Dynamic modeling of rotary blade crack with regard to three-dimensional tip clearance

•Dynamic model of the 3D tip clearance with regard to blade breathing crack is built.•Breathing function of crack considers the coupling of stresses in three dimensions.•Dynamic model of cracked blade is validated numerically and experimentally.•Nonlinearity of breathing crack causes the super-harmonic response of 3D tip clearance.•Blade crack depth, location, and width affect dynamic responses of 3D tip clearance.•Nonlinear damage indicators of 3D tip clearance represent the blade crack severity.