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Erschienen in: Neural Computing and Applications 9/2018

23.02.2017 | Original Article

Prediction of creep curve of HP40Nb steel using artificial neural network

verfasst von: Amitava Ghatak, P. S. Robi

Erschienen in: Neural Computing and Applications | Ausgabe 9/2018

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Abstract

Simulation of creep curves using data obtained from a limited number of short-time creep tests is helpful for predicting the long-time creep life of materials by extrapolation techniques. The present paper demonstrates the application of artificial neural network (ANN) for the prediction of creep curves for HP40Nb micro-alloyed steel. The network consists of stress, temperature and time as the input parameters and the creep strain as the output parameter. The data used are taken from accelerated creep tests carried out at constant temperatures in the range 650–1050 °C and constant stresses 47–120 MPa. The network was trained using a three-layer feed-forward back-propagation network, having a 15-neuron hidden layer, using the Levenberg–Marquardt optimization algorithm. After successful network training, the model was subjected to several tests to demonstrate consistent prediction capability. 98% of the creep strain data could be predicted within an error of ±10% deviation from the experimental values. An additional experiment carried out to check the prediction capability of the model confirms very good prediction capability, with a correlation coefficient of 0.994, by ANN modeling.

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Literatur
1.
Zurück zum Zitat Park DB, Hong SM, Lee KH et al (2014) High-temperature creep behavior and microstructural evolution of an 18Cr9Ni3CuNbVN austenitic stainless steel. Mater Charact 93:52–61CrossRef Park DB, Hong SM, Lee KH et al (2014) High-temperature creep behavior and microstructural evolution of an 18Cr9Ni3CuNbVN austenitic stainless steel. Mater Charact 93:52–61CrossRef
2.
Zurück zum Zitat Hayhurst DR, Vakili-Tahami F, Zhou JQ (2003) Constitutive equations for time independent plasticity and creep of 316 stainless steel at 550 °C. Int J Press Vessel Pip 80:97–109CrossRef Hayhurst DR, Vakili-Tahami F, Zhou JQ (2003) Constitutive equations for time independent plasticity and creep of 316 stainless steel at 550 °C. Int J Press Vessel Pip 80:97–109CrossRef
3.
Zurück zum Zitat Ha VT, Jung WS (2012) Creep behavior and microstructure evolution at 750 °C in a new precipitation-strengthened heat-resistant austenitic stainless steel. Mater Sci Eng A 558:103–111CrossRef Ha VT, Jung WS (2012) Creep behavior and microstructure evolution at 750 °C in a new precipitation-strengthened heat-resistant austenitic stainless steel. Mater Sci Eng A 558:103–111CrossRef
4.
Zurück zum Zitat Ghatak A, Robi PS (2015) Creep behavior and creep life assessment of HP40Nb reformer steel. Int J Res Eng Appl Sci 5:98–105 Ghatak A, Robi PS (2015) Creep behavior and creep life assessment of HP40Nb reformer steel. Int J Res Eng Appl Sci 5:98–105
5.
Zurück zum Zitat Ghatak A, Robi PS (2015) Investigation of micro-structure and creep life analysis of centrifugally cast Fe–Cr–Ni alloy reformer tubes. Manuf Sci Tech 3:155–159 Ghatak A, Robi PS (2015) Investigation of micro-structure and creep life analysis of centrifugally cast Fe–Cr–Ni alloy reformer tubes. Manuf Sci Tech 3:155–159
6.
Zurück zum Zitat Dieter GE (1998) Mechanical metallurgy. McGraw-Hill Book Co., Ltd., London Dieter GE (1998) Mechanical metallurgy. McGraw-Hill Book Co., Ltd., London
7.
