The Analysis of Stress States in Steel Rods Surfaced by Welding

Open access


In work is presented a method of calculating elasto-plastic states in thermally loaded rods, which takes into account phase transformations that occur during surfacing by welding. Kinetics of phase transformations during heating and cooling is limited by temperature values at the beginning and at the end of austenitic transformation, while the progress of phase transformations during cooling is determined on the basis of TTT-welding diagram, basing on Johnson-Mehl-Avrami-Kolomogorov law for diffusional transformations and Koistinen-Marburger for martensitic transformation. Stress state of a bar subjected to thermo-mechanical loads is described assuming the planar cross section hypothesis and using integral equations of stress equilibrium of a bar as well as simple Hook’s law. Dependence of stresses from strains is assumed on the basis of tensile curves of particular structures, taking into account the influence of temperature. Computations of strains and stresses are investigated in a rod made of S235 steel, loaded by thermal fields generated by a point welding heat source of different intensities. The analysis of origination and development of plastic strains is carried out. In order to verify correctness of the model, experimental tests are carried out on a rod made of S235 steel surfaced with GMA method with geometry and welding parameters assumed in numerical simulations. Residual stresses, calculated taking into account phase transformations and for homogenous material model, are compared with experimental results.

[1] J.A. Goldak, A. Oddy, M. Gu, W. Ma, A. Mashai e, E. Hughes, Coupling heat transfer, microstructure evolution and thermal stress analysis in weld mechanics. In: Mechanical Effects of Welding, IUTAM Symposium Lulea, Sweden 1991, Springer Verlag Berlin Heidelberg 1991.

[2] Y. Ueda, J. Rond a, H. Murakawa, K. Ikeuch i, Thermo-mechanical-metallurgical model of welded steel. Part I: Evolution equations for internal material structures, Trans. JWRI 23, 2, 148-167 (1994).

[3] J. Ronda, Y. Estrin, G.J. Oliver, Modelling of welding. Acomparison ofathermo-mechano-metallurgical constitutive model withathermo-viscoplastic material model, J. Mater. Proces. Technol. 60, 629-636 (1996).

[4] J. Ronda, H. Murakawa, G Oliver, Y. Ueda, Thermo-mechanical-metallurgical model of welded steel. Part II: Finite element formulation and constitutive equations, Trans. JWRI 24, 2, 92-113 (1995).

[5] L.E. Lindgren, Finite element modeling and simulation of welding. Part 1: Increased complexity, J. Thermal Stresses 24, 141-192 (2001).

[6] L.E. Lindgren, Finite element modeling and simulation of welding. Part 2: Improved material modeling, J. Thermal Stresses 24, 195-231 (2001).

[7] L.E. Lindgren, Finite element modeling and simulation of welding. Part 3: Efficiency and integration, J. Thermal Stresses 24, 305-334 (2001).

[8] B. Chen, X.H. Peng, J.H. Fa n, S.T. Su n, A viscous-elastoplastic constitutive equation incorporating phasetransformation with the application to the residual stress analysis for welding process, J. Mater. Proces. Technol. 205, 316-321 (2008).

[9] D. Deng, FEMprediction of welding residual stress and distortion in carbon steel considering phase transformation effects, Materials Design 30, 359-366 (2009).

[10] A. Bokota, W. Piekarsk a, Numerical modeling of residual stresses inadual laser beam welding, Metalurgija 49, 2, 156-160 (2010).

[11] W. Piekarsk a, Numerical analysis of thermomechanical phenomena during laser welding process. The temperature fields, phase transformations and stresses. Monographies No 35, Technical University of Czestochowa (2007).

[12] N.O. Okerblom, Welding strains and stresses, Mashgiz, Moscow-Leningrad 1948.

[13] D. Radaj, Heat effects of welding. Temperature field, residual stress, distortion, Springer-Verlag, Berlin 1992.

[14] J. Pilarczyk, J. Pilarczy k, Arc welding and surfacing of metals, Slask sp.zo.o., Katowice 1996.

[15] E. Tasak, Metallurgy of welding, JAK, Cracov 2008.

[16] J. Rhode, A. Jeppso n, Literature review of heat treatment simulations with respect to phase transformation, residual stresses and distortion, Scand. J. Metall. 29, 47-62 (2000).

