Syrigou M, Benson S, Dow RS. Strength of aluminium alloy ship plating under combined shear and compression/tension.

Transcription

1 Syrigu M, Bensn S, Dw RS. Strength f aluminium ally ship plating under cmbined shear and cmpressin/tensin. In: 5th Internatinal Cnference n Marine Structures (MARSTRUCT). 05, Suthamptn, UK: CRC Press. Cpyright: The authrs, 05. Date depsited: 09/09/05 This wrk is licensed under a Creative Cmmns Attributin-NnCmmercial 3.0 Unprted License Newcastle University eprints - eprint.ncl.ac.uk

2 Strength f aluminium ally ship plating under cmbined shear and cmpressin/tensin M.S. Syrigu, S.D. Bensn & R.S. Dw Newcastle University, Newcastle Upn Tyne, UK ABSTRACT: This study investigates the failure mdes, ultimate strength and pst cllapse behaviur f unstiffened aluminium plates under cmbined lads f shear and axial cmpressin/tensin. A nn-linear finite element methd is used t mdel simply supprted plates with restrained and unrestrained edges. The generated stress/strain curves and the interactin diagrams fr cmbined shear and axial cmpressin/tensin lads are presented fr a range f different plate slenderness ratis and tw marine grade aluminium allys: H6 and 608-T6. This study has been carried ut with the aim f incrprating the effect f shear and trsin int the simplified prgressive cllapse methd, which is a well-established apprach fr assessing the ultimate strength f a hull girder. The existing methd is applied t ship hull girders under an assumed pure lngitudinal hgging and sagging bending mment. Extending this methd t incrprate the effects f shear and trsin will imprve its capability fr the analysis f intact and damaged ship structures built frm steel and aluminium where shear and trsin may be significant. INTRODUCTION The ultimate strength f a ship is nrmally defined by the capacity f the main hull girder under lngitudinal hgging and sagging bending mment. Several methds are available t evaluate the ultimate strength and cmpare t the extreme wave induced lading. These include the simplified prgressive cllapse methd (als knwn as the incrementaliterative methd in sme classificatin rules) and nnlinear finite element methd. Bth these methds nrmally cnsider pure lngitudinal bending mment as the principal lad case. Hwever, particularly in the case f damage, lngitudinal bending may nt be the gverning lad cnditin. Trsin and shear frces may appreciably influence the glbal strength. Therefre the effect f cmbined lading is an imprtant factr t be investigated. Lngitudinal bending f a hull girder generates axial cmpressin/tensin n the lngitudinally effective structure. Trsin lads n the hull girder are resisted by the cellular crss sectin f the girder. This principally results in shear frces acting n the cntinuus plating. Therefre cmbined glbal bending and trsin n the hull girder causes cmbined axial cmpressin/tensin and shear lads n the lcal plate structure. Using a nnlinear finite element methd (NLFEM), we investigate the failure mdes, ultimate strength and pst cllapse behaviur f unstiffened aluminium plates under cmbined shear and axial cmpressin/tensin. Results fr steel plates have previusly been published Syrigu et al., (04). The results are cmpared t existing analytical methds t predict cmbined ultimate strength and the parameters which affect the pre and pst cllapse respnse f the plate are defined. The utcme is presented in a useful frmat with the aim f incrprating shear and trsin int the simplified prgressive cllapse methd Smith, (977). The extensin f this methd t accunt fr different lad effects will be particularly useful in a damage scenari, where a quick estimatin f residual strength is essential during recverability and survivability decisin making. BACKGROUND The behaviur f steel plates under axial cmpressin and tensin with typical gemetry equivalent t ship structures has been examined thrughly in the literature. Fr example, Faulkner, (975) derived a highly effective design frmula (based n the Frankland frmula) fr predicting the ultimate strength f a lng plate, which captures elast-plastic cllapse f stcky plate and pst buckling strength f mre slender plating. Test data are presented in several studies, fr example by Frieze et al., (977). Chalmers,

