PROBABILISTIC SURFACE DAMAGE TOLERANCE ASSESSMENT OF AIRCRAFT TURBINE ROTORS

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1 Proeedings of ASE Turbo Expo 2 Power for Land, Sea, and Air June 16 19, 2, Atlanta, Georgia, USA GT2-871 PROBABILISTIC SURFACE DAAGE TOLERANCE ASSESSENT OF AIRCRAFT TURBINE ROTORS ihael P. Enright R. Craig Clung Lu Huyse Yi-Der Lee Gerald R. Leverant Southwest Researh Institute 622 Culebra Road San Antonio, TX Harry R. illwater University of Texas at San Antonio 69 North Loop 164 West San Antonio, TX Simeon H. K. Fith ustard Seed Software Enino Way San Antonio, TX ABSTRACT This paper desribes some of the new surfae damage apabilities in DARWIN T, a probabilisti frature mehanis software ode developed to evaluate the risk of frature assoiated with airraft jet engine titanium rotors/disks. An initial framework is presented in whih a graphial user interfae (GUI) is used to expliitly define the stresses and temperatures at the rak loation for several rak geometries. A summary of the approah used to develop new stress intensity fator solutions for these geometries is also presented, inluding seleted validation results. INTRODUCTION The appliation of probabilisti methods to fraturemehanis-based life predition is beoming inreasingly essential in the aerospae industry. A probabilisti methodology is partiularly well suited to the effiient design of omponents subjeted to rare, ritial (i.e., life-limiting) events, beause it allows the designer to adjust nominal omponent parameters to meet quantitative reliability requirements. Airraft turbine rotors may be subjeted to rare ritial events (e.g., unontained engine failures) due to the presene of metallurgial (e.g., hard alpha) and manufaturing (e.g., surfae damage) defets that an our during the manufaturing proess. To aount for these events, the Rotor Integrity Subommittee (RISC) of the Aerospae Industries Assoiation (AIA) has reommended adoption of a probabilisti damage tolerane approah to supplement the urrent safe life methodology. The reommendation led to the development of a omputer program alled DARWIN T (Design Assessment of Reliability With INspetion), being developed in ollaboration with major engine manufaturers (General Eletri, Honeywell, Pratt & Whitney, and Rolls-Roye). The program omputes the probability-of-frature as a funtion of the number of flight yles, onsidering random defet ourrene and loation, random inspetion shedules, and several other random variables. Both onte Carlo simulation and importane sampling are available for use in probabilisti life preditions. A frature mehanis module, alled Flight_Life, is also inorporated into the ode. In addition, a user-friendly graphial user interfae (GUI) is available to handle the otherwise diffiult task of setting up the problem for analysis and viewing the results. Previous papers [1-6] have foused on the probabilisti methodology for prediting the failure probability assoiated with hard alpha defets. Reently, the ode has been enhaned to inlude new preditive apabilities for surfae damage. An enhaned GUI has been developed to aommodate user defined mission profiles, and work is ontinuing to address fully three-dimensional finite element models. New stress intensity fator solutions for surfae, orner, and through raks at holes and surfae raks in plates have been derived from extensive boundary element analysis. These new solutions employ weight funtions to address aurately the nonlinear stress gradients ommon at stress onentrations and other 1 Copyright 2 by ASE

