The role of Poisson’s ratio in necking of polycarbonate

The numerical modelling of cold drawing in glassy polymers such as Polycarbonate (PC) is extremely sensitive to the shape of the constitutive stress–strain curve due to softening between the upper and lower yield point. This work shows that it is equally important to consider not only stress triaxiality effects but also the role of the nonlinear plastic Poisson’s ratio to accurately model the large deformation process of PC. Experimental results for the plastic Poisson’s ratio for uniaxial tensile tests on axisymmetric specimens are reported. The ratio of transverse to axial strains is measured with a unique combination of contour strain and Digital Image Correlation analysis, indicating that the plastic Poisson’s ratio varies significantly as a function of strain. An extension of Hart’s instability analysis is proposed, which considers the effect of strain-dependent Poisson’s ratio. The resulting 1D theory successfully describes neck formation and subsequent stabilisation as the interplay of cross-section area reduction due to Poisson’s effect and gradients of the stress-strain relationships. This theory delivers an intriguingly simple explanation for the characteristic change of shape of the observed force-elongation plots as strain rate is increased, if viscoplastic effects are considered. Limitations of the approach, including the incompressibility assumption underlying the Bridgman corrections and the scope of the one-dimensional stability analysis, are discussed.