3 (993) presents typical lad shrtening curves fr plates ver a range f nn-dimensinal slenderness which can be used effectively in incremental prgressive cllapse methds. Steel plates subjected t shear are less thrughly examined by Paik & Thayamballi, (003), Eurcde 3 ENV 993--, (005), Alinia et al., (009), Rizz et al., (04) and Zhang et al., (008) and there is very limited research in plates under cmbined cmpressive/tensile and shear lads Harding et al., (977). The parameters which affect their behaviur are the shape and the level f initial imperfectins and als the level f weld induced residual stresses which may be present in a ship-type plate. Hwever, the utcme f the research fr steel plates cannt be applied directly t equivalent aluminium ally plates. Bth the lad shrtening curves and ultimate strength f aluminium plates under axial cmpressin differ frm thse fr steel plates due t the different material stress-strain curve and the influence f the heat affected zne where material clse t a jint is sftened due t the high heat input during welding Bensn, (0). Marine grade aluminium ally plates subjected t in-plane lads were investigated experimentally by Mfflin, (983). Bensn, (0) cmpared Mfflin s results with empirical frmulas suggested by Faulkner, (975), Jhnsn-Ostenfeld (DNV, 00), Eurcde 9 EN 997--, (007) and Paik and Duran, (004). The cmparisn has shwn a very gd crrelatin f all fr lw (equal/less than ) and intermediate ( t.3) slenderness rati (β) but nt fr higher values. T extend this cmparisn, we cmpare the results frm this study fr unrestrained and restrained aluminium ally plates under axial cmpressin/tensin with the fllwing empirical frmulas: Faulkner s frmula fr steel unwelded and uncnstrained plates Faulkner, (975):, () where σ ο = prf yield stress at 0.% ffset strain; β = plate slenderness rati, defined as: b t / () / where b = plate breadth; t = plate thickness; and E = Yung s mdulus. Eurcde 9 class 4 fr marine allys Eurcde 9 EN 997--, (007) : N N ED.0 (3) where N ED = design value f the cmpressin frce; N = design resistance t nrmal frces equal t: N A eff (4) M Fr the purpses f cmparisn with ther theretical frmulas, we assume N ED = N ; γ Μ = safety factr t accunt design uncertainties is taken equal t. Hence: N (5) A eff where σ ο = prf yield stress at 0.% ffset strain; A eff = verall effective area equal t: A eff b 0 t ( b b ) t (6) where b = width f the Heat Affected Zne; t = plate thickness. The reduced factrs f the yield stress in the and f the prf yield stress are: 0 0 (7) 0 C C C (8) where C = 9; C = 98 b (9) t 50 / (0) 0 Paik and Duran s (Paik and Duran, 004): , , C () where σ ο = prf yield stress at 0.% ffset strain; β = plate slenderness rati, defined in equatin. As cncern, aluminium plates subjected t pure shear Eurcde 9 EN 997--, (007) prvides the fllwing frmulas: VED V () where V ED = design value f the shear frce at the crss sectin; V = design shear resistance f the crss sectin. Fr the purpses f cmparisn with ur results, we assume V ED = V, which fr: Nn-slender plates β 39ε, where β is defined by (9) and ε by (0), yielding check is required using the frmula: V A net 3 (3) / M

