1、Best Practices Entry: Best Practice Info:a71 Committee Approval Date: 2000-03-15a71 Center Point of Contact: JSCa71 Submitted by: Wil HarkinsSubject: Fracture Mechanics Reliability Practice: Use a fracture mechanics formulation to estimate the design fatigue life and reliability of metallic or ceram
2、ic structural and mechanical components subject to fluctuating stress. For reusable spacecraft, update the reliability analysis based on in-service inspection and repair data.Programs that Certify Usage: N/ACenter to Contact for Information: JSCImplementation Method: This Lesson Learned is based on
3、Reliability Guideline Number GD-AP-2304 from NASA Technical Memorandum 4322A, NASA Reliability Preferred Practices for Design and Test.Benefit:Consideration of fracture mechanics reliability during the design process can assist in the prevention of failures of structural and mechanical components su
4、bject to fluctuating loads in service. Explicit consideration of the reliability of structural and mechanical components provides the means to evaluate alternate designs and to ensure that specified risk levels are met. Probabilistic fracture mechanics analyses may also be applied to life extension
5、of existing structures, and for problem assessment of in-service fatigue failures.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Potential applications of this method to the Space Shuttle or Space Station include: landing gear, control surfaces, mai
6、n engine components, auxiliary power unit components, external tank and solid rocket booster welds, pressure vessels, propulsion modules, and logistics modules. The method is also applicable to reusable, Shuttle launched payloads or spacecraft such as Spacelab, Spacehab, EURECA, SPAS and Spartan.Sto
7、chastic fracture mechanics analysis provides the basis for analysis consistency between reliability analysis of mechanical systems, such as reliability block diagram analysis, and traditional deterministic fracture mechanics safe life estimation.Implementation Method:The method outlined below is a s
8、tochastic elastic fracture mechanics approach (for metallic or ceramic materials) which neglects any crack retardation or acceleration effects. Composites and other materials with insufficient crack growth data or intractable flaw growth characteristics are not considered. The detailed development o
9、f this approach is essentially the same as that given in references 1 through 6. The purpose of the simplified approach described herein is to illustrate some of the advantages and typical results of a stochastic fracture mechanics analysis. Discussion of technical implementation details, such as th
10、e use of crack growth laws other than the Paris equation (for example, the modified Forman equation reference 15), follows in the technical rationale section.For illustration, a Paris crack growth law is assumed, which may be written in the form of a differential equation. For random applied stress
11、processes, a solution can be written in the form of a limit state function, M, as:refer to D description D (1)in which:Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-refer to D descriptionD Failure is defined to occur when the critical crack length,
12、 ac, is exceeded, so that at failure M0. The probability of failure is then the probability that the limit state function is equal to or less than zero: refer to D descriptionD (2)The first term of Equation 1, the integral, essentially defines the fatigue resistance of the structure against a crack
13、growing from an initial size, ao, to critical size ac. This integral must be evaluated numerically in all but the simplest of cases.Particular forms of the geometry function, Y(a), are available for simple configurations in the literature or from general purpose fracture mechanics software packages.
