Stress Analyses of Mechanically Fastened Joints in Aircraft Fuselages

Transcription

1 Stress Analyses of Mechancally Fastened Jonts n Arcraft Fuselages J.J.M. de Rjck, S.A. Fawaz, J. Schjve 3, R. Benedctus 3 and J.J. Homan 3 Corus RD&T, O BOX 000, 970 CA IJmuden, The Netherlands, Rener.de-rjck@Corusgroup.com USAF Acadamy, 354 Farchld Drve, Sute 6L-55, USAF Acadamy, CO 80840, Scott.Fawaz@usafa.af.ml 3 Delft Unversty of Technology, Kluyverweg, 69 HS Delft, The Netherlands, J.Schjve@lr.tudelft.nl, R.Benedctus@lr.tudelft.nl, J.J.Homan@lr.tudelft.nl Abstract: For mechancally fastened lap-splce jonts and butt jonts n a fuselage structure the domnant loadng condton s ntroduced by the groundar-ground pressurzaton cycle. The hoop load s transferred from one skn panel to the next panel by fasteners n a lap jont or a sngle strap butt jont. The hoop load s offset by eccentrctes n the jont, resultng n secondary bendng. Secondary bendng s hghly dependent on the magntude of the eccentrcty and the flexural rgdty of the jont between the fastener rows. The bendng stresses can be derved wth a one-dmensonal Neutral Lne Model (NLM) as proposed by Schjve. In the present paper ths model s extended to account for load transmsson by rvet rows between the outer rows of the jont whch was gnored n the orgnal model. Stran gage measurements have ndcated that load transmsson occurs n these rows. The extended model covers both monolthc and fbre metal lamnate materals. It can be appled to a wde range from smple to complcated jonts contanng rvets or bolt type fasteners. In case of rveted fasteners, the nfluence of so-called fastener flexblty can be addressed as well. Stran gage measurements on lab specmens and n-servce jonts have supported the analyss to show the most lkely locatons for fatgue crack nucleaton and growth.. INTRODUCTION A thorough understandng of the stresses at the most crtcal fastener row s essental n conductng fatgue and damage tolerance analyss of mechancally fastened jonts. The crtcal fastener row locaton s most susceptble to fatgue crack nucleaton and subsequent crack growth. The domnant loadng condton for rveted lap-splce jonts n an arcraft fuselage structure s ntroduced by the Ground-Ar-Ground (GAG) pressurzaton cycle. The hoop load s transferred from one skn panel to the next panel by fasteners n a lap jont or a sngle strap

2 butt jont. The hoop load s not collnear through the jont because t s offset by eccentrctes n the jont. The eccentrc path of the hoop load causes secondary bendng, see Fgure for a smple case. The total stress n the jont around the rvet holes s then the sum of the hoop stress, stresses due to secondary bendng and bearng stress assocated wth the fastener loads on the holes. Load transmsson by frcton s not consdered here. Secondary bendng s hghly dependent on the magntude of the eccentrcty and the flexural rgdty of the jont between the fastener rows. The theory used to derve the bendng stresses s based on advanced beam theory []. Schjve adopted a smple Neutral Lne Model (NLM) to calculate the tenson and bendng stresses at any locaton n the jont. It s mportant to know the secondary bendng stress for ndcatng the most crtcal rvet row n a lap-splce jont [], [3] n whch the fatgue crack nucleaton wll occur. Well-known problems of multple-ste damage and damage tolerance are assocated wth crack nucleaton at fastener holes. The neutral lne model s a one-dmensonal model n such a way that the out of plane dsplacement of the neutral axs (w(x) n Fgure 3) determnes the behavour of the jont as a sngle structural element. In the smple Neutral Lne Model employed by Schjve load transmsson occurs at the outer rvets only, and load transmsson does not occur by fasteners n the mddle row. The effect of local plastc deformaton was consdered by Schjve n a smple way by assumng that t caused a local rotaton of the neutral lne. A rotaton of caused already a sgnfcant reducton of the maxmum bendng moment n the jont, but load transmsson by the mddle rvet rows was stll gnored. Müller [4] consdered load transfer by all rvet rows n an entrely dfferent way. He ntroduced elastc fastener elements between the two sheets of a FE model. In ths model the mddle row s also transferrng part of the load. The two outer rows were also the more crtcal rows n hs model. The method proposed by Müller s not evaluated here because ths method s based on changng the actual flexural rgdty to a vrtual flexural rgdty. The method s adequate for jonts made of monolthc materals, but does not allow for a correct calculaton of the neutral lne dsplacements for fber metal lamnates (FML) because both the elastc modulus and moment of nerta are changed. In the present paper a new model s ntroduced based on the elastc Neutral Lne Model. However, local plastcty around the rvet holes s assumed to occur. As a consequence, load transfer occurred at each rvet row, whch results n dfferent loads n the two matng sheets of the lap jont. The latter effect s dealt wth by defnng an nternal moment. The load transmsson s dependng on the thcknesses of the sheets and the load on the jont. For llustratve purposes the orgnal Neutral Lne Model s dscussed frst n Secton. for a smple symmetrc lap jont. In Secton. the new model s dscussed for the same lap jont. A comparson s made between the bendng stresses obtaned wth the smple Neutral Lne Model and the present model. The new model can also be appled to more complex splce jonts of both monolthc and fber metal lamnates, e.g. GLARE. In the latter case the multlayer effect on the bendng stffness must be accounted for. Varous results are presented n [6]. In Secton 3 exemplary results are shown for the bendng stress n a sngle strap butt jont of monolthc 04-T3 and for a smlar jont of Glare sheets. The results are compared to stran gage measurements. The paper s completed wth some summarzng conclusons.

