A one-dimensional stress wave model for analytical design and optimization of oscillation-free force measurement in high-speed tensile test specimens

In this work, the phenomenon of the oscillation-free force measurement in a new sample shape, called the Generation III (Gen. III) sample in a previous work, was first physically analyzed. Based on metal physics findings and the classical elastic stress wave theory, a simplified one-dimensional elastic stress wave model was developed. For this model, several assumptions were applied so that the Gen. III sample was modeled by five thin bar sections with different section sizes and material properties. By implementing the derived governing equations in the MATLAB software, which enables the combination with a mathematical optimization algorithm (sequential quadratic programming), both the characteristic of the current Gen. III sample and its sensitivity to the geometric parameters (such as the section sizes of the beams) and the material properties could be calculated. The developed model can not only correctly calculate the principle section design, but also make correct predictions of effects that have been overlooked until know. The model assumptions are thus reasonable. It was found that strain hardening of the sample material has an influence on the geometric parameters of the Gen. III sample. Therefore, the Gen. III sample geometry may be slightly adapted for each material.