In this study, interaction between a main crack and a surrounding layer of cracks is considered. Stress Intensity Factors during these interactions are obtained using Dimensional analysis (DA) based on the J-integral method. Amplification and shielding effects on the resulting stress field are shown. Besides, orientations as well as positions of cracks with respect to the main crack are considered as crucial parameters to quantify these effects. A series of illustrated examples is given and obtained results are compared with those of other researchers.
ChudnovskyAKachanovM. Interaction of a crack with a field of microcracks. Int J Eng Sci1983; 21: 1009–1018.
2.
ChudnovskyADolgopolskyAKachanovM. Elastic interaction of a crack with a microcrack array—I. Formulation of the problem and general form of the solution. Int J Solids Struct1987; 23: 1–10.
3.
ChudnovskyAWuS. Effect of crack-microcracks interaction on energy release rates. Int J Fract1990; 44: 43–56.
4.
KachanovMMontagutELELauresJP. Mechanics of crack microcrack interactions. Mech Mater1990; 10: 59–71.
5.
KachanovM. Elastic solids with many cracks: a simple method of analysis. Int J Solids Struct1987; 23: 23–43.
6.
KachanovM. Elastic solids with many cracks and related problems. Adv Appl Mech1993; 30: 259–445.
7.
YokoboriTYoshidaMKurodaH, et al.Non-linear interaction between main crack and near-by slip band. Eng Fract Mech1975; 7: 377–388.
AourBRahmaniONait-AbdelazizB. A coupled FEM/BEM approach and its accuracy for solving crack problems in fracture mechanics. Int J Solids2007; 44: 2523–2539.
19.
AngWT. A boundary integral solution for the problem of multiple interacting cracks in an elastic material. Int J Fract1986; 31: 259–270.
20.
SihGCLiebowitzH. Mathematical fundamentals of fracture. New York: Academic Press, 1968.
21.
BuckinghamE. On physically similar systems; illustrations of the use of dimensional equations. Phys Rev1914; 4: 345–376.
22.
RiceJ. A path-independent integral and the approximate analyses of strain concentration by notches and cracks. J Appl Mech1968; 35: 379–386.
23.
BakkerA. An analysis of the numerical path dependence of the J-integral. Int J Pressure Vessels Piping1983; 14: 153–179.
24.
Abaqus/Standard, User’s manual, version 6.10 by Hibbit, Karlsson and Sorensen, Pawtucket, Rhode Island, 2010.
25.
IrwinGR. Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech1957; 24: 361–364.
26.
Hamli BenzaharHChabaatM. Cracking in brittle material at presence of a dislocation. Adv Mater Res2014; 919-921: 2043–2047.
27.
TadaHParisPCIrwinGR. The stress analysis of cracks handbook. 3rd ed. New York, USA: ASME Press, 2000.