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°].