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3. VOLUME (THREE-DIMENSIONAL) CRACKS

Next important deviation on theory side is associated with the crack geometry.

Analytical solutions of fracture mechanics concentrate on 2-dimesional problems and two

limit cases of plane stress and plane strain conditions. Although the real fracture

mechanics problems surround crack areas which are curved with stress field in three

dimensions, simply only possible analysis and corresponding solutions are limited to the

2-dimensional idealisation. Solutions based on this idealisation enable further treatment

by fracture mechanics. Here, it should be mentioned that this 2-dimesional approach is

not only limited to the analytical solutions, but is also completely transmitted to the

experimental evaluation of the material parameters. Moreover, the material properties, as

, and crack opening displacement (COD) are evaluated on through crack speci-

mens. Accordingly, one of the basic problems in fracture mechanics is, how on the basis

of knowledge, acquired with the help of 2-dimesional specimens with through cracks,

asses the behaviour of real 3-dimesional structures, e.g. with the surface crack (Fig. 5).

Figure 5: Stress distribution at surface crack tip

Practical experiences show that initiation and growth of fracture in the engineering

structures can be mainly attributed to the surface cracks. Therefore, the surface cracks in

structure are of great practical importance. Especially in thin wall structures with crack

the plastic collapse of the ligament is the most frequent cause for the failure. Except this,

as the through crack causes leakage, the damaged components can be timely excluded

from operation or unloaded, such cracks are in practical application less dangerous. For

that, residual strength of the surface crack ligament and the evaluation of crack critical

length for wall penetration are the most important criteria for the guarantee of “leak-

before-break (LBB)”. Therefore, study of the formula relating to the maximal loading of

the surface crack ligament is an important task of the fracture assessment, especially for

the case of pressurised structures.

It is important to note, that the surface cracks are of small dimensions, always smaller

than wall thickness and are more dangerous, especially when the bursting of vessel may