Effects of plastic anisotropy on localization in orthotropic materials: New explicit expressions for the orientation of localization bands in flat specimens subjected to uniaxial tension

Abstract

This paper presents a theoretical investigation on the inception of plastic localization bands in specimens taken from orthotropic metallic sheets, and subjected to uniaxial tension. For the first time, it is shown that the orientations of the localization bands can be obtained directly from experimental measurements of the uniaxial tensile flow stresses and Lankford coefficients (r-values) of the metallic sheet. In contrast to isotropic materials, it is shown that localization bands equally inclined with respect to the loading axis develop only for the samples of orientations θ* corresponding to the extrema of the uniaxial tensile flow stresses in the plane of the sheet. Moreover, the expression for the bands angle depends solely on the Lankford coefficient r(θ*). For specimen orientations other than θ*, the two localization bands have different inclinations with respect to the loading axis. If for a given specimen orientation experimental values are not available, we show that the orientations of the localization bands can be obtained using the theoretical r-values and uniaxial flow stresses calculated using any orthotropic plastic potential. As an example, explicit expressions for the band angles obtained using Hill (1948) and Cazacu (2018) orthotropic plastic potentials are provided, and further applied to two textured sheets: a 2090-T3 Al alloy, and a 99% Al alloy. The results obtained are compared, and the sensitivity of the orientation of the localization bands to the constitutive model used for description of plastic anisotropy is brought to light.