Development of Models for the Prediction of Mechanical. Properties of Rolled Ribbed Medium Carbon Steel

Transcription

1 ISSN (Paper) ISSN (Online) Development s for the Prediction Mechanical Properties Rolled Ribbed Medium Carbon Steel OYETUNJI Akinlabi. (Corresponding author) Department Metallurgical and Materials Engineering, The Federal University Technology, Akure Nigeria Tel: , akinlabioyetunji@yahoo.com ADEBAYO Abdullah Olawale Department Metallurgical and Materials Engineering The Federal University Technology, Akure Nigeria Tel: , visitabdullah@yahoo.com Abstract The target the contribution is to outline possibilities applying modelling for the prediction mechanical steel properties ribbed medium carbon steel rods. The impact toughness; tensile properties - tensile strength at maximum load, tensile strength at break and yield strength; as well as hardness property medium carbon steels rolled from inland rolling mills were determined experimentally and quantitatively. The experimental data obtained were used to develop models using stepwise techniques (statistical analysis). The precise tool used for development these models was multiple regression analysis (Analysis Varia- ANOVA) and the models were used to obtain the predicted (numerical) values these properties for each the materials investigated. The outcome models enable the prediction mechanical properties the material on the basis decisive parameters influencing these properties. Both the experimental and calculated (numerical) values these properties were subjected to statistical tests namely, paired t-tests, correlation coefficient, standard error, standard deviation and varia; which were found valid within the limit experimental error.. By applying modelling that are combination mathematical and physical analytical methods it will be possible to lower the manufacturing cost, environmental costs and enable the users the products to also confirm the predicted properties easily before use. Keywords: ling; mechanical properties; rolled-ribbed steel; multiple regression analysis, validation and statistical analysis NOMENCLATURE C=Carbon (%), Mn=Manganese (%), Si= Silicon (%), Ni= Nickel (%), Cr = Chromium (%), P= Phosphorus (%), S= Sulphur (%), Cu= Copper (%),

2 ISSN (Paper) ISSN (Online) Co= Cobalt (%), W= Tungsten (%) Fe= Iron (%) Dia= Diameter the steel rods (mm) THV = Transverse Hardness Value (RHN) LHV: = Longitudinal Hardness Value (RHN) TS@L Max = Tensile Strength At Maximum Load (N/mm 2 ) = Tensile Strength At Break (N/mm 2 ) YS= Yield Strength (N/mm 2 ) IS= Impact Strength (J) THV = Transverse Hardness Value Predicted from Type- (RHN) LHV : = Longitudinal Hardness Value Predicted from Type- (RHN) TS@L Max = Tensile Strength At Maximum Load Predicted from Type- (N/mm 2 ) = Tensile Strength At Break Predicted from Type- (N/mm 2 ) YS = Yield Strength Predicted from Type- (N/mm 2 ) IS = Impact Strength Predicted from Type- (J) THV 2 = Transverse Hardness Value Predicted from Type-2 (RHN) LHV 2 : = Longitudinal Hardness Value Predicted from Type-2 (RHN) TS@L Max 2 = Tensile Strength At Maximum Load Predicted from Type-2 (N/mm 2 ) = Tensile Strength At Break Predicted from Type-2 (N/mm 2 ) YS 2 = Yield Strength Predicted from Type-2 (N/mm 2 ) IS 2 = Impact Strength Predicted from Type-2 (J). Introduction Mechanical properties materials are prime interest to the Engineers and the results tests to determine these properties are used for various purposes. They are corn to a variety parties such as producers and consumers materials, research organisations, government agencies, because they have different areas application the material. Consequently, it is imperative that there be some consistency in the manner in which tests are conducted, and in the interpretation results so that appropriate choice materials will be made by the users. The possibility to model the microstructure and mechanical properties ribbed steel components enables the engineers to use the property variation obtained in steel rolled as an input to structural simulation programs such as JAVAS, MATLAB and VISUAL BASIC, and thereby be able to make good progress in proper and accurate measurements. The mechanical properties rolled steels are very sensitive to composition, rolling process, section sizes and solidification behaviour, and thermal treatment. Bringing the rolling process and materials testing closer to the materials designers and end users will lead to a reliable, and optimised design complex geometries the materials. Improvement in the degree integration between processing, metallurgical and mechanical properties steel ribbed can also be achieved by the process. This will lead to a shorter lead-time, right from the first design attempt and sounder components which strengthen the competitiveness the material and rolling industry. The linking between the process, microstructure and mechanical properties has been implemented in commercial simulation stware by various researchers such as Bingji (2009) that worked on development

