# Fatigue Characteristics of Fe-Based Shape-Memory Alloys
## 4 Result and Discussion
### Relationship between Stress Range and Number of Cycles  
As shown in Table 3, the number of cycles of the A-type and B-type alloys at stress range of 700 MPa was 32,018 times and 39,284, respectively. On the other hand, the number of loading cycles of the A-type alloy exceeded two million under stress range of 400 MPa, whereas the number of loading cycles of the B-type alloy was 418,098. [PERSON] et al. [17] and [PERSON] et al. [18] argued that the fatigue strength increases as the yield strength increases. As shown in Section 2.2, the A-type alloy has greater both yield and tensile strength than the B-type alloy. This difference in strength can be confirmed with the optical micrographic (OM) image in Figure 8. For OM analysis, each specimens were mechanically grinded using SiC papers. Subsequently they were polished by 3-\(\upmu\)m, 1-\(\upmu\)m alumina suspension and 0.04-\(\upmu\)m colloidal silica suspension. The specimens for OM were color etched by 0.5% NH\({}_{4}\)HF\({}_{2}\) and 1.2% K\({}_{2}\)S\({}_{2}\)O\({}_{5}\) (mass%) with 100 ml of distilled water. As shown in Figure 8a,b, there is no significant difference in grain size between A-type alloy and B-type alloy, so the difference between grain size and strength according to Hall-Petch relation is considered to be irrelevant. However, as shown in Figure 8c, the strength of the B-type alloy without Ti was decreased due to the presence of many abnormal grain growth which may be formed during reheating step in hot rolling process [19]. On the other hand, abnormal grain growth could be inhibited by the formation of TiC for A-type alloy with Ti addition [14; 20]. For this reason, the A-type alloy has greater strength than the B-type alloy.  
Figure 6: Stress–strain curves according to number of cycle for A-type Fe–SMA. (**a**) 700 MPa; (**b**) 400 MPa.  
Therefore, the fatigue strength of the Fe-SMA is influenced by its strength, so that the A-type alloy with higher strength due to the formation of TiC has lager fatigue strength than the B-type alloy.  
As shown in Figure 9a, as a result of performing a first order regression analysis using the test results, the stress range and the number of loading cycles of the A-type alloy showed the relationship delineated in Equation (1), and the coefficient of determination (R\({}^{2}\)) was 0.9433. Assuming that the fatigue limit of the Fe-SMA (f\({}_{\text{f}}\)) is a stress range that does not break even at two million cycles, it can be obtained by substituting two million into the N value of Equation (1). As a result, the fatigue limit of the A-type alloy was determined to be about 473 MPa. Figure 9b shows the results of the first order regression analysis using the fatigue test results of the B-type alloy. As shown in Figure 9b, the stress range and the number of cycles of the B-type alloy showed the relationship delineated in Equation (2), and the coefficient of determination (R\({}^{2}\)) was 0.8432. The fatigue limit of the B-type alloy calculated in the same way as for the A-type alloy was found to be about 33% less than that of the A-type alloy. This is because the fatigue strength increases as the yield strength increases, as described above.  
\[S=-131.56 logN+1265.8 \tag{1}\]  
\[S=-178.92 logN+1456.9 \tag{2}\]  
Figure 7: M-N relation according to type of alloy. (**a**) A-type; (**b**) B-type.