• DTDHandbook
• Contact
• Contributors
• Sections
• 1. Introduction
• 2. Fundamentals of Damage Tolerance
• 0. Fundamentals of Damage Tolerance
• 1. Introduction to Damage Concepts and Behavior
• 2. Fracture Mechanics Fundamentals
• 3. Residual Strength Methodology
• 4. Life Prediction Methodology
• 5. Deterministic Versus Proabilistic Approaches
• 6. Computer Codes
• 0. Computer Codes
• 1. Structural Analysis
• 2. Life Prediction
• 3. PRobability Of Fracture (PROF)
• 7. Achieving Confidence in Life Prediction Methodology
• 8. References
• 3. Damage Size Characterizations
• 4. Residual Strength
• 5. Analysis Of Damage Growth
• 6. Examples of Damage Tolerant Analyses
• 7. Damage Tolerance Testing
• 8. Force Management and Sustainment Engineering
• 9. Structural Repairs
• 10. Guidelines for Damage Tolerance Design and Fracture Control Planning
• 11. Summary of Stress Intensity Factor Information
• Examples

# Section 2.6.3. PRobability Of Fracture (PROF)

PROF is a computer program that was specifically written to interface with the data that are available as a result of ASIP. PROF runs in the Windows environment using an Excel spreadsheet interface with ASCII data files and two C++ calculation modules. The two calculation modules estimate the probability of failure as a function of flight hours due to either fatigue crack growth at a stress riser and the probability of failure due to discrete source damage in a load path.

The PROF input requirements for estimating failure probability due to fatigue crack growth are:

·        crack growth versus flight hours (a versus T) for the expected stress sequences;

·        a versus K/s at the stress riser;

·        distribution of critical stress intensity factors at the stress riser;

·        distribution of maximum stress per flight experienced at the stress riser;

·        distribution of crack sizes at the stress riser;

·        probability of detection as a function of crack size, POD(a), function for the inspection system used at inspections;

·        distribution of equivalent crack sizes at repaired stress risers; and

·        flight hour intervals between inspections.

PROF projects the crack size distribution using the a versus T relation from the deterministic damage tolerance analysis of ASIP. At an inspection, PROF changes the distribution of crack sizes in accordance with the POD(a) function and the equivalent repair crack sizes. The post-inspection/repair crack size distribution is then projected for the next usage interval. Single flight probability of failure is calculated using the Irwin abrupt fracture criterion. That is, the failure probability is calculated as the probability that the maximum stress intensity factor (combination of the distributions of maximum stress per flight and crack sizes) during the flight exceeds the critical stress intensity factor. This probability is obtained from a triple integration over input distributions.

For failure probability due to discrete source damage, PROF requires the additional input of residual strength as a function of crack size in the remaining critical elements of the load path. The residual strength characterization replaces the stress intensity factor input. PROF again grows the crack size distributions with modifications, as necessary, at inspections. Single flight failure probability is calculated from the distribution of maximum stress per flight, crack size distribution at the critical element and residual strength as a function of crack size. This probability is obtained from a double integration over input distributions.

The output of PROF is stored in an Excel workbook and provides both the single flight failure probability as a function of flight hours and the crack size distributions before and after an inspection. The availability of the crack size distributions permits changing the analysis due to known changes in usage. Further, multiple runs of PROF permit analyzing more complex scenarios such as multiple element damage. See Sample Problems UDRI-2, UDRI-3 and UDRI-4 for examples of the use of PROF for risk analysis of discrete source damage, multiple element damage and corrosion damage scenarios, respectively.

PROF is proprietary to the University of Dayton but is freely available for United States government applications. PROF can be obtained for United States government applications from

Mr. David Banaszak
AFRL/VASM
Wright-Patterson Air Force Base, Ohio 45433

Phone:  (937) 255-6104

For applications not directly related to the United States government, a license for the use of PROF can be arranged. Contact

Dr. Alan Berens
University of Dayton Research Institute
300 College Park
Dayton, Ohio 45469-0120

Phone:  (937) 229-4417

email:    berens@udri.udayton.edu

DARWIN

Design Assessment of Reliability WIth INspection (DARWIN) is a risk analysis program for calculating the probability of failure in turbine engine disks. With a graphical user interface for problem setup and output, DARWIN integrates finite element analysis, fracture mechanics, non-destructive inspection, random defect occurrence and location, and other random variables to assess the risks of rotor fracture. Risk calculations incorporate both Monte Carlo and failure function/fast integration methods.