[17] W. Piekarska, M. Kubiak, A. Bokota, Numerical simulation of thermal phenomena and phase transformations in laser-arc hybrid welded joint, Archives of Metallurgy and Materials 56, 2, 409-421 (2011).

[18] M. Avrami, Kinetics of phase change. I. General theory, J. Chem. Physics 7, 1103-1112 (1939).

[19] H.P. Hougardy, Calculation of the transformation of steels on contionuous cooling, Metallurgy and Foundry 13, 407-439 (1987).

[20] R. Parkitny, J. Wincze k, Modelling of phase transformations during multipass surfacing, In:. Conf. Proc. XXXVIII Sympozjon Modelling in Mechanics, Silesian University of Technology Gliwice, 219-224 (1999).

[21] D.P. Koistine n, R.E. Marburge r, Ageneral equation prescribing the extent of the austenite-martensite transformation in pure iron-carbon alloys and plain carbon steels, Acta Mettall. 7, 59-60 (1959).

[22] A. Bokota, T. Domanski, Numerical analysis of thermo-mechanical phenomena of hardening process of elements made of carbon steel C80U, Archives of Metallurgy and Materials 52, 277-288 (2007).

[23] T. Domanski, A. Bokota, Numerical models of hardening phenomena of to ols steel base on the TTTand CCT diagrams, Archives of Metallurgy and Materials 56, 325-344 (2011).

[24] J. Winczek, Asimplified method of predicting stresses in surfaced steel rods, J. Mater. Proces. Technol. 212, 1080-1088 (2012).

[25] A. Bokota, R. Parkitny, Modelling of thermal, structural and mechanical phenomena in hardening processes of steel elements. In: Informatics in Metal Technology, Silesian University of Technology, Gliwice (2003).

[26] M. Mysliwiec, Thermo-mechanical basis of welding, WN-T, Warszawa 1970.

[27] J. Brózda, J. Pilarczy k, M. Zema n, Welding TTT diagrams of austenite transformations, Slask, Katowice 1983.

[28] J. Winczek, A. Kulawi k, Dilatometric and hardness analysis of C45 steel tempering with different heating-up rates, Metalurgija 51, 1, 9-12 (2012).

[29] J. Gawad, D. Szelig a, A. Bato r, V. Pidvysock- y y, M. Pietrzyk, Interpretation of the tensile test results interpretation based on two criterion optimization, In: Proc. 14. Conf. Kom Plas Tech, Informatics in Metal Technology, ed. M. Pietrzyk et al., Akapit, Cracow, 27-34 (2004).

[30] P.M.M. Vila Real, R. Cazeli, L. Simoesda Sil- v a, A. Santiago, P. Piloto, The effect of residual stresses in the lateral-torsional buckling of steel I-beams at elevated temperature, J. Construct. Steel Research 60, 783-793 (2004).

[31] M. Melander, A Computional and Experimental Investigation of Induction and Laser Hardening, Linkoping Studies in Science and Technology, Dissertation No 124, Linkoping Univeristy (1985).

[32] J. Lian, Z. Jian g, J. Liu, Theoretical model for the tensile work hardening behaviour of dual-phase steel, Mater. Sci. Eng. A147, 55-65 (1991).

[33] Y.M. Kim, S.K. Ki m, N.J. Ki m, Correlation of yield ratio with materials constants of constitutive equation, Mater. Sci. Forum 475-479, 289-292 (2005).

[34] S.K. Kim, Y.M. Ki m, Y.J. Li m, N.J. Ki m, Relationship between yield ratio and the material constants of the swift equation, Metals Materials Int. 12, 2, 131-135 (2006).

Archives of Metallurgy and Materials

The Journal of Institute of Metallurgy and Materials Science and Commitee on Metallurgy of Polish Academy of Sciences

Journal Information

IMPACT FACTOR 2016: 0.571
5-year IMPACT FACTOR: 0.776

CiteScore 2016: 0.85

SCImago Journal Rank (SJR) 2016: 0.347
Source Normalized Impact per Paper (SNIP) 2016: 0.740

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 133 96 4
PDF Downloads 70 61 3