3 x x 3 x 4 a j= x j=3 j= b L L L 3 L 4 Fgure Nomenclature for lap-splce jont geometry Fgure Tensle load causes secondary bendng of the lap-splce jont w e Fgure 3 Neutral lne model wth out-of-plane dsplacement w(x). THE NEUTRAL LINE MODEL FOR A SIMLE LA-JOINT MODEL. Orgnal neutral lne model The orgonal neutral lne model [3] for an smple lap-splce jont s recaptulated here n order to explan the extenson of ths model wth fastener flexblty and the nternal moment concept. The dmensons of the lap-splce jont wth three rvet rows are shown n Fgure. For smplcty symmetry s assumed whch mples that L = L 3 and L = L 4. Both sheets are also smler t a = t b and E = E. If the specmen s loaded n pure tenson then secondary bendng wll occur (Fgure ) and the neutral lne becomes curved due to eccentrctes nherent to lap-splce jonts (Fgure 3). In the orgnal Neutral Lne Model the two sheets between the outer fastener rows are assumed to behave as one ntegral sheet. It mples that load transfer does not occur n the mddle row. Furthermore fastener flexblty s not consdered. Wth the notatons of Fgure the bendng moment can be wrtten as:

4 M x = w () For sheet bendng: d x M x = EI () dx The dfferental equaton thus becomes: d w α w = 0 (3) dx wth α = ( =,) (4) EI The soluton s: w = A snh( α x ) + B cosh( α x ) (5) A and B are solved usng the boundary condtons for the two parts wth length L and L respectvely. x = 0 w x = L w = 0 x = L and x x = L and x = 0 w dw = 0 dx = 0 ( symmetry) = w e dw = dx (6) After substtuton of Eq. (5) n the n Eq. (6) the constants A and B of Eq. (5) can be solved. The bendng moment M x s then obtaned as: M x d w EI dx = The maxmum secondary bendng occurs at the frst fastener row (x = L ). Defnng the bendng factor k b as: k b 6M c σ bendng Wt 6α A = = = (7) σ tenson t Wt the solutons derved n [3] for t a = t b and L = L 3 s:

