After the rotor shaft failure of the aero-engine, the parameters of the engine will change drastically, among which the change of the FAR will affect the parameters related to the combustor and the turbine to a certain extent. To study the rotor shaft failure accident under variable specific heat turbine characteristics, this paper utilizes the elemental potential method to study the change of gas properties, completes the expansion of the turbine characteristics under variable specific heat, takes a particular type of turbofan engine with different flight phases and different rotor shafts after failure as the object of study, and to carry out simulation analysis based on Matlab/Simulink. The simulation results show that after the rotor shaft failure accident, when the FAR reaches the chemically correct fuel–air ratio, the turbine flow rate under the variable specific heat turbine characteristics will decrease to a certain extent compared with the constant specific heat condition. The turbine acceleration will be slower, and the time to reach its rupture speed can be delayed by up to 3.55% according to the degree of intensity of change in the FAR.