Acta Technica Corviniensis

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