Presented to the Israel Annual Conference on Aerospace Sciences, 2009 RISK-ANALYSIS A SUPPLEMENT TO DAMAGE-TOLERANCE ANALYSIS

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1 RISK-ANALYSIS A SUPPLEMENT TO DAMAGE-TOLERANCE ANALYSIS Abraham Brot Engineering Division Israel Aerospace Industries Ben-Gurion Airport, Israel abrot@iai.co.il ABSTRACT Risk-analysis, based on probabilistic considerations, has been developed to determine the risk of a fatigue failure as a function of inspection methods and intervals. If the risk is found to be very small, this may allow the delaying of certain inspections. Risk-analysis can also be used to evaluate the effect of aging on the increased risk of operation. The use of risk-analysis applies a "systems type approach" to fatigue life substantiation. This paper compares two very different risk-analysis computer programs to evaluate the risk of increasing inspection intervals for a typical aircraft structure. It was concluded that riskanalysis can often be used to obtain more favorable inspection thresholds and intervals compared to classical damage-tolerance analysis, without subjecting the structure to excessive risk. Risk-analysis can also be used to evaluate the effect of service life extension on the increased probability of failure. INTRODUCTION Damage-tolerance has been used to substantiate civilian and military aircraft structures for fatigue life for more than 30 years. For the most part, the damage-tolerance approach has proved to be successful in avoiding fatigue failures. At times, aircraft must be inspected earlier, or more often than planned, due to fatigue test findings or changes to the operating mission-mix or loading spectrum. This can be very expensive to the customer, and can have a severe effect on aircraft availability. Risk-analysis, based on probabilistic considerations, can be used to determine the risk of a fatigue failure (at a specific location) as a function of inspection methods and intervals. If the risk is found to be very small, this may allow the delaying of certain inspections. Riskanalysis can also be used to evaluate the effect of aging on the increased risk of operation. The use of risk-analysis applies a "systems type approach" to fatigue life substantiation. Although risk-analysis has been primarily used for military aircraft, the FAA encourages the use of risk-analysis for certain specific instances on civilian aircraft [1]. This paper compares two very different risk-analysis computer programs to evaluate the risk of increasing inspection intervals for a typical aircraft structure. 1

2 CLASSICAL DAMAGE-TOLERANCE ANALYSIS Figure 1 describes the geometry and spectrum loading for an aluminum lug. A classical damage-tolerance analysis (DTA) was performed for the lug using NASGRO v.5 software, and the results are shown in Figure 2. The classical DTA is based on the assumption that the lug has an initial crack of 0.050", and a critical crack length, under a 30 ksi limit load, of 0.119". Inspections are specified to be performed using the "high-frequency eddy-current" (HFEC) method, which has a 90% probability of detection for a crack size of 0.105". The classical DTA method arrives at an initial (threshold) inspection at 3800 flights and subsequent inspection intervals of 500 flights. This inspection schedule will be extremely difficult and costly for the operator. The question is raised whether the inspection intervals can be increased without significantly putting the aircraft at risk? Figure 3 examines the sources of conservatism that are built-in the classical DTA, and identifies three very conservative assumptions: 1. Studies have shown that the probability that an initial crack is equal or greater than 0.050" is less than one in a million. 2. The HFEC method begins to detect cracks much smaller than 0.105" with a 20% probability of detection (POD) for a crack of 0.053" and a 50% POD for a crack of 0.070". 3. The probability that a limit load stress of 30 ksi will occur when the crack size is only 0.119" is highly unlikely. Risk-analysis software can be used to evaluate these (and other) sources of conservatism and calculate the resulting probabilities of failure if these sources of conservatism are relaxed. Gross Stress - (ksi) Exceedances per 20,000 Flights Lug Loading Spectrum P E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 Exceedances Gross Stress Material: 7050-T7351; Required Residual Strength: 30 ksi D = 0.25 ; W = 0.75 ; t = 0.25 Figure 1: Test Case for Analysis 2

