Damage Tolerance Analysis of Aero Structural Components

Transcription

1 Damage Tolerance Analyss of Aero Structural Components In today s structural desgn, fatgue and damage tolerance analyss have become most mportant and challengng task for the desgners because of falure of structure due to dfferent type of damages. Some of these damages have caused a loss of entre structure.e. Whole Arcraft Itself. Ths paper presents detals of, types of damages whch are expected to occur durng manufacturng and n servce nduced damages. Modelng of dfferent type of damages lke Cracks, Dents, Ncks, Gouges, and Scratches, Estmaton of Strength, Lfe usng Fatgue Analyss and Crack Growth usng Lefm approach of components wth defects s very essental for ther acceptablty for the desred functon. In ths presentaton, we share our experences n carryng out the Allowable Damage Lmt (ADL) analyss of metallc materal of a transport arcraft. Metallc materals are wdely used for many arcraft prmary and secondary structural components. However, metallc materals are susceptble to damage, whch can be nduced by servce loads and accdental mpacts. The man focus of the present work s to establsh the analyss procedure to valdate the component s strength, lfe, and resdual strength and nspecton ntervals wth defned defects n t.

2 Damage Tolerance Analyss of Aero Structural Components About the Authors Kran Rao, Sachn Rastog, Hemanth Upadhya, Ashok Sanman, S A Hakeem and K Badar Narayana The team has an average aerospace experence of 5 years and n lead by Kran Rao. Ths team has successfully executed projects on allowable damage lmt for a commercal arcraft program under the gudance of S A Hakeem and K Badar Narayana. 1

3 Damage Tolerance Analyss of Aero Structural Components Table of Contents 1. Introducton 3 2. Damage Tolerance and Allowable Desgn Lmt Analyss 3 3. Types of Damages 5 4. Dfferent Fatgue Desgn Methodologes 6 5. Typcal Examples used to Illustrate ADL and Damage tolerance Concepts 8 6. Concluson Acknowledgement References 11 2

4 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton Introducton Today s economc realty dctates that a fleet must be operated beyond ntended desgn lfe. The estmate materal propertes must be evaluated as precsely as possble wthn all the envronmental condtons to avod falures. For ths reason the arcraft structural ntegrty programs are put n place to provde an ntegrated and systematc approach to arcraft structural engneerng and mantenance. Two major approaches were developed n the past, namely, the safe-lfe and the fal-safe desgn concepts. The safe-lfe approach correlatng the tme to falure of the specmen wth the appled loads characterstcs to predct the tme to falure of real components usng Mnor s rule approach. The other s fal-safe concept, n whch lnear elastc fracture mechancs approach (LEFM) are used to predct the crack stablty, crack growth and hence the mnmal tme between the two nspectons to avod a crack reachng crtcal sze. The later concept called the damage tolerance, whose functon s to asses the effect of cracks n the structure. The analyss of damage tolerance behavor plays an mportant role n the structural ntegrty program. Fg. 1 shows the typcal procedure for damage tolerance analyss used n the present work. Ths paper presents detals of, types of damages, modelng dfferent type of damages, estmaton of ther lfe usng fatgue analyss and crack growth analyss usng LEFM approach. Damage Tolerance and Allowable Desgn Lmt Analyss 2.1 Damage Tolerance Damage tolerance s ablty t ressts fracture from the preexstent cracks for a gven perod of tme and s an essental attrbute of components whose falure could result n catastrophc loss of lfe or property. The damage tolerance addresses two ponts concernng an ntally cracked structure. Frst, t s desred to determne fracture load for a specfed crack sze. Second, t s necessary to predct the length of tme requred for a sub-crtcal crack to grow to the sze that causes fracture at gven load. It s assumed that the crack can extend n a sub-crtcal manner by fatgue and/or stress corroson crackng. 2.2 Allowable Damage Lmt (ADL) Allowable Damage Lmt s the damage that allows an operator to contnue operatng an arcraft wthout any repar. Damage permtted by these data must have no sgnfcant effect on strength and fatgue lfe of the structure, whch must stll be capable of fulfllng ts desgn functon. 3

