Coupled analytical model for temperature-phase transition and residual stress in hot-rolled coil cooling process

The presence of residual stress in hot-rolled strips not only causes flatness defects but also induces subsequent cutting deformation. The residual stress formed during the cooling stage involves the coupling of temperature, phase transition and mechanics, lacks analytical models to reveal the complex mechanisms comprehensively. This paper delves deeply into the mechanism underlying the formation of residual stress during the cooling process of hot-rolled coils by means of analytical modeling. Firstly, discretizing the coil into numerous elements and micro-units along the circumferential and axial directions, converting the multi-physics coupling problem from cylindrical to Cartesian coordinates. In the Hamiltonian system, the exact analytical solution of the three-dimensional temperature field of the coil is derived by using the basic equation. Meanwhile, an alternating coupling algorithm is developed to achieve nonlinear calculation of thermal-metallurgical coupling processes. Furthermore, the relationship between residual stress and eigenstrain caused by thermal metallurgical behavior during cooling is elucidated. Next, the analytical models for axial and radial residual stresses in coil are derived based on the principle of overall deformation coordination. To verify the precision of the analytical model, a multi-physics field coupled finite element model based on measured data validation is established. Finally, the analytical solutions of temperature, microstructure and residual stress distribution are almost consistent with the finite element solutions. The calculation results indicate that axial residual stresses distributed radially are mainly formed inside the coil, with magnitudes concentrated in the range of −100∼60 MPa.