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A Mathematical Model To Predict δ- Ferrite Content In Austenitic Stainless Steel Weld Metals

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Abstract

This paper presents a mathematical model to forecast the level of residual δ ferrite in terms of FN in austenitic stainless steel welds at cooling rates between 10 °C/s up to 103 °C/s. With this aim, two series of austenitic steel specimens were prepared using an electric arc remelt furnace. Whilst the alloying level was kept constant at [Creq+Nieq] = 30 % and [Creq+Nieq] = 40 %, the Creq/Nieq ratio was gradually increased from 1.22 up to 2.00 in each series. For each alloying level, a highly correlated polynomial function (FN vs. Creq /Nieq ), was found, being Creq and Nieq Hammar and Svensson’s equivalents. These experimental results have led to the importance of [Creq +Nieq] and (Creq /Nieq ) variables in the forecast of the residual ferrite content and a general expression including both variables is proposed.

$${\rm \bf FN=54.22-126.26(Cr_{eq}+Ni_{eq})+\lbrack-48.11+37.14(Cr_{eq}+Ni_{eq})\rbrack \Big({Cr_{eq}\over Ni_{eq}}\Big)+\lbrack-0.23+61.95(Cr_{eq}+Ni_{eq})\rbrack \Big({Cr_{eq}\over Ni_{eq}}\Big)^2}$$

The proposed model is able to forecast the level of δ ferrite with a mean error of +1.01 FN within a deviation of +/- 2.12 FN with 95 % probability by just considering the chemical composition of the alloy. This level of error has been proved to be lower than DeLong’s and WRC-1988 diagrams errors. Moreover, the proposed model has also been compared with WRC-1992 diagram and FNN-1999 neural network and it provides a more accurate FN forecast within the range of compositions and cooling rates considered.

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References

  1. Kujanpää V.P. and David S.A.: White, C.L. Formation of hot cracks in austenitic stainless steel welds- solidification cracking, Welding Journal, 1986, vol. 65, no. 8, pp. 203s–212s.

    Google Scholar 

  2. Suutala N., Takalo T. and Moisio T. The relationship between solidification and microstructure in austenitic and austenitic-ferritic stainless steel welds, Metallurgical Transactions A. 1979, vol. 10A, no. 4, pp. 512–514.

    Article  CAS  Google Scholar 

  3. Kujanpää V.P., Suutala N, Takalo T. and Moisio T.: Correlation between solidification cracking and microstructure in austenitic and austenitic-ferritic stainless steel welds, Welding Research International, 1979, vol. 9, no. 2, pp. 55–75.

    Google Scholar 

  4. Lippold J.C. and Savage W.F.: Solidification of austenitic stainless steel weldments: Part III —The effect of solidification behavior on hot cracking susceptibility, Welding Journal, 1982, no. 12, pp. 388s-396s.

  5. Brooks J.A., Thomson A.W. and Williams J.C.: Variations in weld ferrite content due to P and S, Welding Journal, 1983, no. 8, pp. 220s-225s.

  6. Kujanpää V.P, Suutala N.J., Takalo T.K. and Moisio T.J.I.: Solidification cracking — estimation of the susceptibility of austenitic and austenitic-ferritic stainless steel welds, Metal Construction, 1980, vol. 12, no. 6, pp. 282–285.

    Google Scholar 

  7. Suutala N, Takalo T. and Moisio T.: Technical note: Comment on the transformation δ → γ by a massive mechanism in austenitic stainless steel, Welding Journal, 1981, no. 5, pp. 92s-93s.

  8. Suutala N.: Effect of solidification conditions on the solidification mode in austenitic stainless steels, Metallurgical Transactions A., 1983, vol. 14A, no. 2, pp. 191–197.

    Article  Google Scholar 

  9. Kujanpää V.P.: Effects of steel type and impurities in solidification cracking of austenitic stainless steel welds, Metal Construction, 1985, vol. 17, no. 1, pp. 40R–46R.

