A Self-Consistent Approach for Necking Correction in Tensile Specimens With Rectangular Cross-Section Using a Novel Mirror Fixture

Abstract

True stress–true strain cannot be computed beyond necking, unless the effects of necking on the geometry of the tensile specimen and the stress state are accurately quantified. Necking produces a triaxial stress state that does not reflect the true uniaxial flow stress of the material. Therefore, the true stress must be multiplied by a correction factor to correct for the effect of the triaxial stresses and obtain the true uniaxial flow stress. While necking effects are easily quantified for specimens with circular cross-sections, specimens with rectangular cross-sections can exhibit complex necking geometry. In this paper, the necking behavior of pure Sn and Sn-3.5Ag-0.7Cu solders was studied to: (1) quantify necking geometry in rectangular specimens using a novel mirror fixture and a high speed camera during tests conducted at 10−3 to 30 s−1, and (2) develop a self-consistent method of necking correction that incorporates strain rate effects and can be applied to many materials.