5 3 k b = (8) Th + Th wth the hyperbolc functon Th = tanh(α L ) t was shown n [3] that for a long specmen,.e. L sgnfcantly larger then L, the value of Th s practcally equal to. Ths mples that the effect of the length of the specmen on the secondary bendng can be gnored, and the equaton reduces to: k b 3 = (9) + tanh ( α L ) wth: 3σ α = (0) t E The loadng condtons at the ends of the specmen,.e. far away of the overlap regon, were also explored n [3]. If the hnged load ntroducton n s replaced by a fxed clampng (dw/dx = 0 at x = 0) the dfference of the secondary bendng at x = L wth the hnged load ntroducton s neglgble. Ths also apples to a msalgnment when the loads at the two ends of the specmen are appled along slghtly shfted parallel lnes. Values of the bendng factor k b calculated wth (9) for dfferent nput data are shown n Table I. The data n the frst lne of the table apples to the geometry of typcal specmen dmensons. The load corresponds to an appled stress level of 00 Ma. L [mm] 00 L [mm] t [mm] E [N/mm ] k b for an appled stress of 00 Ma Table I Varaton of nput data for symmetrcal lap-splce jont The results n the table show the followng trends: If the row spacng L s reduced from 8 mm to 8 mm, the bendng factor ncreases from.6 to.43 If the sheet thckness s reduced from mm to mm, the bendng factor decreases from.6 to 0.88 If the Elastcty Modulus s ncreased from 7000 Ma (Al-alloys) to 0000 Ma (steel) the bendng factor ncreases from.6 to.49 These trends can be understood as beng related to the bendng flexblty of the overlap regon and the eccentrcty n the jont. It may well be expected that smlar trends wll also

6 apply to lap-splce jonts of fber metal lamnates, whch also apples to the effects of specmen clampng (fxed or hnged and msalgnment).. The model wth the nternal moment to account for load transmsson In the prevous secton load transfer from one sheet to the other sheet of a lap-splce jont occurred only by the fasteners n the st and 3 rd row because fastener flexblty was gnored and the two sheets between the outer rvet rows were consdered as a sngle beam wth a thckness of t a + t b. However, due to the hgh stresses n the sheets around the fastener holes, some plastc deformaton wll occur around the holes. As a result some more rvet tltng wll be possble. Ths wll affect the load transfer and as a consequence load transfer wll also occur by the mddle row. An nternal moment model s presented for solvng ths problem. As an llustraton of the model, t s dscussed here for the same symmetrc lap splce jont dscussed n the prevous Secton.. Because fastener flexblty s now consdered load transmsson from one sheet to the other sheet occurs by all three rows, also the mddle row. The load transmtted by the three rows are T, T and T 3 (see Fgure 4), and because of the symmetry T 3 = T. Moreover, = T + T + T 3 and thus: = T + T () T T T 3 t M T M T M 3 T 3 L L Fgure 4 Smple lap-splce jont wth load transmsson from the upper sheet to the lower sheet causng nternal moments t -T M T Fgure 5 Internal moment as a result of load transfer va the fastener t e M Fgure 6 Moment as a result of the load transfer of orgnal neutral lne model

7 The loads n the varous parts of the jont are ndcated n Fgure 4. In the elementary neutral lne model, the mddle row dd not contrbute to load transmsson (T = 0) and as a consequence T and T 3 were both equal to /. However, due to fastener flexblty, T and - T are no longer equal to / because dfferent tenson loads occur n the upper and lower segments of the overlap of the jont. As a consequence, an nternal moment wll be ntroduced at the fastener rows, M, M and M 3, at the three fastener rows respectvely. In vew of symmetry M 3 = M. The nternal moment M at the frst fastener row s ndcated n Fgure 5. As mentoned earler, the loads n the upper and lower sheet are dfferent due to the load transfer assocated wth dfferent tensle elongatons of the upper and lower sheet. In the neutral lne model the upper and lower sheets between the st and 3 rd rvet row, n the overlap regon, are assumed to act as an ntegral beam subjected to secondary bendng. t M + T T M = T t 3 t = 0 () Ths moment s assocated wth the nfluence of the load transfer of Fgure 5 and thus the neutral lne model wll behave as shown n Fgure 6. For the moment n the second and thrd fastener row usng the same prncple follows that: M M 3 = T t = T t (3) The orgnal neutral lne model calculates the (non-lnear) secondary bendng moment n a jont and assumes a moment ntroduced by the eccentrcty e. The nfluence of the load trasnfer leads to a change of ths moment. The changes per fastener row can be wrtten as: 3 = M = M = M 3 + e + e 3 (4) These changes n moments must be taken nto account when analyzng the deformatons n the jont. Note that for the orgnal neutral lne model, T = 0, T = T 3 = / and e = e 3 = t/, t follows that = 0. The calculaton of T and T s based on the dfferent elongatons of the upper and lower sheetoccurng as a result of fastener tltng. Ths phenomenon s descrbed here by a lnear functon between the appled load () transmtted by a row of fasteners and the dsplacement (δ) occurrng n the jont due to plastc deformaton around the fastener holes. f δ = (5) For the lap-splce jont, the symbol δ s the dsplacement of the lower sheet at a row relatve to the upper sheet, whle s the load assocated wth the relevant nternal moment (T or T ). The symbol f s an emprcally obtaned flexblty constant. For the frst and the second row:

