Issue 29

M. Marino, Frattura ed Integrità Strutturale, 29 (2014) 96-110; DOI: 10.3221/IGF-ESIS.29.10 97 In this paper, a novel constitutive model for SMAs is proposed for describing their pseudo-elasticity properties. Accordingly, stress-induced transformations (SITs) are modeled by addressing isothermal uniaxial tests and by considering direct transformations from a non-oriented lattice arrangement (namely, multi-variant martensite Mm or austenite A) to an oriented one (that is, single-variant martensite in its traction and compression variants, Ms+ and Ms-), and viceversa reverse transformations Ms+/Ms-  Mm/A,[1]. As a notation rule, quantities referred to Ms+ are indicated by the superscript  , and to Ms- by the superscript  , while to direct and reverse transformations by subscripts d (or D ) and r (or R ). Denoting with mf T and af T the zero-stress martensite-finish and austenite-finish characteristic temperatures (namely, Mm is stable at < mf T T and A is stable at > af T T ), the typical SMA non-linear behavior at high temperature, > af T T , and at low-temperature, < mf T T , is addressed. Moreover, an intermediate-temperature range, < < mf af T T T , is also considered by admitting the co-existence of Mm and A at low stress. Present model opens to consider the well-established temperature dependence of transformation strains / / D R    (namely, the strain accumulated during SITs), [6]. Moreover, it is based on a very general phase diagrams with highly non-linear direct/reverse transformation lines / / ( ) d r T    and without the need of fixing a specific form for the interpolation functions describing the stress-temperature dependence (see Fig. 1). In the lack of detailed experimental data, the only assumption on the phase diagram is that there exists a unique temperature value ro T , such that < < mf ro af T T T , at which reverse transformations (both from Ms+ and Ms-) occur at zero stress (that is, the temperature corresponding to = = 0 r r     ). The motivations underlying this work, as well as the novelty of the proposed approach with respect to existing modeling approaches, are elucidated in the following. Figure 1 : Left: typical phase diagram in  - T plane for SMAs. The figure shows the direct SIT lines to Ms+ ( d   ) and to Ms- ( d   ), as well as the reverse ones from Ms+ ( r   ) and from Ms- ( r   ). Moreover, two loading-unloading paths for uniaxial isothermal traction tests are shown at 1 = < mf T T T and 2 = > af T T T . Top right: SMA typical  -  constitutive relationship at 1 = T T and 2 = T T . Bottom right: SMA typical relationships between direct ( D   ) and reverse ( R   ) transformation strains and T . State-of-the-art and proposed improvements Existing constitutive relationships for SMAs can be categorized as either micro, micro-macro or macro models [7]. In this paper, phenomenological macro-models are addressed because these are the most effective for engineering applications, being able to describe SMA global structural behavior without an explicit modeling of micro-scale behavior. Parameters of