4 where γ Μ = safety factr t accunt design uncertainties is taken equal t fr the cmparisn; A net = net effective area equal t: A net b. t b b t (4) Slender plates β > 39ε, where β is defined by (9) and ε by (0), yielding check is required the equatin (3) and buckling check using the fllwing frmula: V (5) bt / 3 M where γ Μ = safety factr t accunt design uncertainties is taken equal t fr the cmparisn; and ν equal t: 7 t k / b (6) but less than: 430 t k and (7) b where b = plate s breadth; a = plate s length; and if α/b, kτ derives frm: b / k a (8) We have previusly investigated the behaviur f simply supprted square steel plates under cmbined axial cmpressive and shear lads (Syrigu et al., 04). These results have already been validated; therefre we apply the same apprach t mdel aluminium allys 5083-H6 and 608-T6 taking int accunt the particularities f the material. 3 FINITE ELEMENT PLATE MODEL 3. Plate characteristics In this study, aluminium allys 5083-H6 and 608-T6 square plates 000x000mm with typical slenderness rati values β = t 6 are mdelled in ABAQUS CAE nn-linear finite element sftware. The finite element mesh is mdelled using quadrilateral shell elements with reduced integratin (S4R). A Heat Affected Zne () f 5mm each has been cnsidered alng the sides f the plate based n Bensn s research (Bensn, 0). A mesh element size f 0x0mm is chsen after mesh cnvergence study. The material prperties f aluminium allys 5083-H6 and 608-T6 are prf yield stress σ 0. =5MPa and σ 0. =60MPa respectively, Yung s mdulus E=70GPa and ν=0.33. The stressstrain curves were btained frm the Ramberg- Osgd mdel apprximatin (Ramberg and Osgd, 943) using knee factr (n) equal t 5 fr aluminium ally 5083-H6 and 30 fr aluminium ally 608-T6 in the fllwing equatin: n 0.00 (9) 0. The reduced stress in the was calculated fr aluminium ally 5083-H6 and 608-T6 respectively as: Y MPa 0. Y MPa The same Ramberg-Osgd relatinship with the same knee factr was used fr the heat affected material as used fr the parent metal. Additinally, the tensile stress was assumed equal t 0.95σ ΥΗΑΖ in each 5mm and the lngitudinal residual stresses were incrprated in the plates. Finally, the imperfectins f the plate were cmprised f single half sine wave distributins in bth directins in rder t incrprate a realistic distrtin f the critical elastic buckling mde with average level f initial imperfectin amplitude: w 0. t (0) 3. Bundary cnditins A cmplex set f bundary cnditins had t be develped t adequately cpe with the cmbinatins f shear and in-plane applied lads n the plate. They are defined as fllws (with reference t Fig. ): 3.. Initial cnditin Edge is fixed in x, y, z Edge, 3 & 4 are fixed in y Edge 3 is cnstrained in x in rder all the ndes t have the same displacement Edge : Unrestrained edge: Linearity in z f the ndes between RPand RP4. Restrained edge: Linearity in z and x f the ndes between RPand RP4. Edge 4: Unrestrained edge: Linearity in z f the ndes between RP and RP3. Restrained edge: Linearity in z and x f the ndes between RPand RP Relaxatin step The residual stress is mdelled using initial stress cnditins at every sectin pint in the mesh. This can cause slight departure frm equilibrium because it is cmbined with initial imperfectins. Therefre an intermediate step withut lad precedes the lad

5 step in rder t ensure self-equilibrating stress distributin Lad The Riks arc length methd is used t increment the lad applicatin, which is carried ut with displacement cntrl n Edge 3 in: z directin fr axial cmpressin/tensin x directin fr shear z and x directin simultaneusly fr cmbined lads f axial cmpressin/tensin and shear. Figure. Stress-strain curves f aluminium ally 5083-H6 plates with unrestrained edges under axial cmpressin/tensin. Figure. Finite Element mdel f square plate. 