Zurück zum Zitat Brnic J, Turkalj G, Canadija M, Krscanski S, Brcic M, Lanc D (2015) Deformation behaviour and material properties of austenitic heat-resistant steel X15CrNiSi25-20 subjected to high temperatures and creep. Mater Des 69:219–229CrossRef Brnic J, Turkalj G, Canadija M, Krscanski S, Brcic M, Lanc D (2015) Deformation behaviour and material properties of austenitic heat-resistant steel X15CrNiSi25-20 subjected to high temperatures and creep. Mater Des 69:219–229CrossRef
8.
Zurück zum Zitat Sawada K, Tabuchi M, Kimura K (2009) Analysis of long-term creep curves by constitutive equations. Mater Sci Eng A 510:190–194CrossRef Sawada K, Tabuchi M, Kimura K (2009) Analysis of long-term creep curves by constitutive equations. Mater Sci Eng A 510:190–194CrossRef
9.
Zurück zum Zitat Ghatak A, Robi PS (2015) A comparative study of constitutive equations for the creep deformation of HP40Nb micro-alloyed steel. Mater Sci Eng A 648:418–427CrossRef Ghatak A, Robi PS (2015) A comparative study of constitutive equations for the creep deformation of HP40Nb micro-alloyed steel. Mater Sci Eng A 648:418–427CrossRef
10.
Zurück zum Zitat Ghatak A, Robi PS (2015) High-temperature deformation behavior of HP40Nb micro-alloyed reformer steel. Metallogr Microstruct Anal 4:508–517CrossRef Ghatak A, Robi PS (2015) High-temperature deformation behavior of HP40Nb micro-alloyed reformer steel. Metallogr Microstruct Anal 4:508–517CrossRef
11.
Zurück zum Zitat Larson FR, Miller J (1952) A time-temperature relationship for rupture and creep stresses. Trans ASME 74:765–771 Larson FR, Miller J (1952) A time-temperature relationship for rupture and creep stresses. Trans ASME 74:765–771
12.
Zurück zum Zitat Ghatak A, Robi PS (2016) Modification of Larson–Miller parameter technique for predicting creep life of materials. Trans Indian Inst Met 69:579–583CrossRef Ghatak A, Robi PS (2016) Modification of Larson–Miller parameter technique for predicting creep life of materials. Trans Indian Inst Met 69:579–583CrossRef
13.
Zurück zum Zitat Manson SS, Haferd AM (1953) A linear time-temperature relation for extrapolation of creep and stress-rupture data. Technical Note 2890. NACA Manson SS, Haferd AM (1953) A linear time-temperature relation for extrapolation of creep and stress-rupture data. Technical Note 2890. NACA
14.
Zurück zum Zitat Orr RL, Sherby OD, Dorn JE (1954) Correlation of rupture data for metals at elevated temperature. Trans Am Soc Met 46:113–128 Orr RL, Sherby OD, Dorn JE (1954) Correlation of rupture data for metals at elevated temperature. Trans Am Soc Met 46:113–128
15.
Zurück zum Zitat Monkman FC, Grant NJ (1956) An empirical relationship between rupture life and minimum creep rate in creep rupture tests. Proc Am Soc Test Mater 56:593–620 Monkman FC, Grant NJ (1956) An empirical relationship between rupture life and minimum creep rate in creep rupture tests. Proc Am Soc Test Mater 56:593–620
16.
Zurück zum Zitat Dobes F, Milicka K (1976) The relation between minimum creep rate and time to fracture. Metal Sci 10:382–384CrossRef Dobes F, Milicka K (1976) The relation between minimum creep rate and time to fracture. Metal Sci 10:382–384CrossRef
17.
Zurück zum Zitat Phaniraj C, Nandagopal M, Mannan SL, Rodriguez P (1991) The relationship between transient and steady state creep in AISI 304 stainless steel. Acta Mater 39:1651–1656CrossRef Phaniraj C, Nandagopal M, Mannan SL, Rodriguez P (1991) The relationship between transient and steady state creep in AISI 304 stainless steel. Acta Mater 39:1651–1656CrossRef
18.
