Conclusion
In this research work, the main objective is to determine the effect of
micro-crack on the semi-infinite crack by determining the strain energy
and limiting the zones of amplification, reduction and sometimes arrest
of propagation of semi-infinite crack. According to the Figures 4-16,
whatever the positioning of the micro-crack compared to semi-infinite
crack, the strain energy values are symmetrical with respect to the
semi-infinite crack tip. The results of strain energy summarized in
Tables 1- 4, show that the zones of amplification, reduction and arrest
of propagation of semi-infinite crack are symmetrical compared to the
point of semi-infinite crack tip. By varying the orientation angles (
and α), the Table 3 summarizes all zones of amplification and reduction
and presents a symmetry in the effect on the propagation of
semi-infinite crack
(\(\text{α\ ϵ}\left[0\ ,\ \pi/2\right]\) symmetrical with\(\text{α\ ϵ}\left[\pi\ ,\ 3\pi/2\right]\) andα ϵ]π/2, π] symmetrical with α ϵ]3π/2,
2π]). According to Table 4, the presence of micro-crack in a
perpendicular position to the semi-infinite crack (that is to say ; α =
π/2 and α = 3π/2), can also arrest the propagation of crack in the zones
; \(\text{θ\ ϵ}\left[0\ ,\ 11\right]\ \), [166° -
192°] and [349° – 360°].