    Google Scholar 

  10. Brooks J.A.: Solidification behavior and cracking susceptibility of austenitic stainless steel welds, Proceedings of the 8th Annual North American Welding Research Conference, Columbus, Ohio, October 1992, pp. 19–21.

  11. Li L. and Messler R.W. Jr.: The effects of phosphorus and sulphur on susceptibility to weld hot cracking in austenitic stainless steels, Welding Journal, 1999, no. 12, pp. 387s-396s.

  12. Brooks J.A, Robino C.V., Headley T.J and Michael J.R.: Weld solidification and cracking behavior of free-machining stainless steel, Welding Journal, 2003, no. 3, pp. 51s-64s.

  13. Brooks J.A., Goods S.H. and Robino C.V. Weld properties of AISI 303 free-machining stainless steel, Welding Journal, 2003, no. 4, pp. 84s-92s.

  14. Shankar V., Gill T.P.S, Mannan S.L and Sundaresan S.: Solidification cracking in austenitic stainless steel welds, Sadhana, 2003, vol. 28, pp. 359–382.

    Article  CAS  Google Scholar 

  15. Katayama S., Fujimoto T. and Matsunawa A.: Correlation among solidification process, microstructure, microsegregation and solidification cracking susceptibility in stainless steel weld metals, Transactions of Japanese Welding Research Institute, 1985, vol. 14, no. 1, pp. 123–138.

    CAS  Google Scholar 

  16. Lundin C.D., Delong W.T. and Spond D.F.: Ferrite-fissuring relationship in austenitic stainless steel weld metals, Welding Journal, 1975, no. 8, pp. 241s-246s.

  17. Lundin C.D., Delong W.T. and Spond D.F.: The fissure bend test, Welding Journal, 1976, no. 6, pp. 145s-151s.

  18. Olson D.L.: Prediction of austenitic weld metal microstructure and properties, Welding Journal, 1985, vol. 64, no. 10, pp. 281s–295s.

    Google Scholar 

  19. Strauss B. and Maurer E.: Die Hochlegierten Chromnickelstahle als nichtrostende Stahle. Kruppsche Monatshefte, 1920, vol. 1, no. 8, pp. 129–146.

    Google Scholar 

  20. Newell H.D. and Fleischmann M.: Hot rolled metal article and method of making same, U.S. patent n∘ 2-118-683, 1938.

  21. Feild A.L., Bloom K.F. and Linnert G.E.: Development of armor welding electrodes: relation of the composition of austenitic (20Cr-10Ni) electrodes to the physical and ballistic properties of armor weldments, OSRD Report n∘ 1636, 1943.

  22. Binder W.O., Brown C.M. and Franks R.: Resistance to sensitization of austenitic chromium-nickel steels of 0.03% max. carbon content, Trans. ASM., 1949, vol. 41, pp. 1301–1346.

    Google Scholar 

  23. Campbell H.C. and Thomas Jr R.D.: The effect of alloying elements on the tensile properties of 25-20 weld metal, Welding Journal, 1946, vol. 25, no. 11, pp. 760s–768s.

    CAS  Google Scholar 

  24. Schaeffler A.L.: Selection of austenitic electrodes for welding dissimilar metals, Welding Journal, 1947, vol. 26, no. 10, pp. 1–20.

    Google Scholar 

  25. Schaeffler A.L.: Welding dissimilar metals with stainless electrodes, Iron Age, 1948, vol. 162, pp. 72.

    CAS  Google Scholar 

  26. Schaeffler A.L.: Constitution diagram for stainless steel weld metal, Metal Progress, 1949, vol. 56, no. 11, pp. 680–680B.

    CAS  Google Scholar 

  27. Delong W.T. and Reid Jr H.F.: Properties of austenitic chromium in austenitic chromium-manganese stainless steel weld metal, Welding Journal, 1957, vol. 37, no. 1, pp. 1–8.

    Google Scholar 

  28. Delong W.T.: A modified phase diagram for stainless steel weld metals, Metal Progress, 1960, vol. 77, no. 2, pp. 99–100B.