3 ISSN (Paper) ISSN (Online) model-intensive web-based rolling mill applications. Study on application artificial intellige methods for prediction steel mechanical properties was carried out by Jan^Íková et al, (2008). Myllykoski, et al (996) studied the development prediction model for mechanical properties batch annealed thin steel strip by using artificial neural network modelling, and Dobrzański, et al (2005) studied methodology the mechanical properties prediction for the metallurgical products from the engineering steels using the Artificial Intellige methods ; and Simecek, and Hajduk (2007) studied the prediction mechanical properties hot rolled steel products. All the works reviewed did not address modelling to predict the following mechanical properties- impact toughness; tensile properties - tensile strength at maximum load, tensile strength at break and yield strength; as well as hardness property rolled ribbed medium carbon steel. Fully know the engineering importa this material in structural industry; it becomes highly imperative that a study on how these properties can rapidly be predicted for the use rolling industries, designers and end users should be investigated. To solve this problem rapidly prediction these mechanical properties rolled ribbed medium carbon steel, a modelling approach was sought; this is rationale behind this work. Therefore, enabling the modelling and integration these processes will lead to substantial shortening the development time, cost reduction and fewer risks. He, the research study the development models for the rapid prediction mechanical properties-tensile Strength At Maximum Load (TS@L Max ), Tensile Strength At Break ), Yield Strength (YS), Transverse Hardness Value (THV), Longitudinal Hardness Value (LHV), and Impact Strength (IS) a very universal engineering material rolled ribbed medium carbon steel, commonly used in various structural engineering designs. While the specific objectives towards achieving the set aim are to determine the chemical compositions the as-received ribbed bars diameters 2 mm, 6 mm 20 mm and 25 mm; experimental determination mechanical properties the medium carbon steel; development models from experimental results and validation for rapid prediction the mechanical properties. 2. Materials and Methods The rolled ribbed medium carbon steel rods used were obtained from Nigerian Rolling Mills. The rods used were 2 mm, 6 mm, 20 mm and 25 mm in diameters. Other materials included abrasive papers and water as coolant. 2. Samples Preparation A mass spectrometric analyzing machine was used to determine the chemical compositions the steel rods in accorda with ASTM E50-00 (2005) standard. The as-received steel samples were machined using lathe machine with coolant into various standard tests specimens for hardness, tensile and impact tests. The standard tensile test specimens were prepared according to ASTM E370 standard specification 30 mm long with a gauge length 70 mm (Oyetunji, 200) while the hardness samples were cut with power hacksaw machine into 20 mm long. The specimens for impact test were machined into standard samples in conformity with the Charpy V-notch impact machine specification (Oyetunji, 200) 2.2 Tests The experimentally determined mechanical properties on the various prepared standard specimens are tested for hardness, tensile strength, breaking strength, yield strength and impact toughness Tensile Test The tensile test specimen shown in Figure was mounted on the Istron universal testing machine at the jaws- one end stationary and the other movable. The machine was then operated which pulled the specimen at constant rate extension. The tensile test were performed in accorda with ASTM E8-09/E8M-09 standards (Oyetunji and Alaneme, 2005) Hardness Test The surface the entire hardness test specimen shown in Figure 2 in which an indentation was to be made were ground using 200 nm grinding papers to make them flat and smooth. A diamond indenter under the

