PSI - Issue 47

Daniela Scorza et al. / Procedia Structural Integrity 47 (2023) 30–36 Scorza et al./ Structural Integrity Procedia 00 (2023) 000–000

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application are: nanoelectronics (to develop efficient microchips and devices), solar panels and hydrogen fuel cells (to increase their efficiency), medicine (for medical implanted devices, like catalysts), and fundamental parts of nanoelectromechanical systems (Chakraverty (2021)). When nanostructures are used to form nanocomposites, the matrix can be: (a) ceramic or metallic, generally used for bridges, boat house, panel of swimming pools, bodies of sport cars, storage tanks, spacecrafts and aircrafts (Naher et al. (2003); Nayak et al. (2019); Ravikumar and Naik (2022)); (b) cementitious, used for example in high strength hydraulic structures (Rahmanzadeh et al. (2018)), structures exposed to blast loading (Nawar et al. (2021)) and, more in general, when concrete with both exceptional mechanical properties and a minimum content of cement are desired (Khalid et al. (2016)); (c) polymeric (Santos et al. (2021)), to build composites with flame-retardant, conductivity, gas-barrier, and optical properties (Rachid et al. (2020)). Although the probability of the presence of defects in nanostructures is quite low, fracture behaviour of nanostructures has been found to differ substantially from that observed in bulk materials (Deng and Barnoush (2018); Iqbal et al. (2012); Jaya et al. (2015); Matoy et al. (2009)). In the present paper, the Mixed-Mode (I+II) static bending behaviour of an edge-cracked cantilever nanobeam is analysed by using the Stress-Driven nonlocal Model (SDM) (Scorza et al. (2021), (2022), (2023)), where the nanobeam is divided into two beam segments connected through a massless elastic rotational spring, located at the cracked transversal section. 2. Formulation Let us consider the edge-cracked cantilever nanobeam shown in Fig. 1 (a), having length L , thickness B , height H , containing a crack of length a at a distance 1 L from the constraint. The crack is assumed to be inclined by an angle θ with respect to the vertical direction. A transversal point load F is applied at the free end. The crack is represented by a massless elastic rotational spring (Fig. 1 (b)) with a stiffness k .

(a)

(b)

y

y

v 2 ( x )

k

v 1 ( x )

θ

O

O

H

x

x

a

B

F

F

L

L

1

1

L

L

Fig. 1. (a) Schematisation of the edge-cracked cantilever nanobeam considered; (b) model with a massless elastic rotational spring representing the cracked transversal section. According to the SDM, the differential governing equations are given by:

( ) (2) 1

M x

1

1

( )

( )

(6) v x

(4) v x

for 0

x L

−

=−

≤ ≤

(1)

1

1

1

2 c

2 c L IE

L

( ) (2) 2

M x

1

1

( )

( )

(6) v x

(4) v x

for

L x L < ≤

−

=−

(2)

2

2

1

2 c

2 c L IE

L