PSI - Issue 68

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

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the assessment of fatigue behaviour for longer lives, usually called the very high cycle fatigue regime (VHCF), of materials typically employed in these industries not only gained interest but also became fundamental.

Nomenclature

a b

interplanar distance

atomic distance

f

frequency

G

shear modulus

L

distance travelled by a dislocation

m material constant related with shear stress and dislocation velocity t time variable T period of a sinusoidal sign V dislocation velocity ν Poisson’s ratio τ shear stress applied into a slip plane τ 0 shear stress required to achieve a dislocation velocity of V 0 = 1 cm / s τ PN Peierls-Nabarro stress ω angular frequency

Nonetheless, the very high fatigue cycle regime, which is typically the region beyond the 10 7 number of cycles, can only be analysed with the help of an ultrasonic machine that can operate at frequencies around 20 kHz , leading to significant reduction in testing time compared to traditional machines (Ghadimi et al , 2021). However, sometimes a frequency e ff ect can be identified in the experimental data obtained at higher frequencies, depending on the material under assessment . As consequence, the fatigue behaviour observed for a certain material can vary with the technology of testing, in particular when ultrasonic fatigue testing systems are considered (Krupp and Giertler , 2022; Brugger et al , 2017; Guennec et al , 2014). Moreover, the level of influence of the frequency e ff ect as well as the nature of variations observed in fatigue behaviour usually change with the material and are di ffi cult to comprehend or predict. Therefore, it is of great importance to address this topic in order to clarify and handle it, which would be fundamental to legitimize the application of ultrasonic fatigue experimental data to analyse real case scenarios involving engineering components (Hong et al , 2023; Zhu , 2015). For example, aluminium alloys, which are typically characterized by an fcc (face-centred cubic) crystal structure, tend to present negligible frequency e ff ect, since the stress required to move a dislocation is considerable low. On the other hand, alloys with bcc (body-centred cubic) crystal structure, such as mild steels, demonstrate higher sensitivity to frequency e ff ect. Nonetheless, this phenomenon can also be influenced by other factors such as the presence of phases or precipitates, the ultimate strength or the sensitivity to strain rate, which increases the complexity of the topic (Hong et al , 2023; Mayer, 2016). In this work, the frequency e ff ect observed in ultrasonic fatigue data is analysed and explained with an emphasis in the characteristics of crystallographic structures. Firstly, the main causes identified in the literature for several authors as responsible for the frequency e ff ect are summarized and critically discussed and explained. Then, the relation between strain rate sensitivity (and consequently frequency e ff ect) and lattice structure characteristics is established based on the Peierls-Nabarro stress, the velocity of dislocations and the shear stress applied into a slip plane. Finally, these concepts are correlated with di ff erent crystals structures and the respective fatigue behaviour described in the literature.

2. An overview on the main causes of frequency e ff ect

Several aspects can be identified as responsible for the frequency e ff ect. One of them is the high strain rate present in fatigue tests performed at high frequencies, since materials can be more or less sensitive to strain rate. Therefore, the mechanical properties, such as the ultimate strength and consequently the fatigue limit, can vary with the strain rate.