Implicit finite element formulations for multi-phase transformation in high carbon steel. (English) Zbl 1388.74101
Summary: An anomalous plastic deformation observed during the phase transformation of steels was implemented into the finite element modeling. The constitutive equations for the transformation plasticity originally proposed by G. W. Greenwood and R. H. Johnson [The deformation of metals under small stresses during phase transformation. Proc. R. Soc. A 283, No. 1394, 403–422 (1965; doi:10.1098/rspa.1965.0029)] and further extended by J. B. Leblond et al. [J. Mech. Phys. Solids 34, 395–409, 411–432 (1986; Zbl 0585.73200); Mathematical modeling of transformation plasticity in steels. I: Case of ideal-plastic phases. II: Coupling with strain hardening phenomena. Int. J. Plasticity 5, 511–572, 573–591 (1989)] were modified to consider the thermomechanical response of generalized multi-phase steel during phase transformations from austenite at high temperature. An implicit numerical solution procedure to calculate the plastic deformation of each constituent phase was newly proposed and implemented into the general purpose implicit finite element program via user material subroutine. The new algorithms include efficient calculation of consistent tangent modulus for the transformation plasticity and application of general anisotropic yield functions without limitation to the isotropic yield function. Besides the thermoelastic-plastic constitutive equations, non-isothermal transformation kinetics was characterized by the Johnson-Mehl-Avrami-Kolmogorov (JMAK) equation and additivity relationship for the diffusional transformation, while the model proposed by Koistinen and Marburger was used for the diffusionless transformation. Numerical verifications for the continuous cooling experiments under various loading conditions were conducted to demonstrate the applicability of the developed numerical algorithms to the high carbon steel SK5.
MSC:
| 74S05 | Finite element methods applied to problems in solid mechanics |
| 74A15 | Thermodynamics in solid mechanics |
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
Keywords:
finite element method; transformation plasticity; constitutive equations; high carbon steelCitations:
Zbl 0585.73200Software:
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