessmet of metal products while i operatio shows their degradatio due to such egative factors [1 3] as wear abrasio, corrosios, ad fatigue. Oe of the metal assessmet methods used for products while i work ad operatio is their hardess testig [5 6]. For the last two decades, metal assessmet methods have bee itesively developed as well as istrumets ad scopes of their applicatio [7 9]. The traditioal use of durometers implies measuremet of product at its several poits, ad the average value of obtaied results should be used to assess the metal hardess. Ekici, Starikov, Muzyka, et al. [10 1] showed that the use of the additioal iformative parameter idetified durig the hardess testig process, amely, the hardess scatterig, allows the improvemet of the metal assessmet method. Util recetly, the implemetatio of this techique has bee restricted by the istrumet uavailability. owever, the productio of high-ed portable durometers with a lower effect o test samples elimiated this restrictio, ad a parallel evaluatio of the average value of hardess ad its certai measure of scatterig is ow beig used i trasportatio, costructio ad other idustries [13 15]. The literature review cocerig the use of other iformative hardess parameters showed the isufficiecy of the data.. Theory Mechaical stresses, corrosios, ad itesive tesile ad compressive forces result i structural modificatios of the surface layers of metals ad alloys. Cotet from this work may be used uder the terms of the Creative Commos Attributio 3.0 licece. Ay further distributio of this work must maitai attributio to the author(s) ad the title of the work, joural citatio ad DOI. Published uder licece by IOP Publishig Ltd 1
IV Iteratioal Coferece o Moder Techologies for No-Destructive Testig IOP Publishig IOP Cof. Series: Materials Sciece ad Egieerig 13 (016) 0100 doi:10.1088/1757-899x/13/1/0100 The followig variats are the most visible maifestatio of these chages: surface roughess (the kid, directio, ad level of mechaical stresses as well as their duratio defie the degree of the surface modificatio. It should be oted that surface roughess ca be both icreased ad decreased); small disorieted fatigue cracks; eplicit, orieted ad rather deep cracks. Such cracks are usually iduced by metal-to-metal cotact of parts by repeated trajectories; corrosio spots (oides, salts of mother metal(s)). The specific desity (relative fractio of corrosio spot area) ad the size of spots deped o the duratio the metal product eposure to such hazardous factors as humidity, acid ad acid solutio vapors, alkalis, ad salt solutios; oide, salt ad other films produced by corrosio. The value of hardess obtaied by a sigle measuremet is aturally cosidered to be radom. The radom variable is completely defied i case its probability desity fuctio F() is kow [16]. The radom variable collectio of characters is divided ito two large groups, amely: measure of locatio ad measure of scatterig. I the work of Kor et al. [16], measures of locatio of radom variable iclude the average value, media Me ad mode Mo. Measures of scatterig of radom variable iclude dispersio σ, mea-square deviatio σ, coefficiet of variatio V, coefficiet of skewess A, ad coefficiet of ecess E. Note 1 I scietific literature, the distributio fuctio of the radom variable is described by differet laws such as logormal, ad Weibull ad Gumbel distributios. These laws are twoparameter distributios which comprise a measure of locatio ad a measure of scatterig. All metioed measures of locatio ad scatterig icludig those i Note 1 ca be used for metal assessmet whe applied to the radom variable. Note. The degree of metal surface uiformity of hardess, sometimes called the coefficiet of uiformity k [1 14], is coected with values of measure of locatio. Note 3. The estimatio of hardess value obtaied by a sigle measuremet depeds o the cotact area betwee the ideter ad the material beig tested. From Note 3 it follows that the smaller the size of ideter the more evidet is the scatterig of hardess. Presetly, the size of ideters ad their peetratio force ca be varied. Depedig o the size of idetatio, hardess, micro-, ad ao-hardess ca be measured. Let us put forward the basic statemets which allow a substatiatio of character of the radom variable used i the capacity of metal product assessmet provided by hardess test methods. Statemet 1. The chage of metal surface properties uder ay impact coditios is caused by its structural modificatio. Statemet. For each of variats of visible maifestatio of chages stated above, the surface layer modified durig the product operatio will possess at least oe hardess parameter regarded as a radom variable, dissimilar to the respective oe of the origial metal. Note 4. Oe iformative parameter of hardess may tur to be isufficiet to provide the metal assessmet. I this case, it is advisable to use two or more iformative parameters. Statemet 3. A samplig parameter of the radom variable selected from the collectio of those to be aalyzed ca be iformatively ecessive i case it is closely coected with oe or more residual parameters. Close coectio betwee radom variables ad y is evaluated usig the correlatio factor r y. Parameters ad y are cosidered to be closely coected i case the correlatio factor r y satisfies the coditio of r 0 r y 1. The lower boud r 0 of this iterval is determied eperimetally. Sice the authors preset techical measuremets, the value r 0 rages betwee 0.85 0.95. It is logically to select such a parameter which is easy to idetify for further aalysis or some argumets ca be put forward i favor of its applicatio i case it possesses a eplicit physical iterpretatio. Cosequece of Statemet 3 I metal assessmet, the samplig y parameter of the radom variable is additioal to the iformative parameter i case it is idepedet of parameter. Let us assume that coectio betwee ad y parameters are egligible at the fulfillmet of 0 r y r 1 coditio. The lower boud r 1 of this iterval is also determied eperimetally. The value r 1 rages betwee 0.1 0..
