As discussed above, the crack length ao will grow to acr
in some life tf, and as
the crack grows the residual strength capability decreases. Experiments have shown that several
parameters affect the crack growth life; the most important of these being the
initial crack size, ao,
the load history, the material properties, and the structural properties. The isolated effect of each parameter on the
crack growth behavior and the residual strength curves will be discussed in
turn using the baseline conditions identified in Figure 2.1.4. The interrelation of these parameters will
be developed in the discussion of life prediction methodology (Section
Figure 2.1.4. Description of Baseline Conditions for
Observed Crack Growth Behavior
Initial Crack Size
– A Measure of Quality
The effect of initial crack size is significant. Given a configuration and loading, the
smaller the initial crack size, the longer the life and the higher the residual
strength capacity at any time. These
observations are displayed in Figure 2.1.5a and b, respectively.
Note that the shape of the crack growth curve (for a given configuration
and loading) remains essentially constant for any given crack growth increment.
Thus, given the crack growth curve for the smaller initial
crack, it is possible to construct the crack growth curve for the baseline
condition. This can be accomplished by
shifting the crack growth curve with a smaller initial crack horizontally to
the left until the curve intersects the vertical axis at the baseline initial
crack size. Also, note that the
residual strength curve for the baseline condition can be constructed from the
curve obtained for the smaller initial crack size.
Figure 2.1.5. Schematic Summary of the Effects of Quality,
Usage, Material, and Geometry on Both the Crack Growth and Residual Strength
Stress History - A Measure of Usage
As an aircraft flies different missions and different
maneuvers, it experiences different loadings.
The magnitude and sequence of aircraft loadings are noted to have a
significant effect on the rate at which cracks grow. The stress history describes the magnitude and sequence of
stresses at one location that results from the sequence of missions or
maneuvers that an aircraft flies. Figure 2.1.5c and d
illustrate the effect that stress history (usage) can have on the crack growth
behavior and residual strength capacity, respectively. While it was not shown, a change in stress
history will normally also change the applied stress level at which fracture
The stress history experienced at each location on the aircraft
will also differ due to changes in bending moment, twisting moment, shear
loading, etc., given a particular crack configuration (e.g., a crack growing
from a fastener hole on a wing). The
loading spectra for a lower surface location is typically more severe than a
corresponding upper surface location; and, therefore, the life for the lower
surface will be significantly shorter than that of the upper surface all other
conditions being equal.
Material Properties - A measure of
Material Resistant to Cracking
Experimentally, it has been shown that for the same loading
condition (i.e., the same number and amplitude of stress cycles) cracks will
grow faster in certain alloys than in others.
The crack growth rate (Da/DN)
can be derived experimentally for each material. Given the same load and geometric conditions, the alloy having
the slower growth rate characteristics (i.e. 2024-T3) will have a longer life (tf) as shown in Figure 2.1.5e.
This material also has some inherent resistance to fracture. The higher this inherent resistance, the
higher the residual strength capacity for any crack length. This effect is described in Figure 2.1.5f.
If the cracks are so small that the fracture process is
controlled by gross yielding, then the residual strength curve is controlled by
a net section failure criterion rather than a fracture criterion. In this case, the material with the highest
yield strength would have the highest residual strength in the region of the
curve controlled by the behavior of the small cracks.
Structural Properties - A Measure
The most complex of the parameters affecting crack growth
behavior are the structural properties.
The structural properties involve such things as crack configuration,
load transfer through fasteners, fastener hole size, part thickness, etc. A substantial amount of experimental work
has been performed to characterize the geometrical effects on life. The effect of a change of hole radius on the
crack growth behavior and on the residual strength capacity is shown in Figure 2.1.5g and h. The structure with the smaller hole, and
thus the smaller stress concentration is noted to have the longer life and
higher residual strength.
As discussed above, there are four major parameters that affect
the crack growth life and residual strength capacity of structures. These parameters are in the realm of quality
(initial crack size), usage (loading history), material (material properties),
and geometry (structural properties). Figure 2.1.6 has been prepared to summarize the
parameters’ effect on life and to illustrate various presentation schemes that
might be employed to compare effects.
Figure 2.1.6. Summary of Schemes Which Illustrate the Sensitivity of Life to
Various Structural Parameters