Skip to main content
SpringerLink
Log in

RETRACTED ARTICLE: Analytical modeling of tensile strength of functionally graded steels

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

This article was retracted on 25 August 2020

This article has been updated

Abstract

In the present study, the tensile strength of ferritic and austenitic functionally graded steel produced by electroslag remelting has been modeled by artificial neural networks. Functionally graded steel containing graded layers of ferrite and austenite may be fabricated via diffusion of alloying elements during remelting stage. Vickers microhardness profile of the specimen has been obtained experimentally and modeled with artificial neural networks. To build the model for graded ferritic and austenitic steels, training, testing and validation using respectively 174 and 120 experimental data were conducted. According to the input parameters, in the neural networks model, the Vickers microhardness of each layer was predicted. A good-fit equation that correlates the Vickers microhardness of each layer to its corresponding chemical composition was achieved by the optimized network for both ferritic- and austenitic-graded steels. Afterward, the Vickers microhardness of each layer in functionally graded steels was related to the yield stress of the corresponding layer and by assuming Holloman relation for stress–strain curve of each layer, they were acquired. Finally, by applying the rule of mixtures, tensile strength of functionally graded steels configuration was found through a numerical method. The obtained results from the proposed model are in good agreement with those acquired from the experiments.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

Change history

  • 25 August 2020

    The Editor-in-Chief has retracted this article

References

  1. Bahr HA, Balke H, Fett T, Hofinger I, Kirchhoff G, Munz D, Neubrand A, Semenov AS, Weiss HJ, Yang YY (2003) Cracks in functionally graded materials. Mater Sci Eng, A 362:2–16

    Google Scholar 

  2. Xu H, Yao X, Feng X, Hisen YY (2008) Dynamic stress intensity factors of a semi-infinite crack in an orthotropic functionally graded material. Mech Mater 40:37–47

    Google Scholar 

  3. Tohgo K, Suzuki T, Araki H (2005) Evaluation of r-curve behavior of ceramic-metal functionally graded materials by stable crack growth. Eng Fracture Mech 72:2359–2372

    Google Scholar 

  4. Rousseau CE, Tippur HV (2000) Compositionally graded materials with cracks normal to the elastic gradient. Acta Mater 48(16):4021–4033

    Google Scholar 

  5. Carpenter RD, Liang WW, Paulino GH, Gibeling JC, Munir ZA (1999) Fracture testing and analysis of a layered functionally graded Ti/TiB beam in 3-point bending. Mater Sci Forum 308–311:837–842

    Google Scholar 

  6. Williamson RL, Rabin BH, Drake JT (1993) Finite element analysis of thermal residual stresses at graded ceramic–metal interfaces, Part I: model description and geometrical effects. J Appl Phys 74:1310–1320

    Google Scholar 

  7. Giannakopoulos AE, Suresh S, Finot M, Olsson M (1995) Elastoplastic analysis of thermal cycling: layered materials with compositional gradients. Acta Metallurgica Mater 43:1335–1354

    Google Scholar 

  8. Kolednik O (2000) The yield stress gradient effect in inhomogeneous materials. Int J Solids Struct 37(5):781–808

    MATH  Google Scholar 

  9. Aghazadeh Mohandesi J, Shahosseinie MH (2005) Transformation characteristics of functionally graded steels produced by electroslag remelting. Metall Mater Trans A 36A:3471–3476

    Google Scholar 

  10. Aghazadeh Mohandesi J, Shahosseinie MH, Parastar Namin R (2006) Tensile behavior of functionally graded steels produced by electroslag remelting. Metall Mater Trans 37A:2125–2132

    Google Scholar 

  11. Nazari A, Aghazadeh Mohandesi J (2010) Modelling impact resistance of functionally graded steels with crack divider configuration. Mater Sci Technol 26:1377–1383

    Google Scholar 

  12. Nazari A, Aghazadeh Mohandesi J (2009) Impact energy of functionally graded steels with crack divider configuration. J Mater Sci Technol 25(6):847–852

    Google Scholar 

  13. Nazari A, Aghazadeh Mohandesi J, Riahi S (2010) Modeling impact energy of functionally graded steels in crack divider configuration using modified stress-strain curve data. Int J Damage Mech. doi:10.1177/1056789510397073

  14. Nazari A, Aghazadeh Mohandesi J, Hamid Vishkasogheh M, Abedi M (2011) Simulation of impact energy in functionally graded steels. Comput Mater Sci 50:1187–1196

    Google Scholar 

  15. Nazari A, Aghazadeh Mohandesi J (2010) Impact energy of functionally graded steels in crack arrester configuration. J Mater Eng Perform 19:1058–1064

    Google Scholar 

  16. Nazari A, Milani AA, Zakeri M (2011) Modeling ductile to brittle transition temperature of functionally graded steels by artificial neural networks. Comput Mater Sci 50:2028–2037