2 surfaes. Risk alulation apabilities have been enhaned to provide failure probability preditions for individual features. This paper desribes some of the new surfae damage features in DARWIN T. An initial framework is presented in whih a graphial user interfae (GUI) is used to expliitly define the stresses and temperatures at the rak loation for several rak geometries. A summary of the approah used to develop new stress intensity fator solutions for several rak geometries (i.e., surfae, orner, and through raks at holes and surfae raks in plates) is also presented, inluding seleted validation results. initial rak loation AN INITIAL FRAEWORK FOR SURFACE DAAGE- BASED RISK ASSESSENT Previous releases have foused on risk assessment of titanium airraft engine rotor disks with inherent (hard alpha) defets. Inherent defets an our anywhere within a disk, so a zone-based risk integration methodology is used to aount for this unertainty [2,4]. The disk is disretized into a number of zones of approximately equal risk, and the total disk risk is approximately equal to the sum of the risks assoiated with the individual zones. Variability in defet size is addressed using established exeedane urves [7]. Under this methodology, stress and temperature information are provided for the entire disk for all of the load steps modeled based on results from finite element analysis. In ontrast, surfae damage is present only on the exterior surfaes of a omponent and is often loated at features (e.g., bolt holes) or along other mahined surfaes. Additional rak geometries were introdued in DARWIN T 4. to model surfae features as shown in Fig. (1). Currently, a featurebased methodology is used to estimate risk, in whih the disk risk is approximately equal to the sum of the risks assoiated with the individual features. For a typial disk, the number of features assoiated with surfae damage assessment is relatively small ompared to the number of zones assoiated with inherent-defet-based assessment. In addition, the stress/ temperature data assoiated with a surfae damage assessment an be obtained at disrete loations (i.e., data are not required for the entire disk). A surfae-damage-based defet distribution is urrently under development by the Rotor Integrity Sub Committee (RISC) of the Aerospae Industries Assoiation (AIA) to address defet size variability. The initial framework for surfae-damage-based risk assessment is shown in Fig. (2). The user defines a mission profile and rak geometry for eah surfae feature in the disk. Inluded in the mission profile definition are the stress, temperature, and stress gradient values at disrete time steps. As shown in Fig. (), the stress gradient an be defined expliitly by the user, or it an be extrated diretly from a 2D finite element model. The number and spaing of gradient points an be adjusted prior to extration. Figure 1. In the DARWIN T 4. release, surfae damage features are modeled as one of the following rak types: (a) surfae rak, (b) surfae rak at a hole, or () orner rak at a hole. (a) (b) () 2 Copyright 2 by ASE

3 Figure 2. Initial framework for surfae damage in DARWIN T (4. release). A mission profile onsisting of stresses and temperatures at the rak loation (and assoiated stress gradients) is defined for eah surfae feature. Figure. Enhaned stress gradient definition apabilities for surfae damage. The stress gradient an be defined expliitly by the user, or it an be extrated diretly from a 2D axisymmetri finite element model. The number and spaing of points along the gradient an be adjusted by the user. Copyright 2 by ASE

4 A summary of the primary differenes in the damage tolerane approah for inherent and surfae-damage-based defets in DARWIN T is indiated in Table 1. It an be observed that the list of differenes is relatively small. In fat, most of the same omputational tools an be applied to both defet types to assess the risk of frature, whih is a major advantage to this approah. Table 1. Summary of the primary differenes in the damage tolerane approah for inherent and surfae-damage-based defets in DARWIN T Defet Type Inherent Surfae Damage Crak Type Embedded, Surfae, Surfae at Surfae, Corner Hole, Corner at Defet Size Variability Stress & Temperature Data FAA Advisory Cirular [7] Hole Under Development by RISC 2D Finite Element User Defined odel Risk basis Volume Based Feature (Geometry) Based A number of other enhanements were added to improve assessment of deterministi rak growth, suh as a user speified initial defet aspet