×

Theoretical and numerical modeling of the thermomechanical and metallurgical behavior of steel. (English) Zbl 1426.74060

Summary: Welding or heat treatment of steel structures generate important heat gradients. These heat gradients are generally very localized and involve local dilations that lead to the appearance of residual strain and stress fields. These fields play a very important role in fatigue life prediction of structures. In addition, thermal cycles induced by welding or heat treatment operations can generate phase transformations within the material. The work presented in this paper describes an anisothermal model for steel where thermomechanical and metallurgical aspects are taken into account. In the proposed model, the thermomechanical behavior of each phase is treated independently and the macroscopic behavior is obtained using a Reuss model. In order to quantify the importance of the TRansformation Induced Plasticity (TRIP: plastic deformation due to the variation of the proportion of phases under applied stress) as well as viscosity, two descriptions are presented: first, the phases are assumed to be elastoplastic; second, the low-temperature phases are considered as elastoplastic whereas the high-temperature phase is assumed to be viscoplastic. For each description the influence of TRIP is considered by comparing results obtained with or without TRIP. These models have been implemented into the numerical code COMSOL Multiphysics by developing new modules capable of simulating phase transformation and inelastic deformation. Numerical simulations show good agreement with experimental data. Moreover, it is shown that taking into account TRIP and assigning for each phase an appropriate behavior improve the predictions of residual displacements and stresses.

MSC:

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74N05 Crystals in solids
74F05 Thermal effects in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics

Software:

