Residual Strength and Fatigue Lifetime of ... - Solid Mechanics

Figure 1.8: Typical fatigue crack growth rate vs. K diagram.
The crack growth rate diagram is divided into an initiation phase (I), a stable crack growth phase
(II) and an unstable crack growth phase (III), as shown in Figure 1.8. The initial phase includes
non-continuous fracture processes with a very low crack growth rate. The stress intensity factor
range in this phase approaches the fatigue crack growth threshold, Kth. The linear intermediate
phase is the most interesting phase due to the linear relation between the logarithm of the crack
propagation rate and the logarithm of the stress intensity factor. This phase covers a large range
of stress intensity factors and crack propagation in this phase is generally more stable than in the
two other phases. The linear phase of the diagram, also named the Paris regime, can be written as
where m is the slope of the linear phase and c is the crack growth rate for K=1.
11
(1.20)
In phase III the crack grows fast and in an unstable manner. The effect of the loading ratio,
R=Fmin/Fmax, on the crack growth rate is shown in Figure 1.8. It is seen for a given crack growth
rate that the K value increases with increased loading ratio. The influence of the loading ratio is
due to the fact that the crack growth is mainly determined by the maximum stress intensity factor
value for each fatigue cycle, Kmax, and its proximity to the fracture toughness of the material, Kc.
In homogeneous materials due to the fact that the crack only experiences opening mode I
loading, the crack growth rate diagram is unique. On the contrary, in an interface due to the
existence of mixed-mode loading at the crack tip and the resistance of other layers toward
kinking of the crack, different crack growth rate relations exist for different mode-mixities.