Page 469 - Biaxial Multiaxial Fatigue and Fracture

Microcmck Propagation Under Non-Proportional MuItiariaI Alternating Loading 453

approach to ascertain the crack growth rate out of the striation wide will be developed. Till this
is finished the fractographical investigations could deliver only qualitative statements.
The results obtained so far fit very well to various crack propagation models, e.g. the model
by McDowell and Bennet [8]. According to this model, the process of crack propagation is
divided into three regimes (cf. Fig. 12). In the first regime, the regime of microcracks, the
crack growth is highly non-linear. The process in this regime includes successive
acceleration/deceleration, as barriers are traversed depending on the microstructure. The mean
value of the crack growth rate is considered to be dependent on the loading level, but nearly
independent of the crack length. The higher the loading level, the weaker is the dependence on
the crack length (cf. Fig. 12). For the mathematical description an average rate is calculated. In
the following regime, the regime of short cracks, which begins at a crack length of several
grain diameters (kd with d as mean grain diameter and k as an integer-valued material
parameter), the dependence of the crack growth rate moves more and more towards the crack
length. This indicates a diminishing role of the microstructure with increasing crack length.
When the crack reaches a sufficient length, it reaches the regime of long cracks (third regime)
and further propagation can be described by linear-elastic fracture mechanics (LEFM).

microcrac ks short cracks long cracks

Fig. 12. Schematic representation of a typical crack growth behaviour depending on the
loading level.

On a higher load level, the crack growth rate of course is higher than that of a lower load level.
However it is even more important that in the regime of micro cracks the dependence on the
microstructure is less pronounced. This is evident from the fact that on a higher load level more
energy is available, which can be used to ovemde microstructural barriers. As a consequence,