4 ISSN (Paper) ISSN (Online) application 60 KN was pressed into the surface. The hardness test was performed with the aid digital Rockwell hardness tester and the machine operational procedure in line with ASTM E8-08b and ASTM E40-07 standards ( Oyetunji and Alaneme, 2005) Impact Test Each test piece shown in Figure 3 was held horizontally on a vice attached to the impact testing machine such that the notched side faced the approaching hammer. The impact test was performed using V-notch pendulum-type impact testing machine in accorda with ASTM A350 / A350M - 0 standards, (Bello et al, 2007; Oyetunji, 200 and Waid and Zantopulous,2000). 3.0 Development In formulating the models, the following conditions were assumed: other elements in the materials were assumed insignificant; the materials samples were as-rolled from the companies; there was normal heating regime the billets in the re-heating furnace; the system was under continuous rolling production; there was no over tension and looping on the rolling line, that is, normal rolling speed; similar rolling scheme was used; and normal water pressure. Statistical analysis was used to develop the models. The results the three tests namely tensile, hardness and impact were analyzed statistically by using a routine for correlation, that is, multiple regression analysis. The computation the multiple regression parameters (coefficients) were obtained with the aid computer in a stepwise technique using the package known as Statistical Package for Social Scie (SPSS). Thereafter, the correlation between the predictors (independent variables) such as sample sizes, percentage carbon, percentage manganese, percentage silicon, percentage phosphorous, percentage sulphur, percentage chromium, percentage nickel, percentage copper, percentage cobalt, percentage tungsten and percentage iron shown in Table with the tensile strength at maximum load, tensile strength at break, yield strength, impact energy and hardness were carried out. They all indicate good correlation. (with correlation coefficient ranges from to ). The multiple regression analysis in accorda with Oyetunji, 200 was used to determine the respective relations for the tensile properties, impact energy and hardness with and without percentage iron for the four materials samples used. Resulting models from multiple regression analysis that predict the mechanical properties medium carbon rolled ribbed steel were presented in Appendix. He, the outcome models that predicted the mechanical properties the rolled ribbed bars as obtained in SPSS (Appendix were presented as equations to 2.The predicted values were manually obtained from these models through the use scientific calculator. MODELS TYPE-I (WITH IRON) : TRANSVERSE HARDNESS VALUE (THV) THV Dia %C %Mn %Si %P %S %Ni -9.22%Cu %Co %W %Fe..() : LONGITUDINAL HARDNESS VALUE (LHV) LHV = Dia %C %Mn %Si %S %Ni %Cu %Co %W %Fe %P...(2)

5 ISSN (Paper) ISSN (Online) : TENSILE STRENGTH AT MAXIMUM LOAD ( ) TS Dia %C %Mn %Si %P %S %Ni %Cu %Co %W %Fe....(3) : TENSILE STRENGTH AT BREAK ) TS@Break = : YIELD STRENGTH (YS) Dia %C %Mn %Si %P %S %Ni %Cu %Co W %Fe = Dia %C %Mn %Si YS %P %S %Ni %Cu %Co +2.8%W -90.6%Fe : IMPACT STRENGTH (IS) %W %Fe....(4)....(5) = Dia *%C %Mn *%Si IS %P %S %Ni %Cu %Co MODELS TYPE-II (WITHOUT IRON) : TRANSVERSE HARDNESS VALUE (THV) = Dia %C +.789%Mn %Si % THV %S %Cr %Ni %Cu %Co +60.0%W : LONGITUDINAL HARDNESS VALUE (LHV) %W.....(6)..(7) = Dia %C %Mn +3.53%Si %P LHV %S % Cr %Ni %Cu %Co C 2 : TENSILE STRENGTH AT MAXIMUM LOAD ( )... (8)

6 ISSN (Paper) ISSN (Online) TSL max 2 = Dia % %Mn %Si %P %S %Cr %Ni %Cu %Co %W D 2 : TENSILE STRENGTH AT BREAK ( ) TS@Break %P %S %Cr %Ni %Cu %Co %W.....(9) = Dia %C %Mn %Si.....(0) E 2 : YIELD STRENGTH (YS) = Dia %C %Mn %Si YS %P %S %Cr %Ni %Cu %Co %W F 2: IMPACT STRENGTH (IS) %Co %W.....() = Dia %C %M n %Si IS %P %S %Cr %Ni %Cu....(2) 3. Validation the Developed s Validation the developed models was carried out in two stages: first by verification through manual computation and second by statistical analysis. The verification was done by using a set predetermined data for the prediction the mechanical properties the specimen. The theoretical (numerical) results obtained were compared to experimental results as shown in Table 2. From the results, it was shown that theoretical and experimental values were approximately equal. To further ascertain the consistency this result, validation by statistical test was carried. The experimental and numerical data each property were subjected to the following statistical tests: Paired t-tests; Correlation Coefficient; and Standard Error Prediction.. The validation tests indicate that there was good agreement between the numerical and experimental values. From the paired t-tests results in Tables 3 8, the pair differe and the standard deviations values were very small. The acceptable interval range was also very narrow and these confirmed that there was no significant differe between the predicted and experimental values. According to Oyetunji (200), a very high positive correlation (R) was observed when the coefficient correlation test was carried out on the predicted and experimental data all the mechanical properties estimated. This was an indication excellent reliability the obtained data. Also, there was none the data that its standard error value was more than 2.72 % for both the predicted and experimental data. This implies good agreement in the two data as the standard error values in Tables 9-4 were considered insignificant and therefore neglected because standard error values were less than 0% (Kusiak and Kuziak,2002; and Oyetunji, 200). There were good agreements between the predicted and experimental data for all validation tests done on the data collected, it can therefore be said that the

