Geometry independent J-Tz domination of three-dimensional steady growing crack-tip fields in ductile materials

•GTN damage model is adopted to simulate quasi-static ductile crack growth behaviours.•The J-Tz solution is extended to quasi-static elastic–plastic growing crack-tip stress fields.•The dominance and geometry independence of the J-Tz solution make it more simply and effectively to ductile fracture problems.