6.1 Damage Tolerance Analysis Procedure

Transcription

1 6. Dmge Tolernce Anlysis Procedure For intct structure the nlysis procedures for Slow Crck Growth nd Fil Sfe structure re essentilly the sme. An initil flw is ssumed nd its growth is nlyzed until filure of the member or lod pth occurs (or instbility nd rrest in Fil Sfe Crck Arrest structure). For intct structure, there re two options for the qulifiction of ech type of structure: depotlevel inspectble or non-inspectble. The differences re in the ssumed initil flws nd the required crck growth life to instbility. These requirements re explined in detil in Section.3. After lod pth filure (or instbility nd rrest), the dmge will be of sufficient size to fford more frequent inspection. As result, there re more options for qulifiction of the structure with remining structure dmge depending upon the inspectbility of the remining structure dmge. The options re: flight evident, ground evident, wlkround visul, specil visul, nd depot level. The required crck-growth life with remining structure dmge present depends upon the inspection intervl, which increses from one () flight to ¼ lifetime. Obviously, these requirements do not pply to slow crck growth structure. Crck rrest cn only occur if there is lod trnsfer from the crcked prt to other members (e.g., seprte member or reinforcements in the cse of Fil Sfe structure). However, lod trnsfer does not utomticlly clssify structure s Fil Sfe structure. Only if such lod trnsfer cn be shown to give crck rrest, nd if the remining structure requirements cn lso be met, cn the structure be qulified s Fil Sfe structure. In ll other cses the structure is considered s Slow Crck Growth structure nd should be qulified on the bsis of Slow Crck Growth requirements. The crck growth nlysis for ll types of structures requires the following steps: Step. Determine the stress-intensity fctor (K) s function of crck size for ech member involved. Possible lod trnsfer must be considered, becuse it my ffect K nd this crck growth. (See Section ). Step 2. Obtin or derive the stress history for the loction under considertion. (See Section 5). Step 3. Obtin bseline crck-growth dt (d/dn s function of K nd R) for ll the mterils involved, e.g., the skin nd the reinforcement members might be fbricted from different mterils. (Section 7 summrizes dt collection progrms). Step 4. Using the results of Steps,, 2, nd 3, clculte the crck-growth curve for ech element, using one of the retrdtion models described in Section 5. Strt with 0.05 inch flw. The result will be s shown schemticlly in Figure

2 Figure 6... Digrmmtic Crck Growth Curve (SCG = Slow Crck Growth, FS = Fil Sfe) Step 5. By using the results of the residul strength nlysis (Section 4), plot the criticl (first instbility) crck sizes, DMC nd LTC, for depot level inspectbility (fil sfe lod P DM ) nd non-inspectble (fil sfe lod P LT ). These re shown in Figure 6... NOTE: Since P DM (nd P LT ) differ for slow crck growth nd for fil sfe ctegorized structure, four criticl crck sizes my hve to be considered. Step 6. For slow crck growth structure, check Figure 6.. to determine: I. whether BD is equl to or greter thn 2 design lifetimes. II. whether CE (or C E) is equl to or greter thn ½ design lifetime. If only I is stisfied, the structure is qulified s slow crck growth, non-inspectble. If only II is stisfied, the structure is qulified s slow crck growth, depot level inspectble structure. If both I nd II re stisfied, it is optionl to qulify the structure s non-inspectble, or inspectble. It should be qulified s non-inspectble to void costly inspections. If neither I nor II is stisfied, there re three options: redesign or lower stress levels until either I or II is stisfied. mke the structure dismountble nd require specil non-destructive inspection. In tht cse the post-inspection flw my be ssumed 0.05-inch insted of 0.25-inch. Then BE should be equl to ½ lifetime for qulifiction s slow crck growth, depot level inspectble structure. demonstrte tht crcks smller thn 0.25-inch cn normlly be detected, nd show tht crck growth from this size to criticl covers ½ lifetime for qulifiction s slow crck growth, depot level inspectble structure. To check for potentil qulifiction s Fil Sfe structure continue with the following steps: Step 7. Check (Figure 6..) to determine: I. whether AF is equl to or greter thn design lifetime. 6..2

