The breaking stress is proportional to the intensity factor ($K_I$), which is in turn proportional to the square root of the force ($F$), the modulus of Elasticity ($E$), and the break length ($l$):

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$\sigma_x(r,\theta)=\displaystyle\frac{K_i}{\sqrt{2\pi r}}\cos\displaystyle\frac{\theta}{2}\left(1-\sin\displaystyle\frac{\theta}{2}\sin\displaystyle\frac{3\theta}{2}\right)$

$\sigma_y(r,\theta)=\displaystyle\frac{K_i}{\sqrt{2\pi r}}\cos\displaystyle\frac{\theta}{2}\left(1+\sin\displaystyle\frac{\theta}{2}\sin\displaystyle\frac{3\theta}{2}\right)$

$\sigma_y(r_p,0)=\displaystyle\frac{K_i}{\sqrt{2\pi r_p}}$

The fracture propagates because its tip has an extremely small radius, which implies very high tension, as tension is proportional to the inverse of the square root of the radius.

The advancement of the fracture can be halted if, at some point, the radius increases, reducing the tension at its tip. This is achieved, for example, through material porosity or the insertion of inhomogeneities that act as stress concentration points.

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