Zurück zum Zitat Dunand DC, Han BQ, Jannsen AM (1999) Monkman-Grant analysis of creep fracture in dispersion-strengthened and particulate-reinforced aluminum. Metall Mater Trans A 30A:829–838CrossRef Dunand DC, Han BQ, Jannsen AM (1999) Monkman-Grant analysis of creep fracture in dispersion-strengthened and particulate-reinforced aluminum. Metall Mater Trans A 30A:829–838CrossRef
19.
Zurück zum Zitat Phaniraj C, Choudhary BK, Rao KBS, Raj B (2003) Relationship between time to reach Monkman-Grant ductility and rupture life. Scr Mater 48:1313–1318CrossRef Phaniraj C, Choudhary BK, Rao KBS, Raj B (2003) Relationship between time to reach Monkman-Grant ductility and rupture life. Scr Mater 48:1313–1318CrossRef
20.
Zurück zum Zitat Phaniraj C, Choudhary BK, Raj B, Rao KBS (2005) A critical damage criterion for creeping solids. J Mater Sci 40:2561–2564CrossRef Phaniraj C, Choudhary BK, Raj B, Rao KBS (2005) A critical damage criterion for creeping solids. J Mater Sci 40:2561–2564CrossRef
21.
Zurück zum Zitat Jones J, MacKay DJC (1996) Neural network modeling of the mechanical properties of Ni based superalloys. In: 8th international symposium on Superalloys, Seven Springs; Pennsylvania; USA; 417–424 Jones J, MacKay DJC (1996) Neural network modeling of the mechanical properties of Ni based superalloys. In: 8th international symposium on Superalloys, Seven Springs; Pennsylvania; USA; 417–424
22.
Zurück zum Zitat Warde J, Knowles DM (1999) Application of neural networks to mechanical property determination of Ni based superalloys. ISIJ Int 39:1006–1014CrossRef Warde J, Knowles DM (1999) Application of neural networks to mechanical property determination of Ni based superalloys. ISIJ Int 39:1006–1014CrossRef
23.
Zurück zum Zitat Warde J, Knowles DM (1999) Use of neural networks for alloy design. ISIJ Int 39:1015–1019CrossRef Warde J, Knowles DM (1999) Use of neural networks for alloy design. ISIJ Int 39:1015–1019CrossRef
24.
Zurück zum Zitat Dumortier C, Lehert P (1999) Statistical modelling of mechanical tensile properties of steels by using neural networks and multivariate data analysis, neural networks in materials science. ISIJ Int 39:980–985CrossRef Dumortier C, Lehert P (1999) Statistical modelling of mechanical tensile properties of steels by using neural networks and multivariate data analysis, neural networks in materials science. ISIJ Int 39:980–985CrossRef
25.
Zurück zum Zitat Datta S, Sil J, Banerjee MK (1999) Petri neural network model for the effect of controlled thermomechanical process parameters on the mechanical properties of HSLA steels, neural networks in materials science. ISIJ Int 39:986–990CrossRef Datta S, Sil J, Banerjee MK (1999) Petri neural network model for the effect of controlled thermomechanical process parameters on the mechanical properties of HSLA steels, neural networks in materials science. ISIJ Int 39:986–990CrossRef
26.
Zurück zum Zitat Haque ME, Sudhakar KV (2002) ANN back-propagation prediction model for fracture toughness in microalloy steel. Int J Fatigue 24:1003–1010CrossRef Haque ME, Sudhakar KV (2002) ANN back-propagation prediction model for fracture toughness in microalloy steel. Int J Fatigue 24:1003–1010CrossRef
27.
Zurück zum Zitat Esfahani MB, Toroghinejad MR, Abbasi S (2009) Artificial neural network modeling the tensile strength of hot strip mill products. ISIJ Int 49:1583–1587CrossRef Esfahani MB, Toroghinejad MR, Abbasi S (2009) Artificial neural network modeling the tensile strength of hot strip mill products. ISIJ Int 49:1583–1587CrossRef
28.