5 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton 2. 3 Types of falures Any structure wll fal due to one or a combnaton of falures such as elastc & nelastc deformatons, bucklng, fatgue, creep, corroson & fracture. Ths paper descrbes the procedure to carry out the damage tolerance analyss wth ntal cracks. Fg. 1 Damage Tolerance Analyss Process 4

6 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton Types of damages Damages may occur due to manufacturng and assemblng errors ncludes gouges, ncks, burrs, scratches & dents. Materal flaws nclude porosty, consttuent partcles, nclusons, forgng or castng defects & mproper thermal/mechancal treatment of basc alloy. Servce nduced damage ncludes cracks, damage due to foregn object ncludes brd strke effects etc. Some typcal damages seen n aero-structural components are shown n Fg. 2 Fg. 2 Typcal damages n aero-structural components 3.1 Smulaton of damages All regons of a component must be able to wthstand damages lke dents, cracks, scratches and gouges, worst case wll be cracks. Fg 3 and 4 show the smulaton of dents and cracks (center crack). Global model wth loads and BCs Local model wth loads & BCs Stress (σxx) plot wth dent Fg. 3 Smulaton of Dent 5

7 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton Global model wth loads and BCs Smulaton of center crack Max. Prncpal Stress Local model Fg. 4 Smulaton of Center Crack by un-connectng nodes Dfferent Fatgue Desgn Methodologes The nterest here s to determne the nfluence of the preexstent cracks on the structural component. In the followng sectons dfferent fatgue desgn concepts are brefly dscussed. a) Infnte Lfe Desgn In ths desgn concept component stresses are kept below the endurance lmt of the materal. The endurance lmt s the maxmum constant ampltude stress that can be appled to a component wthout causng a fatgue falure. Although the endurance lmt concept was useful for solvng the fatgue problems orgnally, ths approach has many serous lmtatons. The endurance lmt, s extremely senstve to the condton of the test specmen. Notches, small scratches, ncks, dngs serve as stress concentratons that quckly cause localzed fatgue crackng and greatly reduce the endurance lmt. Snce, t s mpractcal; to desgn hghperformance structures for nfnte lves by the endurance lmt methodology. It s now accepted that most structures wll have a fnte fatgue lfe. b) Safe-Lfe Desgn The safe-lfe approach treats fatgue as a crack nucleaton process and does not explctly consder the possblty for crack growth. The safe-lfe approach led to several nadequate arcraft desgns n the 1960s; however, ts current use s dscouraged, n the man ar craft structures, except, landng gear and n some helcopter components. c) Damage Tolerance Desgn In order to overcome ths shortcomng of the safe-lfe approach, damage tolerant desgn methods were developed that assume the structure contans ntal cracks. The ntal crack usually based on the nspecton lmts. There are two general approaches, wth varatons, that may be followed to guarantee that the structure does not fal n servce, they are; 6

8 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton. Slow Crack Growth: The slow crack growth desgn crtera select component materal and sets stress levels so that the assumed preexstent crack wll not grow to falure durng servce and s the normal approach for sngle load path structure. For ncreased safety, the allowed servce lfe usually obtaned by dvdng the total crack growth perod by a factor of 2. The component would have to be nspected at ths tme before contnued operaton would be permtted.. Fal-Safe Desgn: Ths desgn concept assumes the possblty of multple load paths and/or crack arrest features n the structure so that a sngle component falure does not lead to mmedate loss of the entre structure. The load carred by the broken member s mmedately pcked up by adjacent structure and total fracture s avoded. It s essental; however, that the orgnal falure be detected and promptly repared, because the extra load they carry wll shorten the fatgue lves of the remanng components. 4.1 Fatgue lfe estmaton usng Fracture of mechancs approach In lnear elastc fracture mechancs (LEFM), most formulas are obtaned usng ether plane stress or plane stran, assocated wth the three basc modes of loadng[1], namely, openng, sldng and tearng. In the present analyss, LEFM approach s assumed where n Stress Intensty Factors (SIF) KI controls the crack growth. Fg 5 depcts a typcal fracture and fatgue behavor of a cracked body. Fg. 5 Fracture and Fatgue behavor of a cracked body The SIF, K s related to appled load, crack sze and geometry of the component. In equaton form t s gven by: K = σ max. F. π. a Where, σ max s appled stress, a s crack sze and F s dmensonless factor ( these factors are well documented for a number of crack confguratons [2-4]. K can be K I, K II or K III dependng upon the type of crack tp deformaton. 7