COMSOL; Code_Aster
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Alberg, H.; Berglund, D.: Comparison of plastic, viscoplastic, and creep models when modelling welding and stress relief heat treatment, Comput. methods appl. Mech. eng. 192, 5189-5208 (2003) · Zbl 1054.74558 · doi:10.1016/j.cma.2003.07.010
[2] Avrami, M.: Kinetics of phase change: general theory, J. chem. Phys. 7, 1103-1112 (1939) · Zbl 0021.04502
[3] Cavallo, N., 1998. Contribution à la validation expérimentale de modèles décrivant la ZAT lors d’une opération de soudage. PhD Thesis, INSA Lyon.
[4] Coret, M.; Combescure, A.: A mesomodel for the numerical simulation of the multiphasic behavior of materials under anisothermal loading (application to two low-carbon steels), Int. J. Mech. sci. 44, 1947-1963 (2002) · Zbl 1015.74501 · doi:10.1016/S0020-7403(02)00053-X
[5] Coret, M.; Calloch, S.; Combescure, A.: Experimental study of the phase transformation plasticity of 16mnd5 low carbon steel under multiaxial loading, Int. J. Plasticity 18, 1707-1727 (2002) · Zbl 1058.74502
[6] Coret, M.; Calloch, S.; Combescure, A.: Experimental study of the phase transformation plasticity of 16mnd5 low-carbon steel induced by proportional and nonproportional biaxial loading paths, Eur. J. Mech. A – solids 23, 823-842 (2004) · Zbl 1058.74502 · doi:10.1016/j.euromechsol.2004.04.006
[7] Costantini, M., 1996. Simulation numérique du soudage par faisceau d’électrons. Contribution au développement d’un modèle prédictif de l’apport d’énergie. PhD Thesis, Université Paris VI.
[8] Denis, S.; Gautier, E.; Simon, A.; Beck, G.: Stress phase transformations interaction, basics principle, modelling, and calculation of internal stresses, Mater. sci. Technol. 1, 805-814 (1985)
[9] Denis, S.; Gautier, E.; Sjöström, S.; Simon, A.: Influence of stresses on the kinetics of pearlitic transformation during continuous cooling, Acta metall. 35, 1621-1632 (1987)
[10] Fischer, F. D.: A micromechanical model for transformation plasticity in steels, Acta metall. Mater. 38, 1535-1546 (1990)
[11] Fischer, F. D.; Sun, Q. P.; Tanaka, K.: Transformation induced plasticity (TRIP), Appl. mech. Rev. 49, 317-364 (1996)
[12] Gautier, E., Simon, A., Beck, G., 1985. Etude du comportement mécanique associé à la transformation martensitique d’alliages de type FE-NI-C sollicités en fluage ou en traction. In: Mc Queen (Ed.), Seventh International Conference on Strength of Metal and Alloys (ICSMA 7), p. 569.
[13] Giusti, J., 1981. Contraintes et déformations résiduelles d’origine thermique. Application au soudage et à la trempe des aciers. PhD Thesis, Université Paris VI.
[14] Greenwood, G. W.; Johnson, R. H.: The deformation of metals under small stresses during phase transformation, Proc. R. Soc. lond. A 283, 403-422 (1965)
[15] Halphen, B.; Nguyen, Q. S.: Plastic and visco-plastic materials with generalized potential, Mech. res. Commun. 1, 43-47 (1974) · Zbl 0347.73035 · doi:10.1016/0093-6413(74)90034-2
[16] Inoue, T.; Wang, Z.: Coupling between stress, temperature and metallic structures during processes involving phases transformations, Mater. sci. Technol. 1, 845-850 (1985)
[17] Johnson, W. A.; Mehl, R. F.: Reaction kinetics in processes of nucleation and growth, Trans. AIME 135, 416-458 (1939)
[18] Karlsson, L.; Lindgren, L. E.: Combined heat and stress – strain calculations, Modeling of casting, welding and advanced solidification processes V, 187-202 (1991)
[19] Koistinen, D. P.; Marburger, R. E.: A general equation prescribing extent of austenite-martensite transformation in pure FE-C alloys and plain carbon steels, Acta metall. 7, 59-60 (1959)
[20] Leblond, J. -B.: Mathematical modelling of transformation plasticity in steels. II: coupling with strain hardening phenomena, Int. J. Plasticity 5, 573-591 (1989)
[21] Leblond, J. -B.; Devaux, J.: A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size, Acta metall. 32, 137-146 (1984)
[22] Leblond, J. -B.; Mottet, G.; Devaux, J. -C.: A theoretical and numerical approach to the plastic behaviour of steels during phase transformations – I. Derivation of general relations, J. mech. Phys. solids 34, 395-409 (1986) · Zbl 0585.73200 · doi:10.1016/0022-5096(86)90009-8
[23] Leblond, J. -B.; Devaux, J.; Devaux, J. -C.: Mathematical modelling of transformation plasticity in steels. I: case of ideal-plastic phases, Int. J. Plasticity 5, 551-572 (1989)
[24] Lemaitre, J.; Chaboche, J. -L.: Mécanique des matériaux solides, (1996)
