Issue 50

V. Iasnii et alii, Frattura ed Integrità Strutturale, 50 (2019) 310-318; DOI: 10.3221/IGF-ESIS.50.26 311 The application of SMAs depends on the phase transformation temperatures, mechanical and functional properties, type of loading (static, cyclic and thermo-mechanical). SMA are increasingly used in machine parts, implants [1, 2]. Due to the high ability to energy dissipation, SMA are used in damping devices for civil engineering [3–6] or other structural elements [7, 8]. As they are subjected to intense cyclic loading during operation, it is important to ensure their reliability and lifetime under low-cycle fatigue [9]. Defects, such as internal subsurface voids, surface scratches which lead to crack initiation, play significant role under low- cycle fatigue [10]. Also, fatigue microcracks can initiate at the martensite–martensite or austenite–martensite interfaces [11]. The martensite– martensite or austenite–martensite interface motion causes the formation of defects in the grain, these defects becoming potential crack initiation areas. Cracks can initiate at the grain boundaries [12]. The cyclical loading affects not only the ability of the material to resist structural fatigue, but also the functional properties. Therefore, it is necessary to know how their functional and structural properties change in order to design reliably the devices and structural elements made of pseudoelastic SMA which operate under fatigue loading. It is also important to take into account the balance between structural and functional fatigue. Under a cyclic loading the residual strain [13] increases and the dissipation energy reduces, thus worsening the efficiency of the damping devices [14]. Residual martensite plates increase with the number of cycles and are considered to be one of the causes of the formation of a residual strain during cyclic loading [15]. Lifetime of SMA can be predicted by stress- [16, 10], strain- [17-19] and energy based criteria [10] of fatigue failure. An overview of the structural fatigue of SMA under mechanical and thermomechanical loading is presented, for instance in the paper [20]. For low - cycle fatigue the strain amplitude and the number of cycles to failure could be represented by the empirical dependence f N      (1) where  and β represent ε a in N f =1 and the slope of the log Δ ε - log N f curve, respectively. For NiTi wire of 0.5 mm in diameter under rotating-bending fatigue test the relationship between  and T is expressed by the following equation [21]: ( ) 10 s a T M s      (2) where T is test temperature; M s – martensite start temperature. Based on the experimental results, the coefficients are determined as β = 0.28, α s = 0.248, a = 0.0032 K -1 [21]. For NiTi tube with outer diameter of 0.9 mm and inner 0.7 mm under rotating-bending fatigue test the dependence of α on T is expressed by the following equation [21]: 0 0 ( ) n m T T      (3) Based on the experimental results, the coefficients are determined as β = 0.25, m = 0.065 K n , n = 0.4, T 0 = 297 K, α 0 = 0.057. A quasi-linear dependence of log Δ W dis on log N f for several values of the mean stress. It is, hence, interesting to approximate experimental results using the following curve [22]: 1 1 dis f W N     (4) where Δ W dis – is dissipation energy per cycle; α and β are material parameters. Numerical results are in good agreement with experimental data for α = 11 and β = −0.377. A damage based fatigue failure model by dividing the total damage sources into three parts, i.e., microcrack initiation, microcrack propagation and martensite transformation induced damage was proposed by Song [23]. The damage variable as the ratio of the accumulated dissipation energy after a prescribed number of cycles to that obtained at the failure life was defined