Fig. 1 Schematic representation of the model and mesh used for the CPFEM simulation

Fig. 2 Comparison between the stress-strain curves obtained from the tensile test and the crystal plasticity based simulation

Fig. 3 Flowchart of deformation and recrystallization calculation process

Fig. 4 Initial microstructure of the as-received DP steel: a the optical microscopic image, b, c the phase map and orientation map used for the CPFEM simulation, respectively

Fig. 5 CPFEM simulation results of the cold-rolled DP steel with the initial strain of 0.69: a distribution of the von Mises stress, b distribution of the total shear strain

Fig. 6 Evolution of the total shear strain in the cold-rolled DP steel simulated by CPFEM at different initial strains: a ε?=?0.35, b ε?=?0.69, c ε?=?1.20. d The statistical distribution of the total shear strain in ferrite and martensite at different initial strains

Fig. 7 Comparison of the deformation microstructure between the micrographs a and the simulations b in the DP steel. Details of the various microstructural constituents are shown in local regions of I-IV

Fig. 8 Simulated microstructure evolution of the recrystallization (left) in the cold-rolled DP steel at ε?=?0.69, T?=?700 °C and the comparison with the optical micrograph observations (right) for different time: a, b t?=?5 s, c, d t?=?10 s, e, f t?=?20 s

Fig. 9 Simulated recrystallization kinetics and the JMAK plot at ε?=?0.69 and T?=?700 °C

Fig. 10 Statistical distribution of the stored deformation energy inside ferrite phase at different initial strains

Fig. 11 Comparison between the experimental and simulated recrystallization kinetics of ferrite with different initial strains at T?=?700 °C

Fig. 12 Simulated resultant microstructures of the recrystallization a, c, e compared with corresponding metallograph results b, d, f under the initial strain of 0.35 a, b, 0.69 c, d and 1.2 e, f