[25] Levitas, V. I.: Structural changes without stable intermediate state in inelastic material. Part I. General thermomechanical and kinetic approaches, Int. J. Plasticity 16, 805-849 (2000) · Zbl 0963.74009
[26] Levitas, V. I.: Structural changes without stable intermediate state in inelastic material. Part II. Applications to displacive and diffusional-displacive phase transformations, strain induced chemical reactions and ductile fracture, Int. J. Plasticity 16, 851-892 (2000) · Zbl 0963.74009 · doi:10.1016/S0749-6419(99)00084-4
[27] Levitas, V. I.; Ozsoy, I. B.: Micromechanical modeling of stress-induced phase transformations. Part 1. Thermodynamics and kinetics of coupled interface propagation and reorientation, Int. J. Plasticity 25, 239-280 (2009) · Zbl 1277.74059
[28] Levitas, V. I.; Ozsoy, I. B.: Micromechanical modeling of stress-induced phase transformations. Part 2. Computational algorithms and examples, Int. J. Plasticity 25, 546-583 (2009) · Zbl 1277.74058
[29] Li, S. H.; Dan, W. J.; Zhang, W. G.; Lindgren, Z. Q.: A model for strain-induced martensitic transformation of TRIP steel with pre-strain, Comput. mater. Sci. 40, 292-299 (2007)
[30] Magee, C.L., 1966. Transformation kinetics, microplasticity and aging of martensite in FE31Ni. PhD Thesis, Carnegie Institute of Technology, Pittsburgh, PA.
[31] Mahnken, R.; Schneidt, A.; Anteretter, T.: Macro modelling and homogenization for transformation induced plasticity of low-alloy steel, Int. J. Plasticity 25, 183-204 (2009) · Zbl 1419.74206
[32] Martinez, M., 1999. Jonction 16MND5-INCONEL 690-316LN par soudage diffusion. Elaboration et calculs des contraintes résiduelles de procédé. PhD Thesis, Ecole Nationale Supérieure des Mines de Paris.
[33] Moumni, Z., 1995. Sur la modélisation du changement de phase à l’état solide. PhD Thesis, Ecole Nationale Supérieure des Ponts et Chaussées, Paris.
[34] Moumni, Z.; Nguyen, Q. S.: A model of material with phase change and applications, J. phys. IV 6, 335-345 (1996)
[35] Moumni, Z.; Zaki, W.; Nguyen, Q. S.: Theoretical and numerical modeling of solid – solid phase change: application to the description of the thermomechanical behavior of shape memory alloys, Int. J. Plasticity 24, 614-645 (2008) · Zbl 1145.74028 · doi:10.1016/j.ijplas.2007.07.007
[36] Nguyen, Q. S.: Stability and nonlinear solid mechanics, (2000) · Zbl 0949.74001
[37] Nguyen, Q. S.; Moumni, Z.: Sur une modélisation du changement de phases solides, CR acad. Sci. 321, 87-92 (1995) · Zbl 0828.73008
[38] Petit-Grostabussiat, S., 2000. Conséquences mécaniques des transformations structurales dans les alliages ferreux. PhD Thesis, INSA Lyon.
[39] Rockaffellar, R. T.: Convex analysis, (1972)
[40] Ronda, J.; Estrin, Y.; Oliver, G. J.: Modelling of welding. A comparison of a thermo-mechano-metallurgical constitutive model with a thermo-viscoplastic material model., J. mater. Process. technol. 60, 629-636 (1996)
[41] Taleb, L.; Petit, S.: New investigations on transformation induced plasticity and its interaction with classical plasticity, Int. J. Plasticity 22, 110-130 (2006) · Zbl 1148.74323 · doi:10.1016/j.ijplas.2005.03.012
[42] Taleb, L.; Sidoroff, F.: A micromechanical modeling of the greenwood – Johnson mechanism in transformation induced plasticity, Int. J. Plasticity 19, 1821-1842 (2003) · Zbl 1098.74550 · doi:10.1016/S0749-6419(03)00020-2
[43] Taleb, L.; Cavallo, N.; Waeckel, F.: Experimental analysis of transformation plasticity, Int. J. Plasticity 17, 1-20 (2001)
[44] Taleb, L.; Petit, S.; Jullien, J. -F.: Prediction of residual stresses in the heat affected zone, J. phys. IV 120, 705-712 (2004)
[45] Trinh, N.T., 2008. Sur la modélisation du comportement thermomécanique et métallurgique des aciers. Application au procédé de soudage et de traitements thermiques. PhD Thesis, Ecole Polytechnique, Paris.
[46] Vincent, Y.; Bergheau, J. -M.; Leblond, J. -B.: Viscoplastic behaviour of steels during phase transformations, CR acad. Sci. 331, 587-594 (2003)
[47] Waeckel, F., 1994. Une loi de comportement thermo-métallurgique des aciers pour le calcul mécanique des structures. PhD Thesis, ENSAM de Paris.
[48] Wolff, M.; Taleb, L.: Consistency for two multi-mechanism models in isothermal plasticity, Int. J. Plasticity 24, 2059-2083 (2008) · Zbl 1297.74025
[49] Wolff, M.; Böhm, M.; Helm, D.: Material behavior of steel – modeling of complex phenomena and thermodynamic consistency, Int. J. Plasticity 24, 746-774 (2008) · Zbl 1144.74319 · doi:10.1016/j.ijplas.2007.07.005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.