Strength, Fracture and Complexity 3 (2005) 61–72 61 IOS Press Snap-back instability in micro-structured composites and its connection with superplasticity Alberto Carpinteri * , Marco Paggi and Giorgio Zavarise Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy Abstract. Instability phenomena occurring in the microstructure of micro-structured composites are numerically investigated. To this aim, an interface constitutive law is proposed to describe both decohesion and contact at bi-material interfaces. These formulations are implemented in the FE code FEAP. Then, by applying dimensional analysis, the nondimensional parameters governing the macroscopic response of the composite are identified. According to this model, transverse debonding with respect to the fiber direction is simulated and the transition from snap-back instability in case of coarse fiber diameters, to a stable mechanical response for finer reinforcements is quantified. These results provide a possible quantitative explanation to the role played by the size of the reinforcement on the instability phenomena experimentally observed during superplastic deformation. Keywords: Fiber reinforced metal matrix composites, snap-back instability, superplasticity, interface debonding, finite element method 1. Introduction The mechanical behavior of micro-structured composites has been experimentally and theoretically proven to be strongly dependent on the size of the reinforcement. In other words, keeping constant the reinforcement volumetric fraction and the mechanical properties of the constituent materials, size ef- fects on the mechanical response are observed by varying the diameter of the fibers/particles. From the technological point of view, an important example where this size effect is noticed is represented by superplasticity. Superplastic behavior is defined as “the ability of a polycrystalline material to exhibit, in a generally isotropic manner, very high tensile elongations before failure” [1]. The occurrence of super- plasticity has been experimentally reported in a very wide range of metallic alloys [2,3], intermetallics [4] and ceramics [4]. More recently, the field of superplasticity has been expanded beyond the tradi- tional metallic alloys to include evidence of superplastic-like behavior in a very wide range of new and advanced materials, such as metal and ceramic matrix composites [5]. Over the last two decades, a lot of attention has been devoted to examining and attempting to explain the physical mechanisms which occur during superplastic deformations. From experiments it is well- established that, when accommodation processes are not rapid enough to meet the requirements imposed by boundary sliding, then stresses which develop at fiber boundaries are not relaxed in a sufficiently rapid way and cavities might nucleate at the interface between matrix and reinforcement. Consequently, * Corresponding author. Tel.: +39 0115644850; Fax: +39 0115644899; E-mail: alberto.carpinteri@polito.it. 1567-2069/05/$17.00  2005 – IOS Press and the authors. All rights reserved