Application of Response Surface Methodology for Modeling the effect of alloying elements on Mechanical Properties of Structural Steel

Transcription

1 Volume : Issue 1 : 015 ISSN (Online): ISSN (Print) : International Journal of Research and Innovations in Science & Technology, SAINTGITS ollege of Engineering, INDIA Research paper, Application of Response Surface Methodology for Modeling the effect of alloying elements on Mechanical Properties of Structural Steel Abhinay Bhatt 1 *, Dr. Mahesh B. Parappagoudar 1 1 Department of Mechanical Engineering, hhatrapati Shivaji Institute of Technology, Durg. *abhinaybhatt@csitdurg.in opyright 015 Abhinay Bhatt and Mahesh B. Parappagoudar.. This is an open access article distributed under the reative ommons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In the present paper an attempt has been made to establish the non-linear input-output relationships to model mechanical properties of structural steel with the help of Response Surface Methodology. entral composite design is utilized to conduct the experiments. Further, surface plots have been developed for response namely Yield strength, Ultimate tensile strength and Elongation. The experiments have been conducted as per central composite design where all process variables are set at three levels. The surface plots showed that alloying elements Manganese, Silicon and arbon have positive contribution towards both responses Ultimate tensile strength and Yield strength. Moreover, analysis of variance test has been conducted to determine the statistical adequacies of the developed models. The alloying elements arbon and Manganese showed more contribution as compared to Silicon. It is to be noted that all the three alloying elements are found to have negative contribution towards the response- Elongation. The developed nonlinear regression models for the responses Yield strength, ultimate tensile strength and elongation have been tested for their prediction accuracy with the help of test cases. The present work is found to be useful to control the mechanical properties of structural steel by varying the major alloying elements. Moreover, most of the surface plots have shown a linear relation with the responses.. Keywords: Alloying elements, Response surface methodology, Structural Steel, Surface plots.. 1. Introduction Structural steel is playing an increasingly important role in traditional and medium density housing with its versatility, strength and competitive price. The alloy steels are normally required when additional properties such as strength, ductility, and toughness or corrosion resistance are desirable in large measure. While changing the proportion of alloying elements the properties are changed. The main alloying elements in structural steel are carbon, manganese and silicon. The responses to measure strength of the steel are Yield strength, Ultimate tensile strength and elongation percentage. It is to be noted that not much of the work is carried in analyzing the effect of alloying elements and modeling of structural steel production by using statistical regression analysis. However, it is found good amount of literature is available on successful application of DOE and RSM tools metal casting. Zyska et. al.[] used two level full-factorial design of experiment to study the effect of squeeze, die temperature and percentage of modifier on percent elongation are tensile strength of squeeze cast components. Further linear and non-linear regression models were successfully applied to establish the input-output relationship in different casting processes, namely cement bonding molding, [3-4], green sand molding[5-6], resin-bonded sand mold[7],sodium-bonded molding system[8],die casting[9-11] and evaporative casting process[1]. A study conducted by Laz ko et al.[13] found that the strength of high strength weldable steel increases significantly as its carbon content increases from 0.05 to % with retention of plasticity and resilience at a sufficiently high level. Babichev et al. [14] found that manganese added to steels containing 1% affects their wearability. The wearability of quenched steels (1% ) and the hardness decrease with increasing amounts of manganese, while in annealed steels containing %, manganese has no effect either on the 1

