Abstract:Gradient-dependent plasticity having characteristic length reflecting heterogeneity was used to deduce analytically non-uniform plastic strain in necked zone, and the external shape of the zone was described because the plastic strain and the plastic extension of the zone regardless of change of volume of the zone was calculated. In addition, the true stress was deduced because the minimum sectional area in the zone can be determined according to the external shape. The advantage of the present analytical results for true stress and true strain curve is that the related parameters have specific physical meanings, such as softening modulus describing brittleness, elastic modulus considering elasticity, characteristic length reflecting the heterogeneity, the gauge length involved in the present model to study the geometrical size effect. Comparisons of the existing experimental results for titanium and Ti-6Al-4V and the present analytical results were carried out and the new model considering microstructures and localized necking was verified. It is found that the brittleness and heterogeneity of Ti-6Al-4V are higher than those of CP titanium. The differences of the propagation velocity of the localized band in two kinds of materials are explained in terms of the different brittleness.