II. Brittle failure
The brittle failure occurs suddenly by cleavage generated during separation of the atoms forming the material [12]. In brittle metals, it is experimentally observed that failure only occurs if the material plasticizes, which shows that microcracks or defects are created during the plasticization of the material [13]. The sudden failure strength of a brittle material is determined by the critical value of the stress intensity factor in mode I ( KI). It varies according to the chemical composition and the property of the cracked material [14]. The stress intensity factor in mode I, can be linearly calculated by the stresses which tend towards infinity at the end of semi-infinite crack [15]. It makes to determine the size of microcrack and effective in stopping of the cracking and consequently controlling the necessary and sufficient qualities [16]. The KI represents a physical characteristic of the material determined experimentally under conditions [17]. In linear elasticity, the distribution of the plane stresses in the vicinity of the semi-infinite crack is expressed in polar coordinates [18] :
\(\sigma_{\text{ij}\left(r,\ \theta\right)}=\frac{K_{\text{ij}\left(r\right)}}{\sqrt{2\pi r}}f_{\text{ij}\left(\theta\right)}\)(1)