3 II. whether CG (or C G) is equl to or greter thn ¼ design lifetime. If either or both of the two conditions re stisfied the structure might qulify s fil sfe structure with the sme possibilities s in Step 6. However, clssifiction still depends upon the following steps. If neither condition is stisfied, either redesign or reduce stress levels. (Note tht the structure would certinly not stisfy Slow Crck Growth requirements.) Step 8. Determine the size of the rrested crck from the residul strength nlysis (Section 4). Step 9. Determine the remining structure dmge s specified in JSSG-2006, the Airplne Dmge Tolernce Requirements. First clculte the stress-intensity fctor s function of crck size. The growth of this dmge is clculted in the sme wy s tht of the initil dmge following Steps through 4. for independent structure, flw of inch should be ssumed in the djcent (uncrcked) member. The remining structure dmge is of the size to which this flw hs grown prior to instbility nd rrest or member filure. two djcent members in Fil Sfe dependent structure hve common source of crcking, so tht both hve 0.02 inch initil flw. If one member fils, the remining structure dmge in the djcent member is obviously of the size to which the 0.02-inch initil flw hs grown prior to instbility of the crck in the first member. in Fil Sfe structure, the crck my rrest in hole. In tht cse the remining structure dmge is simply inch flw t the other side of the hole, plus its growth prior to instbility. If the crck does not rrest in hole, remining structure dmge hs to be mutully greed upon by the USAF nd the contrctor. Step 0. Determine the totl dmge size by combining the results of Steps 8 nd 9. Determine the stress-intensity fctor of this dmge s function of its further growth. Step. Clculte the post-rrest crck propgtion curve, using the stress-intensity fctors determined in Step 0 nd follow the sme procedure s in Steps 2, 3, nd 4. Step 2. By using the results of the residul strength nlysis (Section 4) plot the criticl crck size for the pplicble level of remining structure inspectbility; five levels re vilble. If the life stisfied the requirement for the selected inspection, the structure qulifies s Fil Sfe structure provided tht the residul strength of the remining structure t the moment of rrest is dequte. If neither of these requirements is met, the structure does not qulify. In tht cse, there re two options: redesign (e.g., detil design of djcent structure) or lower stress level. try to qulify the structure s Slow Crck Growth structure by following Steps through 6 (lrger initil flw sizes nd longer crck lives re specified in tht cse). The following exmple illustrtes, in much simplified exmple, the interction of these decisions nd some of the informtion which cn be obtined from the bsic crck growth nlysis. This exmple is illustrtive only nd mny of the simplifying ssumptions would not be vlid for ctul design purposes. 6..3

4 A Simplified Exmple It is not immeditely obvious whether it is lwys dvntgeous to qulify structure s noninspectble. This subsection intends to illustrte in which cses higher design stresses cn be llowed if the non-inspectble qulifiction is selected, nd in which cses n inspectble qulifiction would llow higher design stresses. Subsequently, the other dvntges nd disdvntges of the two cses will be briefly considered. For Slow Crck Growth structure the required crck-growth life for the non-inspectble cse (2 lives from 0.05 inch to criticl) is on the order of four times the required life for depot level inspectbility (/2 lifetime from 0.25 to criticl). The sme holds for Fil Sfe structure ( lifetime from 0.05-inch to criticl, nd ¼ lifetime from 0.25 to criticl). Crck-growth curves usully show shrp rise towrds the end of the life. This rises the question whether the structure would not lwys qulify s non-inspectble if it qulifies s depot level inspectble. For exmple, in Figure 6.., if CG covers ¼ lifetime would not AF be t lest life; nd similrly if CE covers ½ life would not BE t lest cover 2 lives? If this were so, depot-level inspectble structure would lwys qulify s non-inspectble. (A noninspectble structure would not lwys qulify s depot level inspectble, however.) Then the inspectble cse would be superfluous, since the non-inspectble qulifiction would lwys permit the higher design stress. If the initil dmge of 0.05 inch consists of through crcks in skin pnels, it cn esily be shown tht the crck-growth life from initil flw size to filure is lwys more thn four times the life from 0.25 inch (through crck) to filure. However, this does not hold for the cse of crcks t holes. In the following exmple, n pproximte derivtion shows in which cses depot-level inspectble qulifiction would llow higher stresses thn non-inspectble structure, nd vice vers. It should be emphsized tht this exmple is only n pproximtion. The results should not be used s bsis for design; ech new structure should be considered s seprte cse, nd be nlyzed s such. The stress-intensity fctor for crcked hole cn be given s: K = βσ π For simplicity, fourth power lw for crck growth is ssumed: d dn = φc ( K ) 4 where φ is n rbitrry retrdtion fctor, used s n verge for the whole spectrum (it would be different for different spectr, but this is irrelevnt since φ will dispper during the derivtion). The growth rte cn be integrted to give the crck-growth life s: c c N d d = = ( ) 4 φc K π φcσ β 2 i i (6..) 6..4

