Acta Technica Corviniensis

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ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGBecause of the huge size of dates found in such aprocessing of experimental dates, we stopped,focusing on the mechanical feature R p0,2/450 ,which must be guaranteed by the metalmanufacturer, for the analysed steel.The most important feature of this steel categoryat high temperature is the conventional runninglimit at heat. This is the reason why the studyhas been made for establishing combinations ofthe best chemical composition and through theworking process, for the steel to have superiormechanical features. Therefore, the obtainedresults follow the way of the conventionalrunning limit for combinations of three mainelements of the chemical composition. Throughthe multidimensional numerical pattern-makingof the experimental dates, it was tried thefinding of a modeling of the dependent variable,considering the independent variables x, y, z as:222u = C ⋅ x + C ⋅ y + C ⋅ z + C ⋅ x ⋅ y + C ⋅ y ⋅ z612+ C ⋅ z ⋅ x + C ⋅ x + C ⋅ y + C ⋅ z + C783The variation limits of the variable are:94[%C] = 0,16…0,23; [%Mn] = 0,51…0,83;[%Si] = 0,16…0,35; Rp 0,2/450 = 169…255.105[1]The medium values and the medium squaredeviation of the variables are:[%C]:0,18563…0,01886; [%Mn]:0,66375…0,09545;[%Si]:0,235…0,047697; [Rp 0,2/450 ]: 08,95…17,193The correlation coefficient is valued:rf = 0,65599451703118,and the deviation from the regression area is:sf = 12,97668845383391The maximum established on the 50 chargessample is given by:22R p 0.2= 19828,0654 ⋅[%C]− 268,3624 ⋅[%Mn]2+ 571,8135 ⋅[%Si]− 2984,07 ⋅[%C]⋅[%Mn]+ 148,8591 ⋅[%Mn]⋅[%Si]+ 1182,9936 ⋅[%Si]⋅[%C][2]− 5668,4577 ⋅[%C]+ 962,9562 ⋅[%Mn]− 672,8277 ⋅[%Si]+ 472,3753These 4 dimensional surfaces allow a saddlepoint of coordinates:[%C] = 0,19417; [%Mn] = 0,79343; [%Si] = 0,2842;Rp0,2/450 =208,473.The existence of the saddle point is veryimportant as it assures a stability of the featureclose to this point, being it preferable oravoidable. In this case, it is preferable. Thebehavior of these hyper surfaces close to thesaddle point can only be studied as tabular,which means ascribing values on concentricspheres of the studied point to the independentvariable. Because of the fact that this surfacecannot be represented in 4 dimensional spaces,it has been chosen the successive replacement ofeach independent variable, with its mediumvalue, and obtaining the following equations:Rp0.2Cmed22= −268,3624⋅[%Mn]+ 571,8135⋅[%Si]+ 148,8591⋅[%Mn]⋅[%Si]+ 409,0382⋅[%Mn]+ 453,2345⋅[%Si]+ 103,3764Rp0.2Mnmed22= 571,8135⋅[%Si]+ 19828,0654⋅[%C]+ 1182,9936⋅[%Si]⋅[%C]− 74,0225⋅[%Si]− 7649,1341⋅[%C]+ 993,3067Rp0.2Simed22= 19828,0654 ⋅[%C]−268,3624 ⋅[%Mn]−2984,07⋅[%C]⋅[%Mn]− 5390,4542⋅[%C]+ 997,938⋅[%Mn]+ 345,8392[3][4][5]These surfaces which belong to the 3dimensional spaces can be represented andtherefore interpreted by technologists. Thesurfaces are shown in fig.2, fig.3, fig.4, fig.5, fig.6and fig.7. For a more exact analysis, thecorresponding level curves have been shownnext to these. The knowledge of the level curvesallow the establishing of the two independentvariable values, so as R p0,2/450 can be obtained,within the limits required or imposed by thebeneficiary.By looking at the graphs shown in fig.2, andconsidering %C an average, you can estimatethat maximum values of R p0,2/450 feature can beobtained for 0,50% Mn and 0,14% Si, valueswhich are close to the inferior limit of thecomposition imposed by standard. From fig.3,considering % Mn an average, you can say thatmaximum values of R p0,2/450 (230 N/mm²) featurescan be obtained for C concentrations within the0,12 – 0,14% limits and Si within the 0,15 – 0,18%limits, subfields which are close to the inferiorlimit of the composition imposed by standard.From the graphs shown in fig.4, and considering% Si an average, you can estimate that while theC and Mn grow, the R p0,2/450 conventional runninglimit grows as well. The diagrams in fig.5, fig.6342008/ACTA TECHNICA CORVINIENSIS/Tome I
ACTA TECHNICA CORVINIENSIS – BULLETIN of ENGINEERINGand fig.7 show the limits of the maximum field,where the metallurgic engineer can choose theelement percent of the chemical composition,in order to obtain steel having the desiredfeatures of the manufacturer. Knowledge of thelevel curves for these maximum fields allows thecorrelation of the two independent variable (thecontents of the chemical element) so that R p0,2/Tcan be obtained within the limits asked by thebeneficiary.CONCLUSIONThese results allow the establishing of the best C,Mn, Si contents from the chemical compositionof 12VMoCr10, so that, by the end of theelaboration, steel can possess certain imposedmechanical features.The analysis has been done for 3 elements of thechemical composition, being able to enlarge itfor both other elements, depending on thedesired chemical composition and other typesof steel.Taking into consideration that the way in whichone charge is done has a deep importance onthe mechanical features of the steel, knowledgeof these correlations is really significant for theengineer, because he is the one to estimate thevalues of the imposed parameter, depending onthe chemical composition which allows him theadjustment of the chemical composition duringthe elaboration, in order to obtain the featuresdesired by the beneficiary.REFERENCES[1.] LĂPUŞAN, A. – Contributions brought to the studyof steel behavior at high temperature, Doctoralthesis, Timişoara, 2004.[2.] TODEREAN, I. – The mathematical study ofexperimental dates. The Academy Publishing,Bucharest, 1976.[3.] MAKSAY, Şt. – Special Mathematics, ThePolytechnic Publishing, Timişoara, 2001.[4.] TALOI, F. – The optimalization of metallurgicprocess. The Didactics and PedagogicPublishing, Bucharest, 1982AUTHORS & AFFILIATION1.AMALIA ANA DASCĂL1. 2. 3DEPARTMENT OF ENGINEERING & MANAGEMENT,FACULTY OF ENGINEERING HUNEDOARA,UNIVERSITY “POLITEHNICA” TIMISOARA, ROMANIAACTA TECHNICA CORVINIENSIS– BULLETIN of ENGINEERINGcopyright ©UNIVERSITY POLITEHNICA TIMISOARAFACULTY OF ENGINEERING HUNEDOARA5, REVOLUTIEI331128 – HUNEDOARAROMANIAhttp://acta.fih.upt.ro2008/ACTA TECHNICA CORVINIENSIS/Tome I 35
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