The applicability of slip-line field theory to contained elastic-plastic flow around a notch

Abstract

Recent calculations by J.R. Griffiths and D.R.J. Owen (1971) on the growth of the elastic-plastic stresses for the plane strain bending of a V-notched bar reveal an interesting phenomenon : the stress maximum lies some way before the elastic-plastic interface, inside the plastic zone. Later calculations have confirmed this effect, for both work-hardening and perfectly-plastic von Mises and Tresca materials. At low applied loads the calculated stresses conflict with plastic slip-line field theory. This result is important, because it means that notch stresses before general yield cannot readily be deduced by etching up plastically-yielded zones. This paper explains the conflict analytically. © 1971.