Computational integration and experimental validation of a two-length scale model for accurate prediction of steels’ plastic behavior during phase transformation
Restricted accessResearch articleFirst published online June, 2025
Computational integration and experimental validation of a two-length scale model for accurate prediction of steels’ plastic behavior during phase transformation
Transformation plasticity, essential during solid–solid phase transitions, significantly impacts industrial processes like welding and quenching. Accurately simulating these procedures necessitates understanding thermal, metallurgical, and mechanical effects. Leblond et al.’s model offers a foundation, but refinement for mixed isotropic/kinematic hardening is crucial. We enhance this model by introducing characteristic length scales through nonlocal variables, illuminating plastic deformation mechanisms in both phases. Our work includes numerical implementation within a finite element analysis framework and practical applications to phase transformation scenarios involving A.508 cl. 3 and A533 low-alloy steels. Results affirm model robustness and efficiency in predicting phase transformation phenomena, benefiting industrial applications.
InoueTNakanoMKuboT, et al. High accuracy control of a proton synchrotron magnet power supply. IFAC Proceedings Volumes1981; 14(2): 3137–3142.
2.
InoueTWangZ.Coupling between temperature, stress and metallic structures during phase transformation and the analysis of carburized quenching of a steel gear. In: YagawaGAtluriS (eds) Computational mechanics’86. Cham: Springer, 1986, pp. 691–696.
3.
FukumutoMYoshizakiMImatakaH, et al. Three-dimensional FEM analysis of helical gear subjected to the carburized quenching process. Zairyo2001; 50(6): 598–605.
4.
MiyaoKWangZInoueT.Analysis of temperature, stress and metallic structure in carburized quenched gear considering transformation plasticity. J Soc Mat Sci1986; 35(399): 1352–1357.
5.
TalebLSidoroffF.A micromechanical modeling of the Greenwood-Johnson mechanism in transformation induced plasticity. Int J Plast2003; 19: 1821–1842.
6.
GreenwoodGWJohnsonR.The deformation of metals under small stresses during phase transformations. Proc R Soc London Ser A1965; 283(1394): 403–422.
7.
MageeCLPaxtonHW.Transformation kinetics, microplasticity and aging of martensite in Fe-31 Ni. Technical report, Carnegie Institute of Technology, Pittsburgh, PA, 1September1966.
8.
De JongMRathenauG. Mechanical properties of an iron-carbon alloy during allotropic transformation. Acta Metall1961; 9(8): 714–720.
9.
BhadeshiaH.The bainite transformation: unresolved issues. Mater Sci Eng1999; 273–275: 58–66.
10.
BhadeshiaH.Carbon-carbon interactions in iron. J Mater Sci2004; 39: 3949–3955.
11.
LeblondJBMottetGDevauxJC.A theoretical and numerical approach to the plastic behaviour of steels during phase transformations–I. Derivation of general relations. J Mech Phys Solids1989; 34(4): 395–409.
12.
LeblondJBMottetGDevauxJC.A theoretical and numerical approach to the plastic behaviour of steels during phase transformations–II. Study of classical plasticity for ideal-plastic phases. J Mech Phys Solids1986; 34(4): 411–432.
13.
LeblondJBPerrinGDevauxJ.Bifurcation effects in ductile metals with nonlocal damage. J Appl Mech Trans ASME1994; 61: 236–242.
14.
EnakoutsaKLeblondJBPerrinG.Numerical implementation and assessment of a phenomenological nonlocal model of ductile rupture. Comput Methods Appl Mech Eng2007; 196: 1946–1957.
15.
EnakoutsaK.Modéle non-locaux en rupture ductile des métaux. PhD Thesis, Université Pierre et Marie Curie (Paris VI), Paris, 2007.
16.
EnakoutsaKLeblondJB.Numerical implementation and assessment of the GLPD micromorphic model of ductile rupture. Eur J Mech A Solids2009; 28: 445–460.
17.
AhadFEnakoutsaKSolankiK, et al. Nonlocal modeling in high velocity impact failure of aluminum 6160-T6. Int J Plast2013; 55: 108–132.
18.
EnakoutsaK.Some new applications of the GLPD micromorphic model for ductile fracture. Math Mech Solids2012; 19(3): 242–259.
19.
EnakoutsaKSolankiKAhadF, et al. Using damage delocalization to model localization phenomena in Bammann-Chiesa-Johnson metals. J Eng Mater Technol2012; 134(4): 041014.
20.
EnakoutsaKSolankiKAhadF, et al. Damage smoothing effects in a delocalized rate sensitivity model for metals. Theor Appl2012; 2(5): 051005.
21.
EnakoutsaK.An analytic benchmark solution to the problem of a generalized plane strain hollow cylinder made of micromorphic plastic porous metal and subjected to axisymmetric loading conditions. Math Mech Solids2015; 20(9): 1013–1025.
22.
EnakoutsaKLiY.Mastering the art: proficient finite element implementation and robust evaluation of a strain-hardening porous ductile material crack growth prediction model at finite strain. Appl Math Model2024; 132: 73–108.
23.
EnakoutsaK.Analytical applications and effective properties of a second gradient isotropic elastic material model. Z Angew Math Phys2015; 66: 1277–1293.
24.
EnakoutsaKBillsYL.Moving from theory to application: evaluating the numerical implementation of void shape effects and damage delocalization in the modeling of ductile fracture in porous plastic metals. Math Mech Solids2024; 29: 1432–1456.
25.
Pijaudier-CabotGBazantZP.Nonlocal damage theory. J Eng Mech1987; 113: 1512–1533.
26.
DesalosY.Comportement mécanique et dilatométrique de l’austénite métastable de l’acier A533. Technical Report 95349401, IRSID, Institut de La Recherche de la Siderurgie, 1981.
27.
CoretMCallochSCambescureA.Experimental study of the phase transformation plasticity of 16MND5 low carbon steel under multiaxial loading. Int J Plast2002; 18(12): 1707–1727.
28.
CoretMCallochSCambescureA.Experimental study of the phase transformation plasticity of 16MND5 low carbon steel induced by proportional and nonproportional biaxial loading paths. Eur J Mech A Solids2004; 23(5): 823–842.
29.
GreenwoodGWJohnsonRH.The deformation of metals under small stresses during phase transformations. Proc R Soc London Ser A1965; 283: 403–422.
30.
LeblondJB.Simulation numérique du soudage-modélisation mathématique des transformations métallurgiques-état d’avancement des travaux. Technical report, Framatome Internal Report #TM/C DC/80.066, 1980.
