Numerical simulation of transient and residual stresses caused by laser hardening of slender elements

A mathematical and numerical model of progressive laser hardening with regard to influence of thermal field and phase transformation under transient and residual axial stresses field is presented. The thermal field was determined on the basis of the diffusion-convection equation which was solved by a suitable superposition of Greens function. TIT diagrams were chosen as a basis for describing phase transformations during the heating and cooling process. The stresses were determined on the base of model of plastic flow with isotropic hardening. The changes in thermomechanical parameters of material as a function of phase contents and thermal field were considered in the stress calculations.