Issue 21

C. Maletta et alii, Frattura ed Integrità Strutturale, 21 (2012) 5-12 ; DOI: 10.3221/IGF-ESIS.21.01 8 F INITE ELEMENT MODELING inite Element Analyses (FEA) have been carried out, by using a commercial FE software code and a special SMA constitutive model [16, 17] in order to study the microstructural evolution during indentation tests as well as to estimate the evolution of the indentation response of the alloy as a function of the test temperature. In particular, two-dimensional axisymmetric FE analyses were carried out by exploiting the axisymmetry of the indenter, while the sample was assumed to be a cylinder with radius equal to 10 times the diameter of the indenter, in order to avoid boundary effects [18]. The model, illustrated in Fig. 2, consists of approximately 50400 2D four-noded quadrilateral elements. The figure also illustrates that a very fine mesh has been used to model the contact region in order to capture the high stress gradient and the complex non-linear effects due to plastic deformation and stress-induced transformation mechanisms, in addition to those due to the contact. This model results from a preliminary convergence study, which was developed by analyzing a standard elastic-plastic material; in particular, systematic comparisons between numerical results and elastic-plastic contact theory have been carried out in order to obtain an optimal balance between accuracy and computational efficiency. Figure 2 : Axisymmetric FE model used to analyze the indentation process. Subsequently, the constitutive model for SMAs, which is directly implemented in the numerical code, was calibrated using the thermo-mechanical parameters illustrated in the previous section, while linear elastic behavior has been adopted for the diamond indenter (elastic constant: E=1141 GPa,  =0.07). The numerical results were compared with the experimentally measured load-displacement curves and, subsequently, the influence of test temperature on the indentation response of the SMA has been numerically analyzed, as described in the following section. R ESULTS AND DISCUSSIONS Preliminary FE analysis reliminary FE studies have been carried out to investigate the phase transition mechanisms in the indentation region as well as to understand better the main differences with respect to conventional elastic-plastic metals. Fig. 3.a illustrates the transformation boundaries in the contact region, for a maximum load of 300 mN, which have been obtained from the FE simulations by comparing the von Mises equivalent stress with the characteristic transformation stresses of the SMA. Starting from the outer region, a fully untransformed austenitic zone is observed (A), i.e. where the von Mises stress is below the start transformation stress s AM    . The area B represents the transformation zone, i.e. von Mises stress between s AM  and f AM  and consequently the volume fraction of martensite is between 0 and 1. Finally, C and D represent the fully transformed martensitic regions, i.e. where the von Mises stress is higher than the transformation stress, f AM  ; however, in C only elastic deformation of the martensitic structure is observed while in D the local stress exceeds the yield stress of martensite and permanent deformation is observed leading to stabilization of the martensite. This stabilized martensite does not revert to austenite on unloading. It is worth noting that the contours in F P