Prediction of shear localization during large deformation of a continuous cast Al–Mg sheet

In this work, a novel continuum solid mechanics approach has been proposed to predict shear band formation in uniaxial tension, utilizing both plane stress and three-dimensional analyses. The approach postulates a heterogeneous distribution of mechanical properties through the starting material. This may be attributed to the second-phase particles, textural banding or grain size variability of the sheet material. The model is used to study the effect of such heterogeneity on the development of shear localization with increasing strain. We also consider how such a model depends on the constitutive equations that are used. It is found that the Voce equation offers realistic predictions of necking and shear localization whilst the Hollomon equation fails to do so over a realistic range of deformation. The location of necking in each structure is controlled by the largest zone of soft material. The influence of the distribution, size and geometry of soft zones have been extensively studied. The amount of inhomogeneity required to precipitate localization is determined and confirmed using the Marciniak–Kuczynski method. The predicted force–displacement curves, limit strains to failure and the shear band angles all agree well with experimental observations.