3 Crack Size (in) Initial Crack (0.050 ) Crack Growth, Initial to Critical (NASGRO Run) Detectable Crack Size (90% POD) using HFEC (0.105 ) Flights 1000 Flights Critical Crack Size under limit load of 30 ksi (0.119 ) Figure 2: Classical Damage-Tolerance Analysis (Resulting in an initial inspection at 3800 flights and subsequent inspections every 500 flights) Crack Size (in) Probability that initial crack is less than 1 in a million 20% POD Crack Growth, Initial to Critical (NASGRO Run) Detectable Crack Size (90% POD) using HFEC (0.105 ) 50% POD Flights 1000 Flights Critical Crack Size under limit load of 30 ksi (0.119 ) Limit load is unlikely to occur Figure 3: Sources of Conservatism in the Classical Damage-Tolerance Analysis PERFORMING RISK-ANALYSIS USING PROF SOFTWARE PRobability Of Fracture (PROF) risk-analysis software was developed by the University of Dayton Research Institute (UDRI). PROF is based solely on crack growth and it establishes the probabilities of failure mathematically. PROF was specifically developed for the use of the USAF, but is commercially available for other users. (Version 3 was released in December 2005.) The basic principle of the methodology used in PROF is shown schematically in Figure 4. An initial crack size statistical distribution is assumed by the user to be representative of the fleet for a specific location on the aircraft. These cracks grow under spectrum loading, as is shown schematically in Figure 4. During periodic inspections, some of the cracks are detected and the parts are repaired. A small portion of the cracks may reach their critical size, and may fail if a sufficiently high overload occurs. 3

4 Figure 4: Basic Methodology used in PROF Several studies have been performed to establish the equivalent initial flaw size (EIFS) distribution for typically manufactured aircraft structures [2], [3]. Some of the results of these studies are shown in Figures 5 7. Equivalent initial flaw sizes were determined by the USAF and others using fractographic analysis of aircraft fatigue failures and crack growth calculations. These are called equivalent flaws or cracks, because they are so small that the rules of linear elastic fracture mechanics do not apply. Figure 5: Distribution of Initial Flaw Sizes for A-7D and F-4C/D Aircraft [2] Figure 6: Distribution of Initial Flaw Size for Reamed Countersunk Fastener Holes [2] 4

5 Figure 7: Equivalent Initial Flaw Sizes Found by NAVAIR on P-3C Fleet [3] Figure 8 shows a family of two-parameter Weibull distributions that can be used to characterize the EIFS distributions. The AB-1 distribution was recommended as a conservative yet realistic standard (having a probability of 1 in a million for exceeding a initial crack.) [4]. Distributions AB-2 or AB-3 are more compatible with the USAF s A-7D and F-4 C/D data, as is shown in Figure 8. This present study used all five EIFS distributions shown in Figure 8. Table 1 contains the Weibull parameters that define these distributions. Table 1: Weibull Parameters Defining the Distributions Distribution Alpha Beta (in) AB AB AB AB AB Failure criteria were established for the risk-analysis by extending the loading spectrum to a level that can be expected to be exceeded once every ten lifetimes, as is shown in Figure 9. A Gumbel extreme-value distribution was used to extrapolate the spectrum data, as shown in Figure 9. The probability of crack detection (POD) distribution used in the risk-analysis for the highfrequency eddy-current (HFEC) inspection method is based on tests sponsored by the FAA [5]. This distribution is shown in Figure 10. 5

6 Exceedance Probability 1.E+00 50% 1.E-01 Exceedance Probability 1.E-02 1.E-03 1.E-04 1.E-05 AB-5 A-7D Data F-4C/D Data AB-1 Initial Cracks AB-2 Initial Cracks AB-3 Initial Cracks AB-4 Initial Cracks AB-5 Initial Cracks AB-4 AB-3 AB-2 AB-1 1.E Crack Size - in Figure 8: Initial Crack Exceedance Distributions Exceedances per 20,000 Flights Extrapolated Data using Gumbel Extreme Value Distribution Gross Stress - (ksi) Loading Spectrum E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 Exceedances Figure 9: Loading Spectrum Extended Using a Gumbel Extreme-Value Distribution 6