ratio, and the apability to speify the defet distribution in terms of initial rak area, length, or depth (among other enhanements). In addition, a rak animation feature was added (Fig. (4)) that allows the user to visualize rak growth. DEVELOPENT OF STRESS INTENSITY FACTOR SOLUTIONS FOR CRACKS AT HOLES Earlier versions of DARWIN T, whih were foused on inherent material anomalies, ontained stress intensity fator (K) solutions for raks in simple retangular plates. Available geometries inluded elliptial embedded raks, semi-elliptial surfae raks, quarter-elliptial orner raks, and edge and embedded through raks. However, the surfae damage problem is urrently foused on bolt holes, and so additional K solutions for raks emanating from holes were required. Numerous K solutions for raks at holes are available in the literature, but these solutions are generally for simple remote loads suh as uniform tension, bend, or pin loading. In ontrast, DARWIN T requires the apability to address a general nonlinear stress gradient on the rak plane. Therefore, it was neessary to develop a new set of weight funtion solutions for the geometries of interest. Figure 4. A new rak animation feature allows the user to visualize rak growth. In this partiular example, an embedded elliptial rak transitions to beome a semielliptial surfae rak. The stress intensity fator solution for the embedded rak expliitly aounts for the effet of the free surfae. Weight Funtion ethod A weight funtion (also known as influene funtion or Green s funtion) formulation enables the evaluation of stress intensity fators (SIFs) by integrating over the rak surfae a produt of the applied stress in the unraked body with the weight funtion for the raked struture. The analytial forms for weight funtions an be derived for some simple geometries, but approximate weight funtion forms are used for 4 Copyright 2 by ASE

5 omplex onfigurations, espeially with free surfaes. In DARWIN T 4., a one-dimensional weight funtion is employed to determine the SIFs resulting from a stress gradient varying in only the rak depth diretion (away from the hole). The frature mehanis modules in DARWIN T 4. for a enter surfae rak (CSC) at a hole and a orner rak (CC) at a hole utilize the approximate weight funtion proposed by Glinka [8-1]. The weight funtion at the -tip (the maximum depth position for the surfae rak, or the tip on the plate surfae for a orner rak) is W x 2 ( ) 1 2 x x x The weight funtion at the a-tip (the rak tip in the bore of the hole for either a surfae or orner rak) is W a 2 1 x 1a x 2a x a x 2 The variable x is the distane normal to the hole axis measured from the loation where the rak emanates (the root of the hole). The parameters 1, 2,, et. depend on the geometrial parameters and are defined by referene solutions. At the -tip, 1, 2, and are defined by [9] 24 1 ( 4Y 6Y1 ) 2Q Y 2Q 1 4 and at the a-tip, 1a, 2a, and a are given by by 1a 2a a 4Q 4Q ( F 18F ) ( 6F 9F ) ( 1 ) 1a 1 2a Q is the shape fator for an elliptial rak approximated Q ( a ) ( a ) ,, a 1 a > 1 and F, F 1, Y and Y 1 are normalized SIFs or the referene solutions. F, F 1 are obtained at the a-tip, and Y and Y 1 are at the -tip. The subsripts identify the two assoiated referene (1) (2) () (4) (5) loads on the rak surfaes: denotes uniform tension, and 1 denotes a linearly dereasing bending stress σ r (x) x/1. The stress intensity fators at the a- and -tips, K a,, an thus be determined by diret integration as K W a, a, σ ( x) where σ(x) is the univariant stress applied on the rak surfae, and the integration is arried out from x to x. The weight funtion for a through rak at a hole in an infinite plate is analytially derived based on the ross setional hoop stress distribution for a hole in an infinite plate subjeted to remote tension given by [11], and the assoiated SIF equation for a through rak at a hole approximated by Shijve [12]. The rak opening stress is given by σ r ~ ( x ) dx 1 1 ~ 2 ~ 4 ( 1 x ) 2 ( 1 x ) where x ~ denotes the normalized x oordinate with respet