Finite element method (FEM), using a viscoplastic constitutive model proposed by Yoshida [Int. J. Plasticity 16 (2000) 359], has been applied to simulate the propagation of Lüders band for an annealed low-carbon steel strip under uniaxial tension test. By reducing the thickness of corresponding element, additional stress concentration is introduced into the FEM model. Calculated results show that the formation and propagation of Lüders band are affected by the level of stress concentration existing at the ends of the specimen.

For annealed mild steel that exhibits yield-point phenomena under uniaxial tension, physical equations expressing the strain-rate dependencies of the strain and the Lüders-band velocity have been proposed in this work. In these expressions, both the Lüders strain and the Lüders-band velocity increase with gauge-length strain rate in the form of exponent functions. The proposed equations have been verified by our experimental data of uniaxial tension on mild steels, as well as by those reported by some other researchers. The proposed equations may provide a simple method to determine the stress-rate sensitivity exponent, in the equation of stress-dependent dislocation velocity, which is usually difficult to be measured by experiments.