Geometric analysis of thinning during superplastic forming

Two original geometric models applicable to the superplastic forming of prismatic die shapes are presented in this study: the uniform thickness model which determines the average of the final thickness, and the variable thickness model, which gives a first approximation of the thickness distribution by assuming sticking contact with the die. The variable thickness approach demonstrates the important contribution of the die geometry to the thinning process by monitoring the sequence of contact events throughout the process. These two models relate to the limits of the friction regime between the superplastic material and the die, i.e. perfect sliding for the uniform thickness model (lubrication and/or low pressures/low strain rates) and sticking contact for the variable thickness model (no lubricant and/or high pressures/high strain rates). Predictions of the pressure-time profiles required to form the component are also derived from the second model and were successfully applied to the manufacture of dental prostheses in titanium alloy (Ti-6A1-4V). The development and the implementation of this geometric study have been greatly and elegantly simplified by the introduction of complex numbers to represent the different geometric parameters.