A model for the through-thickness fatigue crack closure

Constraint and thickness effects on fatigue crack growth has long been recognized and many efforts have been made to explain the transformation from plane stress to plane strain domination. However, most of them are based on empirical relations and failed to provide rational description of the effect of thickness on fatigue crack growth. In the present paper, a theoretical model for through-thickness fatigue crack closure is proposed on the basis of the complex function method developed by Budiansky and Hutchinson (1978) in plane stress. By introducing a constraint factor, the Budiansky and Hutchinson's model is extended to the through-thickness cracked bodies with the upper and lower limits of plane strain and plane stress. Effects of the stress ratio and stress constraint factor can be calculated quantitatively and the comparison of the present model with Newman's formula shows fairly good agreement. Further comparison with available data for finite thickness specimen from numerical simulations and experimental investigations shows that the difference of the present results is less than 10% from the three-dimensional finite element results and less than 6% from the experimental data in a large range of thickness.