Determining material true stress–strain curve from tensile specimens with rectangular cross-section

Abstract

The uniaxial true stress logarithmic strain curve for a thick section can be determined from the load–diameter reduction record of a round tensile specimen. The correction of the true stress for necking can be performed by using the well-known Bridgman equation. For thin sections, it is more practical to use specimens with rectangular cross-section. However, there is no established method to determine the complete true stress–logarithmic strain relation from a rectangular specimen. In this paper, an extensive three-dimensional numerical study has been carried out on the diffuse necking behaviour of tensile specimens made of isotropic materials with rectangular cross-section, and an approximate relation is established between the area reduction of the minimum cross-section and the measured thickness reduction. It is found that the area reduction can be normalized by the uniaxial strain at maximum load which represents the material hardening and also the section aspect ratio. Furthermore, for the same material, specimens with different aspect ratio give exactly the same true average stress–logarithmic strain curve. This finding implies that Bridgmans correction can still be used for necking correction of the true average stress obtained from rectangular specimens. Based on this finding, a method for determining the true stress–logarithmic strain relation from the load–thickness reduction curve of specimens with rectangular cross-section is proposed.