Quantitative analysis on the onset of necking in rate-dependent tension

• Measurement theory on the strain hardening index and the strain rate sensitivity index.
• The general analysis on the capability of uniform deformation of material.
• The critical relation of strain rate to uniform strain.
• The prediction of the onset of necking at specific strain path.

Quantitative analysis on the onset of necking of Zn–5%Al alloy at 340 °C in rate-dependent tension is developed based on Hart’s criterion, through accurately measuring the values of the strain hardening index (n) and the strain rate sensitivity index (m). A critical relation of strain rate to uniform strain is derived and then is verified to be an essential mechanical parameter for characterizing the capability of uniform deformation of rate-dependent materials. The prediction of the onset of necking at specific strain paths with strain rates, tensile velocities and loads agrees well with the critical relation, which suggests the validity of instability analysis in this study. The critical relation indicates that the onset of necking is dependent only on the final values of strain and of strain rate in tension, and is independent of strain path, deformation condition or strain history, which is of great significance for the increase of formability and the reduction of forming time in superplastic forming process. Additionally, it is proved that the tension at constant load is a very effective approach for precisely establishing the critical relation, due to not involving test data at others strain paths.