The projection paths on the π-plane under the newly defined principal coordinate system of several typical tension-torsion loading paths were given. A new multiaxial fatigue damage parameter was proposed based on the projection path on the π-plane. With the non-proportional additional hardening effect being considered

a prediction method of the non-proportional cyclic hardening coefficient was proposed and a new non-proportionality description was defined. Furthermore

a multiaxial effective stress gradient factor was defined by combining the tension stress gradient and the torsion stress gradient of finite element elastic analysis

and a multiaxial notch fatigue life prediction model was developed based on the multiaxial stress gradient effect. The multiaxial notch fatigue test results of GH4165 alloy at 650℃ were used to verify the proposed model. On the basis of analytical study

conclusions can be drawn as follow：(1) the proposed multiaxial fatigue damage parameter is suitable for multiaxial fatigue and uniaxial fatigue with a clearly physical meaning；(2) the equivalent stress gradient factor can be determined only by elastic finite element analysis

which is suitable for practical application；(3) the predicted multiaxial fatigue lives of GH4169 alloy using the proposed model agree better with the experimental results

which are almost within two-time scatter band of the test results.