The intersection of a slip-plane and a stress-free boundary: Application to inhomogeneous yielding

A n analysis is presented for the stable formation of a localized yield-zone within an elasticallydeformed material. The interaction of the yield zone, the stress-free boundary from which this zone originates, and the far-field stress gradient in the elastic body is discussed. A distribution of edge dislocations on a slip-plane is employed as a model for the yield zone. The results of the analysis are compared to four-point bend-test data from mild steel bars. In the analysis, upper and lower yield-point data are used as the controlling parameter values for the formation of this zone. The predicted length of the yield region and the stress distribution around the region are in agreement with the experimental data. From the results of the analysis, a location for the formation of a second yield-zone is suggested. The distance between yield zones is obtained and compared to the observed separation distance in the experiment.