    Google Scholar 

  17. Nazari A, Milani AA (2011) Ductile to brittle transition temperature of functionally graded steels. Int J Damage Mech. doi:10.1177/1056789511398270

  18. Nazari A, Milani AA (2011) Modeling ductile-to-brittle transition temperature of functionally graded steels by gene expression programming. Int J Damage Mech. doi:10.1177/1056789511406561

  19. Nazari A, Milani AA (2011) Ductile to brittle transition temperature of functionally graded steels with crack arrester configuration. Mater Sci Eng, A 528:3854–3859

    Google Scholar 

  20. Nazari A, Milani AA (2011) Modeling ductile to brittle transition temperature of functionally graded steels by fuzzy logic. J Mater Sci 46:6007–6017

    Google Scholar 

  21. Nazari A, Aghazadeh Mohandesi J, Riahi S (2011) Modified modeling fracture toughness of functionally graded steels in crack divider configuration. Int J Damage Mech 20:811–831

    Google Scholar 

  22. Aghazadeh Mohandesi J, Nazari A, Hamid Vishkasogheh M, Abedi M (2010) Modeling fracture toughness of functionally graded steels in crack divider configuration. Model Simul Mater Sci Eng 18:075007 (13 pp)

    Google Scholar 

  23. Nazari A, Aghazadeh Mohandesi J, Riahi S (2011) Fracture toughness of functionally graded steels. J Mater Eng Perform. doi:10.1007/s11665-011-9945-9

  24. Nazari A, Aghazadeh Mohandesi J, Riahi S (2011) Modeling fracture toughness of functionally graded steels in crack arrester configuration. Comput Mater Sci 50:1578–1586

    Google Scholar 

  25. Nazari A, Aghazadeh Mohandesi J (2011) Modeling tensile strength of oblique layer functionally graded austenitic steel. Comput Mater Sci 50:1425–1431

    Google Scholar 

  26. Nazari A, Riahi S (2010) Effect of layer angle on tensile behavior of oblique layer functionally graded steels. Turkish J Eng Environ Sci 34:17–24

    Google Scholar 

  27. Nazari A, Aghazadeh Mohandesi J, Tavareh S (2011) Microhardness profile prediction of a graded steel by strain gradient plasticity theory. Comput Mater Sci 50:1781–1784

    Google Scholar 

  28. Nazari A, Aghazadeh Mohandesi J, Tavareh S (2011) Modeling tensile strength of austenitic graded steel based on the strain gradient plasticity theory. Comput Mater Sci 50:1791–1794

    Google Scholar 

  29. Nazari A, Mojtahed Najafi SM (2011) Prediction Charpy impact energy of bcc and fcc functionally graded steels in crack divider configuration by strain gradient plasticity theory. Comput Mater Sci 50:3178–3183

    Google Scholar 

  30. Nazari A, Mojtahed Najafi SM (2011) Prediction impact behavior of functionally graded steel by strain gradient plasticity theory. Comput Mater Sci 50:3218–3223

    Google Scholar 

  31. Nazari A (2011) Modeling Charpy impact energy of functionally graded steel based on the strain gradient plasticity theory and modified stress–strain curve data. Comput Mater Sci 50:3350–3357

    Google Scholar 

  32. Nazari A (2011) Application of strain gradient plasticity theory to model Charpy impact energy of functionally graded steels. Comput Mater Sci 50:3410–3416

    Google Scholar 

  33. Nazari A (2011) Strain gradient plasticity theory to predict the input data for modeling Charpy impact energy in functionally graded steels. Comput Mater Sci 50:3442–3449

    Google Scholar 

  34. Nazari A (2011) Simulation of impact energy in functionally graded steels by mechanism-based strain gradient plasticity theory. Comput Mater Sci. doi:10.1016/j.commatsci.2011.07.010

  35. Nazari A (2011) Simulation Charpy impact energy of functionally graded steels by modified stress–strain curve through mechanism-based strain gradient plasticity theory. Comput Mater Sci. doi:10.1016/j.commatsci.2011.07.027

  36. Nazari A (2011) Application of strain gradient plasticity theory to model Charpy impact energy of functionally graded steels using modified stress–strain curve data. Comput Mater Sci. doi:10.1016/j.commatsci.2011.07.057

  37. Nazari A (2011) Modeling fracture toughness of ferritic and austenitic functionally graded steel based on the strain gradient plasticity theory. Comput Mater Sci 50:3238–3244

    Google Scholar 

  38. Nazari A (2011) Strain gradient plasticity theory for modeling JIC of functionally graded steels. Comput Mater Sci. doi:10.1016/j.commatsci.2011.06.038

  39. Pala M, Ozbay O, Oztas A, Yuce MI (2005) Appraisal of long-term effects of fly ash and silica fume on compressive strength of concrete by neural networks. Constr Build Mater 21(2):384–394

