“…Consequently, the fatigue life was successfully predicted for the four tested non-proportional loading paths (NPR1, NPR2, NPR3, NPR4) of different and complex shapes ( Figure 2 ) and for one proportional loading path (Prop). Furthermore, the common complex measures of the non-proportional loading effect on fatigue life, such as non-proportional factors [ 79 , 80 , 81 , 82 ], integral approaches [ 66 , 72 , 82 ] and enclosing surface methods [ 83 , 84 ], are not needed.…”