PSI - Issue 66

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

411

6

As can be noted, independent of  , two cracks behave as two independent single cracks for values of the normalised distance greater than 1.0 (that is, the stiffness of each spring tends to that of a single spring), whereas the two cracks influence each other for lower values of d H , thus resulting in an increase of the stiffness. Moreover, the relative deflection of the microbeams with 0.2, 0.4  = , and 0.6 is plotted in Figure 2(b) against the normalised distance, d H , for two values of 1 x L  = , (that is, 0.08 and 0.3 ), being such a relative deflection defined as ratio between the deflection of the microbeam with two cracks and that of the same microbeam with a single crack at 1 x x = . In such a Figure, it can be seen that the relative deflection reaches its maximum for 0.6 d H = independent of  and  . Furthermore, it is worth noticing that, for each value of d H and  analysed, the maximum relative deflection is obtained for the microbeam with 0.6  = . Finally, it can be observed that the relative deflection values obtained for 0.08  = are always greater than those computed for 0.3  = independent of both  and d H . 5. Conclusions In the present paper, the formulation of a novel nonlocal analytical model for the simulation of the mechanical behaviour of nanobeams containing multiple edge-cracks has been presented. In particular, the case of a double cracked microbeam has been studied and a parametric analysis has been performed by investigating the influence of the relative crack depth,  , the normalised distance between cracks, d H , and the relative position of the first crack,  . According to the results obtained, the following conclusions can be summarised: (i) independent of  and  , the maximum deflection is achieved for 0.6 d H = ; (ii) for each value of d H and  analysed, the maximum relative deflection is obtained for 0.6  = ; (iii) the relative deflection values obtained for 0.08  = are always greater than those computed for 0.3  = independent of both  and d H . Acknowledgements The work of Andrea Carpinteri, Camilla Ronchei, Sabrina Vantadori and Andrea Zanichelli is supported by Italian Ministry of University and Research (P.R.I.N. National Grant 2020, Project code 2020EBLPLS; University of Parma Research Unit). References Ansys Workbench 2021 R2, https://www.ansys.com/products/ansys-workbench (last access 18-06-2024). Attia, MA, Matbuly, MS, Osman, T, AbdElkhalek, M., 2024. Dynamic analysis of double cracked bi-directional functionally graded nanobeam using the differential quadrature method. Acta Mechanica 235, 1961 – 2012. Deng, Y, Barnoush, A., 2018. Hydrogen embrittlement revealed via novel in situ fracture experiments using notched micro-cantilever specimens. Acta Materialia 142, 236-247. Loya, J, López-Puente, J, Zaera, R, Fernández-Sáez, J., 2009. Free transverse vibrations of cracked nanobeams using a nonlocal elasticity model. Journal of Applied Physics 105, 044309. Qing, H., Tang, Y., 2023. Size-dependent fracture analysis of Centrally-Cracked nanobeam using Stress-Driven Two-Phase Local/Nonlocal integral model with discontinuity and symmetrical conditions . Engineering Fracture Mechanics 282, 109193. Romano, G, Barretta, R., 2017. Nonlocal elasticity in nanobeams: the stress-driven integral model. International Journal Engineering Science 115, 14 27. Scorza, D, Vantadori, S, Luciano, R., 2021. Nanobeams with internal discontinuities: A local/nonlocal approach. Journal of Nanomaterials 11, 2651. Scorza, D, Luciano, R, Vantadori, S., 2022. Fracture behaviour of nanobeams through Two-Phase Local/Nonlocal Stress-Driven model. Composite Structures 280, 114957. Scorza, D, Luciano R, Caporale, A, Vantadori, S., 2023a Nonlocal analysis of edge-cracked nanobeams under Mode I and Mixed-Mode (I + II) static loading. Fatigue & Fracture of Engineering Materials & Structures 46, 1426 – 1442. Scorza, D, Carpinteri, A, Ronchei, C, Zanichelli, A, Luciano, R, Vantadori S., 2023b. A nonlocal elasticity theory to model the static behaviour of edge-cracked nanobeams. Frattura Ed Integrità Strutturale 18, 280 – 291. Vantadori, S., Ronchei, C., Scorza, D., Zanichelli, A, 2024. Mechanical behaviour of multiple edge-cracked nanobeams by taking into account the multiple cracks effects. Fatigue & Fracture of Engineering Materials & Structures, in press . Zhang, P, Qing, H., 2024. Stress-driven nonlocal integral model with discontinuity for size-dependent buckling and bending of cracked nanobeams using Laplace transform. Mechanics Based Design of Structures and Machines, 1 – 23.