14、 For unique structural details, other approaches are available to determine Y(a), such as detailed finite element modeling of the cracked structure. The second term of Equation 1 defines the accumulated “damage“ caused by the applied stress process. A random stress process is characterized by its po
15、wer spectral density and may be described as being narrowband (slowly varying random) or as wideband. In either case closed form approximations for the second term of Equation 1 are available. If the stress process is deterministic or if time histories of the stress process are available time domain
16、 methods, such as rainflow cycle identification reference 10, approximations are available for determining the factors in the second term of Equation 1. It should be noted that all of the terms in Equation 1 may be treated as random or uncertain. This enables the modeling of all the sources of uncer
17、tainty pertinent to the problem, such as crack size and location, scatter in crack growth data, etc. Subsequent sensitivity analyses can be used to determine which variables contribute the most to the fatigue life uncertainty and require treatment as random, and which variables may be considered as
18、fixed (deterministic). Sensitivity analysis can also indicate the parameters for which further data collection could reduce the overall uncertainty in the fatigue life.Modern reliability methods, the so-called First-Order Reliability Method (FORM) or Second-Order Reliability Method (SORM), are avail
19、able in commercial computer programs to solve Equation 2. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Monte Carlo or more sophisticated simulation techniques are also available references 1, 7, 8, and 9. In particular, PROBAN 1 has been available
20、 commercially from Det Norske Veritas (Oslo, Norway) since 1986 and has been used extensively in the offshore oil industry. PROBAN is available for UNIX and VAX/VMS based workstations. STRUREL is a PC/Windows based application available from RCP, GmBH, of Munich, Germany. RELACS is a similar package
21、 available from REA, Inc., of Golden, Colorado. A NASA-funded application called NESSUS, which runs on UNIX workstations and mainframes, is available from the Lewis Research Center. The commercial codes are recommended because of better user-interfaces and better user support. Monte Carlo approaches
22、 generally require direct programming for the solution for the specific problem under study.For a structure or mechanism in service, the results of inspections may be incorporated into the analysis and the estimated failure probabilities updated to show the change in reliability based on the additio
23、nal information on existing crack size. For each inspection, two outcomes are possible: either no crack is detected, or a crack is detected and its size or length is measured. Figure 1 is an example analysis result (from reference 1) showing reliability as a function of time for which inspections we
24、re assumed at 10 and 20 years, with no crack detected at 10 years, but a 4.0 mm crack detected at 20 years. Note that with the new information gained from inspection at t=10 years, the reliability is shown to increase as no crack was found. After inspection at t=20 years, reliability is also shown t
25、o increase even though a small crack was detected, but only for a short time. The increase at t=20 years can be attributed to the discovery that the crack length was less than the critical crack length for the structure, but it should also be noted that the reliability decreases much faster with the
26、 uncertainty tied to the presence of a flaw. Inspection of structures and the new information that is gained can essentially reset the reliability, and even though a crack may be discovered, this new information can lead to increased inspections, which can lengthen the life of the item. However, a c
27、rack detection generally decreases the reliability, as in this case after about t=22 years.Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-refer to D descriptionD Technical Rationale:A stochastic fracture mechanics approach to fatigue gives an estima
28、te of the reliability of structural and mechanical components as a function of time in service and allows the reliability estimate to be updated if the results of in-service inspections and/or in-service load data are available references 1 and 2. The procedure may also be used to optimally schedule
29、 inspections, and to compare the adequacy of different inspection types or quality levels references 1 and 2. Type and quality of repair techniques may also be compared and selected to maintain a desired reliability level. Updating of these analyses as actual inspections or repairs occur is also pos
30、sible references 2 and 3. The application of in-service reliability estimates is dependent on the availability of some form of flight load data and accessibility to the structure or mechanism for inspection. Without such data no updating of the initial design reliability analysis is possible.The pri
31、mary intent of this guideline is to make available to the NASA reliability engineering Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-discipline the engineering mechanics-based methods for estimating the reliability of structural and mechanical comp
