A strain-dependent model for the coefficient of friction in the tool-blank interaction in superplastic forming

Superplastic forming (SPF) is an advanced sheet metal forming process adopted mainly in the aerospace and automotive industries, as well as for biomedical applications, thanks to its capacity to replicate very complex geometries. Since it basically consists in blowing a metal sheet with a gas pressure into dies at elevated temperature, the study of the tribological issues plays a fundamental role in the understanding of the forming technology. In particular, the evaluation of the coefficient of friction (COF), which takes into account friction phenomena between the sheet and the die surface, is essential to obtain qualitatively satisfying final results preserving tools lifetime. Although a constant COF is usually assumed in SPF modelling, the determination of the real values of COF is very challenging because of its dependence on several parameters, and available test methods are often inadequate to properly assess all those dependences. For these reasons, a new test method is proposed and the evaluation of strain-dependent values of COF through a mathematical model is attempted in this work. Both experimental results, acquired from specifically designed closed-die forming tests, and numerical ones, from finite element modelling of the SPF process, are employed for the calibration of the mathematical model through the evaluation of the thickness distribution in the formed specimens.