Plastic Deformation and Ductile Fracture at an Angled Slit in a Sheet Under Tension

摘要

A theoretical solution is obtained for the growth of narrow plastic zones and for the initiation of ductile fracture at the ends of an angled slit in a metal sheet under remote uniform tension. The theoretical model assumes two distinct regions: narrow plastic zones at the ends of the slit caused by necking of the sheet, and a surrounding elastic region. The direction of the narrow plastic zones is assumed to be normal to the remote tension regardless of the slit angle. The length of the plastic zones is assumed to be governed by Dugdale's hypotheses of yield stress attainment along the plastic zone-elastic region boundary and continuity of stress at the end of the plastic zone. Finally, fracture initiation is postulated to occur at the ends of the slit when the ratio of slit opening displacement to plate thickness attains a critical value representative of the material ductility. Experimental results on hard-rolled copper sheets support the assumptions and closely match the predicted results.