8 δ = f T δ = f T (6) The fastener flexblty dsplacements and the tensle elongatons of the upper and lower sheet (ΔL upper and ΔL lower ) must be compatble, see Fgure 7. L+ΔL upper T T T T L+ΔL lower δ δ Fgure 7 Force dstrbuton when effected by fastener flexblty The tensle elongatons follow from the stress stran relaton: ΔL = ξ load wth ε = ΔL = L S E = load AE L ξ = (7) AE where A s the cross sectonal area. For the lap-splce jont n Fgure 7 t mples: ΔL ΔL upper lower = ξ = ξ T ( T ) (8) The compatblty between the tensle elongatons and fastener flexblty dsplacements s easly obtaned from Fgure 7: ( L + ΔL ) L (9) + ΔLupper = δ + lower δ Wth L = 8 mm, A = 00 mm and E = 7000 N/mm the ξ-value s: ξ = mm N The emprcal fastener flexblty accordng to Huth [7] s: f = mm N

9 The value of T can now be calculated by substtuton of Eqns 6 and 8 n 9, and T follows from Eqn.. The results obtaned are: ξ + f T = ξ + 3 f f T = ξ + 3 f (0) Wth the above-mentoned value of ξ and f the results for T and T are: T = 705 T = 5896 Ths load transmsson s llustrated by Fgure 8. As a result of the fastener flexblty the frst fastener row transmts 35 % (705 N) of the load, the second row 30 % (5896 N) and the thrd row agan 35 % L L L 3 L 4 Fgure 8 load transfer n the smple lap-splce jont accountng for fastener flexblty The calculaton of the nternal moment s entrely dependent on the locaton of the neutral axs of the lap-splce jont [6]. The nternal moment s therefore a functon of both the load transfer and the geometrc lay-out of the jont. In case of a monolthc jont the neutral lne s located at the center of each element of the lap-splce jont. The moments can then be calculated usng e = -t/ and Eqn. 3 and 4: 3 = 5896 Nmm = 79 Nmm = 5896 Nmm The bendng factor was calculated n the prevous Secton. for the smple lap jont wthout consderng rvet tltng. The bendng factor wll now be derved for the same lap splce jont accountng for rvet tltng and load transmsson by all fastener rows.

10 art art L L t e M t x x Fgure 9 Secondary bendng n the smple symmetrc lap-splce jont wth the nternal moments at the frst fastener row For art n Fgure 9 the equatons for the bendng moment and the dsplacements w(x) are smlar to the Eqn. - 4 wth the soluton gven n Eqn. 5. Wth the condton that w(x ) = 0 for x = 0, t s easly found that B = 0. The equaton for w(x ) thus becomes: w x ) = A snh( α ) () ( x For art the nternal moment must be ncluded: M x d w = w () ( x ) = EI dx x The soluton of ths dfferental equaton s: ( x ) = A snh( α x) + B cosh( α x) + (3) w The boundary condtons at the frst fastener row (x = L and x = 0) are: ( w ) = ( wx ) + x e x = L x = L (4) dw dx dw = dx x = L x = 0 (5) At the end of art another condton for reasons of symmetry s: ( x = =L w ) 0 (6) The constants A, A and B can now be solved after substtuton of Eqns and 3 n Eqns. 4 to 6. Wth the boundary values of the hyperbolc functon wrtten as: S = snh( αl ) C = cosh( αl ) Th = tanh( α L )

