Abstract

A theoretical model for predicting elastic-plastic, plane strain stress distributions in notched bars under bend loading has been developed by combining the elastic solutions of Neuber with the slipline field solutions of Hill. The model is used to calculate the plastic zone size as a function of the externally applied load (moment), the yield stress σ isec and geometrical parameters such as root radius, notch depth, and ligament depth. The theoretical predictions are found to be in very good agreement with experimentally measured values of the plastic zone size in notched bars of high nitrogen steel. The fracture strength of notched bars of varying geometries was measured at cryogenic temperatures and the value of K IC was determined. It is shown that the value is consistent with a fracture criterion based on the attainment of a critical tensile stress σ f ∗ over a small volume in front of the notch. Unstable fracture occurs when the plastic zones have spread to a critical distance such that the maximum tensile stress level in the plastic zone is raised from σ isecup toσ f ∗. The model therefore relates the notch strength of bars containiag various notches to the material's intrinsic fracture characteristics. It is found that there is an effective minimum root radius of about 0.002 in. which governs the fracture toughness of specimens containing sharper notches and cracks.

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