Page 369 - Biaxial Multiaxial Fatigue and Fracture

Three-Dimensional Crack Growth: Numerical Evaluations and Experimental Tests 353

is denoted by Smin. Locating the minimum of S(e) with respect to 8 is carried out numerically
using the bisection method by solving:

The equivalent stress intensity factor, Keq, can be calculated from the minimum strain density
factor as:

The incremental size. Determination of the incremental size posses two problems: the first is the
determination of the amount of each increment in terms of a reference size, the second is the
relationship between the maximum incremental size and other incremental sizes along the crack
front.
It is stated in the hypothesis (3) of the strain energy density criterion that the length ro of the
initial crack extension is assumed to be proportional to Smin such that Sm,,,lro remains constant
along the crack front. Since the strain energy factor Smin is proportional to the square power of
the equivalent stress intensity factor Kes, the incremental size at the crack front point under
consideration is given by:

where mar{K,,} is the maximum SIF equivalent evaluated at a set of discrete point along the
front, and Aa- is the incremental size at the point corresponding to the mar{Keq} which is
chosen beforehand as being the maximum distance from the crack front to the opposite side of
the element containing the crack front as in Fig. 13 . The above expression is used for standard
crack growth.
Crack increment

Crack front

Fig. 13. Maximum incremental distance.