Criterion of geometric instability of plastic strain during tension of thin specimens

A long thin rod of a uniform cross-section is considered for its deformation. A problem on geometric softening is analyzed rigorously: the stress-strain equation is derived which gives constant rate tension of long thin samples and allows for the possiblt dependence of the sample cross-section on time and coordinate along the specimen axis. The instability criterion is found for solutions of this equation against local cross-section variations. This geometric instability criterion is compared with experimental data for low-temperature serrated deformation