    Google Scholar 

  29. Long C.J. and Delong W.T.: The ferrite content of austenitic stainless steel weld metal, Welding Journal, 1973, vol. 52, no. 7, pp. 281s–297s.

    Google Scholar 

  30. Delong W.T.: Ferrite in austenitic stainless steel weld metal, Welding Journal, 1974, no. 7, pp. 273s-286s.

  31. Reid H.F. and Delong W.T.: Making sense out of ferrite requirements in welding stainless steels, Metal Progress, 1973, no. 6, pp. 73-77.

  32. Kotecki D.J.: Extension of the WRC Ferrite Number system, Welding Journal, 1982, vol. 61, no. 11, pp. 352s–361s.

    Google Scholar 

  33. Kotecki D.J.: Ferrite control in duplex stainless steel weld metal, Welding Journal, 1986, no. 10, pp. 273s-278s.

  34. Siewer T.A., McCowan C.N. and Olson D.L.: Ferrite Number prediction to 100 FN in stainless steel weld metal, Welding Journal, 1988, vol. 67, no. 12, pp. 289s–298s.

    Google Scholar 

  35. McCowan C.N., Siewert T.A and Olson D.L.: Stainless steel weld metal: Prediction of ferrite content, WRC Bulletin, 1989, no. 342, 36 pages.

  36. Kotecki D.J. and Siewert T.A.: WRC-1992 Constitution Diagram for stainless steel weld metals: a modification of the WRC-1988 Diagram, Welding Journal, 1992, no. 5, pp. 171s-178s.

  37. Feldstein J.: The WRC Diagram, Svetsaren,1993, vol. 47, no. 2, pp. 36–39.

    Google Scholar 

  38. Kotecki D.J.: A martensite boundary on the WRC-1992 diagram, Welding Journal, 1999, vol. 78, no. 5, pp. 181s–192s.

    Google Scholar 

  39. Kotecki D.J.: Martensite prediction in stainless steel weld cladding, Paper presented at the Stainless Steel World Conference, 1999, no. 2, pp. 573–583.

  40. Balmforth M.C. and Lippold J.C.: A new ferritic-martensitic stainless steel constitution diagram, Welding Journal, 2000, vol. 79, no. 12, pp. 339s–345s.

    Google Scholar 

  41. Vasudevan M., Murugananth M. and Bhaduri A.K.: Application of Bayesian neural network for modeling and prediction of ferrite number in austenitic stainless steel welds, On line, Retrieved November 2nd 2004, Available at: http://www.msm.cam.ac.uk/phasetrans/2001/Ferrite_number.pdf.

  42. Vitek J.M., Iskander Y.S., Oblow E.M.: Improved ferrite number prediction in stainless steel arc welds using artificial neural networks — part 1: neural network development, Welding Journal, 2000, no. 2, pp. 33s-40s.

  43. Vitek J.M., Iskander Y.S. and Oblow E.M.: Improved ferrite number prediction in stainless steel arc welds using artificial neural networks — part 2: neural network results, Welding Journal, 2000, no. 2, pp. 41s-50s.

  44. Vitek J.M., David S.A. and Hinman C.R.: Improved ferrite number prediction model that accounts for cooling rate effects — part 1: model development, Welding Journal, 2003, no. 1, pp. 10s-17s.

  45. Vitek J.M., David S.A., Hinman C.R.: Improved ferrite number prediction model that accounts for cooling rate effects- Part 2: model results, Welding Journal, 2003, no. 2, pp. 43s-50s.

  46. Hammar Ö. and Svensson U.: Influence of steel composition on segregation and microstructure during solidification of austenitic stainless steels, Solidification and casting of metals, Conference, The Metals Society, 1979, pp. 401–410.

  47. ASTM E1306-94 (Reapproved 2004) Standard Practice for Preparation of Metal and Alloy Samples by Electric Arc Remelting for the Determination of Chemical Composition, Philadelphia: ASTM International, 2004.

