Three-dimensional crack tip constraint of shallow cracks in tension and bending

Two-dimensional plane strain approaches in fracture mechanics have been used to characterize crack tip constraint of cracked geometries from deep to shallow cracks but neglected out-of-plane crack tip constraint effect. To address the effect of thickness and crack length in three-dimensional crack tip constraint, fully constrained geometries of notched bend bars and unconstrained geometries of center cracked tension panels of deep to shallow cracks in non-hardening and hardening elastic-plastic crack tip fields have been examined. From the results, it is found that thickness affects the crack tip constraint of deep and shallow cracks by changing the shape of the plastic zones and hence the normal stresses at the crack tip. The reduction of crack length from deep to shallow cracks in fully constrained and unconstrained crack tip fields by maintaining the ratio of B/(W-a) through an increase in thickness caused the normal stresses at the crack tip to increase marginally and led to a reduction of the toughness of the shallow cracked geometries. The change in the toughness due to the change in crack length and thickness can be characterized through a J-Delta sigma technique which is based on a crack tip constant stress sector difference fields approach.

Automated summary

The study found that the thickness affects the crack tip constraint of deep and shallow cracks by changing the shape of the plastic zones and the normal stresses at the crack tip. Increasing thickness while maintaining the ratio of B/(W-a) leads to a marginal increase in normal stresses at the crack tip and reduction in toughness of the shallow cracked geometries.