Zurück zum Zitat Yescas MA (2003) Prediction of the Vickers hardness austempered ductile irons using neural network. Int J Cast Metal Res 15:513–521CrossRef Yescas MA (2003) Prediction of the Vickers hardness austempered ductile irons using neural network. Int J Cast Metal Res 15:513–521CrossRef
29.
Zurück zum Zitat Hassan AM, Alrashdan A, Hayajneh MT, Mayyas AT (2009) Prediction of density, porosity and hardness in aluminum-copper-based composite materials using artificial neural network. J Mater Process Tech 209:894–899CrossRef Hassan AM, Alrashdan A, Hayajneh MT, Mayyas AT (2009) Prediction of density, porosity and hardness in aluminum-copper-based composite materials using artificial neural network. J Mater Process Tech 209:894–899CrossRef
30.
Zurück zum Zitat Evans M (1999) Method for improving parametric creep rupture life of 2.25Cr-1Mo steel using artificial neural networks. Mater Sci Tech 15:647–658CrossRef Evans M (1999) Method for improving parametric creep rupture life of 2.25Cr-1Mo steel using artificial neural networks. Mater Sci Tech 15:647–658CrossRef
31.
Zurück zum Zitat Yoo YS, Jo CY, Jones CN (2002) Compositional prediction of creep rupture life of single crystal Ni base superalloy by Bayesian neural network. Mater Sci Eng A 336:22–29CrossRef Yoo YS, Jo CY, Jones CN (2002) Compositional prediction of creep rupture life of single crystal Ni base superalloy by Bayesian neural network. Mater Sci Eng A 336:22–29CrossRef
32.
Zurück zum Zitat Yoo YS, Kim IS, Kim DH, Jo CY, Kim HM, Jones CN (2004) The application of neural network to the development of single crystal superalloys. Superalloys 2004:942–950 Yoo YS, Kim IS, Kim DH, Jo CY, Kim HM, Jones CN (2004) The application of neural network to the development of single crystal superalloys. Superalloys 2004:942–950
33.
Zurück zum Zitat Wang N, Tu ST, Xuan FZ (2013) A novel prediction method of creep rupture life of 9–12% chromium ferritic steel based on abductive network. Eng Fail Anal 31:302–310CrossRef Wang N, Tu ST, Xuan FZ (2013) A novel prediction method of creep rupture life of 9–12% chromium ferritic steel based on abductive network. Eng Fail Anal 31:302–310CrossRef
34.
Zurück zum Zitat Frolova O, Roos E, Maile K, Müller W (2011) Representation of the heat specific creep rupture behaviour of 9% Cr steels using neural networks. Trans Mach Learn Data Mining 4:1–16 Frolova O, Roos E, Maile K, Müller W (2011) Representation of the heat specific creep rupture behaviour of 9% Cr steels using neural networks. Trans Mach Learn Data Mining 4:1–16
35.
Zurück zum Zitat Johnston RE (2011) Neural networks for critical high temperature component life prediction. Mater Sci Tech 27:108–114CrossRef Johnston RE (2011) Neural networks for critical high temperature component life prediction. Mater Sci Tech 27:108–114CrossRef
36.
Zurück zum Zitat Ghafir MFA, Li YG, Wang L (2014) Creep life prediction for aero gas turbine hot section component using artificial neural networks. J Eng Gas Turb Power 136:031504-1–031504-9 Ghafir MFA, Li YG, Wang L (2014) Creep life prediction for aero gas turbine hot section component using artificial neural networks. J Eng Gas Turb Power 136:031504-1–031504-9
37.