2 Volume : Issue 1 : 015 hardness or the wearability. A study by Kharitonov et al.[15] found that the plasticity and resilience of aged steel N18K9M5T containing more than 0.% of Si decrease as a result of the negative effect of this element on these properties of the steel in the aged state.[16] Townsend conducted experiments and he found that Phosphorus, Silicon, hromium, arbon, opper, Nickel, Tin, and Molybdenum are beneficial to corrosion resistance.. Methodology The methodology to study the influence of process parameters and to establish non-linear input-output relationships of mechanical properties of structural steel has been explained in the following steps. 1. Identify the important process parameters and their feasible limits. Decide on the number of replicates.. Develop the design matrix based on the number of variables and their levels chosen. 3. onduct the experiments with the input variable combination as per design matrix and record corresponding response values. There are three input variables (three alloying elements) namely percentage composition of arbon, Manganese and Silicon. The responses (output) measured are Yield strength, Ultimate tensile strength and percentage elongation. Table 1. Process Parameters and their levels Parameters Notation Levels Low (-) Medium(0) High (+) % arbon A % Manganese B % Silicon It is to be noted that the manufacture and preparation of test specimen has been carried out at Bhilai Steel Plant, Bhilai, India. The material used in the experimental work is structural steel (IS 06 E50B).The major alloying elements, namely carbon, manganese, silicon with their low, medium and high level values are presented in Table 1. The operating range of each parameters (i.e. alloying element) is decided based on the literature and by consulting industry experts. However in the experimental analysis and testing, the alloying elements namely sulphur, phosphorus and aluminium are not considered as these are present in very small amount. The test specimen were prepared as per the standards and experiments were conducted to measure YS, UTS and % elongation. The test is carried out as per ASTM E8/E8M Determining the Adequacy of the Developed Models The non-linear regression model will be developed using the data collected as per the central composite design. The effect of individual parameters and their interaction terms are examined by conducting a significance test. The adequacies of the models are tested with the help of Analysis of variance (ANOVA) technique. Surface plots are used to understand the relationships of process parameters and their interaction with responses. Further, they are utilized to study the contribution of process parameters by using MINITAB software. 3. Result and Discussion This section discusses the non-linear regression models developed for effect of alloying elements on mechanical properties of structural steel using MINITAB software. 3.1 Response- Yield Strength To examine the effect of various input parameters and their interaction terms on Yield strength, a significance test (refer to Table ) has been conducted. As the P values of the responses A, B, B and A*B are found to be less than 0.05(corresponding to 95% confidence level),these factors are considered to make significant contribution on the response-yield strength. Table 3 shows the results of ANOVA performed for testing the significance of the factors on Yield strength. It is important to note that A,B and are found to be significant on Yield strength as the value of P is found to be less than 0.05.Moreover the coefficient of correlation for this model is seen to be equal to 0.98.

3 Volume : Issue 1 : 015 Table. Results of the significance test for the non-linear model of Yield strength Term oef SE oef T P onstant A B A B A*B A* B* Table 3. Results of ANOVA for the response- Yield Strength Source DF Seq SS Adj SS Adj MS F P Regression Linear A B Square A B Interaction A*B A* B* Residual Error Lack-of-Fit Pure Error Total Surface plot for the response-yield strength obtained by varying manganese and silicon is presented in Figure 1. It has been observed that increase in manganese and silicon have resulted in the rapid increase in response value. Moreover, maximum yield strength value is reached with both alloying elements set at their maximum value. It is to be noted that the response yield strength changes linearly with both manganese and silicon. S ur fa c e P lo t o f Y S v s, S u r f a c e P l o t o f Y S v s, H o ld V alu es 0.16 H o ld V a lu e s Y S 3 0 Y S Figure 1 With Manganese and silicon Figure With carbon and silicon Surface Plot of Yield strength Surface plot for the response-yield strength obtained by varying carbon and silicon is shown in Figure. It has been observed that increase in carbon and silicon has resulted in the rapid increase in the response value. The maximum yield strength value is attained when both carbon and silicon are set at their maximum value. The surface plot of Yield strength changes linearly with both carbon and silicon.surface plot for the response-yield strength obtained by varying carbon and manganese is shown in Figure 3. It has been observed that increase in carbon and manganese has resulted in rapid increase in response value. The maximum value of Yield strength is reached when both alloying elements are set at their maximum value. The response yield strength changes linearly with both carbon and manganese. 3. Response-Ultimate tensile strength The significance test shows that the linear term %, Mn% and interaction terms %*%, Mn%*Mn%, Si%*Si%, %*Mn%, %*Si% and Mn%*Si% are found to make non-significant contributions on ultimate tensile strength as 3

