Fatigue crack propagation threshold values have been determined with t
wo experimental methods, i.e., the constant R method and the constant
K(max) method. Three materials, namely Al7075-T7351 and Ti6Al4V STA in
the LT- and TL-orientations, and a Ti-turbine disk material (IMI 685)
in the CR-orientation, were investigated. The paper is divided into 3
parts. In the first part the test conditions, the experimental result
s and the conclusions drawn from the experimental results are presente
d, namely that the three different functional dependencies of DELTAK(t
h) on R cannot be reconciled with present continuum mechanics concepts
. In the second part, some facts used in conjunction with the da/dN -
DELTAK(eff) methodology are applied to the non-propagation condition D
ELTAK(th). Parameters such as K(op), the threshold DELTAK(T), and a pa
rameter ''K(LL)'' are investigated by numerical modelling of their ind
ividual influence on the DELTAK(th) versus R curves. This modelling wo
rk shows that the individual DELTAK(th) versus R curves are primarily
dependent on the K(op) behavior of the respective material. Further, i
t is shown that the threshold DELTAK(T) is a constant value, independe
nt of any particular cyclic loading condition. In the third part of th
e paper, the DELTAK(eff) concept is applied to the experimental result
s obtained in the first part. Using either experimentally or semi-empi
rically determined K(op) functions and the measured DELTAK(T) values,
the DELTAK(th) versus R curves of the three materials investigated wer
e accurately reconstructed. It follows that the DELTAK(th) versus R cu
rves of the individual materials are the natural consequence of the dr
iving force for fatigue crack propagation, namely DELTAK(eff).