to the radius of the hole R, and the assoiated normalized SIF for remote tension is defined by f r ξ 1.9ξ.59 2 ( ξ 1) 2 2ξ ( 1 ξ) 2 ξ.2 ξ 1 where ξ symbolizes the normalized rak length, /R [1]. The weight funtion for a through rak at a hole under an arbitrary univariant stress variation, σ(x), an then be derived as w ( x ) β ( ξ ) i 2 (6) (7) (8) 5 ~ ~ 1 x, ξ 1 (9) i 2ξ i 1 ξ where i varies from 1 to 5, and β i s are tabulated as a funtion of rak depth. The SIF is expressed in terms of an integral over the whole rak depth: K ξ ( ξ ) R ( ~ x ) w ( ~ x, ) d~ σ ξ x (1) Note that finite thikness (a/t) effets are inluded expliitly in the weight funtion formulation for the surfae and orner raks. Finite plate width effets for all three geometries are not inluded in the DARWIN T 4. solutions, but are being added in DARWIN T 5. with engineering approximations. Referene Solutions Numerial methods were used to generate highly aurate referene solutions for the approximate weight funtion 5 Copyright 2 by ASE

6 formulation. The referene solutions for two-dimensional raks at holes were derived using the FADDD frature mehanis software, a general boundary element (BE) ode for three-dimensional linear elasti frature analysis [14]. FADDD inludes a novel rak-tip element that allows the omputation of SIFs diretly from the nodal information along the rak front. The BE approah uses fewer elements than finite element (FE) approahes, substantially reduing the modeling effort while maintaining exeptional auray [15,16]. To failitate the use of FADDD, SwRI developed supplemental proedures for pre- and post-proessing. Referene solutions were generated at a wide range of ombinations of geometrial aspet ratios: R/t.25, 1, and 2; a/t.1,.2,.5,.8, and.9; and a/.5, 1, 2.5, 5, and 1. Figure 5 shows an example model for a orner rak at a hole. Nine-node double urved path elements were used. A single model typially ontained fewer than 11 elements. F(φ) R/t1 a/t.5 a/ φ/ (a) FADDD Raju-Newman FE Comparisons and Validation To verify the weight funtion formulation, the SIFs evaluated at the a- and -tips by the weight funtion method using the stress gradient around a hole in a plate subjeted to remote tension were ompared with independent FADDD results using the same meshes and the same nonlinear stress field. The omparisons were performed for all aspet ratio ombinations onsidered. The differenes were less than 1%. F(φ) These FADDD results for uniform remote tension were further evaluated by omparison with the Raju-Newman FE solutions for raks at holes under uniform remote tension [17]. Sample omparisons are shown in Fig. 6. Here F(φ) is the normalized SIF, K/( a/φ). FADDD and Raju-Newman results ompared favorably in many ases. In those ases where signifiant inonsistenies were observed, FE omputations using the ommerial ode FEA-Crak were performed as an independent hek. To ahieve similar resolution to FADDD, FEA-Crak omputations used at least 6 elements. The FADDD results were onfirmed by the R/t2 a/t.8 a/ φ/ (b) FADDD Raju-Newman FE FEA-Crak 2.5 F(φ) R/t1 a/1 a/t.2 FADDD Raju-Newman FE FEA-Crak () 2φ/ Figure 5. Example FADDD model (a/1, a/t.8, R/t1). The detailed mesh is shown for the rak surfae only. Figure 6. Seleted normalized SIF results from FADDD, Raju-Newman, and FEA-Crak for enter surfae rak (a-b) and orner rak () at a hole in a plate under remote tension. 2φ/ denotes the angular position around the rak perimeter. 2φ/ or 2 is the a-tip in the bore, and 2φ/ 1 is the -tip. 6 Copyright 2 by ASE

