Example 3

The pressure differential acting on the fuselage of an aircraft varies with altitude. At sea level, the pressure differential is 0. At higher altitudes, the pressure differential increases in order to maintain a comfortable atmosphere for passengers and crew. It is conservative to assume that a typical flight consists of a single pressurization cycle. Figure 1 shows a series of flights that each consist of a constant amplitude loading cycle where the pressure differential is assumed to be 0 at takeoff and to reach its maximum value of 15 ksi at maximum altitude.

Figure 1. Simplified loading spectrum

The fuselage has a circular penetration with a 3 inch diameter. For this analysis, the chosen crack geometry is a radial through crack at the edge of the hole subject to an applied tensile stress. Since the fuselage is large compared to the hole diameter, the following stress intensity factor solution is used:

where

and

The fuselage skin is manufactured from 0.050 inch thick aluminum. Since the stress ratio associated with the load spectrum is zero (R = 0), the Paris equation shall be used to describe the crack growth rate:

where the material constants C and n are given in terms of ksi and inches by:

(1) Calculate the number of cycles to failure and determine an acceptable inspection interval, assuming an initial crack length of 0.050 inches and using an apparent fracture toughness value of Kc = 100 ksi-in^1/2 data for 0.050 inch 2024-T3 aluminum sheet.

Solution

The first step in determining the number of cycles to failure is to calculate the critical crack length a_c, which is given by:

Since b is a function of crack length, an iterative procedure is required. To solve for a_c using the ETBX Fatigue Crack Growth module, it is first necessary to define a beta correction table, which defines b values associated with given crack lengths. The b values used in the solution are listed here. A screen shot of the beta correction table is shown in Figure 2 .

A picture of the module input form to calculate a_c is shown in Figure 3. Module output is shown in Figure 4. The critical crack length is calculated to be 27.78 inches.

The number of cycles to failure is calculated by choosing the Paris solution and entering ai = 0.050 inches and af = 27.78 inches. The contants C and n are based on units of ksi and inches, and thus all module inputs are expressed in those units. The stress range Ds = (15 ksi - 0 ksi) = 15 ksi. The stress intensity correction factor, b, is given in the beta correction table. The input form is shown in Figure 5.

The number of cycles to failure is computed to be 23897. This factor can be divided by 2 to obtain an inspection interval of 11948 pressurization cycles. A plot of the calculated crack length versus number of cycles is shown in Figure 6. The crack length at 11948 cycles is greater than 3 inches, which can be easily detected in a visual inspection.

Figure 2. Beta correction factor input

Figure 3. Module input form for calculation of critical crack length

Figure 4. Module output for critical crack length calculation

Figure 5. Module input form for cycles to failure calculation

Figure 6. Crack length calculation