Probabilistic Approach To Damage Tolerance Design Of .

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Probabilistic Approach to Damage Tolerance Design ofAircraft Composite StructuresKuen Y. Lin * and Andrey V. Styuart†University of Washington, Seattle, WA, 98195-2400A probabilistic approach to determine design parameters for damage-tolerant compositeaircraft structures has been developed. The main criterion for acceptance of a structure is aspecified probability of failure. The development of this approach is motivated by theincreasing use of damage-sensitive composite aircraft structures. The resulting probabilisticmodel takes into account a probabilistic assessment of in-service accumulated damage, theability of non-destructive inspection methods to detect such damage, the residual strengthdegradation of damaged structure, quality of repair and loads/temperatures expectedbetween damage initiation and detection/repair. The special attention has been paid to theavailability of input probabilistic data and the possibility to obtain such data at reasonablecost. Computing tools and algorithms for the probabilistic analysis have been developed. Thevalidity of the approach has been demonstrated on several existing structural components.The main result of the study is that the reliability of a damage-tolerable composite structurecan be assessed on a quantitative basis, allowing aircraft manufacturers, operators and flightcertification authorities to establish the maintenance service guidelines and estimate thereasonable inspection intervals. Engineers can use this methodology in the future as a guideto establish design and inspection criteria while considering structural risk and maintenancecost at the same.Nomenclatureαβb, BGH(x)Flmax(x,t) Φ0 ND PDF PD(D) Pf , POF SiT ti shape parameterscale parameterparameter of exponential PDFparameter of residual strength curvefrequency of exceeding the level xcumulative probability distribution function of maximum load x per time ttabulated Gauss-Laplace functionnumber of damages per lifeprobability density functionprobability of detecting a damage/defect with a size greater than aprobability of failurestrength through ith intervaltemperature, Ktime intervalI. IntroductionAircraft reliability and risk engineering analysis methods and design tools have been developed for more than 30years. In particular the research focus has been to develop probabilistic methods and tools for application inaircraft programs, because many key engineering parameters are in fact probabilistic in nature like material propertyvalues, gust load, damage size, etc. Although probabilistic technology offers an advanced approach to design, itcontrasts significantly with the classical safety factor deterministic design process. For this reason, designorganizations have been very reluctant to adopt even standard probabilistic methods or include them as part of their*†Professor, Department of Aeronautics and Astronautics, Box 352400, AIAA Associate Fellow.Acting Assistant Professor, Department of Aeronautics and Astronautics, Box 352400.1American Institute of Aeronautics and Astronautics

analysis capability. Other reasons cited are the complexity of failure modes, limited damage databases, and safetyissues.Current aircraft design and certification philosophies are based on deterministic approaches which use safety andknockdown factors for various design conditions such as moisture, temperature, loading, and damage. Because ofhigher scatter in composite material properties and sensitivity of composite structures to impact damage, traditionalmethods have led to very conservative designs and service guidelines for composite structures. In essence, thecurrent approach assumes that a “worst-case scenario” for each design condition occurs simultaneously. The result isa substantial weight and cost penalty which reduce the durability, lightweight, and performance advantages ofcomposites.2As the use of composite materials in aircraft structures are becoming more widespread, a greater need exists todetermine the reliability of aircraft structures subject to accidental damage. Foreign object damage (FOD), groundvehicle collisions and lightning strikes are but a few examples of accidental damage that an aircraft structure mustface during its operational lifetime. By using a nondeterministic approach, the structural failure risks associated withaccidental damage events can be assessed quantitatively, allowing aircraft manufacturers, operators, and flightcertification authorities to better evaluate and predict the damage tolerance and safety of an aircraft structure.The primary candidate package for solving this problem has been the most advanced NASA/SwRI productIPACS-NESSUS software7-19. However the study of its capabilities has been revealed that the advanced FPImethods incorporated into this software do not work with the discrete variables such as the number of damages orthe number of inspections to detect damage. The other candidates have been the “Level of Safety” method proposedby Lin, et al.5 and “Probabilistic Design of Composite Structures” method by Styuart, et al20. The approachpresented here combines those two methods. However the NESSUS package has been used in a current study forobtaining the probabilistic characteristics of initial and residual strength.The reliability assessment method presented in this paper enables the utilization of service experience to take fulladvantage of the benefits of using composites. The potential of this method to increase structural safety and reducemaintenance cost is not however, limited to composite structures.Past reliability and structural risk studies have focused on fatigue of aging aircraft, which is mainly an issueunique to metal structures. Composite structures are fatigue and corrosion resistant, but are much more sensitive todamage threats because of brittle behavior during failure. Furthermore, there may be no visible evidence of damageto composite structures, even though significant internal damage has been sustained. Many probabilisticmethodologies incorporating micromechanics, laminate theory, manufacturing defects, operating environment, andimpact damage have been proposed for composite structures, but few however, have addressed the important issuesof inspection intervals and damage detection capability.The present study is based on a probabilistic failure analysis with the consideration of parameters such asinspection intervals, statistical data on damages, loads, temperatures, and damage detection capability, residualstrength of the new, damaged and repaired structures. The inspection intervals are formulated based on theprobability of failure of a structure containing damages and the quality of a repair.II. Reliability FormulationModern damage tolerance philosophies require that damage accumulated during the service life of a component bedetected and repaired before the strength of the component is degraded beyond some design threshold. Thefollowing simple example describes some fundamental concepts of probabilistic structural analysis and design: theassessment of the probability of failure for deterministically defined residual strength history as shownschematically in Fig 1. Let us assume that every structural component in an infinite fleet has this residual strength Rhistory. The initial R is equal to 1.5. At the instant t0 the damage of size D occurs and R is decreased to the value1.1. At the time instant t1 the damage is repaired and strength fully restored. There is three intervals ti of constantstrength Si. Then the failure may happen only because of the random external load exceeding the structural strength.The probability of failure per life is expressed asN 3Pf 1 [1 Pf ( Si , ti )]i 1where Pf(Si,ti) is a probability of failure per ith interval.2American Institute of Aeronautics and Astronautics(1)

