| Abstract: | When stretched under uniaxial stress, ductile polymers usually exhibit unstable plastic deformation, which embodies two phases: (a) yielding with the formation of a neck and (b) cold-drawing with the propagation of necking shoulders. The mechanical state associated with this deformation behavior is analyzed. The discussion is divided into three parts. The first part is a general treatment of the constitutive function of flow stress in the plastic state, in which a series of relations among various characterizing parameters are formulated. The second part provides three mechanical criteria for necking deformation and propagation of necking shoulders: the condition of unstable plastic deformation requiring $ D_P = - \left( {\partial {{\ln \dot \varepsilon } \mathord{\left/ {\vphantom {{\ln \dot \varepsilon } {\partial \varepsilon }}} \right. \kern-\nulldelimiterspace} {\partial \varepsilon }}} \right)_P < 0 $ the stabilizing deformation mode, which requires $ \gamma _p = \left( {{{dD_p } \mathord{\left/ {\vphantom {{dD_p } {d\varepsilon }}} \right. \kern-\nulldelimiterspace} {d\varepsilon }}} \right)_P > 0 $ and the obvious localization of unstable plastic deformation. The third part describes a mathematical model which can be used in calculations to fit the contour of the necking shoulder. This model is developed according to rational considerations for the relation of In $ \dot \varepsilon $ to ε. Experimental data on PE rod specimens are well fitted by this model. © 1993 John Wiley & Sons, Inc. |
