Issue 23

C. Maletta et alii, Frattura ed Integrità Strutturale, 23 (2013) 13-24; DOI: 10.3221/IGF-ESIS.23.02 19       1 0 2 1 lim 2 2 1 1 IM M IA r K r K              (12) Eq. 12 shows that IM K can be expressed ad a function of IA K ,  and of the Young’s modulus ratio  . However, it is worth noting that the knowledge of the extent of transformation region, in terms of A r , is required to calculate both IA K and IM K and an iterative approach is required to calculate these parameters as described in [25]. Fig. 6a shows the values of IA K and IM K , normalized with respect to the applied SIF I K a      , as a function of the transformation strain, L  , and for different values of the transformation stress, AM  , for an alloy with 0.3   , 40 A E GPa  and 0.5   . Note that the same curves are used to represent IA K and IM K , as / IM IA K K is a constant depending on the elastic properties of the alloy, as shown in eq. 12. The figure illustrates that both IA K and IM K increase with increasing the transformation strain, and this effect is more evident when decreasing the transformation stress, as a direct consequence of the increase of the transformed region near the crack tip [23]. Furthermore, IA K is always greater than I K  , with / 1 IA I K K   when AM   and 0 L   , i.e. in the case of linear elastic materials. In addition, the martensitic SIF, IM K , is always smaller than I K  , which indicates a reduction of the stresses at the very crack tip if compared with linear elastic materials. Fig. 6b, illustrates the effects of the testing temperature on both IA K and IM K for a commercial superelastic NiTi alloy. The figure shows that a decrease of both SIFs is observed when increasing the temperature, as a direct consequence of the increase of the transformation stress. In particular, a reduction of about 20% is observed in the temperature range between 273 K and 343 K, which correspond to a range of transformation stress between about 90 MPa and 800 MPa. However, IA K and IM K decrease rapidly from 273 K to 290 K, while a small variation, i.e. of about 2%, is observed when the temperature is above 290 K. This effect is a direct consequence of the increase of the transformation stress with increasing the temperature, which causes a marked reduction of the transformation region, as discussed in [23], and, consequently, IA K approaches to the applied SIF I K  , i.e. the alloy behaves like a linear elastic material. Furthermore, it is worth noting that the temperature range is limited by a lower bound, min T , which corresponds to a transformation stress equal to zero, and by an upper bound min d T M  , which represents a characteristic maximum temperature for stress induced transformation. a) b) Figure 6 : Martensitic and austenitic SIFs, IA K and IM K , normalized with respect to the applied SIF, I K  , as a function of: a) the transformation strain  ( L  ) and for different values of the transformation stress ( t AM r    ), b) the testing temperature ( T ) [25]. The reference model has been recently modified in [26] to overcome one of the basic limitation, i.e. the assumption of constant stress transformation. In fact, it has been demonstrated that the slope of the stress-strain transformation plateau increases under specific loading conditions, such when increasing the loading rate or under cyclic loads [30]. To this aim,