The basic hypothesis of the fracture mechanics approach to fatigue is that crack growth rate data can be described as a function of a stress-intensity factor (K) parameter associated with the fatigue loading.  For constant amplitude loading, the parameter is the stress-intensity factor range (DK); and for steady-state variable amplitude loading histories, the parameter might be a root mean square value of the stress-intensity factor (K_rms).  Once the basic hypothesis has been verified, crack growth data can be generated using relatively simple specimens; such data are independent of stress level, crack length, and structural test geometry, and thus can be related to the behavior of complicated structural geometries through the use of the stress-intensity factor.  The transferability of the crack growth rate data using the stress-intensity factor has provided a semi-inverse procedure for estimating the stress-intensity factor for complicated crack problems.

The semi-inverse procedure depends on the availability of two pieces of information: 

(1)·                       crack growth rate data for the structure for which the stress-intensity factor will be estimated, and

(2)·                       crack growth rate versus stress-intensity factor type data collected for the material subjected to the same type of loading history to which the structural crack has been exposed. 

The semi-inverse procedure relies on using the structure’s crack growth rate (information item 1) to interpolate the material’s crack growth rate/stress-intensity factor relationship (information item 2) to estimate the structure’s stress-intensity factor.  Figure 7.4.4 provides a schematic illustrating how the two information items are used to obtain the structure’s stress-intensity factor relationship.

Figure 7.4.4.  Semi-Inverse Fatigue Crack Growth Rate Determination of Stress-Intensity Factors

Grandt and coworkers [Grandt & Sinclair, 1972; Grandt & Hinnerichs, 1974] have applied the semi-inverse procedure to a number of problems of Air Force interest.  Figure 7.4.5 describes the results for a radially cracked cold-worked hole that was subjected to two different levels of remote loading.  It can be seen from the figure that the stress-intensity factor values obtained from the semi-inverse procedure (the data points) describe a relatively smooth function and closely approximate the analytical results marked linear superposition.  Due to the cold-working operation, the stress-intensity factor is also seen to be substantially below that associated with the open hole configuration (curve marked Bowie), which well demonstrates the benefit of cold working.

Figure 7.4.5.  Stress-Intensity Calibration for a 0.26 Inch Diameter Hole Cold-worked to Achieve a 0.012 Inch Diametrical Interference in 7075-T6 Aluminum Alloy (0.25 Inch Thick)