    Google Scholar 

  40. Pak J, Jang J, Bhadeshia HKDH, Karlsson L (2009) Optimization of neural network for Charpy toughness of steel welds. Mater Manuf Proces 24:16–21

    Google Scholar 

  41. Cottrell GA, Kemp R, Bhadeshia HKDH, Odette GR, Yamamoto T (2007) Neural network analysis of Charpy transition temperature of irradiated low-activation martensitic steels. J Nuclear Mater 367–370:603–609

    Google Scholar 

  42. Yeh IC (1998) Modeling of strength of HPC using ANN. Cement Concrete Res 28(12):1797–1808

    Google Scholar 

  43. Lai S, Sera M (1997) Concrete strength prediction by mean of neural networks. Constr Build Mater 11(2):93–98

    Google Scholar 

  44. Lee SC (2003) Prediction of concrete strength using artificial neural networks. Eng Struct 25(7):849–857

    Google Scholar 

  45. Hong-Guang N, Ji-Zong W (2000) Prediction of compressive strength of concrete by neural networks. Cement Concrete Res 30(8):1245–1250

    Google Scholar 

  46. Dias WPS, Pooliyadda SP (2001) Neural networks for predicting properties of concretes with admixtures. Constr Build Mater 15(7):371–379

    Google Scholar 

  47. Oztas A, Pala M, Ozbay E, Kanca E, Caglar N, Asghar Bhatti M (2006) Predicting the compressive strength and slump of high strength concrete using neural network. Constr Build Mater 20(9):769–775

    Google Scholar 

  48. Akkurt S, Ozdemir S, Tayfur G, Akyol B (2003) The use of GA-ANNs in the modelling of compressive strength of cement mortar. Cement Concrete Res 33(7):973–979

    Google Scholar 

  49. Mukherjee A, Biswas SN (1997) Artificial neural networks in prediction of mechanical behavior of concrete at high temperature. Nucl Eng Design 178(1):1–11

    Google Scholar 

  50. Nazari A, Riahi S (2010) Computer-aided prediction of physical and mechanical properties of high strength cementitious composite containing Cr2O3 nanoparticles. NANO 5(5):301–318

    Google Scholar 

  51. Nazari A, Riahi S (2011) Prediction split tensile strength and water permeability of high strength concrete containing TiO2 nanoparticles by artificial neural network and genetic programming. Compos Part B Eng 42:473–488

    Google Scholar 

  52. Nazari A, Riahi S (2011) Computer-aided design of the effects of Fe2O3 nanoparticles on split tensile strength and water permeability of high strength concrete. Mater Design 32:3966–3979

    MATH  Google Scholar 

  53. ASTM E8 (2001) Standard test methods for tension testing of metallic materials, annual book of ASTM standards. ASTM, Philadelphia, PA

    Google Scholar 

  54. Ince R (2004) Prediction of fracture parameters of concrete by artificial neural networks. Eng Fract Mech 71(15):2143–2159

    Google Scholar 

  55. McCulloch WS, Pitts W (1943) A logical calculus of the ideas immanent in neural nets. Bull Math Biophys 5:115–137

    MathSciNet  MATH  Google Scholar 

  56. Rosenblatt F (1962) Principles of neuro dynamics: perceptrons and the theory of brain mechanisms. Spartan Books, Washington, DC

    MATH  Google Scholar 

  57. Rumelhart DE, Hinton GE, William RJ (1986) Learning internal representation by error propagation. In: Rumelhart DE, McClelland JL (eds) Proceeding parallel distributed processing foundation, vol 1. MIT Press, Cambridge

    Google Scholar 

  58. Liu SW, Huang JH, Sung JC, Lee CC (2002) Detection of cracks using neural networks and computational mechanics. Comput Meth Appl Mech Eng 191(25–26):2831–2845

    MATH  Google Scholar 

  59. Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Nat Acad Sci 79:2554–2558

    MathSciNet  MATH  Google Scholar 

  60. Suratgar AA, Tavakoli MB, Hoseinabadi A (2005) Modified Levenberg–Marquardt method for neural networks training. World Acad Sci Eng Technol 6:46–48

    Google Scholar 

  61. Nazari A (2011) Application of artificial neural networks for analytical modeling of Charpy impact energy of functionally graded steels. Neural Comput Appl. doi:10.1007/s00521-011-0761-9

Download references

Author information

Authors and Affiliations

  1. Department of Materials Science and Engineering, Saveh Branch, Islamic Azad University, Saveh, Iran

    Ali Nazari

Authors
  1. Ali Nazari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ali Nazari.

About this article

Cite this article

Nazari, A. RETRACTED ARTICLE: Analytical modeling of tensile strength of functionally graded steels. Neural Comput & Applic 23, 787–799 (2013). https://doi.org/10.1007/s00521-012-0995-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-012-0995-1

Keywords

Search

Navigation