7 ISSN (Paper) ISSN (Online) developed models were reliable and valid. And they can be used to predict the mechanical properties rolled ribbed medium carbon steels that were studied. 3.2 s with and without Iron A critical observation both types-models developed was made. This revealed that the type-2, that is, models without iron inclusive predicted the observed value more accurately than the type- (models with iron inclusive). This could be seen as calculated and shown in Tables 8 4 as the standard error the models for types- and 2 models indicated. The standard errors values the predicted values from developed models and experimental values were very close and are less than 0%. This shows that both the experimental values and predicted values from developed models were valid (Kusiak and Kuziak, 2002; and Oyetunji, 200). Though, both models types are valid, but type-2 predicted almost exactly the same values the mechanical properties-tensile Strength At Maximum Load (TS@L Max ), Tensile Strength At Break ), Yield Strength (YS), Transverse Hardness Value (THV), Longitudinal Hardness Value (LHV), and Impact Strength (IS) rolled ribbed medium carbon steel rods as the experimental values. He, type-2 models are more preferred for perfect accuracy and reliability with insignificant error prediction. 4. Conclusions In the field research oriented on metallurgical technologies control with the aim to optimize a quality materials by applying models for predicting mechanical properties rolled ribbed steel rods after experimental works, models were developed and manually tested. These models predicted final mechanical properties-tensile Strength At Maximum Load (TS@L Max ), Tensile Strength At Break ), Yield Strength (YS), Transverse Hardness Value (THV), Longitudinal Hardness Value (LHV), and Impact Strength (IS) rolled ribbed medium carbon steel rods on the basis the knowledge chemical steel compositions, steel rods section diameters 2 mm, 6 mm, 20 mm and 25 mm; and the conditions rolling ribbed medium carbon steel bar. Thus from the results, the following conclusions were drawn; The multiple regression analysis is a powerful tool (Analysis Varia- (ANOVA)) to develop models that predict theoretically the mechanical properties rolled ribbed medium carbon steel rods. The predicted and experimental values were in good agreement with each other. The models developed are excellent in predicting the mechanical properties the materials studied. The models type-2 (models without iron inclusive). is more accurate than the models type- (models with iron inclusive). in predicting the mechanical properties rolled ribbed medium carbon steel rods. Referes ASTM E Standard. Hardness conversion tables for metals relationship among brinell hardness, Vickers hardness, Rockwell hardness, superficial hardness, knoop hardness, and scleroscope. ASTM E 8-08b- Standard Test Methods for Rockwell Hardness Metallic Materials. ASTM E (2005) Standard Practices for Apparatus, Reagents, safety consideration for Chemical Analysis Metals, Ores, and Related Materials. ASTM E 8-09/ E 8M-09 Standard Test Methods for Tension Testing Metallic Materials. ASTM E370 Standard Test Methods and Definitions for Mechanical Testing Steel Bello, K.A;, S.B. Hassan, M. Abdulwahab,. Shehu L.E. Umoru, A. Oyetunji, and I.Y.Suleiman (2007). Effect Ferrite-Martensite Microstructural Evolution on Hardness and Impact Toughness Behaviour High Martensite Dual Phase Steel. Australian Journal Basic and Applied Scies, (4): Pp Bingji Li (2009). Development -intensive Web-based Rolling Mill Applications, AISTech 2009 Proceedings - Volume II Pp

