Predicting ductile fracture during extended Miyauchi shear testing using analytical model

Abstract

In the fracture forming limit diagram, it is known that the major strain at fracture increases with increasing the minor strain at fracture in sheet shear testing. In this study, ductile fracture during an extended Miyauchi shear testing was predicted using an analytical model. First, an extended Miyauchi shear testing was proposed, in which the angle between the line segment that connects two neighboring notch roots and the tensile direction of the specimen was set to be an arbitrary value between zero and π/2. Next, an analytical model for the extended Miyauchi shear testing was proposed, in which the deformation of the sheet before localized necking and that after localized necking were analyzed in the region surrounding the line segment connecting two neighboring notch roots, and ductile fracture was predicted. Finally, the major strain at fracture and the minor strain at fracture obtained by the experiment for nine angles between zero and π/2 were compared with those calculated using the analytical model and those calculated using the ellipsoidal void model proposed previously by the author. Special attention was paid to the effect of prestrain which was imparted to the sheet by rolling on ductile fracture. When the angle is equal to zero, the major strain at fracture and the minor strain at fracture obtained by the experiment, agreed with those calculated using the analytical model, and did not agree with those calculated using the ellipsoidal void model.