IV Iteratioal Coferece o Moder Techologies for No-Destructive Testig IOP Publishig IOP Cof. Series: Materials Sciece ad Egieerig 13 (016) 0100 doi:10.1088/1757-899x/13/1/0100 3. Eperimetal With a view to assess the iformativeess of parameters describig the radom variable, a series of hardess tests was coducted for steel specimes eposed to differet types of eteral actios. Specimes of differet steel types were tested havig average value of hardess ragig from 80 to 00 B. Calibratio measuremets were coducted by Briell hardess of 100 ad 184 B. ardess measuremets are characterized by the high-quality treatmet of the surface. Therefore, the effect eerted by the surface roughess o the hardess properties assessmet as a radom variable, is miimized. ardess tests were carried out with the dyamic ideter TEMP-4 i compliace with recommedatios give by techical specificatios ad guidelies. The origial samplig was provided for each test specime usig Briell hardess ( 1,, 3,..., ), where is the volume of samplig ( 00). I all, seve specimes were tested. Measures of locatio ad scatterig of the radom variable were estimated for each specime. All samplig parameters were subsequetly cosidered as radom variables. I accordace with the Cosequece of Statemet 3, the idepedece (level of depedece) of these values was verified by couples of parameters. At the first stage of the eperimetal data processig the followig parameters of the radom variable were estimated: the average value ; media Me; ad mode Mo. These parameters ca be obtaied from [16]: i1 i, 1 i Me 1, i Me f (Mo ) ma f ( ). (1) Alog with measures of locatio, measures of scatterig were determied: mea-square deviatio σ, coefficiet of variatio V, coefficiet of skewess A, ad coefficiet of ecess E. Scatterig parameters [16] ca be obtaied form i i1 σ m3 m4 σ, V, A, E 3 3. () m m where m k is the cetral k-order samplig momet of the value aalyzed. It ca be foud from [16]: m k k i i. (3) Accordig to ote, parameters of the assumed radom distributio ca act as measures of locatio ad scatterig. I the umber of scietific papers devoted to the study of stregth of materials, it is assumed that or l radom variables are Weibull-distributed. The radom variable is Weibull-distributed [16] i case its distributio fuctio is described by equatio 4: k F( ) 1 e. (4) I additio to (1) ad (), the locatio of the radom variable will be characterized by λ ad λ l parameters, while its scatterig by k ad k l parameters. 3
IV Iteratioal Coferece o Moder Techologies for No-Destructive Testig IOP Publishig IOP Cof. Series: Materials Sciece ad Egieerig 13 (016) 0100 doi:10.1088/1757-899x/13/1/0100 Weibull distributio parameters k ad λ ca be obtaied usig the method of matchig momets. Two iitial momets ad are to be obtaied for the radom variable. Weibull distributio parameters k ad λ are obtaied from [17]: 1 k, 1 1 k 1 1 k 0 z1 t, ( z) t e dt. (5) I [11 13], the authors describe the method of estimatio of the coefficiet k l : l i l i l i1 i1 l, l. (6) 1 Gumbel approimatio for k parameter is as follows: l 0,4343d k. (7) It is assumed that the larger values of k ad k l coefficiets provide the low level of hardess scatterig ad the better structural orgaizatio ad the lower degree of damage. Ulike the larger, the smaller values of k ad k l coefficiets provide the highest degree of damage. It was show i [11 13] that the level of scatterig measures of metal property to be idetified, icludig hardess, ca correspod to aother statistical criteria. I the preset work, the