Slip-Line Field Solution of Shallow Notched Bar Due to Three Point Loading : The Case of Shallow Notch Depth

抄録

In this report, four types of slip-line field solutions are presented for the initial plastic yielding of a shallow notched bar bent as in the Charpy test. The slip-line field is statically indeterminate because it is uniquely determined by both of stress and velocity boundary conditions. Then making use of the analogy of Hencky's equation and Geiringer's equation, we studied the method of solution of a statically indeterminate problem when the profile of the base characteristic lines on the hodograph or the normal velocity components along the base slip-line in the physical plane are given. Using this method, slip-line field, constraint factor and maximum tensile stress are calculated. From the coincidence of the field of critical depth calculated by this method with the corresponding field of a deeply notched bar, we conclude that our method is appropriate.