32、onents. Use of such methods would allow for consistency of models and data between the reliability and structural/mechanical engineering disciplines within NASA. A stochastic fracture mechanics approach provides a “physics-of-failure“ basis for estimating the reliability of components subject to fat
33、igue and fracture. This enables fault tree or reliability block diagram analyses, or probabilistic risk assessments, for structural and mechanical components in spacecraft systems to be performed using the same data and engineering mechanics models as the NASA accepted, deterministic fracture analys
34、is procedures reference 14. For example, the mean time to failure for a pressure vessel girth weld (as may be needed for a propulsion system reliability block diagram analysis) estimated using probabilistic fracture mechanics would be rationally consistent with the safe-life analysis performed to me
35、et current NASA fracture control and safe-life analysis requirements.The approach outlined herein is a simplified formulation that neglects load interaction effects, such as retardation, by using the Paris crack growth law. If a Paris equation is properly fit to the basic crack growth data, the resu
36、lting deterministic safe life estimate will be more conservative (shorter) than the estimated life resulting from a fracture analysis which incorporates retardation. The current NASA accepted practice in fracture mechanics analysis uses the computer program NASA/FLAGRO, which includes interaction ef
37、fects. Load interaction effects may be included in a stochastic fracture mechanics analysis by using crack growth laws such as the modified Forman equation found in NASA/FLAGRO. For example, a FORM/SORM formulation which included the modified Forman equation has been used to study aircraft durabilit
38、y and damage tolerance reference 14. A direct Monte Carlo solution implementing the modified Forman equation may also be found in references 7, 8, and 9. Issues related to the implementation, applicability, and accuracy of FORM/SORM and Monte Carlo methods are beyond the scope of this guideline. In
39、general, if a fracture mechanics reliability analysis is to be performed and it has been determined from a preliminary deterministic fracture analysis thatthe Paris formulation is inadequate, the modified Forman equation (as in NASA/FLAGRO) should be used following either the approach described in r
40、eference 14 or in references 7, 8, and 9.Two critical parameters in any fracture analysis, deterministic or stochastic, are the size, location and distribution of initial flaws or cracks, and the ability of nondestructive evaluation (NDE) techniques to detect a flaw or crack smaller than a certain s
41、ize. NASA has established standard NDE flaw sizes for Space Transportation System (STS) payloads reference 14. Two recent NASA research projects, one directed at establishing NDE probability of detection (POD) data, and one directed at gathering initial flaw distribution data, also may provide addit
42、ional data for modeling initial flaws and NDE quality.Deterministic fracture analysis practice uses relatively large safety or “scatter“ factors to account for the many inherent sources of uncertainty or error, such as analytic model inadequacies, inaccuracy of stress intensity predictions, and the
43、scatter of experimental crack growth data. Stochastic analysis methods extend the accepted deterministic methods by allowing (or forcing) the analyst to explicitly account for these uncertainties by treating them as random variables (or process or fields), requiring Provided by IHSNot for ResaleNo r
44、eproduction or networking permitted without license from IHS-,-,-the analyst to consider the likely range and distribution of the parameters. Both the deterministic and the stochastic analysis will suffer from the same shortcomings of model inadequacy, etc. The stochastic model has the advantage of
45、addressing the uncertainties specifically using probability and statistical theory, while the deterministic approach addresses uncertainty in a general manner through the use of the safety or scatter factor. Use of a stochastic approach and a reliability based design criteria can be beneficial in av
46、oiding over- or under-conservatism that may result from the use of a deterministic safety factor approach.References:1. PROBAN-2: Example Manual, Report No. 89-2025, A.S Veritas Research, Hovik, Norway, August, 19892. Madsen, H.O., Skjong, R.K., and Kirkkemo, F., “Probabilistic Fatigue Analysis of O
47、ffshore Structures - Reliability Updating Through Inspection Results“, A.S Veritas Research, Hovik, Norway3. Madsen, H.O., Skjong, R.K., Tallin, A.G., and Kirkemo, F., “Probabilistic Fatigue Crack Growth Analysis of Offshore Structures, with Reliability Updating Through Inspection“, Society of Naval
48、 Architects and Marine Engineers, Proceedings, Marine Structural Reliability Symposium, Arlington, VA, October 5-6, 19874. Wirsching, P.H., Torng, T.Y., and Martin, W.S., “Advanced Fatigue Reliability Analysis“, International Journal of Fatigue, Vol. 13, No. 5, 1991, pp. 389-3945. Wu, Y.-T., Burnsid
49、e, O.H., and Dominguez, J., “Efficient Probabilistic Fracture Mechanics Analysis“, Numerical Methods in Fracture Mechanics: Proceedings of the Fourth International Conference, Luxmoore, A.R., Owen, D.R.J., Rajapakse, Y.P.S., and Kanninen, M.F., Eds., Pineridge Press, Swansea, U.K., 19876. Veers, P.S., Winterstein, S.R., Nelson, D.V., and Cornell, C.A., “Variable-Amplitude Load Mode
