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.