4 RESULTS 4. Ally 5083-H6 The lad shrtening curves f unrestrained and restrained plates are shwn in Figure and 3 respectively. The very stcky plates (β=) under axial cmpressin are independent frm the bundary cnditins n the unladed edges f the plate, i.e. unrestrained r restrained, s there is n change in their ultimate strength. Hwever, the behaviur f slender plates alters due t the bundary cnditins. Restrained plates have higher ultimate strength and stiffness in cmparisn with the unrestrained plates. This phenmenn becmes strnger as the plate becmes mre slender. The restrained plates which are subjected t tensin present als higher stress and stiffness in cmparisn with the unrestrained but almst at the same level all plates, independently their slenderness rati (β). Figure 4 and 5 shw the shear stress-shear strain curves fr unrestrained and restrained plates. The behaviur f the stcky plates (β= & β=) is nt affected by the different bundary cnditins n the unladed edges f the plate. Slender plates, β=3-6, present gradual reductin in their critical shear stress in bth cases but with higher levels f critical shear stress and stiffness fr the restrained plates in cmparisn with the crrespnding unrestrained. Figure 3. Stress-strain curves f aluminium ally 5083-H6 plates with restrained edges under axial cmpressin/tensin. The ultimate strength f unrestrained and restrained plates under axial cmpressin is cmpared with Faulkner s (), Eurcde 9 (4) and Paik and Duran s () theretical frmulas in Figure 6. The graph f the F.E. results fr the unrestrained plates shws a gd crrelatin with Faulkner s and Eurcde 9 results. The graph f the stcky F.E. restrained plates has the same tendency but it alters fr slender plates. Paik and Duran s graph fr slender plates is clse t Faulkner s, Eurcde 9 and the F.E. graph fr unrestrained plates, but with different slpe. Stcky plates (β=, ) are nt particularly affected by the bundary cnditins f the unladed edges. The restrained slender plates sustain higher values f direct stress in cmparisn with the unrestrained. This behaviur is expected and agrees with ther studies fr

6 steel plates, Harding s (Harding et al., 977) and the authrs previus study (Syrigu et al., 04). critical shear stress fr nn-slender plates (β=-) accrding t Eurcde s 9 equatin (3) is higher than the F.E. results but bth graphs fllw the same pattern, a straight hrizntal line. The buckling shear stress f slender plates (β=3-6) derives frm equatin (5) and its graph shws similar tendency with ur F.E. results. Figure 4. Shear stress-shear strain curves f aluminium ally 5083-H6 plates with unrestrained edges under pure shear. Figure 6. Cmparisn f F.E. results with theretical frmulas fr aluminium ally 5083-H6 plates under axial cmpressin Figure 5. Shear stress-shear strain curves f aluminium ally 5083-H6 plates with restrained edges under pure shear. Figure 7 shws the graphs f the critical shear stress against plate slenderness (β) f the F.E. results fr restrained and unrestrained plates under pure shear and accrding t Eurcde 9 (3) & (5). Stcky plates (b=, ) subjected t shear are als independent frm the bundary cnditins at the edges. The restrained slender plates withstand higher levels f critical shear stress than the unrestrained. Hwever, the graphs fr bth bundary cnditins have similar curvature. Eurcde s 9 frmula, (3), fr nn-slender plates estimates the critical shear stress due t yield. Additinal, buckling check is required fr slender plates using frmula (5) fr slender plates. The estimated Figure 7. Cmparisn f F.E. results with theretical frmulas fr aluminium ally 5083-H6 plates under pure shear. Figures 8 and 9 present the interactin diagram f axial cmpressive/tensile and shear lads fr aluminium ally 5083-H6 plates with unrestrained and restrained edges. Each pint depicts the peak direct stress and the peak shear stress f plates under these cmbined lads. In cases where either the direct r shear stress cmpnents have failed t reach a peak value, limitatins are set fr the interactin relatinship. In this case values f either direct r shear

