Modes of fracture

Definition

Let a body in $\R^3$ contain a crack whose faces are locally planar near a point $P$ of the crack front. Choose an orthonormal frame $e_1, e_2, e_3$ at $P$ as follows. The vector $e_1$ lies in the crack plane, is perpendicular to the front and points ahead of the crack. The vector $e_2$ is normal to the crack plane, and $e_3$ is tangent to the front. Let $[u] = u^+ - u^-$ be the jump of the displacement between the upper face ($x_2 > 0$) and the lower face ($x_2 < 0$) near $P$. The crack-tip deformation is in

1. mode I (opening) when $[u]$ is parallel to $e_2$;
2. mode II (in-plane shear, sliding) when $[u]$ is parallel to $e_1$;
3. mode III (out-of-plane shear, tearing) when $[u]$ is parallel to $e_3$.

A general deformation is a mixed mode, a superposition of the three.