7 Probability of Crack Detection POD Crack size (inches) Figure 10: Probability of Detection Distribution for HFEC Inspections [5] The crack growth characteristics were calculated by NASGRO v.5 software, starting from a " equivalent crack, and including estimated retardation effects. Crack growth, under the lug spectrum shown in Figure 1, will require about 180,000 flights to grow from " to 0.173", with about 166,000 flights required to grow up to a crack size of 0.010". The principal output of PROF is the hazard-rate (Figure 11) and the probability of failure since the previous inspection (Figure 12). The hazard-rate is defined as the probability of failure during next flight. The USAF has established hazard-rate criteria as 10-7 being a totally acceptable hazard rate. Hazard rate peaks ranging from 10-7 to 10-5 can be acceptable if their occurrences are limited, while hazard-rates that exceed 10-5 are never acceptable [6]. The hazard-rate function, shown in Figure 11 exhibits a saw-tooth behavior. This is due to the periodically scheduled inspections for cracks. At each inspection, the probability of crack detection is governed by the distribution shown in Figure 10. As a result of the detection of the largest cracks (and their repair), the hazard-rate drops significantly and then begins to increase again as the aircraft accumulates additional flights. At the next inspection, the process repeats. The probability of failure since the previous inspection, shown in Figure 12, behaves in a similar manner, with the same saw-tooth behavior. The USAF has not defined criteria for acceptable probabilities of failure. Another important parameter, the overall probability of failure (from time zero) is not displayed by PROF, but it can be calculated from the individual probabilities of failure that are displayed in the output. This function increases monotonically, as is shown in Table 3. 7

8 Figure 11: Hazard-Rate as a Function of Service Life (PROF Output) Figure 12: Probability of Failure as a Function of Service Life (PROF Output) 8

9 Table 2: PROF Results for Lug Analysis Based on a 30,000 Flight Service Life Initial Crack Distribution Peak Hazard Rate * Overall Probability of Failure * AB E % AB E % AB E % AB E % * - Based on an inspection threshold of 10,000 flights and an inspection interval of 2,000 flights. Spectrum overloads, per Gumbel Distribution are included. Table 3: PROF Results for Lug Analysis Based on AB-2 Initial Crack Distribution Service Life (Flights) Peak Hazard Rate * Overall Probability of Failure * 15, E % 20, E % 25, E % 30, E % * - Based on the AB-2 initial crack distribution, an inspection threshold of 10,000 flights and an inspection interval of 2,000 flights. Spectrum overloads, per Gumbel Distribution, are included. The results of the risk-analysis, performed for the lug test case, are shown in Tables 2 and 3. Table 2 shows the peak hazard-rate and the overall probability of failure of the lug, for four equivalent initial crack distributions, AB-1 to AB-4, for a 30,000 flight service life. (AB-5 was found to be extremely mild, so the results are not shown.) All the PROF analyses were based on an initial HFEC inspection at 10,000 flights and subsequent intervals of 2,000 flights. All four distributions meet the USAF hazard-rate criterion (peak hazard rate less than 10-5 ), but the overall probability of failure seems excessive (1.21%) for distribution AB-1. Table 3 shows the peak hazard-rate and overall probability of failure for distribution AB-2, as a function of service life. As expected, both the peak hazard-rate and overall probability of failure increase with increased service life. The results shown in Table 3 indicate that very reasonable results can be obtained by limiting the service life of the lug to 20,000 flights. The PROF risk-analysis results show that inspection thresholds and intervals (10,000 and 2,000 flights respectively) can be significantly increased above those determined through classical damage-tolerance analysis (3,800 and 500 flights respectively), without exposing the structure to excessive risk. Risk-analysis also provides a tool to evaluate the effect of service life on the risk of failure, a parameter that is totally absent in the classical damage-tolerance analysis. It should be noted that the initial crack distribution is not accurately known for any specific application and can only be estimated. Therefore, risk-analysis can be a valuable tool when it 9

