Numerical implementation of a thermo-elastic-plastic constitutive equation in consideration of transformation plasticity in welding

Finite element analysis of welding processes, which entail phase evolution, heat transfer and deformations, is considered in this paper. Attention focuses on numerical implementation of the thermo-elastic–plastic constitutive equation proposed by Leblond et al. [J. Mech. Phys. Solids 34(4) (1986a) 395; J. Mech. Phys. Solids 34(4) (1986b) 411] in consideration of the transformation plasticity. Based upon the multiplicative decomposition of deformation gradient, hyperelastoplastic formulation is borrowed for efficient numerical implementation, and the algorithmic consistent moduli for elastic–plastic deformations including transformation plasticity are obtained in the closed form. The convergence behavior of the present implementation is demonstrated via a couple of numerical examples. � 2004 Published by Elsevier Ltd.

[1]  P. Tekriwal,et al.  Transient and Residual Thermal Strain-Stress Analysis of GMAW , 1991 .

[2]  J. Devaux,et al.  Mathematical modelling of transformation plasticity in steels I: Case of ideal-plastic phases , 1989 .

[3]  G. J. Oliver,et al.  Comparison of applicability of various thermo-viscoplastic constitutive models in modelling of welding , 1998 .

[4]  Heng Xiao,et al.  Some basic issues in traditional Eulerian formulations of finite elastoplasticity , 2003 .

[5]  T. Hughes.  Generalization of selective integration procedures to anisotropic and nonlinear media , 1980 .

[6]  J. Devaux,et al.  A theoretical and numerical approach to the plastic behaviour of steels during phase transformations—I. Derivation of general relations , 1986 .

[7]  Valery I. Levitas,et al.  Thermomechanical theory of martensitic phase transformations in inelastic materials , 1998 .

[8]  Michael Ortiz,et al.  A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations , 1985 .

[9]  Wing Kam Liu,et al.  Nonlinear Finite Elements for Continua and Structures , 2000 .

[10]  T. Inoue,et al.  Determination of thermal-hardening stress in steels by use of thermoplasticity theory , 1978 .

[11]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multiplicative decomposition. part II: computational aspects , 1988 .

[12]  John W. Cahn,et al.  Transformation kinetics during continuous cooling , 1956 .

[13]  J. Leblond.  Mathematical modelling of transformation plasticity in steels II: Coupling with strain hardening phenomena , 1989 .

[14]  Lakhdar Taleb,et al.  A micromechanical modeling of the Greenwood–Johnson mechanism in transformation induced plasticity , 2003 .

[15]  J. C. Simo,et al.  A framework for finite strain elastoplasticity based on maximum plastic dissipation and the multipli , 1988 .

[16]  G. W. Greenwood,et al.  The deformation of metals under small stresses during phase transformations , 1965, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[17]  M. Ortiz,et al.  Formulation of implicit finite element methods for multiplicative finite deformation plasticity , 1990 .

[18]  A. Bertram.  Finite thermoplasticity based on isomorphisms , 2003 .

[19]  J. Devaux,et al.  A theoretical and numerical approach to the plastic behaviour of steels during phase transformations—II. Study of classical plasticity for ideal-plastic phases , 1986 .

[20]  John Goldak,et al.  Transformation Plasticity and Residual Stresses in Single-Pass Repair Welds , 1992 .

[21]  V. Levitas.  Structural changes without stable intermediate state in inelastic material. Part I. General thermomechanical and kinetic approaches , 2000 .

[22]  Alain Combescure,et al.  Experimental study of the phase transformation plasticity of 16MND5 low carbon steel under multiaxial loading , 2002 .

[23]  J. C. Simo,et al.  Associated coupled thermoplasticity at finite strains: formulation, numerical analysis and implementation , 1992 .

[24]  C. L. Magee,et al.  TRANSFORMATION KINETICS, MICROPLASTICITY AND AGING OF MARTENSITE IN FE-31 NI. , 1966 .

[25]  Heng Xiao,et al.  A consistent finite elastoplasticity theory combining additive and multiplicative decomposition of the stretching and the deformation gradient , 2000 .

[26]  Jean-Baptiste Leblond,et al.  A new kinetic model for anisothermal metallurgical transformations in steels including effect of austenite grain size , 1984 .

[27]  J. Christian,et al.  The theory of transformations in metals and alloys , 2003 .