II. 2 Different modes of fracture
The semi-infinite crack can propagates according to three modes of displacement of the lips of the opening [22]. It can also be propagated according to the mixed mode representing the superposition of two or three modes [23]. Figure 2 illustrates the three modes of displacement of the crack lips. In the first mode of fracture (Mode I), the surfaces of the semi-infinite crack tends to step aside perpendicularly with respect to the plane of crack [24]. Mode II is considered, if the surfaces of the semi-infinite crack slide between it parallel to the plane of crack [25]. On the other hand, mode III occurs when the surfaces of semi-infinite crack slide between it perpendicular to those of mode II [26].
Fig.2 three modes of fracture
For each mode of fracture, the stress intensity factor is determined as a function of the component of constraints. When the point of application of constraints tends towards zero (r → 0), the stress intensity factor is found as follows:
\(\left\{\par \begin{matrix}K_{I}=\operatorname{}\sqrt{2\pi r}\sigma_{22}\\ \\ K_{\text{II}}=\operatorname{}\sqrt{2\pi r}\sigma_{21}\\ \\ K_{\text{III}}=\operatorname{}\sqrt{2\pi r}\sigma_{23}\\ \end{matrix}\right.\ \) (4)