In damage mechanics it is well-known that localization zones are often precursors of macro-cracks. Correspondingly, in fracture mechanics extended experimental investigations (e.g.
Klemm and Kalthoff, 1984
Bertram and Kalthoff, 2003
) have shown that at the tip of a crack there is no stress singularity, instead, in front of the crack a small process zone can be observed caused by intensive dislocation motion in the case of ductile materials as metals or by intensive microcracking in the case of brittle materials as limestone or granite. At the same time high temperatures develop in the process zone. The size of the process zone depends strongly on the material properties. For glass the process zone is very small, but a very high temperature can be measured there. Another essential feature is the fact that the process zone evolves with high speed, if the crack moves with high speed.