PSI - Issue 68

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

904

4

3. Lattice crystal structure, strain rate and frequency e ff ect

As mentioned above, the magnitude of strain rate e ff ect (and frequency e ff ect) is influenced by the susceptibility of a material to plastic deformation, or in other words, by the resistance of dislocations to move under cyclic loading. The resistance to plastic deformation as function of lattice structure can be quantified throughout the Peierls-Nabarro stress (Hong et al , 2023). As consequence, the variability of frequency e ff ect observed in di ff erent materials can be explained with it. The Peierls-Nabarro stress ( τ PN ) is the critical stress required to move a dislocation through the lattice unit cell and is given by the following equation: where G is the shear modulus, ν is the Poisson’s ratio, a is the distance between atomic planes (interplanar distance) and b is the atomic distance (Hertzberg , 1996; Hong et al , 2023). An can be observed in Fig. 2, the normalized Peierls-Nabarro stress is inversely proportional to the ratio between interplanar distance and atomic distance ( a / b ). Hence, for lattice structures with higher values of a / b , the stress re quired to induce plastic deformation is lower. Nonetheless, it is important to note that this stress is defined considering dislocation without obstacles which could hinder this movement. Thus, metallographic structures such as inclusions, interstitials or second phases are not included in this stress and can change the dislocation behaviour significantly (Hu et al , 2018). Additionally, data points of aluminium and iron crystals collected from (Kamimura et al , 2013), representing two di ff erent lattice structures, fcc and bcc structures, were also plotted in Fig. 2. The tendency verified in this plot is in accordance with the behaviour described until now for di ff erent types of materials. The frequency e ff ect in aluminium alloys, which are typically characterized by an fcc crystal structure, is negligible since the stress require to move dislocations is considerable low. This observation is explained by high planar density, which corresponds to smaller atomic distances, and a larger number of slip systems (combination of slip planes and directions). As consequence, aluminium alloys are easily to deform plastically, even at high frequencies of testing (Hong et al , 2023). τ PN = 2 G 1 − ν exp − 2 π a (1 − ν ) b (1)

Fig. 2. Evolution of normalized Peierls-Nabarro as function of a / b for di ff erent Poisson’s coe ffi cients together with experiential data for di ff erent crystals: aluminium (Al) and iron (Fe) (data from (Kamimura et al , 2013))

On the other hand, the fatigue behaviour of mild steel alloys, which exhibit a bcc or body centred tetragonal (bct) structure, is a ff ected by frequency e ff ect, since they demonstrate higher strengths at ultrasonic frequencies. In bcc