A novel very-high-cycle-fatigue life prediction model with interior microstructure induced cracking behavior of Inconel-713C superalloy at 25 °C, 750 °C and 1000 °C

•Fatigue lives with interior failure are longer at 750 °C and shorter at 1000 °C.•Interior crystallographic plane cracking behavior belong to Mode I & Ⅱ cracking.•Climbing, bypassing and shearing mechanisms are remarkable at elevated temperature.•Threshold value and transition crack size are lower at 1000 °C.•A crystallographic version of FIP controlled crack initiation life is proposed.