7 FEA-Crak results. Note that the older Raju-Newman FE solutions, whih employed fewer degrees of freedom, are less aurate at free surfaes due to the relatively oarse meshes used. FUTURE WORK Additional work is urrently underway to broaden the generality of these solutions in future versions of DARWIN T. Planned enhanements inlude the effets of an off-enter surfae rak, a finite width plate, and a hole that is off-enter in the plate. A new weight funtion formulation is also being developed that will address a fully bivariant stress field in the rak plane. In addition, a apability for modeling surfae damage based on -dimensional finite element geometry is urrently under development. ACKNOWLEDGENTS This work was supported by the Federal Aviation Administration under Cooperative Agreement 95-G-41 and Grant 99-G-16. The authors wish to thank the FAA Tehnial Center projet managers, Brue Fenton and Joe Wilson, for their ontinued diligene and enouragement and Tim ouzakis of the FAA Engine and Propeller Diretorate for his ontinued support. The ongoing ontributions of the Industry Steering Committee (Darryl Lehmann, Pratt & Whitney; Jon Tshopp, General Eletri; Ahsan Jameel, Honeywell; Jon Dubke, Rolls-Roye) are also gratefully aknowledged. REFERENCES [1] illwater, H.R., Fith, S., Wu, Y.-T., Riha D.S., Enright,.P., Leverant, G.R., Clung, R.C., Kuhlman, C.J., Chell, G. C., Lee, Y.-D., 2, A Probabilistially-Based Damage Tolerane Analysis Computer Program for Hard Alpha Anomalies in Titanium Rotors, Proeedings of the 45th ASE International Gas Turbine & Aeroengine Tehnial Congress, unih, Germany, ay 8-1. [2] Wu, Y.-T., Enright,.P., and illwater, H.R., 2, Effiient and Aurate ethods for Probabilisti Analysis of Titanium Rotors, Proeedings of the 8th ASCE Joint Speialty Conferene on Probabilisti ehanis and Strutural Reliability, Notre Dame, IN, CD-RO Proeedings (Kareem, Haldar, Spener, and Johnson, eds.), paper PC2-221, 6 pages. July [] Leverant, G.R., Clung, R.C., illwater, H.R., and Enright,.P., 22, A New Tool for Design and Certifiation of Airraft Turbine Titanium Rotors, Proeedings of the 47th ASE International Gas Turbine & Aeroengine Tehnial Congress, Amsterdam, The Netherlands, June -6. [4] Wu, Y.-T., Enright,.P., and illwater, H.R., 22, Probabilisti ethods for Design Assessment of Reliability with Inspetion, AIAA Journal, AIAA, 4 (5), [5] Leverant, G.R., Clung, R.C., illwater, H.R., and Enright,.P., 2, A New Tool for Design and Certifiation of Airraft Turbine Rotors, Journal of Engineering for Gas Turbines and Power, ASE (aepted). [6] Clung, R.C., Enright,.P., illwater, H.R., Leverant, G.R., and Hudak, S.J., 2, A Software Framework for Probabilisti Fatigue Life Assessment, Probabilisti Aspets of Life Predition, AST STP 145, W.S. Johnson and B.. Hillberry, Eds., AST International, West Conshohoken, PA (in press). [7] "Advisory Cirular - Damage Tolerane for High Energy Turbine Engine Rotors," U.S. Department of Transportation, Federal Aviation Administration, AC.14-1, Washington, DC, Jan 21. [8] Glinka, G., and Shen, G., 1991, Universal Features of Weight Funtions for Craks in ode I, Engineering Frature ehanis., 4, [9] Shen, G., and Glinka, G., 1991, Weight Funtions for a Surfae Semi-Elliptial Crak in a Finite Thikness Plate, Journal of Theoretial and Applied Frature ehanis., 15, [1] Kiiak, A. Glinka, G., and Eman,., 1998, Weight Funtions and Stress Intensity Fators for Corner Quarter- Elliptial Crak in Finite Thikness Plate subjeted to in- Plane Loading, Engineering Frature ehanis, 6, [11] Timoshenko, S.P., and Goodier, J.N., 197, Theory of Elastiity, rd Edition, Graw-Hill, New York. [12] Shijve, J., 198, Stress Intensity Fators of Hole Edge Craks. Comparison between One Crak and Two Symmetri Craks, International Journal of Frature, 2, R111-R115. [1] Wu, X.-R., and Carlsson, A.J., 1991, Weight Funtions and Stress Intensity Fator Solutions, Pergamon Press, New York. [14] Xiao, L., and ear,.e., 1998, FADDD User s anual, Dept. of Engrg. ehanis, University of Texas at Austin. [15] Li, S., ear,.e., and Xiao, L., 1998, Symmetri Weak- Form Integral Equation ethod for Three Dimensional Frature Analysis, Computer ethods in Applied ehanis and Engineering., 151, [16] Li, S., and ear,.e., 1998, "Singularity-Redued Integral Equations for Disontinuities in Linear Elasti edia," International Journal of Frature, 9, [17] Raju, I.S., and Newman, J.C., Jr., 1979, Stress-Intensity Fators for Two Symmetri Corner Craks, Frature ehanis, AST STP 677, Amerian Soiety of Testing and aterials, Copyright 2 by ASE