Zurück zum Zitat Chatzidakis S, Alamaniotis M, Tsoukalas LH (2014) Creep rupture forecasting for high performance energy systems. In: 5th international conference on information, intelligence, systems and applications, IISA 2014, USA, 95–99 Chatzidakis S, Alamaniotis M, Tsoukalas LH (2014) Creep rupture forecasting for high performance energy systems. In: 5th international conference on information, intelligence, systems and applications, IISA 2014, USA, 95–99
38.
Zurück zum Zitat Robi PS, Dixit US (2003) Application of neural networks in generating processing map for hot working. J Mater Process Tech 142:289–294CrossRef Robi PS, Dixit US (2003) Application of neural networks in generating processing map for hot working. J Mater Process Tech 142:289–294CrossRef
39.
Zurück zum Zitat Banerjee S, Robi PS, Srinivasan A (2012) Prediction of hot deformation behavior of Al–5.9%Cu–0.5%Mg alloys with trace additions of Sn. J Mater Sci 47:929–948CrossRef Banerjee S, Robi PS, Srinivasan A (2012) Prediction of hot deformation behavior of Al–5.9%Cu–0.5%Mg alloys with trace additions of Sn. J Mater Sci 47:929–948CrossRef
40.
Zurück zum Zitat Gupta VK, Kwatra N, Ray S (2007) Artificial neural network modeling of creep behavior in a rotating composite disc. Eng Comput 24:151–164CrossRef Gupta VK, Kwatra N, Ray S (2007) Artificial neural network modeling of creep behavior in a rotating composite disc. Eng Comput 24:151–164CrossRef
41.
Zurück zum Zitat Sarkar A, Sinha SK, Chakravartty JK, Sinha RK (2014) Artificial neural network modelling of in-reactor diametral creep of Zr2.5%Nb pressure tubes of Indian PHWRs. Ann Nucl Energy 69:246–251CrossRef Sarkar A, Sinha SK, Chakravartty JK, Sinha RK (2014) Artificial neural network modelling of in-reactor diametral creep of Zr2.5%Nb pressure tubes of Indian PHWRs. Ann Nucl Energy 69:246–251CrossRef
42.
Zurück zum Zitat Ghatak A, Robi PS (2016) Effect of temperature on the microstructure and hardness of service exposed 25Cr35NiNb reformer tubes. Trans Indian Inst Met 69:823–827CrossRef Ghatak A, Robi PS (2016) Effect of temperature on the microstructure and hardness of service exposed 25Cr35NiNb reformer tubes. Trans Indian Inst Met 69:823–827CrossRef
43.
Zurück zum Zitat Shariat MH, Faraji AH, Ashraf Riahy A, Alipour MM (2003) In: Advanced creep failure of HP modified reformer tubes in an ammonia plant. J Corros Sci Eng 6. Paper H012 preprint 69 Shariat MH, Faraji AH, Ashraf Riahy A, Alipour MM (2003) In: Advanced creep failure of HP modified reformer tubes in an ammonia plant. J Corros Sci Eng 6. Paper H012 preprint 69
44.
Zurück zum Zitat Ul-Hamid A, Tawancy HM, Mohamed AI, Abbas NM (2006) Failure analysis of furnace radiant tubes exposed to excessive temperature. Eng Fail Anal 13:1005–1021CrossRef Ul-Hamid A, Tawancy HM, Mohamed AI, Abbas NM (2006) Failure analysis of furnace radiant tubes exposed to excessive temperature. Eng Fail Anal 13:1005–1021CrossRef
45.
Zurück zum Zitat Yoon KB, Jeon DG (1998) Oxidation failure of radiant heater tubes. Eng Fail Anal 6:101–112CrossRef Yoon KB, Jeon DG (1998) Oxidation failure of radiant heater tubes. Eng Fail Anal 6:101–112CrossRef
46.
Zurück zum Zitat Guan K, Xu H, Wang Z (2005) Analysis of failed ethylene cracking tubes. Eng Fail Anal 12:420–431CrossRef Guan K, Xu H, Wang Z (2005) Analysis of failed ethylene cracking tubes. Eng Fail Anal 12:420–431CrossRef
47.
