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

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.