authors verify the validity of this statemet. At the secod stage, verificatio of the availability, directio, ad closeess of correlatio betwee parameters of the radom variable was carried out usig the correlatio aalysis. I case of samplig ( 1,,, ) ad (y 1, y,, y ) for ad y radom variables, the correlatio factor r y takes the form r y y y y. (8) The sig ad the absolute value of a correlatio factor describe the directio ad the magitude of the relatioship betwee two variables. The radom variables ad y ru over all possible locatio ad scatterig parameters, respectively. I equatios 3, the umber equals to the umber of specimes. Seve specimes ( = 7) are sufficiet merely for a prelimiary study of the problem. The estimatio of the coefficiet of uiformity k based o equatio 5, is rather complicated ad requires a prelimiary costructio of the additioal fuctio of k. I equatio 5 this fuctio is epressed by the right had side of the equatio. Mathcad iteded for the verificatio, validatio, documetatio of egieerig calculatios, ca be a alterative for solvig this problem. 4. Results ad discussio Table 1 gives the results of statistical processig of eperimetal data o Briell hardess of specimes. Table 1 cotais the values of parameters of the radom variable locatio, amely: Me, Mo, λ ad λ l. Also there are give parameters of σ, V, A, E, k, k l, which determie the hardess scatterig. Parameters of locatio ad scatterig of were idetified usig equatios 1 ad 5 7. 4
IV Iteratioal Coferece o Moder Techologies for No-Destructive Testig IOP Publishig IOP Cof. Series: Materials Sciece ad Egieerig 13 (016) 0100 doi:10.1088/1757-899x/13/1/0100 Table 1. A summary table of samplig parameters of. Measure Parameter Specime umber 1 3 4 5 6 7 Locatio 100.8 184. 119. 16.0 16.4 177.8 19.3 Me 101. 184.3 11.7 14.3 18.9 177.6 191.4 Mo 97.1 184.3 11.7 1.7 134.0 183. 187.3 λ 111.7 04 13 139.6 139.9 197 13 λ l 106.9 189. 19.3 138. 139.7 191.5 03.1 Scatterig σ 7.13 5.19 1.00 15.93 19.07 15.90 1.06 V 0.0708 0.08 0.1006 0.163 0.1509 0.0894 0.067 A 0.984 0.46 0.603 0.144 0.839 0.88 0.197 E 3.90 1.78 0.47 0.81.09 1.37 0.36 k 17.485 44.917 1.103 9.51 7.935 13.697 19.817 k l 5.104 0.131 5.359 4.446 3.841 6.11 9.014 I order to aalyze iformativeess of oe or aother parameter of the radom variable B ad idetify the ecessive parameters, oe ca use the correlatio aalysis. It should be oted that the samplig volume is isigificat. owever, it may tur to be eough to determie iformativeess of the suggested process of hardess testig. The correlatio factor r y is calculated from equatio 8. ere radom variables ad y ru over all parameters of the radom variable, amely:, Me, Mo, λ, λ l, σ, V, A, E, k, ad k l. Correlatio factor values for hardess parameters are give i table. Table. Correlatio factor values for hardess parameters. Parameters Me Mo λ λ l σ V A E K K l 1.00 0.99 1.00 1.00 0.1 0.55 0.5 0.35 0.55 0.64 Me 1.00 0.99 1.00 1.00 0.1 0.54 0.5 0.34 0.55 0.64 Mo 0.99 0.99 0.99 0.99 0.05 0.48 0.7 0.3 0.51 0.61 λ 1.00 1.00 0.99 1.00 0.1 0.55 0.5 0.35 0.55 0.64 λ l 1.00 1.00 0.99 1.00 0.03 0.47 0.8 0.39 0.47 0.57 σ 0.1 0.1 0.05 0.1 0.03 0.88 0.0 0.38 0.80 0.69 V 0.55 0.54 0.48 0.55 0.47 0.88 0.0 0.18 0.87 0.80 A 0.5 0.5 0.7 0.5 0.8 0.0 0.0 0.63 0.17 0.08 E 0.35 0.34 0.3 0.35 0.39 0.38 0.18 0.63 0.19 0.05 k 0.55 0.55 0.51 0.55 0.47 0.80 0.87 0.17 0.19 0.98 k l 0.64 0.64 0.61 0.64 0.57 0.69 0.80 0.08 0.05 0.98 From table, the followig itermediate coclusios ca be draw relative to mutual parameter depedecies which characterize the radom variable. 