Abstract: A theoretical analysis is performed for fatigue crack closure based on a modified strip yield model and the complex function method developed by Budiansky and Hutchinson (1978) in plane stress. By introducing a reasonable constraint factor, Budiansky and Hutchinson's model is extended to the general stress state with the upper and lower limits of plane strain and plane stress. The present theory can be easily extended to analyze the closure in the through thickness crack growing. Effects of the stress ratio and stress constraint factor can be calculated quantitatively, and the comparison of the present model with available data from two and three dimensional finite element simulations and experimental investigations shows quite good agreement. The explicit equations for the opening stress can be applied in engineering.

Key words: str ess state, fatigue cr ack clo sur e, constraint, opening str ess r atio, thickness effect, t hr oug hthicknesscr acks