Simulating superplastic forming Javier Bonet a, * , Antonio Gil a , Richard D. Wood a , Rajab Said a , Richard V. Curtis b a Civil and Computational Engineering Centre, School of Engineering, Department of Civil Engineering, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK b The Guy’s, King’s and St. Thomas’s Hospitals Medical and Dental Institute, Dental Biomaterials, Guy’s Campus, St. Thomas’ Street, London SE1 9RT, UK Received 10 April 2004; received in revised form 15 March 2005; accepted 18 March 2005 Abstract This paper reviews the numerical simulation of the superplastic forming of thin sheet from early attempts with simplified geometries through to general finite element techniques. A summary of the classical finite flow formulation of the problem is presented together with a detailed exposition of the incremental flow formulation. Pressure cycle control and contact algorithms are formulated in detail and a number of applications presented. Finally some practical simulation issues are discussed followed by brief conclusions. Ó 2006 Elsevier B.V. All rights reserved. Keywords: Superplastic forming; Numerical simulation; Finite element analysis; Thin sheet; Dental prostheses 1. Introduction Superplasticity is a characteristic of some fine-grained (3–5 lm) alloys and ceramics to exhibit, under certain process conditions, very high ductility resulting in large tensile deformation before fracture. Such materials are formed at high tem- peratures, typically of the order of half the absolute melting temperature, and at specific strain rates or flow stresses. Since the material behaviour during forming is viscoplastic high dimensional precision can be achieved with little or no spring- back associated with cold forming. Superplastic forming (SPF) is widely used in aerospace industries to form a variety of complex, very light, structurally strong thin sheet components often very resistant to adverse in-service conditions. Typical superplastically formed components are shown in Fig. 1. 1 In particular the popular titanium aluminium vanadium alloy, Ti–6Al–4V, is able to diffusion bond (SPF-DB), whereby material coming into contact during SPF fuses together to form a bond having the strength of the parent alloy. Consequently a single SPF manufacturing process can produce complex cel- lular structural components without the need for welding or rivetting parts together. SPF can also be used to forge solid components such as turbine disks and hybrid solid and thin shell components such as fan blades. Although originally pio- neered by the aircraft industry SPF is increasingly used in the automotive industry and more recently for the construction of dental and medical prostheses where high precision is paramount. Thin sheet SPF dominates the industry and the man- ufacturing process can be described with reference to Fig. 2a. At its simplest a thin sheet, typically the alloy Ti–6Al–4V, is clamped into a furnace, induction heated to a temperature of about 927 °C and blow formed by an argon gas pressure, in the order of 2 MPa, into the die, see Fig. 2a. This produces a flow stress of about 10 MPa which is considerably lower than the mechanical yield strength of 900 MPa. Insofar SPF occurs at a specific temperature and strain rate the furnace must maintain the temperature during the forming period 0045-7825/$ - see front matter Ó 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.cma.2005.03.012 * Corresponding author. Tel.: +44 1797 295 689; fax: +44 1792 295 676. E-mail addresses: j.bonet@swansea.ac.uk (J. Bonet), r.d.wood@swansea.ac.uk (R.D. Wood), richard.curtis@kcl.ac.uk (R.V. Curtis). 1 Fig. 1 courtesy of (a) Aeromet UK, (b) Formtech Gmb, (c) Authors. www.elsevier.com/locate/cma Comput. Methods Appl. Mech. Engrg. 195 (2006) 6580–6603