11 The three equatons are: B = A S α A = AC α A S + B C + e + = 0 (7) The most crtcal bendng moment occurrng at the frst fastener row s obtaned as: M d w = EI dx = (8) x L x = L Wth α = the result for the bendng factor becomes: EI k b 6M c σ bendng Wt 6α A = = = (9) σ tenson t Wt After solvng A and realzng that t = t and e = - t / for the smple lap-splce jont, a further evaluaton leads to: 6 3 t + C k b = (30) Th + Th It should be noted that for = 0,.e. no fastener flexblty and nternal moments, Eqn. 30 reduces to the prevous Eqn. 9. Results of the calculatons of k b wth fastener flexblty (Eqn. 30) are shown n Table II for smlar values of L, L, t, E used prevously. L [mm] 00 L [mm] t [mm] E [N/mm ] f [mm/n] k b for an appled stress of 00 Ma Wth f Wthout f E E E Table II Varaton of nput data for symmetrcal lap-splce jont, f calculated usng Huth [7] ths also effects the load transfer through the fastener rows.

12 The last column of Table 3 ncludes the results for the same lap jont as calculated n Secton. where tltng of fasteners was not consdered. A comparson between the bendng factors obtaned wth and wthout ncludng fastener flexblty s made n the last two columns of Table II. It turns out that the bendng factor s reduced by the fastener flexblty whch agrees wth expectatons about flexblty effects recalled earler. However, the reducton s relatvely small, just a few percent wth one excepton for t =.0 mm (reducton 7%). The trends of k b noted n the prevous secton do not change when the nfluence of load transfer s taken nto account. Changng the overlap length from 8 mm to 8 mm stll ncreases the bendng factor k b. A decrease n sheet thckness results n a decrease n bendng stffness and thus n a lower k b. Increasng the Modulus of Elastcty for the jont results n a hgher bendng factor k b. In summary: The fundamental assumpton of the present nternal moment model s that the load dstrbuton n the two sheets s related to deformatons assocated wth fastener flexblty n order to arrve at compatblty equatons from whch the load dstrbuton can be calculated. The load dstrbuton then reveals the load transmtted by the fastener rows from whch the nternal moments can be derved. In the present secton, a calculaton was made for the most smple case of a symmetrc lap-splce jont to llustrate the basc procedure. Smlar calculatons can be made wth the same model for other jonts wth a more complex geometry and other materals ncludng fber metal lamnates. 3. RESULTS In ths secton results are presented for surface stress levels n two butt splce jonts and one n servce lap splce jont. Fgure 0 shows calculated and measured results of stress levels n an Al-04 T3 Clad butt splce jont. Only one overlap of the symmetrc smple strap jont s shown. The calculatons provde a contnuous curve of the varaton of the stress level along the jont. The stran gage measurements gve a number of local stress values only. Outsde the overlap the agreement between calculaton and measurement s very good. Insde the overlap the agreement s less, but t should be realsed that the neutral lne model s a one dmensonal model whch does not take nto account the non-homogenous stress dstrbuton n the wdth drecton Fgure shows a smlar comparson for a fber metal lamnate butt-splce jont. The trends are practcally the same as for the Al-04 T3 Clad butt splce jont,.e. agan a very good agreement outsde the overlap area, and a qualtatvely correct trend nsde the overlap.

13 Butt jont: Fgure E- Stran gage pattern: Fgure E-6 Appled stress: 04 Ma 50 Stran gage data Neutral lne model s.g. 3 Surface stress [Ma] s.g. 6 s.g. 8 s.g.9 s.g t 8 9 t Locaton [mm] Fgure 0 Butt jont results from stran gages at the lower sde of the butt splce jont, sheet thckness t = 4.0 mm, t = 4.0 mm and materal Al 04-T3 Clad Stran gage data Neutral lne model Butt jont: Fgure E- Stran gage pattern: Fgure E-6 Appled stress: 8 Ma Load transfer s.g. 3 Surface stress [Ma] 00 s.g. 6 s.g. 9 s.g. 50 s.g t t Locaton [mm] Fgure Butt jont surface stress representaton for stran gages at the upper surface, sheet thckness t = 4.5 mm, t = 4.5 mm and materal sheet s Glare 3-6/5-0.5 and sheet s Glare B-6/5-0.5

