<div>In this paper, it is important to illustrate that, for the LCF of
metallic materials, a “stress quantity” calculated based on the
<i>linear-elastic analysis</i> of the studied component is taken to be a
<i>mechanical quantity, S</i>, to establish a relation of the
<i>mechanical quantity, S,</i> to the fatigue life, <i>N</i>, is
practicable. Based on the practicability, a prediction equation, for a
low/medium/high cycle fatigue life assessment of metallic materials, is
proposed. The prediction equation is a stress invariant based one, in
which the computation of stress invariant is on the basis of the
<i>linear-elastic analysis</i> of the studied component. Using
experimental data of plain specimens reported in literature, it is
proved that the prediction equation is both accurate and high efficient.
In addition, the prediction equation in conjunction with the Theory of
Critical Distances and <i>linear-elastic notch mechanics</i> are
combined to establish the fatigue life estimation equation of the
notched components. Finally, using experimental data of the fatigue life
of 16MnR steel, validation verification of the notch fatigue life
prediction equation is given.</div>