Most structural failures typically occur at stress levels significantly lower than the yield strength of the material under the time-varying loads. In this research, we present a high cycle fatigue failure constrained design process considering the modified Goodman theory, the Gerber theory and the SWT criteria combined with the stress constrained topology optimization scheme using P-norm correction method. The phase field design method with double well potential functions is used to implement structural design and the modified P-norm stress is employed for a design constraint. The earlier studies determined the Stress correction factor arbitrarily. To complement this point, we propose the determination method of Stress correction factor considering loading effects related to axial stress component. As a result, we can derive optimization results having small gray scale regions and their maximum stress becomes close to the allowed stress. Also, we can design the more reasonable structure due to introducing the Stress correction factor.