Effects of specimen geometry and surface defect on high and very high cycle fatigue of TC17 alloy

•Specimen geometry has great influence on crack initiation and fatigue performance.•Fatigue strength of plate specimen is lower for the same artificial surface defect.•A model is proposed for effects of specimen geometry and defect on fatigue strength.•Rough area feature is observed at artificial surface defect on the fracture surface.•Nanograins are observed in the rough area at artificial surface defect.