Averaged strain energy density and J-integral for U- and blunt V-shaped notches under torsion

Abstract

Analytical solutions for the J-integral and the strain energy density (SED) averaged over a control volume are presented for U- and blunt V-shaped notches under torsion. The influence of the notch tip radius and the notch opening angle are fully included in the new proposed relationships. These expressions take advantage of some recent solutions for the stress fields ahead of blunt notches under Mode III loading and can be seen as a synthesis of the efforts carried out during the last years by the present authors on this topic. Afterwards, the expressions are applied to a recent set of experimental data from cracked, notched and plain specimens tested under torsion at low temperature $$(-60\,^{\circ }\hbox {C})$$ . The large scatter shown by notched specimens in terms of maximum elastic stresses strongly reduces when the J-integral or the local SED are used in combination with the specific control volumes.