8 ISSN (Paper) ISSN (Online) Dobrzański, L.A.; M. Kowalskiand and J. Madejski (2005). Methodology the mechanical properties prediction for the metallurgical products from the engineering steels using the Artificial Intellige methods. Journal Materials Processing Tech, Vols 64-65, pp AMPT/AMME05 Part 2. Jan^íková, Z. ; V. Roubí^ek, and D. Juchelková (2008). Application Artificial Intellige Methods For prediction steel mechanical properties. METABK (METALURGIJA ) 47(4) UDC UDK :620.7: :608.4= ISSN PP Kusiak, J. and Kuziak, R. (2002), ling microstructure and mechanical properties steel using the artificial neural network. Journal Materials Processing Technology,27 (), Pp5-2. Myllykoski, P.; J. Larkiola and J. Nylander (996). Development Of Prediction For Mechanical Properties Of Batch Annealed Thin Steel Strip By Using Artificial Neural Network ling. Journal Materials Processing Technology Vol. 60 Issues -4. Pp Oyetunji, A. and Alaneme K. K. (2005). Influe the Silicon Content and Matrix Structure on the Mechanical Properties Al-Si Alloy. West Indian Journal Engineering. Vol.28. No., Pp Oyetunji, A. and Adebisi, J.A. (2009). Development Stware for Rapid Estimation Corrosion Rate Austempered Ductile Iron in corrosive media. Australian Journal Basic and Applied Scies, ISINET Publication Vol 3 (3) Pp Oyetunji, A. (200). ling the Impact Properties Grey Cast Iron Produced from CO 2 and Steel Moulds Journal Applied Scie Research, ISINET Publication Pakistan. Vol. 6(5), Pp Simecek, P. and Hajduk, D. (2007). Prediction Mechanical Properties Hot Rolled Steel Products. Journal Achievement in Materials and Manufacturing Engineering. Vol. 20, Issues -2. Pp Wain, GM.and Zantrtropulos, H. (2000). The effects OD curvature and sample flattening ontransverse Charpy V-Notch Impact toughness high Strength Steel Tubular product. ASTM (SEDL/ST P 0380-EB/STP4402S) Standard and Engineering Digital library (SEDL) Symposia paper. P2. Table Chemical Compositions the Rolled Ribbed Medium Carbon Steels used in the Research and Predictors (Independent Variables) X Diameter (mm X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 0 X X 2 %C %Mn %Si %P %S %Cr %Ni %Cu %Co %W %Fe

9 ISSN (Paper) ISSN (Online) Table 2: Transverse Hardness Value ( Experimental and Numerical Data) with models type- (models with iron inclusive) rolled ribbed medium carbon steel using Chemical Compositions in Table S/ Diameter Remark No (mm) Numerical (Exp. Value- Exp. Value value Numerical Value) A Insignificant B Insignificant C Insignificant D Insignificant E Insignificant F Insignificant G Insignificant H Insignificant

10 ISSN (Paper) ISSN (Online) I J K L Insignificant Insignificant Insignificant Insignificant Table 3. Pair t-test Analysis that Determine the Acceptable Confide Interval Range Transverse Rockwell Hardness Value A (THV) Rolled Ribbed Medium Carbon Steel. S Transver Pair Square Mean Varia Mean Stand Con / N se Rockwel nc e Pair Pair Pair Varia Pair ard Devia fide l (d 2 ) Var (d) tion Inte ( d ) Hardnes (Sd) rval (Var ( d ) s (d) Value A ( ) Rolled Ribbed Medium (99. 9%) Carbon Steels (THV) THV 5.096E E E E E E-3 E- Deg ree Fre edo m t v(0.0 0) Acceptable Interval ( d + t v(- ) Sd) Lower Upper Limit Limit E E THV E-2.035E E E E E E-

11 ISSN (Paper) ISSN (Online) Table 4: E-3 E- 2 Pair t-test Analysis that Determine the Acceptable Confide Interval Range Longitudinal Rockwell Hardness S/ N Longitu dinal Rockwe ll Hardnes s Value A Rolled Ribbed Medium Carbon Steels (LHV) air P (d) Square Pair (d 2 ) Value A (LHV) Rolled Ribbed Medium Carbon Steel. Mean Pair ( d ) Varia Pair nc e Var (d) Mean Varia Pair (Var ( d ) Standard Deviation (Sd) Confi de Interv al ( ) (99.9 %) Degre e Freed om t v(0.00 ) Acceptable Interval ( d + t v(- ) Sd) Lower LHV LHV E- Limit Upper Limit E Table 5.Pair t-test Analysis that Determine the Acceptable Confide Interval Range Tensile Strength at maximum Load (TS@Lmax) Rolled Ribbed Medium Carbon Steel. S/ N Tensile Strength at Maximu m Load Rolled Ribbed Medium Carbon Steels (TS@L max) Pair (d) Square Pair (d 2 ) Mean Pair ( d ) Varia Pair nc e Var (d) Mean Varia Pair (Var ( d ) Standard Deviation (Sd) Confi de Interv al ( ) (99.9 %) Degre e Freed om t v(0.00 ) Acceptable Interval ( d + t v(- ) Sd) Lower TS@Lm Limit Upper Limit