Zurück zum Zitat Ghanem MM, Elbatahgy AM (2003) Catastrophic failure of liquefied ammonia gas cylinder. Mater Perform 42:52–55 Ghanem MM, Elbatahgy AM (2003) Catastrophic failure of liquefied ammonia gas cylinder. Mater Perform 42:52–55
48.
Zurück zum Zitat De Silveira TL, Le May I (2006) Reformer furnaces: materials, damage, mechanisms and assessment. Arab J Sci Eng 31:99–119 De Silveira TL, Le May I (2006) Reformer furnaces: materials, damage, mechanisms and assessment. Arab J Sci Eng 31:99–119
49.
Zurück zum Zitat Swaminathan J, Guguloth K, Gunjan M, Roy P, Ghosh R (2008) Failure analysis and remaining life assessment of service exposed primary reformer heater tubes. Eng Fail Anal 15:311–331CrossRef Swaminathan J, Guguloth K, Gunjan M, Roy P, Ghosh R (2008) Failure analysis and remaining life assessment of service exposed primary reformer heater tubes. Eng Fail Anal 15:311–331CrossRef
50.
Zurück zum Zitat Nagesh DS, Datta GL (2002) Prediction of weld bead geometry and penetration in shielded metal-arc welding using artificial neural networks. J Mater Process Tech 123:303–312CrossRef Nagesh DS, Datta GL (2002) Prediction of weld bead geometry and penetration in shielded metal-arc welding using artificial neural networks. J Mater Process Tech 123:303–312CrossRef
51.
Zurück zum Zitat Çaydaş U, Hasçalık A (2008) A study on surface roughness in abrasive water jet machining process using artificial neural networks and regression analysis method. J Mater Process Tech 202:574–582CrossRef Çaydaş U, Hasçalık A (2008) A study on surface roughness in abrasive water jet machining process using artificial neural networks and regression analysis method. J Mater Process Tech 202:574–582CrossRef
52.
Zurück zum Zitat McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in neurons activity. Bull Math Biophys 5:115–133MathSciNetCrossRef McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in neurons activity. Bull Math Biophys 5:115–133MathSciNetCrossRef
53.
Zurück zum Zitat Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Networ 5:989–993CrossRef Hagan MT, Menhaj MB (1994) Training feedforward networks with the Marquardt algorithm. IEEE Trans Neural Networ 5:989–993CrossRef
54.
Zurück zum Zitat Ghatak A (2015) Creep correlation of micro-alloyed HP40Nb reformer steel. Dissertation, Indian Institute of Technology Guwahati Ghatak A (2015) Creep correlation of micro-alloyed HP40Nb reformer steel. Dissertation, Indian Institute of Technology Guwahati
55.
Zurück zum Zitat Garson GD (1991) Interpreting neural-network connection weights. Artif Intell Expert 6:47–51 Garson GD (1991) Interpreting neural-network connection weights. Artif Intell Expert 6:47–51
56.
Zurück zum Zitat Elmolla ES, Chaudhuri M (2011) The use of artificial neural network (ANN) for modelling, simulation and prediction of advanced oxidation process performance in recalcitrant wastewater treatment. In: Hui CLP (ed) Artificial Neural Networks-Application. InTech, Europe, chapter 6 Elmolla ES, Chaudhuri M (2011) The use of artificial neural network (ANN) for modelling, simulation and prediction of advanced oxidation process performance in recalcitrant wastewater treatment. In: Hui CLP (ed) Artificial Neural Networks-Application. InTech, Europe, chapter 6
Metadaten
Titel
Prediction of creep curve of HP40Nb steel using artificial neural network
verfasst von
Amitava Ghatak
P. S. Robi
Publikationsdatum
23.02.2017
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 9/2018
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-017-2851-9

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