7 stress at strain values f ε/ε ο = r γ/γ ο = are used t define the failure stresses fr the interactin diagram. the differences between the tw allys will be analysed. Figure 8. Interactin diagram f aluminium ally 5083-H6 plates with unrestrained edges under axial cmpressin and shear. Figure 0. Stress-strain curves f aluminium ally 608-T6 plates with unrestrained edges under axial cmpressin/tensin. Figure 9. Interactin diagram f aluminium ally 5083-H6 plates with restrained edges under axial cmpressin and shear. In Figure 8, the tensile direct stress is very clse fr all unrestrained plates (β=-6), instead f the ultimate cmpressive stress which decreases depending n plate s slenderness rati. Very stcky plates (β=) fllws the Mises yield criterin and very slender plates (β=3, 4, 5, 6) develp high insensitivity t shear. Buckling remains the dminate reasn f failure fr lw prprtins f shear t axial cmpressive lad and shear starts t affect plate s strength when it reaches apprximately the 50% f shear yield stress. The behaviur f plates with slenderness rati β= is similar t the behaviur f stcky plates but withut verifying the Mises yield criterin. The interactin diagram f the restrained plates in Figure 9 has similar pattern with this f the unrestrained plates (Fig. 8). Hwever, the restrained slender plates (β=-6) present higher values f cmpressive and tensile stress. Very stcky plates β= cmply with Mises criterin and less stcky plates β=, 3 behave in a similar manner. The influence f shear lad t the axial cmpressive strength is greater in slender plates (β=4, 5, 6) and shear buckling ccurs fr lwer prprtins f shear and mre slender plates than in the unrestrained case. 4. Ally 608-T6 The equivalent graphs fr aluminium ally 608-T6 plates with unrestrained and restrained edges have als been generated. These are presented in the fllwing Figures 0-7, but because they are very similar t the aluminium ally 5083-H6 results, nly Figure. Stress-strain curves f aluminium ally 608-T6 plates with restrained edges under axial cmpressin/tensin. Figures 0 and shw the lad shrtening curves fr unrestrained and restrained plates respectively under axial cmpressin and tensin and there is n difference with Figures and 3 fr aluminium ally 5083-H6. Figures and 3 shw the shear stress-shear strain curves fr aluminium ally 608-T6 plates with unrestrained and restrained edges and there is n nticeable difference with Figures 4 and 5 which depict the equivalent curves fr aluminium ally 5083-H6.

8 frm ally 608-T6 present insensitivity f cmpressive strength t shear fr lwer prprtins (40%) f the critical shear stress. Figure. Shear stress-shear strain curves f aluminium ally 608-T6 plates with unrestrained edges under pure shear. Figure 4. Cmparisn f F.E. results with theretical frmulas fr aluminium ally 608-T6 plates under axial cmpressin. Figure 3. Shear stress-shear strain curves f aluminium ally 608-T6 plates with restrained edges under pure shear. Since the results f the ultimate direct and critical shear stress fr aluminium ally 608-T6 are very clse t these fr aluminium ally 5083-H6, it is expected t generate similar graphs fr the theretical cmparisn. S, the graphs in Figures 4 and 5 in which the ultimate strength and the critical shear stress f ur F.E. results are cmpared with theretical frmulas, actually verify the graphs in Figures 6 and 7. The interactin diagram f axial cmpressive/tensile and shear lads fr restrained aluminium ally 6083-T6 (Fig. 7) is almst identical t the 508-H6 diagram (Fig. 9). Hwever, fr unrestrained edges, the interactin diagrams f aluminium allys 5083-H6 and 608-T6 in Figure 8 and 6 are similar t, but slender plates (β=4, 5, 6) Figure 5. Cmparisn f F.E. results with theretical frmulas fr aluminium ally 608-T6 plates under pure shear. Figure 6. Interactin diagram f aluminium ally 608-T6 plates with unrestrained edges under axial cmpressin and shear.

