A Simple Procedure for the Post-Necking Stress-Strain Curves of Anisotropic Sheet Metals

Abstract

Modelling the anisotropic plasticity of a metal requires the derivation of various experimental flow curves from specimens machined along different orientations and, depending on the anisotropy model, tested under different loading modes (tension, compression, torsion). The derivation of stress–strain curves from tensile experiments is a common practice within the uniform straining range but still presents some uncertainties after necking onset. Modern sheet metals, for structural applications where significant energy absorption is required, may exhibit early necking and prolonged post-necking ductility; when such alloys also exhibit pronounced anisotropy, the derivation of their flow curves may be challenging, whatever the loading mode or the specimen direction. This work examines the experimental procedures for determining the true-stress–true-strain curve and the anisotropic strain ratio, extended over the post-necking range and up to failure, from representative tensile tests along the rolling direction of PHS-1800 steel and aluminum 6181 alloy. The validity ranges of different standard procedures for stress–strain derivation are investigated to understand when and how fast the typical true-stress–true-strain data start to depart from the effective material response. Other considerations, based on simple experimental and post-processing procedures, aim at a procedure delivering useful information about the material response over the post-necking range and up to failure. The procedure to retrieve post-necking true curves and anisotropy ratios is then applied to tensile tests at static, intermediate, and high strain rates on the two sheet metals of interest.

Keywords

• sheet metals
• true strain
• true stress
• anisotropy
• lankford coefficients