Large Deformation of Notched Perfectly Plastic Tensile Bars

Solutions are obtained for the large, nonsteady deformation of U-notched rigid/perfectly plastic tensile bars in the plane and axisymmetric deformation modes. The solution for the plane mode is shown to be unique. The solutions for both modes are obtained by a general finite-difference method whose accuracy is assessed by examining different mesh sizes in both iterative and noniterative schemes. The solutions may be useful for estimating local stresses and strains in ductile fracture tests even though comparison of calculated and observed deformations indicates some discrepancies due to the neglect of hardening in the theory. The theory does successfully predict yield loads as well as the sharpening of blunt notches and the blunting of acute notches which is observed in axisymmetric tests. It also shows that the largest strains in the plane mode occur on the rigid/plastic boundary reaching a maximum at the surface while those in the axisymmetric mode occur at the center of the root plane. The tensile stresses are maximum at the center of the minimum section for both modes. These results suggest an explanation for the initiation of the shear-type fractures and the cup-cone fractures which are commonly observed in the plane and axisymmetric modes, respectively.