If the stress state of the crack and the displacement direction of the crack surface are taken as the classification criteria, the cracks can be divided into three types, as shown in Figure 1.

Mode I crack is subjected to tensile stress in Y-axis direction, which will make the crack open up and down, also known as open crack; mode II crack is subjected to stress in x-axis direction, which will make the crack slip back and forth, also known as slip crack; mode III crack is subjected to stress in z-axis direction, which will make the crack tear left and right, also known as tear crack. Among the three kinds of cracks, mode I open crack is the most harmful, because it is the most likely to cause low stress brittle fracture.

The displacement of three-dimensional crack front is shown in Figure 2. Set the first normal of crack front as N and the second normal as B. the tangent direction can be determined by the vector product of B and n. When θ = – π, the expression of stress intensity factor described by the displacement of crack front is as follows:

Where, μ C1, μ C2 and μ C3 are the displacements in B, N and τ directions of the crack front respectively.