Issue 69

S. Cao et alii, Frattura ed Integrità Strutturale, 69 (2024) 1-17; DOI: 10.3221/IGF-ESIS.69.01

International Journal of Fracture, 139(2), pp. 169-196. DOI: 10.1007/s10704-006-7135-9. [50] Ren, W. and Xu, J. (2017). Fractal characteristics of concrete fragmentation under impact loading. Journal of Materials in Civil Engineering, 29(4), 04016244. DOI:10.1061/(ASCE)MT.1943-5533.0001764. [51] Feng, P., Liu, B., Tang, R., Wei, M., Zhang, Y. and Li, H. (2022). Dynamic fracture behaviors and fragment characteristics of pre-compressed flawed sandstones. International Journal of Mechanical Sciences, 220, 107162. DOI: 10.1016/j.ijmecsci.2022.107162. [52] Duggan, T. V., Byrne, J., Duggan, T. V. and Byrne, J. (1977). Fracture Mechanics and Fatigue Crack Propagation. Fatigue as a Design Criterion, pp. 112-147. DOI: 10.1007/978-1-349-03222-8_6.

N OMENCLATURE E

: Young’s modulus (MPa); : Half-crack center angle (º); : Cylinder radius (mm); : Shear modulus (MPa);

α R G

κ

: Kolosov constant; : Poisson’s ratio;

ν

( x , y , z ) ( i , j , k )

: Global basis;

: Local basis defined by crack; : x direction displacement vector (mm); : y direction displacement vector (mm); : z direction displacement vector (mm); : i direction displacement vector (mm); : j direction displacement vector (mm); : k direction displacement vector (mm);

U V W

u v

w

ū v̄

: i -direction displacement in the equivalent system (mm); : j -direction displacement in the equivalent system (mm);

A n B n

: Coefficients of the expansion; : Coefficients of the expansion; : Half crack length, a = αRπ/180 º (mm);

a

L h

: Cylinder length (mm); : Cylinder thickness (mm);

: Stress intensity factor of mode I crack (MPa ‧ mm 0.5 ); : Stress intensity factor of mode II crack (MPa ‧ mm 0.5 );

K I

K II

F

: Dimensionless stress intensity factor;

D N T N E N R S

: Number of data points ;

: Last term in the Williams expansion;

: Excess of the number of data points over the number of terms in Williams expansion;

: Data selecting ring radius (mm); : Rigid body rotation to the crack tip

φ c

17