Issue 67

D. Scorza et alii, Frattura ed Integrità Strutturale, 67 (2024) 280-291; DOI: 10.3221/IGF-ESIS.67.20

Influence of  on transverse displacement Let us consider a crack at the centre of the nanobeam, that is,  =L 1 /L= 0.5. Three values of  , that is, 0.3, 0.5 and 0.6, are examined. The results in terms of transverse displacement are reported in Fig. 3(a) for  = 22°.5 and in Fig. 3(b) for  = 45°. Moreover, the results determined by applying the local beam theory (that is,  = 0.0) are also reported. It can be observed that the transverse displacements computed according to the nonlocal theory are smaller than those obtained from the local one, independent of crack depth and crack orientation. More precisely, for  =22°.5 (Fig. 3(a)), the nonlocal values of v 2 /H in correspondence of x/L= 1.0 are about 14.30%, 13.44% and 12.63% smaller than the local ones, for  equal to 0.3, 0.5 and 0.6, respectively. For  =45°(Fig. 3(b)), the displacement decreases become equal to about 14.46%, 14.01% and 13.64% for  equal to, respectively, 0.3, 0.5 and 0.6. Moreover, for  =22°.5 (Fig. 3(a)), the nonlocal values of v 2 /H in correspondence of x/L= 1.0 increase of about 7.47% and 15,40% for  increasing from 0.3 to 0.5 and from 0.3 to 0.6, respectively, whereas such increments are equal to about 3.74% and 6.97% for  =45° (Fig. 3(b)).

5

0.25

(a)

(b)

0.3  Loc. Nonl.

0.3  Loc. Nonl.

0.5 0.6

0.5 0.6

2

0.20

5

0.15

v 1 / H or v 2 / H

1

0.10

5

0.05

NORMALISED DISPLACEMENT,

0.0 0.2 0.4 0.6 0.8 1.0 NORMALISED ABSCISSA, x/L 0.00

0.0 0.2 0.4 0.6 0.8 1.0 NORMALISED ABSCISSA, x/L 0

Figure 3: Normalised transverse displacement along the nanobeam axis for  = 0.5 and  equal to: (a) 22°.5 and (b) 45°, for different values of the relative crack depth  and according to both the nonlocal and the local beam theory. Finally, by comparing Fig. 3(a) with Fig. 3(b), the nonlocal values of v 2 /H in correspondence of x/L= 1.0 decrease of about 1.26%, 4.69% and 8.47% for  equal to 0.3, 0.5 and 0.6, respectively, when the value of  is made to vary from 22°.5 to 45°. Influence of  on transverse displacement Let us consider a crack characterized by a relative crack depth  = 0.5. Three values of  , that is, 0.25, 0.50 and 0.75, are examined. The results in terms of transverse displacement are reported in Fig. 4(a) for  =22°.5 and in Fig. 4(b) for  =45°. Moreover, the results for  = 0.0 are also reported. It can be observed that the transverse displacements computed according to the nonlocal theory are smaller than those obtained from the local one, independent of the crack location and crack orientation. More precisely, for  =22°.5 (Fig. 4(a)), the nonlocal values of v 2 /H in correspondence of x/L= 1.0 are about 12.14%, 13.44% and 14.36% smaller than the local ones, for  equal to 0.25, 0.50 and 0.75, respectively. For  =45°(Fig. 4(b)), such displacement decreases become equal to about 13.23%, 14.01% and 14.52% for  equal to 0.25, 0.50 and 0.75, respectively.

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