Analysis of Necking Deformation of Isotropy Elastic-Plastic Material with Linear Plastic Stress-Strain Relationship in Uniaxial Tensile Testing

The necking deformation characteristics of the isotropy elastic-plastic material with linear plastic stress-strain relationship in the uniaxial tensile testing are studied by elastic-plastic finite element method. The results indicate that when the ratio Δl/r_c⁰ of the necking displacement to the initial necking radius increases, that the ratio r_c/r_c⁰ of the smallest sectional radius to the initial necking radius decreases exponentially, that the ratio z_ip/r_c⁰ of the distance from minimal sectional to inflection point to the initial necking radius decreases exponentially, that the ratio r_ip/r_c⁰ of the sectional radius at inflection point to the initial necking radius decreases exponentially, and that the tangent slope k^ip_tat the inflection point increases exponentially. The function of the ratio l_n⁰/r_c⁰ of the half initial necking length to the initial necking radius and the ratio T₂/σ₀¹ of plastic deformation coefficient to critical value of flow stress is a double exponential distribution. The relationship between k^ip_t and the cotangent cotα2 of the half necking opening angle is linear.