Two-phase theory for the superplastic ¯ow Miguel Lagos*, He ctor Duque Departamento de FõÂsica, Facultad de Ciencias, Universidad de Chile, Casilla 653, Santiago, Chile Received in ®nal revised form 1 May 2000 Abstract We discuss a theoretical approach to the stress induced motion of vacancies in a poly- crystalline material and its connection with superplastic ¯ow, put forward recently by us. After introducing an alternate formulation, the theory is applied to explain the temperature dependent stress-strain rate curves exhibited by some representative alloys. The agreement with experiment is remarkable. We also employ it to study the rate of cavity growth in two superplastic copper alloys that exhibit particularly strong cavitation. # 2001 Elsevier Science Ltd. All rights reserved. Keywords: Superplasticity; A. Grain boundaries; A. Phase transformation; A. Voids and inclusions 1. Introduction Superplastic materials are polycrystalline solids that under appropriate conditions of temperature and strain rate can undergo extensive, neck-free tensile deformation prior to fracture. Superplastic samples subjected to tensile stresses beyond the elastic limit enter a deformation regime characterized by uniform strains of thousands of percent, instead of failing after a plastic elongation of a few percent. The phenom- enon takes place for temperatures within a speci®c range, starting near half the melting point, and strain rates between bounds that are typically 10 5 and 10 1 s 1 . The physical origin of superplasticity constitutes a fascinating scienti®c problem because it causes hard solid materials to behave in many respects as liquids, without leaving the solid structure. Superplastic materials have actual or potential technical importance because they generally produce parts exhibiting outstanding mechanical properties and allow for International Journal of Plasticity 17 (2001) 369±386 www.elsevier.com/locate/ijplas 0749-6419/01/$ - see front matter # 2001 Elsevier Science Ltd. All rights reserved. PII: S0749-6419(00)00041-3 * Corresponding author.