5 In this eqution, i is the initil flw size, c is the criticl crck size, nd β is function of crck length nd hole dimeter. For the non-hole cse where β ws independent of crck length (for simplicity ssume β = ), it would follow tht: Also: N = 2 4 π φcσ N N LT DM idm i c cdm (6..2) ilt clt = (6..3) where the subscript LT refers to the non-inspectble cse, nd DM refers to the depot-level inspectble cse. Using the proper function for β for rdil crck t hole, Eqution 6.. ws evluted to give the equivlent of Eqution For Slow Crck Growth structures, ilt = 0.05-inch nd idm = 0.25 inch. The criticl crcks clt nd cdm were tken equl, becuse the lst prt of the crckgrowth curve is very steep, (i.e., the difference in life would only be smll if clt cdm ). For Fil Sfe structures, ilt = 0.25 inch. Also here clt nd cdm were tken equl. On the bsis of these numbers, the equtions were numericlly evluted s function of the criticl crck size ( c ) for vrious hole sizes. The results re shown in Figures 6..2 for Slow Crck Growth nd 6..3 for Fil Sfe. The bsciss gives c ; it could be converted into K Ic (or K c ) since K c= πβ 2 Ic 2 2 σ DM Figure Design Curve for Slow Crck Growth Structure For crcks t holes, the rtio N LT /N DM becomes smller thn 4 bove certin vlue of c (when the mteril hs sufficiently high toughness). The lrger the hole dimeter, the smller the crck size t which N LT /N DM <4. In view of the smll initil crck size (more life is spent in crck growth to 0.25 inch) these numbers re somewht lrger for Fil Sfe structures (Figure 6..3). 6..5

6 Figure Design Curve for Fil Sfe Structure In the regime N LT /N DM > 4, it is esier to qulify the structure s non-inspectble. If the totl life from i to c just covers two lifetimes ( life for Fil Sfe structure, the life from 0.25 to c will fll short of ½ life (¼ life for Fil Sfe structure). The crck-growth life might be so long tht it still qulifies s both inspectble nd non-inspectble. Tht mens tht the structure is oversized. As n exmple, consider Slow Crck Growth structure with c = 0.35-inch nd D = 0.2-inch. According to Figure 6..2 this would hve N LT /N DM 6. For the structure to qulify s depotlevel inspectble, N DM hs to be t lest ½ life. Then N LT would be t lest 3 lives (N LT /N DM = 6), wheres 2 lives would be dequte to qulify s non-inspectble. If crck-growth is ssumed pproximtely inversely proportionl to σ 4 (since d/dn = C K 4 ) the design stress could be incresed by fctor of (3/2) /4.. The structure would still qulify s Slow Crck Growth, non-inspectble, but not ny more s depot-level inspectble (N DM would only be /3 life). On the other hnd, if the toughness were high enough to give c = 0.75 inch, n inspectble structure could be designed to higher stress. For D = 0.2 inch, the rtio N LT /N DM would be on the order of 2.5 (Figure 6..2). If N LT would still be equl to 2 lives, then N DM would be 2/2.5 = 0.8 life. In order to qulify for depot-level inspectbility, the stress could be rised by fctor of (0.8/0.5) /4 =.2. In tht cse, N DM would be ½ life, but N LT would only be 2.5 x 0.5 =.25 lives. Hence, qulifiction s non-inspectble would require 2 percent lower stress thn qulifiction s depot-level inspectble. Similr exmples cn be given for Fil Sfe structure. The smller initil crck sizes work slightly in fvor of the non-inspectble qulifiction. It should be borne in mind, however, tht the primry crck-growth requirements here my not be decisive for the design, becuse the remining structure dmge requirements hve to be met lso. As might be expected, longer criticl crck sizes fvor qulifiction s depot-level inspectble t higher llowble stresses thn qulifiction s non-inspectble. Longer criticl crck sizes re lso beneficil for the totl crck-growth life. Therefore, qulifiction s non-inspectble is more esily ttinble with high toughness mterils. A depot-level inspectble structure hs dvntges nd disdvntges. Sfety is ensured by sufficiently slow growth of crcks of inspectble sizes (lrge criticl crck size) nd by periodic inspections. However, the necessity of inspection is burden to the opertor, nd it my mke 6..6

7 the design less ttrctive. Besides, sfety does depend on the dequcy of inspections. If crck is not detected in timely mnner, filure will still occur. Non-inspectble structures will generlly be somewht hevier. Sfety is ensured by sufficiently long crck-growth life. The indequcies nd deficiencies of the dmge tolernce nlysis (which re the sme s for inspectble structure) re not prtly compensted by periodic inspections. If the crck growth nlysis would be fctor 2 in error, ctstrophic filure might still occur within one lifetime. This could be prevented if the structure were inspectble. The ltter considertions re less pplicble to Fil Sfe structures. Their sfety is ensured by dequte remining structure dmge behvior, nd by the fct tht the lrge dmge fter lod pth filure (or instbility nd rrest) is esier to detect. Consequently, pre-instbility requirements cn be less stringent, nd re more of economicl significnce thn in the cse of Slow Crck Growth structure. 6..7