Analysis of the Effects of Shape Deviation on Necking Deformation of Isotropy Elastic-Plastic Materials with Linear Plastic Constitutive Relationship in Uniaxial Tensile Testing

The effects of shape’s deviation on the necking deformation of the isotropy elastic-plastic material with the linear plastic stress-strain relationship in the uniaxial tensile testing are studied by elastic-plastic finite element method. The results indicate that with the increasing of the tangent of the shape’s deviation angle tanβ, both the critical value of total elongation of necking △L_n/L₀ and the initial necking sectional radius’s ratio r_c⁰/R_t decrease linearly, and the initial necking sizes’ ratio l⁰_n/r_c⁰ increases retardedly as parabolic function. The shape’s deviation has no effect on the relationship between the minimal sectional radius’s ratio r_c/r_c⁰ and the displacement’s ratio △l/r_c⁰ during necking, and the r_c/r_c⁰ decreases exponentially with the increase of △l/r_c⁰. The shape’s deviation has an obvious effect on the relationship between the ratio of the distance from necking minimal section to inflection point to the initial necking sectional radius z_ip/r_c⁰ and the displacement’s ratio △l/r_c⁰ during necking, but has no obvious effects on the relationship between the ratio of the sectional radius at inflection point to the initial necking sectional radius r_ip/r_c⁰ and the △l/r_c⁰, and the relationship between the slopes of tangent line at inflection point k^ip_t and △l/r_c⁰. With the increase of △l/r_c⁰, the r_ip/r_c⁰ decreases exponentially acceleratively and the k^ip_t increases exponentially acceleratively.