12 ISSN (Paper) ISSN (Online) ax 2 TS@Lm ax Table 6: Pair t-test Analysis that Determine the Acceptable Confide Interval Range Tensile Strength at Break (TS@Break) Rolled Ribbed Medium Carbon Steel. S / N Tensile Strength at Break Rolled Ribbed Medium Carbon Steels (TS@Break) Pair (d) Square Pair (d 2 ) Mean Pair ( d ) Varia Pair nc e Var (d) Mean Varianc e Pair (Var ( d ) Standard Deviation (Sd) Confid e Interval ( ) (99.9% ) Degre e Freed om t v(0.00 ) Acceptable Interval ( d + t v(- ) Sd) Lower Upper Limit Limit TS@Break TS@Break Table 7.Pair t-test Analysis that Determine the Acceptable Confide Interval Range Yield Strength (YS) Rolled Ribbed S / N Yield Strength Ribbed Medium Rolled Carbon Steels ( YS) Medium Carbon Steel. air P Differ e (d) Square Pair (d 2 ) Mean Pair ( d ) Varianc e Pair Var (d) Mean Varia Pair nc e (Var ( d ) Standard Deviation (Sd) Confid e Interval ( ) (99.9% ) Degre e Freed om t v(0.00 ) Acceptable Interval ( d + t v(- ) Sd) Lower YS YS E E E Table 8.Pair t-test Analysis that Determine the Acceptable Confide Interval Range Impact Toughness (IS) Rolled Ribbed Medium Carbon Steel. S / Impact Strength air P Square Pair Mean Pair Varianc e Mean Standard Deviation Confiden ce Degre e Limit Acceptable Interval Upper Limit

13 ISSN (Paper) ISSN (Online) N Rolled Ribbed Medium Carbon Steels ( IS) Differ e (d) (d 2 ) ( d ) Pair Var (d) Varianc e Pair (Var (Sd) Interval ( ) (99.9%) Freed om t v(0.00 ) ( d + t v(- ) Sd) Lower Upper Limit Limit ( d ) IS E- 3.0 E- 2.5E-2.558E IS E-.7E-.4E-2.83E Table 9: Correlation Coefficient and Standard Error Analysis Transverse Rockwell Hardness Value A Rolled Ribbed Medium Carbon Steel S/N TRANSVERSE HARDNESS CORRELATION STANDARD VALUE (THV) OF ROLLED COEFFICIENT OF ERROR OF RIBBED MEDIUM CARBON MODELS MODELS STEELS THV THV Table 0: Correlation Coefficient and Standard Error Analysis Longitudinal Rockwell Hardness Value A Rolled Ribbed Medium Carbon Steel S/N LONGITUDINAL CORRELATION STANDARD HARDNESS COEFFICIENT OF ERROR OF VALUE (LHV) OF MODELS MODELS ROLLED RIBBED MEDIUM CARBON STEELS LHV LHV Table.Correlation Coefficient and Standard Error Analysis Tensile Strength at maximum Load Rolled Ribbed Medium Carbon Steel S/N TENSILE STRENGTH AT CORRELATION STANDARD

14 ISSN (Paper) ISSN (Online) MAXIMUM LOAD OF ROLLED RIBBED MEDIUM CARBON STEELS Tensile Max COEFFICIENT OF ERROR MODELS MODELS OF Load 2 Tensile Max Load Table 2: Correlation Coefficient and Standard Error Analysis Tensile Strength at Break Rolled Ribbed Medium Carbon Steel S/N TENSILE STRENGTH AT CORRELATION STANDARD BREAK OF ROLLED RIBBED COEFFICIENT OF ERROR OF MEDIUM CARBON STEELS MODELS MODELS (TS@Break) Tensile Break Tensile Break Table 3: Correlation Coefficient and Standard Error Analysis Yield Strength Rolled Ribbed Medium Carbon Steel S/N YIELD STRENGTH OF CORRELATION STANDARD ROLLED RIBBED MEDIUM COEFFICIENT OF ERROR OF CARBON STEELS (YS) MODELS MODELS Yield Strength Yield Strength Table 4: Correlation Coefficient and Standard Error Analysis Impact Toughness Rolled Ribbed Medium Carbon Steel S/N IMPACT STRENGTH OF CORRELATION STANDARD ROLLED RIBBED MEDIUM COEFFICIENT OF ERROR OF CARBON STEELS (IS) MODELS MODELS Impact Strength E- 2 Impact Strength E- APPENDIX!