9 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton 4.2 PARIS MODEL A lnear relatonshp between log da dn vs. log ΔK s observed between these two asymptotes, s used for fatgue crack growth predctons by Pars [5] equaton n the equaton da = C. ( ΔK ) n dn Where C & n are materal / Pars constants. Typcal Examples used to Illustrate ADL and Damage tolerance Concepts MSC Nastran s used for addressng all the ADL and damage tolerance problems. The von-mses stresses are used to establsh the margn of safety (MOS) for statc strength, fatgue and crack growth loadng envronments gven wth these examples. Confguraton: A panel of dmenson 21 X 21 s consdered for analyss wth a hole of dameter 3.0 to smulate the effect of damages lke dents, cracks, scratches and gouges, crtcal beng the crack, thckness of the panel s Damage s smulated by removng the materal at the center of the plate. Fg 6 shows the dmensons, FE model of the panel. Materal propertes: The materal consdered s T 6242, wth Elastc Modulus, E (ps) = 1.482E+07 and Posson's Rato = Materal allowable: F RT = 143 ks at RT, F RT= 136 ks at RT. Temperature reducton factor at 800 F = 0.72 for F tu and 0.6 for F ty 5.1 Comparson of Stress Dstrbuton to valdate the model The stress estmated (Fg 6) for the present problem s valdated aganst avalable reference solutons [7], these calculatons are gven below; Total load appled n X-drecton, P = lb Area of cross-secton, far from hole, A = 21 x 0.02 => 0.42 n 2 Appled stress, σ = / 0.42 => ps Maxmum stress from FE analyss, σ max = ps Stress Concentraton Factor, SCF, K tg (from FE results) = σ max / σ K tg = / => 3.24 Stress Concentraton Factor, SCF, K tg [7] = 3.09 There about 4.85 % dfference, ths makes reasonably good comparson and ths mesh densty s consdered for further analyss. 5.2 Statc strength estmaton For ths problem, the stress resultant forces Nx, Ny and Nxy are estmated from the global soluton and converted as approprate nodal forces based on the panel dmenson. Fg. 6 shows the loads and BCs for the panel wth resultng von-mses stress dstrbuton 8

10 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton Fg. 6 Geometry, appled loads and stress dstrbuton Strength estmaton: Usng the maxmum stress (von-mses) obtaned from the analyss, statc margn of safety (MOS) obtaned for 8000F as 1.48 and 1.95 for lmt and ultmate loads respectvely. 5.3 Fatgue lfe estmaton Ths allows us to calculate the damage for lmt load usng the maxmum von-mses stress estmated for confguraton shown n Fg 6. The estmated number of cycles s very large. Fg 7 shows the typcal S-N data for the gven materal ndcatng the current stress level and the expected lfe. From the below fg. t s seen that there no damage produced for the gven lmt load. Fg. 7 S-N data for T-6242 Materal 5.4 Damage Tolerance Desgn usng fracture mechancs approach Materal constants and allowable: The materal constants and allowable (nearest values from NASGROW 3.0 [8] are chosen) for T-6242 are taken as Yeld Strength = 138 ks, fracture toughness, K IC = 50 ks n and the Pars constants C = 2.52E-09 (n/cycle) (ks n) -n and n = For the estmaton of fatgue crack growth lfe the panel s assumed to contan ether center or edge crack as shown n Fg 8. Based on panel sze, thckness, and maxmum stress observed n the locaton and usng smple Pars type crack growth law. The number of elapsed cycles for the defect to grow from the ntal value to a value where the stress ntensty factor (SIF) reaches to fracture toughness of the materal or the crack sze for whch the net secton stress reaches the materal yeld. Knowng the allowable number of cycles based on C checks the lfe s estmated. A routne based on Pars crack growth law for lfe estmaton s gven below (for Center Crack) 9

