PSI - Issue 66

Daniela Scorza et al. / Procedia Structural Integrity 66 (2024) 406–411 Author name / Structural Integrity Procedia 00 (2025) 000 – 000

410

5

of the corresponding geometric shape function *

i f . In particular, in the present procedure, *

i f is computed for a

nanobeam with two identical edge-cracks under a constant bending moment (so that 1 2 * * * f f f = = ) by varying both the distance between the cracks and the crack depth. To this aim, a 2D model of the above cracked nanobeam is created by means of the commercial software Ansys Workbench 2021 R2 (2021) in order to estimate the stress intensity factor (SIF) through the displacement field around the crack tip. Then, the geometric shape function is determined by equating the SIF defined according to LEFM with the SIF obtained by the linear regression applied to the numerical results. Details may be found in Ref. (Vantadori et al., 2024). Finally, after * i f is estimated, the elastic rotational spring stiffness i k can be obtained as the reciprocal of the elastic compliance computed through Eq. (7). 4. Parametric analysis The present nonlocal analytical model had been already validated by considering an experimental campaign available in the literature, related to bending tests performed on cantilever microbeams containing a single edge crack (Deng and Barnoush, 2018). Since an almost perfect agreement between experimental data and analytical results was obtained regarding the elastic behaviour of the microbeam (Vantadori et al., 2024), the geometrical and loading configurations as well as the material properties employed for the validation are hereafter used as starting point for a parametric analysis related to a microbeam containing two edge-cracks. Therefore, a cantilever microbeam, made of a pure FeAl intermetallic single crystalline alloy and having geometrical sizes B H L   equal to 3x3x12  m 3 , is considered by assuming the presence of two cracks with the same depth, which are distant d each other. The material input data are (Vantadori et al., 2024): material characteristic length (linked to the material grain size) 3 μm c L = ; elastic modulus 75.9GPa E = ; Poisson’s ratio 0.3  = . Finally, a force F equal to 880  N is assumed to be applied at the microbeam free end. In the following, different values of both the normalised distance between cracks, d H , (ranging between 0.01 and 3.6) and the relative crack depth, a H  = , (that is, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7 and 0.8 ) and two values of the relative position of the first crack, 1 x L  = , (that is, 0.08 and 0.3 ) are examined. Firstly, by considering the above seven relative crack depths, the value of the spring stiffness, 1 2 k k k = = , computed as is detailed in Section 3, is plotted in Figure 2(a) as a function of the normalised distance d H . Note that, for each  value examined, the spring stiffness related to a single cracked microbeam is also reported by a dashed line.

7.0

1.5

0.08 0.3 



STIFFNESS, k [Nm  rad] (x10 -7 ) 2.0 4.0 6.0 5.0 3.0 1.0

1.4

0.6 0.2 0.4



1.3

0.2

1.2

0.3

1.1

0.4 ... 0.8

RELATIVE DEFLECTION [-]

0.0

0.0 0.6 1.2 1.8 2.4 3.0 3.6 NORMALISED DISTANCE, d/H [-] 1.0

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 NORMALISED DISTANCE, d/H [-]

Fig. 2. (a) Spring stiffness vs the normalised distance between the cracks; (b) relative deflections vs the normalised distance