PSI - Issue 68

Rita Dantas et al. / Procedia Structural Integrity 68 (2025) 901–907 Rita Dantas / Structural Integrity Procedia 00 (2024) 000–000

906

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In order to simplify Eq. 8, a variable change defined as x = 2 π f t and dx 2 π f

= dt , is introduced, which results in the

following relation between L and f :

V 0

τ τ 0

m π/ 2 0

1 2 π f

( sin ( x )) m dx

(9)

L =

Subsequently, Eq. 9 was plotted for di ff erent values of m and assuming τ/τ 0 = 1 . 01, as can be seen in Fig.3 (b). Thus, it is concluded that the dislocation displacement is inversely proportional to frequency, which can be depicted as a decrease in fatigue damage with the increase of frequency. This statement is in agreement with experimental results where the frequency e ff ect is significant, since the increase in fatigue strength is justified by the decrease in L for higher frequencies (Hong et al , 2023; Zhao et al , 2012).

Fig. 3. Influence of dislocation velocity in shear stress (a) Velocity as function of shear stress for di ff erent values of m and τ 0 (b) Distance travelled by a dislocation as function of frequency e ff ect for di ff erent value of m and τ/τ 0 = 1 . 01

Nevertheless, Eq. 9 also fails into account for obstacles that restrain dislocations movement and reduce the distance travelled, leading to the diminish of frequency e ff ect in fatigue behaviour.

4. Conclusions

Within the scope of this work, the frequency e ff ect observed in ultrasonic fatigue experimental data of certain metal alloys was addressed with a focus on the characteristics of crystallographic structures. Moreover, a critical overview and discussion of the main causes of frequency e ff ect identified in fatigue data was also presented. The frequency e ff ect can be explained by material causes such as the strain rate sensitivity, the ultimate strength, the lattice structure or even the mechanism of failure observed. On the other hand, several aspects related with the test typology can also induce a frequency e ff ect in fatigue data such as the risk volume (since each testing system can require di ff erent specimen’s geometries), the heat generation due to frequency of testing or the typology of machine control during the fatigue tests. Nonetheless, the causes of frequency e ff ect promoted by the system of testing can be reduced or corrected, while the material factors remain and need to be assessed to taking into account during fatigue data analysis. Thus, in this work, the relation between the materials crystal structure and the frequency of loading was explored, to comprehend the characteristics that influence the level of sensitivity to frequency e ff ect exhibited by certain alloys. In this way, it was concluded that in several metal alloys, the frequency e ff ect can be explained with the Peierls Nabarro stress and more extensively comprehended by establishing a relation between the distance travelled by a dislocation and the frequency of loading (which was derived from the equation developed by Stein and Low (1960) for the velocity of a silicon crystal). For example, in certain metal alloys with a fcc crystal structure, such as aluminium