9 7 REFERENCES Figure 7. Interactin diagram f aluminium ally 608-T6 plates with restrained edges under axial cmpressin and shear. 5 CONCLUSIONS The results shwn in the abve figures serve t understand the behaviur f unrestrained and restrained aluminium allys 5083-H6 and 608-T6 plates under cmbined lads f axial cmpressin/tensin and shear. The main cnclusins f this study are: The behaviur f very stcky plates (β=) is independent frm the cnstraints at their sides and fllws the Mises yield criterin: / / Less stcky plates (β=) independently frm their cnstraints and restrained plates (β=3) have similar behaviur with stcky plates but withut verifying the Mises yield criterin: / /. Slender plates β=4, 5, 6 with r withut restrained edges and β=3 plates with unrestrained edges present insensitivity t lw prprtins f shear t axial lad and in higher levels fr the unrestrained case. All plates, except the very stcky β=, sustain mre direct and critical shear stress and becme stiffer when their edges are restrained. Plate s strength depends directly n its slenderness rati (β) fr cmpressive lads, but it is nt particularly affected by β fr tensile lads. Bth aluminium allys 5083-H and 608-T6 present very similar behaviur. The nly remarkable ntice is that aluminium ally 608-T6 slender unrestrained plates shw insensitivity t shear fr lwer prprtins f shear t axial lad 0.4τ ο than 5083-H6 plates. Alinia, M.M., Habashi, H.R., Khrram, A., 009. Nnlinearity in the pstbuckling behaviur f thin steel shear panels. Thin-Walled Struct. 47, Bensn, S., 0. Prgressive Cllapse Assessment f Lightweight Ship Structures. Newcastle University. Chalmers, D.W., 993. Design f Ships Structures. HMSO, Lndn. DNV, 00. Rules fr Classificatin f High Speed, Light Craft and Naval Surface Craft. Det Nrske Veritas. Eurcde 3 ENV 993--, 005. Design f steel structures, part. General rules and rules fr buildings. British Standard Institutin, Lndn. Eurcde 9 EN 997--, 007. Design f Aluminium Structures, part. General structural rules. British Standard Institutin, Lndn. Faulkner, D., 975. A review f effective plating fr use in the analysis f stiffened plating in bending and cmpressin. J. Ship Res. 9, 7. Frieze, P.A., Dwling, P.J., Hbbs, R.E., 977. Ultimate Lad Behaviur f Plates in Cmpressin, in: Steel Plated Structures. Crsby Lckwd Staples, Lndn, pp Harding, J.E., Hbbs, R.E., Neal, B.G., 977. Ultimate Lad Behaviur f Plates under Cmbined Direct and Shear Inplane Lading, in: Steel Plated Structures. Crsby Lckwd Staples, Lndn, pp Mfflin, D., 983. Plate Buckling in Steel and Aluminium. University f Cambridge. Paik, J., Duran, A., 004. Ultimate Strength f Aluminium Plates and Stiffened Panels fr Marine Applicatins. Mar. Technl. Vl.4, 08. Paik, J., Thayamballi, A., 003. Ultimate limit state design f steel-plated structures. Jhn Wiley & Sns Ltd, Chichester, UK. Ramberg, W., Osgd, W.R., 943. Descriptin f stress-strain curves by three parameters. Natinal Advisry Cmmittee Fr Aernautics, Washingtn DC. Rizz, N.A. ds S., Amante, D. d A., Estefen, S., 04. Ultimate shear strength f stiffened panels fr ffshre structures, in: ASME 04 33rd Internatinal Cnference n Ocean, Offshre and Arctic Engineering. Presented at the OMAE 04, San Francisc, Califrnia, USA. Smith, C.S., 977. Influence f lcal cmpressive failure n ultimate lngitudinal strength f a ship s hull., in: Practical Design f Ships and Other Flating Structures. Presented at the Internatinal Sympsium n Practical Design f Ships and Other Flating Structures., Tky, Japan. Syrigu, M.S., Bensn, S.D., Dw, R.S., 04. Strength f Ship Plating under Cmbined Shear and Cmpressin. Presented at the ASRANet, Glasgw. Zhang, S., Kumar, P., Rutherfrd, S.E., 008. Ultimate shear strength f plates and stiffened panels. Ships Offshre Struct. 3, ACKNOWLEDGEMENTS This study was perfrmed under an Office f Naval Research grant. We wuld like t thank ONR fr their cntinuing supprt f this wrk.