15 ISSN (Paper) ISSN (Online) Regression for Transverse Hardness Value Variables Entered/Removed b Variables Entered X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr a a. All requested variables entered. Variables Removed Method. Enter b. Dependent Variable: Y TRANSVERSE HARDNESS VALUE (THV) (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X7 %Cr X8 %Ni X9 % Cu X0 %Co X %W Coefficients a Unstandardized Standardized B Std. Error Beta t Sig a. Dependent Variable: Y TRANSVERSE HARDNESS VALUE (THV) Regression for Longitudinal Hardness Value Variables Entered/Removed b Variables Variables Entered Removed Method X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr. Enter a. All requested v ariables entered. b. Dependent Variable: Y2 LONGITUDINAL HARDNESS VALUE (LHV)

16 ISSN (Paper) ISSN (Online) Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr b. Dependent Variable: Y2 LONGITUDINAL HARDNESS VALUE (LHV) (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X7 %Cr X8 %Ni X9 % Cu X0 %Co X %W Coefficients a Unstandardized Standardized B Std. Error Beta t Sig a. Dependent Variable: Y2 LONGITUDINAL HARDNESS VALUE (LHV) Regression for Tensile Strength at Maximum Load Variables Entered/Removed b Variables Entered X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr a a. All requested v ariables entered. b. Dependent Variable: Y3 TS@max Variables Removed Method. Enter

17 ISSN (Paper) ISSN (Online) Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr b. Dependent Variable: Y3 TS@max (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X7 %Cr X8 %Ni X9 % Cu X0 %Co X %W a. Dependent Variable: Y3 TS@max Coefficients a Unstandardized Standardized B Std. Error Beta t Sig Regression for Tensile Strength at Break Variables Entered/Removed b Variables Entered X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr a a. All requested v ariables entered. b. Dependent Variable: Y4 T S@break Variables Removed Method. Enter Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr

18 ISSN (Paper) ISSN (Online) Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr b. Dependent Variable: Y4 T S@break (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X7 %Cr X8 %Ni X9 % Cu X0 %Co X %W a. Dependent Variable: Y4 T S@break Coefficients a Unstandardized Standardized B Std. Error Beta t Sig Regression for Yield Strength (Y.S) Variables Entered/Removed b Variables Entered X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr a a. All requested v ariables entered. Variables Removed Method. Enter b. Dependent Variable: Y5 YIELD STRENGTH (Y.S) Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr

19 ISSN (Paper) ISSN (Online) Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr b. Dependent Variable: Y5 YIELD STRENGTH (Y.S) (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X7 %Cr X8 %Ni X9 % Cu X0 %Co X %W Coefficients a Unstandardized a. Dependent Variable: Y5 YIELD STRENGTH (Y. S) Standardized B Std. Error Beta t Sig Regression for Impact Strength Variables Entered/Removed b Variables Entered Tungsten, Copper, Diameter, Manganese, Silicon, Phosphorus, Cobolt, Nickel, Carbon, Sulphur, Chromium a a. All requested v ariables entered. Variables Removed b. Dependent Variable: Impact Strength Method. Enter Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), Tungsten, Copper, Diameter, Manganese, Silicon, Phosphorus, Cobolt, Nickel, Carbon, Sulphur, Chromium

20 ISSN (Paper) ISSN (Online) Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), Tungsten, Copper, Diameter, Manganese, Silicon, Phosphorus, Cobolt, Nickel, Carbon, Sulphur, Chromium b. Dependent Variable: Impact Strength (Constant) Diameter Carbon Manganese Silicon Phosphorus Sulphur Chromium Nickel Copper Cobolt Tungsten Unstandardized a. Dependent Variable: Impact Strength Coefficients a Standardized B Std. Error Beta t Sig Regression for Transverse Hardness Value Variables Entered/Removed b Variables Entered X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P a a. Tolera =.000 limits reached. Variables Removed Method. Enter b. Dependent Variable: Y TRANSVERSE HARDNESS VALUE (THV) Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P

21 ISSN (Paper) ISSN (Online) Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y TRANSVERSE HARDNESS VALUE (THV) (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X8 %Ni X9 % Cu X0 %Co X %W X2 %Fe Coefficients a Unstandardized Standardized B Std. Error Beta t Sig a. Dependent Variable: Y TRANSVERSE HARDNESS VALUE (THV) X7 %Cr Excluded Variables b Collinearity Partial Statistics Beta In t Sig. Correlation Tolera. a a. Predictors in the : (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y TRANSVERSE HARDNESS VALUE (THV) Regression for Longitudinal Hardness Value Variables Entered/Removed b Variables Entered X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P a a. Tolera =.000 limits reached. Variables Removed b. Dependent Variable: Y2 LONGITUDINAL HARDNESS VALUE (LHV) Method. Enter