10 is used in a comparative study. When one needs to perform an absolute study, it is best to use a family of initial crack distributions, such as those shown in Figure 8, and try to draw conclusions from the results of all of the distributions. This procedure was followed for the results shown in Table 2. PERFORMING RISK-ANALYSIS USING INSIM SOFTWARE INspection SIMulation (INSIM) risk-analysis software was developed by IAI. It uses probabilistic (Monte-Carlo) simulations to establish the probability of failure for a specific location. INSIM considers the crack-initiation life in addition to the crack growth life. (Version 2.4 of INSIM was released in August 1995.) A detailed description of INSIM can be found in [7] and [8]. Figure 13 contains a typical output from an INSIM run. In order to perform the INSIM run for this application, it was necessary to calculate the mean crack-initiation life of the lug. The stress-concentration factor (based on the net-stress) was calculated to be 4.61, and the mean crack-initiation life was calculated, using a strain-life analysis, as 46,000 flights, based on the spectrum shown in Figure 1. Two primary differences exist between PROF and INSIM, making a comparison of results difficult: PROF considers crack growth life only while INSIM considers both crack-initiation and crack growth effects, with a transition at a crack size of 0.010". PROF calculates hazard-rate and probability of failure as a function of service life while INSIM calculates only the overall probability of failure. Figure 13: INSIM Run Output Containing the Results of One Million Simulations 10

11 In order to reconcile these differences, the following operations were performed: Each initial crack distribution has a median crack size (50% of cracks exceed this value), as is shown in Table 4 and Figure 8. Using the crack growth curve from the lug analysis, the number of flights required for a median crack to grow to 0.010" was calculated. This value is also shown in Table 4, and is assumed to be comparable to the crack-initiation life used in INSIM. The comparison between PROF and INSIM results were based on the overall probability of failure which is output by INSIM and can be calculated from the PROF results. Table 4: Median Crack Size and Crack Growth Life for Each Distribution Initial Crack Distribution Median Crack Size (inches) Crack Growth Life (Median Crack to 0.01") AB ,000 flights AB ,000 flights AB ,000 flights AB ,000 flights On this basis, the comparison between the PROF and INSIM results were calculated and are shown in Figure 14. The results, presented in Figure 14 show reasonable correlation between both methods of analysis % INSIM Solution 1.000% AB-1 PROF Solution Probability of Failure 0.100% AB-2 AB % 0.001% 10,000 30,000 50,000 70,000 90, , ,000 AB-4 Crack-Initiation Life [INSIM] or Crack Growth Life from a Median Initial Crack until 0.01" [PROF] (Flights) Figure 14: Comparison of Results for Risk-Analysis Performed by PROF and INSIM 11

12 SUMMARY AND CONCLUSIONS Risk-analysis can often be used to obtain more favorable inspection thresholds and intervals compared to classical damage-tolerance analysis, without subjecting the structure to excessive risk. Risk-analysis can be used to evaluate the effect of service life extension on the increased probability of failure. PROF and INSIM results showed reasonable correlation when compared on the basis of crack-initiation life (for INSIM) and crack growth life from a median crack to inch (for PROF). RERERENCES [1] FAA Advisory Circular C, "Damage Tolerance and Fatigue Evaluation of Structure", Federal Aviation Administration, [2] Swift, T., "Verification Methods for Damage Tolerance Evaluation of Aircraft Structures", Proceedings of the 12 th Symposium of the International Committee on Aeronautical Fatigue (ICAF), Toulouse, [3] Iyyer, N. et al "Managing Aging Aircraft Using Risk Assessment Models Lessons Learned from P-3C Fleet", Proceedings of the 24 th Symposium of the International Committee on Aeronautical Fatigue (ICAF), Naples, [4] Torng, T. Y. et al, "B1 Maintenance Schedule Impact Based on Risk Assessment Results", Proceedings of the 2007 USAF Aircraft Structural Integrity Program (ASIP) Conference, Palm Springs, [5] Spencer, F. W., "Eddy Current Inspection Reliability at Airline Inspection Facilities", Proceedings of the 1994 USAF Aircraft Structural Integrity Program (ASIP) Conference, San Antonio, [6] Gallagher, J. P., "A Review of the Philosophies, Processes, Methods and Approaches that Protect In-Service Aircraft from the Scourge of Fatigue Failures", Proceedings of the 24 th Symposium of the International Committee on Aeronautical Fatigue (ICAF), Naples, [7] Brot, A., "Evaluating Strategies for Minimizing Fatigue Failures in Metallic Structures", Proceedings of the 2004 USAF Aircraft Structural Integrity Program (ASIP) Conference, Memphis, [8] Brot, A., "Using Probabilistic Simulations in Order to Minimize Fatigue Failures in Metallic Structures", Proceedings of the 45 th Israel Annual Conference on Aerospace Sciences,