11 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton Fg. 8 Unformly loaded center and edge cracked panel Plate Wdth, W = 21.0, Intal Crack Sze, a = 3.0 and thckness of the panel, t = 0.02 Crack Confguraton= through crack Max Stress, σ max = ks, Mn Stress, σ mn = 0 ks Half crack sze, a a o = = 1.5, half Plate wdth, w b = = Appled Stress, σ app = σ max - σ mn = ks Fnal half crack sze based on Net Secton Stress, σ a = n b 1 max = 9.70 σ y 5.5 Fatgue Crack Growth Estmaton for Center Crack a F Δ K = a 1 + Δ a = da Δ N da Δ N ( dn ) N = = avg = F σ = 0 = C app [ Δ K ] Δ = Δ a da Δ N dn da N avg π. a n a b da + Δ N 2 1 a b Where, a Half crack sze at th teraton, Δa Step sze for crack growth, F Shape Functon, ΔK - fracture toughness, (da/dn) rate of crack growth, (dn) - no. of cycles for crack to grow Δa and N - No. of cycles for crack to grow from a 0 to a. a b 3 10

12 Interlamnar Stress Calculaton n Lamnates Usng an 8 Noded Brck Element Based on Mxed Fnte Element Formulaton Fg. 9 Fatgue crack growth Center crack and Edge crack For the gven confguraton usng the above procedure, the crack growth both for CCT and edge crack confguratons are obtaned, the same s gven n Fg 9 from the number of cycles and the allowable cycles for the panel, the MOS and the total number of nspecton ntervals are selected. Concluson Ths paper dscusses the mportance of fatgue and damage tolerance analyss procedures, whch are domnant factors n the arcraft structural desgn process as well as the followng n servce lfe. These concepts are llustrated wth typcal examples. Acknowledgement The authors are thankful to TCS Management n specfc to Aerospace Practce & Smulaton Practce for ther motvaton & contnuous support and provdng us the opportunty to share the knowledge. References 1. D Brock, Elementary Engg. Fracture Mechancs, Martnus Njhoff Pub., G C Sh, Hand book of SIF, Lehgh Unversty Pennsylb. USA H Tada et al., SIF and analyss of cracks Del research Hellertow. 4. D P Rook and D J Cartwrght, Compendum of SIF, HMSO, London, P C Pars et al., A ratonal analytc theory of fatgue, the trends n Engg. Vol 13, No.1, MIL-HDBK-5F Stress Concentraton Factors by Peterson 8. Fatgue Crack Growth Computer Program NASGRO VERSION 3.0, JSC-22267B, Reference-manual, and Oct

13 About Aerospace Practce TCS has been executng projects for goodrch snce August 2003 n the areas of Aero Structures, Landng Gear, Wheels & Brakes and Host & Wnch etc. The Goodrch team currently has 25 ndustry bread desgn and Analyss Engneers. Goodrch team works closely wth Aerospace Practce on Nche areas. About Tata Consultancy Servces (TCS) Tata Consultancy Servces Lmted s an IT servces, busness solutons and outsourcng organzaton that delvers real results to global busnesses, ensurng a level of certanty no other frm can match. TCS offers a consultng-led, ntegrated portfolo of IT and ITenabled servces delvered through ts unque Global Network TM Delvery Model, recognzed as the benchmark of excellence n software development. A part of the Tata Group, Inda's largest ndustral conglomerate, TCS has over 89,000 of the world's best traned IT consultants n 47 countres. The company generated consoldated revenues of US $4.3 bllon for fscal year ended 31 March 2007 and s lsted on the Natonal Stock Exchange and Bombay Stock Exchange n Inda. For more nformaton, vst us at tcs.aerospace@tcs.com All content / nformaton present here s the exclusve property of Tata Consultancy Servces Lmted (TCS). The content / nformaton contaned here s correct at the tme of publshng. No materal from here may be coped, modfed, reproduced, republshed, uploaded, transmtted, posted or dstrbuted n any form wthout pror wrtten permsson from TCS. Unauthorzed use of the content / nformaton appearng here may volate copyrght, trademark and other applcable laws, and could result n crmnal or cvl penaltes. Copyrght 2007 Tata Consultancy Servces Lmted