A closed-form small-scale yielding collinear strip yield model for strain hardening materials

A closed-form extension to the Dugdale strip yield model allowing the consideration of strain hardening effects under small-scale yielding conditions has been developed. This model incorporates a nonuniform singular plastic zone cohesive stress which is a function of the material strain hardening exponent n and is an extension of a numerical model developed by M. Hoffmann and T. Seeger [The Crack Tip Opening Displacement in Elastic-Plastic Fracture Mechanics, pp. 57–77. Workshop on the CTOD Methodology, Geesthacht, Germany (1985)]. The model presented employs an empirical modification of the Hoffmann and Seeger cohesive stress distribution. This modification results in improved crack surface displacement predictions. In addition, the degree of material hardening which may be considered has been extended. Attention is confined to the center cracked panel; however, the model employs weight function techniques and is applicable to arbitrary two-dimensional cracked geometries under plane stress for which a weight function is available. Closed-form analytical expressions for the plastic zone size and crack surface displacement are presented for a center cracked panel, and comparisons are made with displacements from the more rigorous HRR solution and finite element predictions.