22 ISSN (Paper) ISSN (Online) Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y2 LONGITUDINAL HARDNESS VALUE (LHV) (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X8 %Ni X9 % Cu X0 %Co X %W X2 %Fe Coefficients a Unstandardized Standardized B Std. Error Beta t Sig a. Dependent Variable: Y2 LONGITUDINAL HARDNESS VALUE (LHV) X7 %Cr Excluded Variables b Collinearity Partial Statistics Beta In t Sig. Correlation Tolera. a a. Predictors in the : (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y2 LONGITUDINAL HARDNESS VALUE (LHV) Regression for Tensile Strength at Maximum Load

23 ISSN (Paper) ISSN (Online) Variables Entered/Removed b Variables Entered X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P a Variables Removed Method. Enter a. Tolera =.000 limits reached. b. Dependent Variable: Y3 TS@max Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y3 TS@max (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X8 %Ni X9 % Cu X0 %Co X %W X2 %Fe a. Dependent Variable: Y3 TS@max Coefficients a Unstandardized Standardized B Std. Error Beta t Sig

24 ISSN (Paper) ISSN (Online) X7 %Cr Excluded Variables b Collinearity Partial Statistics Beta In t Sig. Correlation Tolera. a a. Predictors in the : (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y3 TS@max Regression for Tensile Strength at Break Variables Entered/Removed b Variables Entered X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P a a. Tolera =.000 limits reached. b. Dependent Variable: Y4 T S@break Variables Removed Method. Enter Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P

25 ISSN (Paper) ISSN (Online) Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y4 T S@break (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X8 %Ni X9 % Cu X0 %Co X %W X2 %Fe a. Dependent Variable: Y4 T S@break Coefficients a Unstandardized Standardized B Std. Error Beta t Sig X7 %Cr Excluded Variables b Collinearity Partial Statistics Beta In t Sig. Correlation Tolera. a a. Predictors in the : (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y4 T S@break Regression for Yield Strength (Y.S)

26 ISSN (Paper) ISSN (Online) Variables Entered/Removed b Variables Entered X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P a a. Tolera =.000 limits reached. Variables Removed Method. Enter b. Dependent Variable: Y5 YIELD STRENGTH (Y.S) Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y5 YIELD STRENGTH (Y.S) (Constant) X DIAMETER (mm) X2 %C X3 %Mn X4 %Si X5 %P X6 %S X8 %Ni X9 % Cu X0 %Co X %W X2 %Fe Coefficients a Unstandardized a. Dependent Variable: Y5 YIELD STRENGTH (Y.S) Standardized B Std. Error Beta t Sig

27 ISSN (Paper) ISSN (Online) X7 %Cr Excluded Variables b Collinearity Partial Statistics Beta In t Sig. Correlation Tolera. a a. Predictors in the : (Constant), X2 %Fe, X9 % Cu, X8 %Ni, X %W, X4 %Si, X2 %C, X0 %Co, X3 %Mn, X6 %S, X DIAMETER (mm), X5 %P b. Dependent Variable: Y5 YIELD STRENGTH (Y.S) Regression for Impact Strength Variables Entered/Removed b Variables Entered Iron, Copper, Nickel, Tungsten, Silicon, Carbon, Cobolt, Manganese, Sulphur, Diameter, Phosphorus a Variables Removed a. Tolera =.000 limits reached. b. Dependent Variable: Impact Strength Method. Enter Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), Iron, Copper, Nickel, Tungsten, Silicon, Carbon, Cobolt, Manganese, Sulphur, Diameter, Phosphorus Regression Residual Total ANOVA b Sum Squares df Mean Square F Sig a a. Predictors: (Constant), Iron, Copper, Nickel, Tungsten, Silicon, Carbon, Cobolt, Manganese, Sulphur, Diameter, Phosphorus b. Dependent Variable: Impact Strength

28 ISSN (Paper) ISSN (Online) (Constant) Diameter Carbon Manganese Silicon Phosphorus Sulphur Nickel Copper Cobolt Tungsten Iron Unstandardized a. Dependent Variable: Impact Strength Coefficients a Standardized B Std. Error Beta t Sig Chromium Excluded Variables b Collinearity Partial Statistics Beta In t Sig. Correlation Tolera. a a. Predictors in the : (Constant), Iron, Copper, Nickel, Tungsten, Silicon, Carbon, Cobolt, Manganese, Sulphur, Diameter, Phosphorus b. Dependent Variable: Impact Strength Summary Adjusted Std. Error R R Square R Square the Estimate.000 a a. Predictors: (Constant), X %W, X9 % Cu, X DIAMETER (mm), X3 %Mn, X4 %Si, X5 %P, X0 %Co, X8 %Ni, X2 %C, X6 %S, X7 %Cr

29 ISSN (Paper) ISSN (Online) V notch Figure 3. V-notch Impact Test Piece

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