Necking in rectangular tensile bars approximated by a 2-D gradient dependent plasticity model

Abstract

Necking and post-necking of a uniaxially stretched tensile test specimen with a rectangular cross-section is investigated. The analysis is based on an enhanced 2-D plane stress finite element model, where the third dimension (the thickness effect) is taken into account by an incorporated length scale. The length scale, fixed with respect to the current deformed state, is incorporated in the continuum description by a finite strain version of a gradient dependent J 2-flow theory. A convincing agreement with the true 3-D post-necking behaviour is obtained by this approximative 2-D plane stress model. The model gives a realistic prediction of the development of the post-necking zone in the tensile bar. Furthermore, the model is found to capture the transition from a dominating diffuse necking mode for a tensile bar with a square cross section to a dominating oblique localised necking mode for a wide strip; effects which can not be captured by an analysis based on a conventional (local) plane stress model.