Results and discussions
In this research, the results of strain energy found during the
positioning of micro-crack with respect to the semi-infinite crack,
limit areas of amplification, reduction and sometimes arrest of the
propagation of semi-infinite crack.
- According to Figures 4 (a, b) - 8 (a, b), whatever the positioning of
micro-crack compared to the semi-infinite crack
(\(\forall\alpha\ \epsilon\left[0\ ,\ 2\pi\right]\ \text{and\ }\ \forall\theta\ \epsilon\left[0\ ,\ 2\pi\right]\)),
the values of strain energy are symmetrical with respect to the point
of semi - infinite crack.
- From Figure 4 (a, b), in case of the micro-crack is parallel with
respect to the semi-infinite crack ( = 0 et = π), the strain energy is
zero if this micro-crack is located on the axis y-y ( = 90° and =
270°), and reaches the maximum value when this micro-crack is located
in axis x-x ( = 0° et = 180°).
- On other, the Figure 5 (a, b) represents a micro-crack perpendicular
to the semi-infinite crack ( = π/2 et = 3π/2). The strain energy is
zero if the micro-crack is located on the x-x axis and reaches
the maximum value when this micro-crack is located on the y-yaxis.
- Figures 9-12 represent variation of the strain energy and consequently
the amplification or reduction of the propagation of semi-infinite
crack according to the orientation of micro-crack around itself and
around semi-infinite crack. The Table 1 summarizes the areas of
amplification, reduction and also arrest of propagation of the
semi-infinite crack.
Table 1 area of amplification, reduction and arrest of the propagation
of the semi-infinite crack