As discussed above, the crack length a_o will grow to a_cr in some life t_f, 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, a_o, 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 2.4). 

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 Curves

Stress History - A Measure of Usage and Location

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 occurs.

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 (t_f) 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 of Geometry

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.

Summary of Effects

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