Fig. 1. Schematic of laser quenching

Fig. 2. 3D model of laser quenching substrate based on Voronoi method

Fig. 3. Locations of nano-indentation measurement. (a) Schematic; (b)--(d)real measurement locations

Fig. 4. Distribution of grain non-uniformity coefficient. (a) Statistical result; (b) standardization result

Fig. 5. Introduction method of grain heterogeneity and result. (a) Flow chart of program; (b) 3D model of laser quenching substrate with grain heterogeneity

Fig. 6. Finite element model of laser quenching with grain heterogeneity and its calculation process. (a) Finite element model; (b) calculation process

Fig. 7. Temperature distributions in quenching substrate at different quenching moments. (a) 0.01 s; (b) 0.35 s;(c) 0.7 s; (d) after natural cooling for 300 s

Fig. 8. Comparison of temperature distribution in cross section with experimental result

Fig. 9. Thermal stress distributions of laser quenching model with grain heterogeneity at different moments. (a) 0.01 s; (b) 0.35 s; (c) 0.7 s; (d) after natural cooling for 300 s

Fig. 10. Temperature and thermal stress curves of grains during laser quenching. (a) Schematic of grain locations; (b) grain temperature versus time; (c) thermal stress versus time

Fig. 11. Stress distributions in local grains. (a) Positions and mechanical properties of selected grains; (b) stress distribution in selected grains