4 Volume : Issue 1 : 015 their values are seen to be more than 0.05.The surface plots are also drawn for the response-ultimate tensile strength. The coefficient of correlation for this model is seen to be equal to S u r f a c e P l o t o f U T S v s, S u r f a c e P l o t o f U T S v s, U T S U T S Figure 4 with silicon and manganese Figure 5 With silicon and carbon Surface Plot of Ultimate tensile strength Surface plot for the response-ultimate tensile strength obtained by varying manganese and silicon is presented in Figure 4. It has been observed that increase in manganese and silicon have resulted in the rapid increase in response value. Moreover, maximum ultimate tensile strength value is reached with both alloying elements set at their maximum value. It is to be noted that the response ultimate tensile strength changes linearly with both manganese and silicon. Surface plot for the response-ultimate tensile strength obtained by varying silicon and carbon is presented in Figure 5. It has been observed that increase in silicon and carbon have resulted in the rapid increase in response value. Moreover, maximum ultimate tensile strength value is reached with both alloying elements set at their maximum value. It is to be noted that the response ultimate tensile strength changes linearly with both silicon and carbon. S u r f a c e P l o t o f U T S v s, U T S Figure 6 Surface Plot of Ultimate tensile strength with manganese and carbon Surface plot for the response-ultimate tensile strength obtained by varying manganese and carbon is presented in Figure 6. It has been observed that increase in manganese and carbon have resulted in the rapid increase in response value. Moreover, maximum ultimate tensile strength value is reached with both alloying elements set at their maximum value. It is to be noted that the response ultimate tensile strength changes linearly with both manganese and carbon. 3.3 Response-Percentage elongation The significance test shows that only the terms Mn% and interaction term Mn%*Mn% are found to make significant contribution to the response percentage elongation as their values are less than The surface plots are also drawn for the response-percentage elongation. The coefficient of correlation for this model is seen to be equal to S u r f a c e P l o t o f % e v s, % e Figure 7 Surface Plot of percentage elongation with silicon and manganese Surface plot for the response-percentage elongation obtained by varying silicon and manganese is shown in Figure 7.It has been observed that increase in manganese and silicon have resulted in gradually decrease in the value of percentage elongation. Moreover, maximum percentage elongation is reached with both alloying elements set at their minimum value. It is to be noted that the response-percentage elongation changes non-linearly with both silicon and manganese. 4

5 International Journal of Research and Innovations in Science and Technology Volume : Issue 1 : 015 S u r f a c e P l o t o f % e v s, % e Figure 8 Surface Plot of percentage elongation with silicon and carbon Surface plot for the response-percentage elongation obtained by varying silicon and carbon is shown in Figure 8. It has been observed that increase in carbon has resulted in gradual decrease in the value of percentage elongation. But increase in silicon has resulted in very small decrease in percentage elongation. Moreover, maximum percentage elongation is reached with both alloying elements set at their minimum value. It is to be noted that the responsepercentage elongation changes non-linearly with both silicon and carbon. S u r f a c e P l o t o f % e v s, % e Figure 9 Surface Plot of percentage elongation with manganese and carbon Surface plot for the response-percentage elongation obtained by varying carbon and manganese is presented in Figure 9. It has been observed that increase in carbon has resulted in gradual decrease in percentage elongation. But increase in manganese has resulted in very small decrease in the value of the response-percentage elongation..it is to be noted that the response-percentage elongation changes non-linearly with both manganese and carbon. 3.4 Testing of the non-linear model The non-linear model is tested by developing regression equations for the responses obtained from 10 test cases. The regression equation obtained for Yield strength (YS), Ultimate tensile strength (UTS) and percentage elongation (E%) are represented by equation (1), () and (3) respectively. YS * A * B * * A B * * AB 347.* A * B UTS * A * B * 597.1* A 6.1* B * 46.88* AB 40.78* A 63.89* B % E * A 43.88* B 35.17* 77.9* A 18.08* B 39.65* 6.04* AB 13.89* A 13.89* B Test case Table 4. Percentage deviation of the responses-yield strength, Ultimate tensile strength and percentage elongation % Mn% Si% Exp Value (a) YS (in Mpa) UTS (in Mpa) %E % % Equ. Exp Equ. Exp Equ. Deviation Deviation Value Value Value Value Value (a-b) (a-b) (b) (a) (b) (a) (b) ax100 ax100 (1) () (3) % Deviation (a-b) ax It can be seen from Table 4 that the maximum percentage deviation is -3.41% for the response of Yield strength(ys), -3.38% for the response of Ultimate tensile strength(uts) and -3.7% for the response of percentage elongation. So the model is accepted. 5

