A sequentially coupled thermo-mechanical model has been developed to investigate the residual stresses of DP600 dual phase steel welded by a Nd:YAG laser process. A numerical cellular automaton (CA) model has been firstly built to simulate the microstructure evolution during a laser welding. The obtained CA microstructure orientation results are input into a finite element model (FEM) as material anisotropic parameters together with a corresponding constitutive law characterizing the material behavior taking into account the dual phase ferrite-martensite hardening, the temperature sensitivity and the strain rate influence. The numerical residual stresses predicted by the proposed coupled CA-FEM model have variations close to those of experimental observation.

The anisotropy of dual phase DP600 steel has been analyzed both from the solidification process using the numerical CA model and from the base metal thermo-mechanical behavior influence using a sequentially coupled thermal-elastic-plastic model and a plane anisotropy theory. It is observed that the residual stress longitudinal to welding direction is more influenced by the material anisotropy and the temperature sensitivity. The analysis of DP600 coupled anisotropy model consists of two parts:

I. Anisotropy of weld: The developed numerical CA model take into account welding temperature field history, the nucleus density, nucleus position and diffusion behavior. The obtained dendrites solidification directions are applied to analyze the microstructure evolution during the welding process and to compute the orthotropic elastic constants of DP600 weld. The martensitic phase properties and the orientations of the weld material are input into a FEM taking into account the corresponding anisotropy.

 II The anisotropy of base metal: A lot of specimens undergoing tensile tests along three different orientations corresponding to 0°, 45°and 90° with the plate rolling direction have been performed. In a classical way the plane anisotropy of steels uses the Hill-48 theory and the corresponding parameters are estimated according to the Lankford computation method. A specific thermo-mechanical rheological law is proposed for formulation of the equivalent stress starting from constitutive models proposed in previous works by A. Gavrus.

The experimental method used to estimate the residual stresses by X-Ray diffraction uses the estimation of the distance between crystallographic planes as an internal strain gauge. The diffractometer used for these studies was equipped with a 4 circle goniometer - (Seifert MZ VI - TS) and a PSD detector.

All the obtained results during this study lead to a better understanding of the relationship between the laser welding process and the welding microstructure, residual stresses and global weld quality. From analysis of the proposed simulation models, several conclusions can be drawn:

• Hardening: the classical Voce or Ludwick model are found unable to perfectly describe the observed material behavior of DP600 dual phase steel in the range of plastic strain from 0 to 0.2. A proposed synthesis rheological model is used to describe in a physical sense the obtained experimental stress-strain curves.
• Temperature sensitivity: the proposed formulation shows a good accordance with the obtained experimental data. The temperature sensitivity is found to have an important influence on residual stresses simulation.
• Strain rate: a strain rate sensitivity model is generated based on experimental data obtained at room temperature. As a first approximation, the strain rate sensitivities for high temperatures are supposed to be the same as that for room temperature. The obtained strain rate sensitivity model is input into FEM model and numerical simulation results of residual stress are compared with the FEM model supposing the unit strain rate sensitivity.
• Anisotropy: the weld anisotropy has little influence while the base metal anisotropy has an important influence on numerical residual stress distribution.