Pergamon Ira. J. Mech.Sci. Voi.36, No. 4, pp. 297-309, 1994 EhcvietScience Ltd Printed i 0 Great Britain. 0020-7403/94 $6.00 + 0.00 PRESSURE-CONTROL ALGORITHMS FOR THE NUMERICAL SIMULATION OF SUPERPLASTIC FORMING J. BONET,* R. D. WOOD* and R. COLLINS* *Department of Civil Engineering, Engineering Building, University College of Swansea, Singleton Park, Swansea SA2 8PP, Wales, U.K.; )British Aerospace, Civil Aircraft Division, Bristol, U.K. (Received 11 December 1992; and in revised form 10 September 1993) Al~trtet--Superplastic forming is a manufacturing process whereby certain materials under the correct conditions of temperature and strain rate exhibit high ductility and can be blow-formed into a die to produce components that are typically very light and strong. It is crucially important, in the process, to be able to control the pressure cycle in order to obtain the optimum strain rate. This paper considers methods for calculating the pressure cycle which may be incorporated into a finite element program for simulating the forming process. I. INTRODUCTION Materials such as titanium and aluminium alloys, metal matrix composites and ceramics, when subject to the fight conditions of temperature and strain rate, can exhibit the phenomena known as superplasticity [1-4]. In contrast to conventional ductile metals, materials which deform superplastically are substantially less susceptible to strain localization. As a consequence, extremely large tensile elongations can be achieved and at a flow stress much less than that occurring in traditional hot-forming operations. Superplastic forming (SPF) of thin-sheet titanium alloy Ti-6AI-4V is currently being used in the aerospace industry to produce very complex, light and strong components. A typical SPF operation is shown in Fig. 1, where the central web has been formed by a process known as diffusion bonding. A superplastic material behaves essentially as a non-Newtonian viscous fluid, where the stress is primarily a function of the strain rate. The ability of the material to sustain ex- treme elongation without necking is crucially dependent upon the gradient m of the log-stress/log-strain-rate relation. In order to achieve maximum formability, the strain-rate sensitivity index m must be a maximum. As deformation progresses, grain growth occurs and the stress-strain-rate relationship slowly changes, see Fig. 2. Current practice seems to indicate that it is desirable to attempt to control the pressure so that, generally throughout the sheet, a constant strain rate is maintained. But as the grain size evolves, the stress-strain-rate relations clearly indicate that the optimum strain rate should shift in order to maintain the maximum value of m. The problem of controlling the pressure cycle is well known to any glassblower; blow too hard and the glass will burst, blow too gently and not much will happen! A glassblower knows intuitively just how hard to blow in order to maximize the strain-rate sensitivity index m. In the aerospace industry, the development of the SPF process and the emergence of some measure of volume production has been increasing since the late 1970s. But during this period the manufacturing process engineers have had to rely heavily on experience and some simple numerical calculations [5-7] in order to estimate the optimum pressure-time cycle. For simple parts, such as hemispheres, which do not contain 3D comers, the result of a simple pressure-cycle calculation may not be critical. But with the increasing success of SPF and the resulting demand for ever more complex parts, such an approach is no longer justified. For complex superplastically formed components, achieving a rapid forming time is less important than achieving a well-formed part. In these circumstances the a priori calculation of the pressure cycle becomes crucially important. Although it is possible to devise formulations for specific cases of SPF, such as a circular diaphragm [8], it is now evident (see Refs [9, 10] and references therein), that the generality of a formulation deriving from the finite element method can make an important HS 36:4-B 297