14 The results shown n Fgure are from a four rvet row lap-splce jont wth extra doublers and a longtudnal stffener attached wth only one fastener row. Stran gages for ths jont were attached one nch to the rght of row A. The results for ths specmen were obtaned by Fawaz [8]. Four dfferent jonts were used to obtan stran gage data. Wth the method descrbed n ths paper, the load transfer dstrbuton over the four fastener rows s as follows; 5% load transfer from the skn-materal nto the doubler. The second fastener row transfers agan 5% load from the skn and doubler sheet to the other sheet and doubler. Each fastener row carres 5% of the appled load. As shown for the other jonts before, the stresses outsde the overlap regon are predcted wth great accuracy, even for ths more complcated jont wth doublers. 8 6 Row A Normal Stress (ks) Tensle stress Bendng stress Tensle stress (stran gage data) Bendng stress (stran gage data) Appled Load (lbs) Fgure Normal stress one nch to the rght of row A 4. CONCLUSIONS. The nternal moment concept gves a good representaton of the load transfer occurrng n mult-row jonts. The calculaton of the load transfer can be made for complcated lap-splce and butt jonts n both monolthc and lamnated sheet materals. The calculated and the expermental stress levels agreed very well outsde the overlap area of the jonts, whle ndcatve results were obtaned n the overlap area. The results provde a base for further research nto mproved fastener flexblty equatons and load transfer.. The nfluence of the fastener flexblty s of less mportance than prevously expected. 3. Addng doublers and strngers do not offer complcatons. Only those parts addng bendng stffness to the jont need to be taken nto account.

15 4. The present experence ndcates that the neutral lne model s a very powerful tool to use n the early stages of jont desgn. It gves a good pcture of crtcal bendng stresses n a jont. LIST OF SYMBOLS Latn Greek A Area [mm ] A, B Constants for solvng dfferental eq. [mm] e Eccentrcty [mm] E Young s modulus [Ma] f Fastener flexblty [mm/n] I Moment of nerta [mm 4 ] k b Bendng factor [-] L Length [mm] M, M x Moment [Nm] M nternal Internal moment [Nm] Appled force [kn] t Thckness [mm] T Load transfer [kn] w Dsplacement neutral axs [mm] W Wdth [mm] x x-coordnate [mm] y y-coordnate [mm] α Stffness rato [Ma] δ Dsplacement [mm] δ f, Dsplacement of fastener [mm] Δ Dsplacement of sheet [mm] σ b Bendng stress [Ma] σ bendng Bendng stress [Ma] σ tenson Tensle stress [Ma] ξ j, Stffness rato [mm/n] REFERENCE LIST [] Gere, J.M. and Tmoshenko, S.. (99), Mechancs of Materals, Chapman & Hall, London. [] Hartman, A. and Schjve, J. (968), Effects of dmensons of rveted lap jonts and sngle-strap butt jonts on secondary bendng (n Dutch). NLR-TR-6806, Amsterdam, Natonal Aerospace Laboratory [3] Schjve, J. (97), Some Elementary Calculatons on Secondary Bendng n Smple Lap Jonts, NLR-TR-7036, Amsterdam, Natonal Aerospace laboratory [4] Müller, R..G. (995), An Expermental and Analytcal nvestgaton on the Fatgue Behavour of Fuselage Rveted Lap Jonts, The Sgnfcance of the Rvet Squeeze Force, and a Comparson of 04-T3 and Glare 3, Ds. Delft Unversty of Technology

16 [5] De Rjck, J.J.M. and Fawaz, S.A. (00), A Smplfed Approach for Stress Analyss of Mechancally Fastened Jonts, 4 th Jont DoD/FAA/NASA Conference on Agng Arcraft [6] Rjck, J.J.M. (005), Stress Analyss of Fatgue Cracks n Mechancally Fastened Jonts, Ds. Delft Unversty of Technology [7] Huth, H. (986), In: ASTM ST 97; Influence of Fastener Flexblty on the redcton of load transfer and Fatgue Lfe for Multple-Row jonts, p. -50 [8] Fawaz, S.A. (000), Equvalent Intal Flaw Sze Testng and Analyss of Transport Arcraft Skn Splces, In: Fatgue and Fracture of Engneerng Materals and Structures, Vol. 6 p