Fully Open Cracks that are Stationary or Growing

If the left-hand side of (4.1.9) is zero at a given value of x, then t) is continuous over the x-axis at that point. This will be true if A (x, t ) is zero for all in particular off the crack face. 

The region of the x-axis off the crack face will sometimes be denoted by the complement of F(t) on the. x-axis. 

Some standard terminology will occasionally be used. If the stresses on the crack face are purely normal, the crack is said to be subject to opening mode or Mode I displacement, or it is simply referred to as a Mode I crack. If the stresses are purely shear, the crack is subject to sliding mode or Mode II displacement, while if the stresses are perpendicular to the plane, we have tearing mode or Mode III displacement [Irwin (1960), Sih and Liebowitz (1968), Sneddon and Lowengrub (1969) for example]. In this Chapter, we consider mainly Mode I displacement and, to a certain extent. Mode II. Tearing mode cracks, which are typically the simplest to analyze, are considered briefly in Chap. 7, in the context of inertial problems. 

2 Fully Open Cracks that are Stationary or Growing 

In this case, C(t) is empty and F(t) is expanding or stationary. This is an example of the type of problem covered by the Extended Correspondence Principle discussed in Sect. 2.6 so that we expect to obtain solutions closely related to the corresponding elastic solutions. From (4.1.6b) we have that 

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Fully Open Cracks that are Stationary or Growing 145 Equations (4.2.11, 12) imply that... 

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