6 Volume : Issue 1 : onclusion In the present work, the effect of three alloying elements namely arbon, Manganese and Silicon on the mechanical properties of structural steel is studied. Response surface methodology, entral composite design is used to analyze the process. It is interesting to note that alloying elements arbon, Manganese and Silicon have positive influence on mechanical properties like Ultimate tensile strength and Yield Strength. Whereas, all alloying elements have negative contribution on the response like Percentage elongation. The influence of alloying elements arbon and Manganese is more compared to Silicon on all the responses. The experimental data collected as per central composite design has been utilized to develop the non-linear regression (input-output and relations) models for the responses Yield strength, Ultimate tensile strength and percentage elongation. These models have been tested for their statistical adequacy with the help of ANOVA test. Further, the performance of the models have been tested by considering ten test cases. The test results showed absolute average deviation values equal to 1.918%, 1.585%, 1.459% for the responses Yield strength, Ultimate tensile strength and percentage elongation. The requirement of mechanical properties i.e. strength and ductility(% elongation) varies depending on applications. It is to be noted that the increase in alloying elements namely manganese, carbon and silicon will increase Yield strength and Ultimate tensile strength whereas reduce percentage elongation (ductility). Hence, the present situation may be considered for the pareto optimal front development where number of optimum solutions can be determined. Presently the authors are working on this aspect. From the present work it can be concluded that the statistical tool Design of experiments and Response surface methodology can be used to effectively model and analyze the mechanical properties of structural steel. Moreover, the results are found to be useful for the foundry men to select the quantity of alloying element in order to develop the required mechanical properties. References [1] Douglas. Montgomery, Design and analysis of Experiments, John Wiley and sons, June 007. [] Zyska A,Konopka Z, Lagiewka M and Nadolski M (013), Optimization of squeeze parameters and modification of AlSi7Mg alloy, Archives of Foundry Engineering, 13(), [3] Parappagoudar MB, Pratihar DK and data GL (008), Linear and non-linear modeling of cement-bonded moulding and system using conventional statistical regression analysis, Journal of Materials Engineering and Performance,17(4), [4] Mandal A and Roy P. (006), Modeling the compressive strength of molasses-cement sand system using design of experiments and back propagation neutral network, Journal of Materials Processing Technology,180(1), [5] Parappagoudar MB, Pratihar DK and Datta GL (007), Non-linear modeling using central composite design to predict green sand mould properties, Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering manufacture,1(5), [6] Parappagoudar MB, pratihar DK and data GL (007), Linear and non-linear statistical modeling of green sand mould system, International Journal of cast metals research, 0(1), 1-13 [7] Surekha B, rao DH, Rao G, Vundavilli PR and Parappagoudar MB (01), Modeling and analysis of resin bonded sand mould system using design of experiments and central composite design, J.Manuf. Sci. Prod.,1(1), [8] Parappagoudar MB, Pratihar DK and Datta GL(011),Modeling and analysis of sodium silicate-bonded moulding sand system using design of experiments and response surface methodology, Journal for Manufacturing Science & Production,11(1-3),1-14 [9] Verran Go,Mendes RPK and Rossi Ma (006), Influence of injection parameters on defects formation in die casting Al1Si1, 3u alloy: Experimental results and numeric simulation, Journal of materials processing technology,179(1), [10] Verran Go,Mendes RPK and dalla Valentina LVO(008),DOE applied to optimization of aluminium alloy die castings, Journal of materials processing technology,00(1),10-15 [11] hiang KT, Liu NM and Tsai T (009), Modeling and analysis of the effects of processing parameters on the performance characteristics in the high pressure die casting process of Al-SI alloys, The International Journal of Advanced 7% Si alloy castings, Journal of materials processing technology,18(1), manufacturing Technology,41(11-1), [1] Kumar S, Kumar P and Shan HS (007), effect of evaporative pattern casting process parameters on the surface roughness of Al-7% Si alloy castings, Journal of materials processing technology,18(1), [13] V. G. Laz'ko, V. N. Nikitin, N. I. Karchevskaya. Effect of carbon content on the structure and mechanical properties of highstrength weldable steel 03G4NMAF, Metal Science and Heat Treatment, March 1986, Volume 8, Issue 3, pp [14] M.A.Babichev, A.A.Velikanova.Effect of the concentration of manganese on the wearability of steel, Metal Science and Heat Treatment, May 1964, Volume 6, Issue 6, pp [15] V. A. Kharitonov,N. I. Popova,V. F. Shishov. Effect of silicon and titanium on the mechanical properties of steel N18K9M5T, Metal Science and Heat Treatment, March 1984, Volume 6, Issue 3, pp [16] H. E. Townsend, Effects of Alloying Elements on the orrosion of Steel in Industrial Atmospheres. orrosion: June 001, Vol. 57, No. 6, pp