Engineering definitions of small crack and long crack at fatigue limit under tensile mean stress and a prediction method for determining the fatigue limit of a cracked Mg alloy

•Three types of crack size were introduced from the viewpoint of fatigue limit.•The fatigue limits for each size were shown based on physical foundations.•The mean stress effect on the fatigue limit of the cracked specimen was formulated.•Engineering approximations were used for the formulation.•Approximation errors were found to be almost within 10%, even for Mg alloy.

A simple method was proposed for evaluating the influence of mean stress on the fatigue limit of a cracked specimen using engineering approximations. Three types of crack sizes were introduced for evaluation: an “extra small crack,” a “small crack,” and a “long crack”. The threshold stress intensity factor range was shown for each size based on crack non-propagation behavior using physical foundations. The effect of mean stress on the fatigue limit of the cracked specimen was formulated, and fatigue tests were performed on a magnesium alloy to check the approximation errors, which were found to be almost within 10%. Furthermore, the small-long crack transition was characterized experimentally.