Figure 1. Random Residual Strength Life HistoryLet us assume the load exceedance curve looks like that in Figure 2.1 .0 0 E 0 6Number of Exceedances per Life1 .0 0 E 0 51 .0 0 E 0 41 .0 0 E 0 31 .0 0 E 0 21 .0 0 E 0 11 .0 0 E 0 01 .0 0 E -0 100 .511 .521 .0 0 E -0 21 .0 0 E -0 31 .0 0 E -0 41 .0 0 E -0 5LoadFigure 2. Load Exceedance CurveThe cumulative probability distribution function of maximum load per time ti may be written as [16]Fl max ( Si , ti ) e Ht ( Si )ti(2)It is easy to find from Figure 1, Figure 2 and (1.2) that Pf(S1,t1) Pf(S3,t3) 6.12 10 , Pf(S2,t2) 4.26 10 andthe summary Pf 4.26 10-2.-6-2Let's make now the picture more realistic. This means: The number of damages per life may be more or less than one. There may be several different types of damage (e.g. through crack, indentation, delamination, disbonding, etc.) Damage occur at random time Damages have different sizes There may be several different types of inspection (pre-flight visual inspection, maintenance inspection, etc.) Time of damage existence (damage life) depends on the frequency of inspections and the capability of inspectionto detect damage.Fig. 3 shows one history of the random damage size vs. time. Two types of damage are supposed: Delaminationand hole. The damage size realization may be converted into residual strength realization and probability of failurecalculated with equation (1). Such a procedure should take into account a number of deterministic and randomvariables discussed in the next two sections.3American Institute of Aeronautics and Astronautics

1.1Damage Size0.90.7DelaminationHole0.50.30.1-0.1 3. Damage Size Lifetime HistoryIII. Deterministic VariablesIn order to make the input data obtainable and simple we follow the current practice and introduce somedeterministic categorization for loads/failure modes, damage types and inspection types.A. Deterministic Load cases/Failure modesIn accordance with the majority of current structural design practices, the analysis of strength/rigidity of anaircraft structure is carried out for a finite set of conditions (e.g. various points on the V-G velocity-accelerationdiagram for wing). They are called design load cases (DLC). There are many load cases, but for each particularsubstructure the engineer selects only a few critical cases. These cases are closely related to the potential failuremodes of the structure under anticipated loading conditions. Usually this set of design cases is selected bycomparing the external loads (bending moment, torque, and shear force) for various design conditions. Further, theselected set of cases is verified with finite element model. Frequently, the load cases are closely related to thesegments of the flight profile. E.g. flap load cases divided into take-off and landing ones.B. Deterministic classification of defects/damagesThe information on defects/damages should be treated similarly to the load information by introduction of finiteset of damage types. Different types of defect/damage may be taken like hole, delamination, surface dents, etc. Theuser may use his own classification. This classification should be related to the availability of methods of predictionof residual strength depending on the size of damage and the availability is the statistical data for every damagetype. The selection of damage types depends also on the type of load realized in the considered site, e.g., if onlytension stress takes place there, primary attention should be paid to through damage, and delamination is of minorimportance.C. Deterministic description of inspection/repairThere may be several types of inspection. They are distinguished by the inspection method and the inspectionschedule. Currently the time of inspection is deterministic variable defined by the array if inspection times throughthe life. One type of inspection is always defined: pre/post-flight inspection. In case the latter is not specified inmaintenance documentation, we believe that it still exists but has low resolution.IV. Random VariablesIn considering the structural integrity of a structural component containing damages/defects, the potentialrandom variables include number of damages, damage/defect size, time to detect/repair damage, load, and strengthproperties. The effectiveness of the inspections is also among the potential random variables. The effectiveness of aninspection can be characterized by its probability of detection (POD) distribution. Nine random variables areconsidered in the current methodology:(1) Number of damages per life ND, for each type of damage(2) Time of damage initiation.(3) Damage/defect size D, for each type of damage(4) Time ti from damage initiation to repair that is a random function of damage size and damage schedule4American Institute of Aeronautics and Astronautics

(5)(6)(7)(8)(9)Initial failure load (initial strength), for each load caseResidual strength of damaged structure, for each type of damage and each load caseFailure load of repaired structure, for each type of damageStructural load for each load caseStructural temperatures T at the instants when maximum external loads occurredMost of the above mentioned variables are described by optional PDF or exceedance curve except twovariables having fixed PDFs: the damage event is assumed to be a very rare and therefore the variable ND isdescribed by Poisson distribution and the number of inspection to detect damage is described by geometric PDF.A. Probabilistic description of loadsAs we have already mentioned in section II, we describe the external loads in terms of exceedance curves andthen use equation (1.2) to obtain the CPF of maximum load per certain time. In a modern practice of fatigueanalysis, a prediction of fatigue life of most fatigue critical sites of structure is carried out by comparing the numberof cycles (time) to crack initiation as obtained in laboratory fatigue tests of specimens, with cumulative damage inoperation. This cumulative damage is predicted on the statistical basis as cumulative load occurrence, versusexceedance curve (Fig.2). It is not eas