Abstract
Ferritic steel bars—25 mm in diameter—were welded by transient liquid phase bonding (TLPB) using Fe-based amorphous metallic foils as filler material. The resulting residual stress (RS) field shows a low peak magnitude—of 147 MPa—as measured by neutron diffraction. The most distinctive feature of TLPB is the heat input delivered simultaneously at the whole joint that allows much lower cooling rates compared with arc welding (AW). Therefore, the elapsed time between 800 and 500 °C (t 8/5) was particularly long reaching 390 s. As a result, a low RS peak magnitude (147 MPa) was obtained in the as-welded condition. This value is well below the RS peak magnitude obtained with AW which typically attain the yield strength of the base metal (276 MPa). The numerical simulation of RS at the welded bars was performed by a thermal and mechanical analysis. It shows that TLPB produced a large austenized region, low cooling rates and a remarkable t 8/5. Consequently, the large volume in which the heat input is delivered is the driving force to reduce RS peak magnitudes. From the mechanical analysis, it was found that the simulated RS was in good agreement with the measured RS. Therefore, the proposed numerical simulation model can be used to predict RS in TLPB weldments.
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Notes
It is worth noting that the usefulness of measuring RS by ND depends on the specimen dimensions. For small specimens, the gauge volume for ND can be very large (e.g.: It may capture both the fusion zone and the heat affected zone).
AC1 is the temperature which corresponds to the boundary between the ferrite-cementite field and the fields containing austenite and ferrite, while AC3 is the temperature which corresponds to the boundary between the ferrite-austenite and austenite fields (during heating of ferritic steels).
References
Oliveira JP, Barbosa D, Fernandes FMB, Miranda RM (2016) Tungsten inert gas (TIG) welding of Ni-rich NiTi plates: functional behavior. Smart Mater Struct 25:03LT01. https://doi.org/10.1088/0964-1726/25/3/03LT01
Oliveira JP, Crispim B, Zeng Z et al (2019) Microstructure and mechanical properties of gas tungsten arc welded Cu-Al-Mn shape memory alloy rods. J Mater Process Technol 271:93–100. https://doi.org/10.1016/j.jmatprotec.2019.03.020
Martin AC, Oliveira JP, Fink C (2020) Elemental effects on weld cracking susceptibility in AlxCoCrCuyFeNi high-entropy alloy. Metall Mater Trans A 51:778–787. https://doi.org/10.1007/s11661-019-05564-8
Hemmesi K, Farajian M, Boin M (2017) Numerical studies of welding residual stresses in tubular joints and experimental validations by means of X-ray and neutron diffraction analysis. Mater Des 126:339–350. https://doi.org/10.1016/j.matdes.2017.03.088
Balakrishnan J, Vasileiou AN, Francis JA et al (2018) Residual stress distributions in arc, laser and electron-beam welds in 30 mm thick SA508 steel: a cross-process comparison. Int J Press Vessel Pip 162:59–70. https://doi.org/10.1016/j.ijpvp.2018.03.004
Haigh RD, Hutchings MT, James JA et al (2013) Neutron diffraction residual stress measurements on girth-welded 304 stainless steel pipes with weld metal deposited up to half and full pipe wall thickness. Int J Press Vessel Pip 101:1–11. https://doi.org/10.1016/j.ijpvp.2012.08.003
Duvall DS, Owczarski WA, Paulonis DF (1974) TLP bonding: a new method for joining heat resistant alloys. Weld J 53:203–214
Kaplan D, Murry G (2008) Thermal, metallurgical and mechanical phenomena in the heat affected zone. Metallurgy and mechanics of welding. ISTE, London, pp 89–131
Fitzpatrick ME, Lodini A (2003) Analysis of residual stress by diffraction using neutron and synchrotron radiation. CRC Press, London
Withers PJ (2013) Synchrotron X-ray diffraction. Practical residual stress measurement methods. John Wiley & Sons Ltd, Chichester, pp 163–194
ASTM A29/A29M–20 (2020) Standard specification for general requirements for steel bars. Carbon and Alloy, Hot-Wrought. https://doi.org/10.1520/A0029_A0029M-20
ASTM E8/E8M-21 (2021) Standard test methods for tension testing of metallic materials. https://doi.org/10.1520/E0008_E0008M-21
Pirling T, Bruno G, Withers PJ (2006) SALSA—a new instrument for strain imaging in engineering materials and components. Mater Sci Eng A 437:139–144. https://doi.org/10.1016/j.msea.2006.04.083
ISO 21432:2019 (2019) Non-destructive testing—standard test method for determining residual stresses by neutron diffraction
Richard D, Ferrand M, Kearley GJ (1996) Analysis and visualisation of neutron-scattering data. J Neutron Res 4:33–39. https://doi.org/10.1080/10238169608200065
Behnken H, Hauk V (1986) Berechnung der roentgenographischen Elastizitaetskonstanten (REK) des Vielkristalls aus den Einkristalldaten fuer beliebige Kristallsymmetrie. Zeitschrift für Met 77:620–626
Spooner S, Wang X-L (1997) Diffraction peak displacement in residual stress samples due to partial burial of the sampling volume. J Appl Crystallogr 30:449–455. https://doi.org/10.1107/S0021889897000174
