Prediction of the Lüders band in fine grained steel strips under uniaxial tension

The Lüders band and the other regions outside the Lüders band in fine grained steel strips are treated as two phases in equilibrium in the present paper. The discontinuities of stress and deformation gradient across interfaces between the Lüders band and the other regions are considered, and the continuities of traction and displacements across interfaces and the Maxwell relation are imposed. The governing equations for two-phase piecewise-homogeneous deformations are obtained. The analysis is reduced to finding the minimum value of the loading at which governing equations have a unique, real, physically acceptable solution. As an illustration, the trilinear stress–strain response under uniaxial tension for fine grained steel used by other authors is applied to calibrate the three-dimensional elastoplastic model, the Maxwell stress, the inclined angle of the Lüders band, the kinking angle of the strip and the strain and stress in the Lüders band are predicted numerically. The predictions are in reasonable agreement with experimental measurements. The analysis also explains why the Lüders band can spread along the length of the displacement-controlled specimen under the constant Maxwell stress plateau as observed in experiments.