Analysis of the stress concentration factor for a shallow notch by the slip-line field method

Abstract

The relationships correlating the local stress and strain at the tip of a notch, the nominal stress expressed by the so called Neuber's rule and Moski and Glinka's equivalent energy density method are studied for a shallow notch,using the slip-line field method proposed in plastic mechanics, and an elastic-plastic solution for the area close to the notch. An elastic-perfect plastic material model is also used. It is found that for lower stress amplitude Moski and Glinka's method is with a good accuracy; however, the relative deviations of the actual stress concentration factors calculated by these two methods to the theoretical stress concentration factor are not small, even up to 20% for higher stress amplitude as the size of the plastic zone around the notch approaches the value of the radius of the notch curvature. While the geometric mean of the two expressions mentioned above can be considered as a reasonable expression to correlate the local stress-strain and the nominal stress, and thus the corresponding actual equivalent stress concentration factor can be evaluated, of which the relative deviations to the theoretical stress concentration factor is shown to be <5%, if the size of plastic zone close to the notch is not greater than the value of the radius of curvature of the notch.