Effects of shape and size of tensile specimens on the stress-strain relationship of sheet-metal

In the industrial forming of sheet-metals, knowledge of the mechanical properties of the work-metal is of major importance, as these properties determine the suitability of the material for a particular forming route, and the limitations of the processes employed. Likewise, the effects of the shape and size of the specimens of the uniaxial tensile test — by far the most commonly employed test — used to determine the mechanical properties need to be understood, in order that appropriate allowances can be made for such effects. In this paper is reported an investigation carried out on the stress—strain relationship of sheet-metal derived from uniaxial tensile tests in which the process parameters, namely, specimen width, thickness, as well as the angle between the loading direction and the rolling direction of the sheet, are varied. By fitting the experimental data to the familiar Hollomon equation, σ = Kηn, and using statistical significance tests, it is found that values of the coefficients K and n are influenced by specimen thickness, loading direction, and width, in that order of significance. That the values of work-hardening coefficients in the Ludwik equation, σ = σy + Cηm, are dependent on these variables is also observed. A mathematical model based on the Hollomon equation is attempted to further depict the response of K and n to process parameter changes.