  48. Valiente Bermejo M.A.: Modelització del nivell de ferrita δ (FN) als acers inoxidables austenítics sotmesos a fusió per arc electric, Modelization of δ-ferrite content (FN) in austenitic stainless steels under electric arc conditions, PhD. University of Barcelona, Department of Materials Science and Metallurgical Engineering, June 2010, ISBN 978-84-693-5713-2 (in Catalan).

  49. ASTM E1306-07 Standard practice for preparation of metal and alloy samples by electric arc remelting for the determination of chemical composition, Philadelphia: ASTM International, 2007.

  50. EN ISO 8249:2000, Welding, Determination of Ferrite Number (FN) in austenitic and duplex ferritic-austenitic Cr-Ni stainless steel weld metals, 2000.

  51. Kotecki D.J.: Predicted and measured FN in specifications — A position statement of the experts of IIW Commission IX, Doc. IIW-1420, Welding in the World, 1999, vol. 43, no. 2, pp. 8–10.

    CAS  Google Scholar 

  52. Iamboliev T., Katayama S. and Matsunawa A.: Interpretation of phase formation in austenitic stainless steel welds, Welding Journal, 2003, no. 12, pp. 337s-347s.

  53. Elmer J.W., Allen S.M. and Eagar T.W.: Microstructural development during solidification of stainless steel alloys, Metallurgical Transactions A., 1989, vol. 20A, pp. 2117–2131.

    Article  CAS  Google Scholar 

  54. Suutala N. Effect of Solidification Conditions on the Solidification Mode in Austenitic Stainless Steels. Metallurgical Transactions A. 1983, vol. 14A, no. 2, pp. 191–197.

    Article  Google Scholar 

  55. Elmer J.W., Allen S.M. and Eagar T.W. The influence of cooling rate on the ferrite content of stainless steel alloys, Proceedings of the 2nd International Conference on Trends in Welding Research, Gatlinburg, 14–18 May 1989, Tennessee: ASM International, 1989, pp. 165–170.

    Google Scholar 

  56. Anderson T.D., Perricone M.J., DuPont J.N. and Marder A.R.: The influence of molybdenum on stainless steel weld microstructures, Welding Journal, 2007, vol. 86, no. 9, pp. 281s–292s.

    Google Scholar 

  57. Inoue H., Koseki T., Ohkita S. and Tanaka T.: Effect of solidification on subsequent ferrite-to-austenite massive transformation in an austenitic stainless steel weld metal, ISIJ International, 1995, vol. 35, no. 10, pp. 1248–1257.

    Article  CAS  Google Scholar 

  58. Lippold J.C. and Kotecki D.J. Welding metallurgy and weldability of stainless steels, New Jersey: Wiley-Interscience, 2005, ISBN 0-471-47379-0.

    Google Scholar 

  59. Nakao R., Fukumoto S., Fuji M. and Takeuchi H.: Evaporation of Alloying Elements and Behavior of Degassing Reactions of High Chromium Steel in Electron Beam Melting. ISIJ International. 1992, vol. 32, no. 5, pp. 685–692.

    Article  CAS  Google Scholar 

  60. Block-Bolten, A. and Eagar T.W.: Metal vaporization from weld pools, Metallurgical Transactions B, 1984, vol. 15B, pp. 461–469.

    Article  CAS  Google Scholar 

  61. Jenkins N.T., Mendez P.F. and Eagar T.W.: Effect of Arc welding electrode temperature on vapor and fume composition, ASM International, Trends in Welding Research Conference, Ohio, 2005, 6 pages.

  62. Jenkins N.T and Eagar T.W.: Chemical analysis of welding fume particles, Welding Journal, 2005, vol. 84, no. 6, pp. 87s–93s.

    Google Scholar 

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    María Asunción Valiente Bermejo

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Valiente Bermejo, M.A. A Mathematical Model To Predict δ- Ferrite Content In Austenitic Stainless Steel Weld Metals. Weld World 56, 48–68 (2012). https://doi.org/10.1007/BF03321381

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