1. All parameters of the radom variable locatio, amely, Me, Mo, λ, λ l, are strictly depedet o each other; correlatio factors are close to zero; the depedecies are strog ad direct.. The mea-square deviatio σ does ot deped o ay locatio parameter of the radom variable ; the absolute values of the correlatio factor do ot eceed 0.1. 3. The correlatio factor V weakly depeds o all parameters of locatio. These depedecies are iverse; the absolute values of the correlatio factor rage from 0.47 to 0.55. 4. Depedece betwee skewess A ad ecess E coefficiets ad locatio parameters is practically abset; the absolute values of the correlatio factor are less tha 0.39. 5. Depedece betwee coefficiets k ad k l is direct ad takes the iterfacial positio betwee medium ad weak depedecies; the absolute values of the correlatio factor rage from 0.57 to 0.64. 5
IV Iteratioal Coferece o Moder Techologies for No-Destructive Testig IOP Publishig IOP Cof. Series: Materials Sciece ad Egieerig 13 (016) 0100 doi:10.1088/1757-899x/13/1/0100 6. The scatterig parameters show the followig depedecies: direct σ V depedece with 0.88 correlatio factor; iverse σ k depedece with 0.8 correlatio factor; V depedece o both k ad k l with 0.8 0.87 correlatio factor. 5. Implicatios From the itermediate coclusios stated above it follows that: 1. All of, Me, Mo, λ, λ l parameters ca be used as a measure of locatio of the radom variable. owever, it is more feasible to use sice it is easily idetified. All other locatio parameters of the radom variable ca be used to eclude radom errors i calculatios.. Parameters σ, A, E ca be used as a measure of scatterig. All other scatterig parameters show a strog depedece o locatio parameters. It is more feasible to use a mea-square deviatio as a parameter least depedet o ay locatio parameter. 6. Coclusio The eperimets showed that i metal assessmet, the mai iformative characteristics of hardess testig process are its average value ad mea-square deviatio for measure of locatio ad measure of scatterig, respectively. All other parameters ca be used to improve the metal assessmet methods. For this improvemet it is epediet to develop multi-chael durometers, the appropriate algorithms of eperimetal data visualizatio ad processig. Ackowledgemet This work was fiacially supported by The Miistry of Educatio ad Sciece of the Russia Federatio i part of the sciece program. Refereces [1] Jacobs J J et al 009 J. Am. Acad. Orthop. Surg. 17 () 69 76 [] Zhag S W et al 004 Wear 56 6 3 [3] Abosrra L et al 011 Costructio ad Buildig Materials 5 (10) 3915 395 [4] ashemi S 011 Mater. Sci. Eg. A. 58 1648 1655 [5] Aboutalebi F et al 011 It. J. Adv. Mauf. Techol. 53 157 165 [6] ołowaty J M ad Wichtowski B 013 Structural Egieerig Iteratioal 3 51 518 [7] Parasız S A et al 011 Joural of Maufacturig Processes 13 153 159 [8] Zhag S et al 01 Machiig Sciece ad Techology 16 (3) 473 486 [9] ussaiova I et al 011 Iteratioal Joural of Materials ad Product Techology 40 (40) 58 74 [10] Ekici R et al 010 Materials & Desig 31 (6) 818 833 [11] Starikov M et al 011 Trasport 6 (3) 55 6 [1] Muzyka N R ad Shvets V P 014 Stregth of Materials 46 (1) 105 109 [13] Lebedev A A et al 007 Stregth of Materials 39 (6) 567 571 [14] Lebedev A A et al 011 Stregth of Materials 43 (5) 506 514 [15] a W et al 01 Materials Trasactio 53 () 390 394 [16] Kor G A ad Kor T M 1994 adbook of Mathematics for Egieers ad Researchers (Moscow: Nauka) [17] Gupta R D ad Kudu D 001 Biometrical Joural 43 (1) 117 130 6