Hutchings MT, Withers PJ, Holden TM, Lorentzen T (2005) Introduction to the characterization of residual stress by neutron diffraction. CRC Press, Boca Raton
Snyder MD, Bathe K-J (1981) A solution procedure for thermo-elastic-plastic and creep problems. Nucl Eng Des 64:49–80. https://doi.org/10.1016/0029-5493(81)90032-7
Ueda Y, Murakawa H, Ma N (2012) Chapter 3—mechanical simulation of welding. In: Ueda Y, Murakawa H, Ma N (eds) Welding deformation and residual stress prevention. Butterworth-Heinemann, Boston, pp 55–98
Rammerstorfer FG, Fischer DF, Mitter W et al (1981) On thermo-elastic-plastic analysis of heat-treatment processes including creep and phase changes. Comput Struct 13:771–779. https://doi.org/10.1016/0045-7949(81)90040-7
Suman S, Biswas P (2020) Comparative study on SAW welding induced distortion and residual stresses of CSEF steel considering solid state phase transformation and preheating. J Manuf Process 51:19–30. https://doi.org/10.1016/j.jmapro.2020.01.012
Favennec Y, Labbé V, Bay F (2003) Induction heating processes optimization a general optimal control approach. J Comput Phys 187:68–94. https://doi.org/10.1016/S0021-9991(03)00081-0
Labridis D, Dokopoulos P (1989) Calculation of eddy current losses in nonlinear ferromagnetic materials. IEEE Trans Magn 25:2665–2669
Di Luozzo N, Fontana M, Arcondo B (2012) Modelling of induction heating of carbon steel tubes: mathematical analysis, numerical simulation and validation. J Alloys Compd 536:S564–S568. https://doi.org/10.1016/j.jallcom.2011.12.084
Elmer FEM (2021) Open source multiphysical simulation software. http://www.elmerfem.org/. Accessed 27 Jul 2022
BS EN 1993-1-2:2005 (2005) Eurocode 3: design of steel structures - Part 1–2: General rules - structural fire design
Iuchi T, Furukawa T, Wada S (2003) Emissivity modeling of metals during the growth of oxide film and comparison of the model with experimental results. Appl Opt 42:2317. https://doi.org/10.1364/AO.42.002317
Churchill SW, Chu HHS (1975) Correlating equations for laminar and turbulent free convection from a horizontal cylinder. Int J Heat Mass Transf 18:1049–1053. https://doi.org/10.1016/0017-9310(75)90222-7
Raithby GD, Hollands KGT (1975) A General Method of Obtaining Approximate Solutions to Laminar and Turbulent Free Convection Problems. In: Irvine TF, Hartnett JP (eds). Elsevier, Amsterdam, pp 265–315
de Souza NE, Perić D, Owen D (2008) Finite elements in small-strain plasticity problems. Computational methods for plasticity. John Wiley & Sons Ltd, Chichester, pp 191–263
Code_Aster (2021) Analysis of structures and thermomechanics for studies & research. https://code-aster.org/spip.php?rubrique2. Accessed 27 Jul 2022
Liu T, Long M, Fan H et al (2018) Dilatometric determination of four critical temperatures and phase transition fraction for austenite decomposition in hypo-eutectoid steels using peak separation method. J Mater Res 33:967–977. https://doi.org/10.1557/jmr.2017.484
Stang AH, GreenspanNewman MSB (1946) Poisson’s ratio of some structural alloys for large strains. J Res Natl Bur Stand 37:211–221. https://doi.org/10.6028/jres.037.012
Chandler H (1995) Heat treater’s guide: practices and procedures for irons and steels, 2nd ed. In: ASM international, materials Park, Ohio
O’Brien A (2004) Welding handbook, vol 2. American Welding Society, Miami
Di Luozzo N, Doisneau B, Boudard M et al (2014) Microstructural and mechanical characterizations of steel tubes joined by transient liquid phase bonding using an amorphous Fe–B–Si interlayer. J Alloys Compd 615:S18–S22. https://doi.org/10.1016/j.jallcom.2013.11.161
Di Luozzo N (2014) Transient liquid phase diffusion welding of metallic parts. https://tel.archives-ouvertes.fr/view/index/identifiant/tel-01297617. Accessed 3 Sep 2022
Acknowledgements
This work was partly supported by the Universidad de Buenos Aires [Grant No. 20020170200266BA]. Neutron experiments were performed at the Institut Max von Laue—Paul Langevin (ILL), Grenoble, France under beam time grant https://dx.doi.org/10.5291/ILL-DATA.DIR-169. The authors acknowledge Metglas® for providing the filler material.
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NDL contributed to conceptualization, methodology, software, formal analysis, investigation, writing—original draft, writing—review & editing, visualization, supervision, project administration and funding acquisition. SC contributed to methodology, software, validation, investigation, data curation, writing—review & editing. MB contributed to investigation and writing—review & editing. MF contributed to resources and writing—review & editing.
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Di Luozzo, N., Cabeza, S., Boudard, M. et al. Measurement and simulation of residual stresses in transient liquid phase bonded ferritic steels. J Mater Sci 57, 20833–20849 (2022). https://doi.org/10.1007/s10853-022-07911-4
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DOI: https://doi.org/10.1007/s10853-022-07911-4