UTC R170. Modeling of Composite Hydrogen Storage Cylinders Using Finite Element Analysis. K. Chandrashekhara

Transcription

1 Modeling of Composite Hydrogen Storage Cylinders Using Finite Element Analysis by K. Chandrashekhara UC R7 A University ransportation Center Program at Missouri University of Siene & ehnology

2 Dislaimer he ontents of this report reflet the views of the author(s), who are responsible for the fats and the auray of information presented herein. his doument is disseminated under the sponsorship of the Department of ransportation, University ransportation Centers Program and the Center for Infrastruture Engineering Studies UC program at the University of Missouri - Rolla, in the interest of information exhange. he U.S. Government and Center for Infrastruture Engineering Studies assumes no liability for the ontents or use thereof. NUC ###

3 ehnial Report Doumentation Page. Report No.. Government Aession No. 3. Reipient's Catalog No. UC R7 4. itle and Subtitle Modeling of Composite Hydrogen Storage Cylinders Using Finite Element Analysis 5. Report Date February 8 6. Performing Organization Code 7. Author/s 8. Performing Organization Report No. K. Chandrashekhara 9. Performing Organization Name and Address Center for Infrastruture Engineering Studies/UC program Missouri University of Siene & ehnology 3 Engineering Researh Lab Rolla, MO Sponsoring Organization Name and Address U.S. Department of ransportation Researh and Speial Programs Administration 4 7 th Street, SW Washington, DC Work Unit No. (RAIS). Contrat or Grant No. DRS98-G- 3. ype of Report and Period Covered Final 4. Sponsoring Ageny Code 5. Supplementary Notes 6. Abstrat Pressurized hydrogen storage ylinders are ritial omponents of hydrogen transportation systems. Composite ylinders have pressure/thermal relief devies that are ativated in ase of an emergeny. he diffiulty in aurately analyzing the behavior of a filament wound omposite storage ylinder derives from ontinually varying orientation of the fibers. In the proposed researh, a finite element model will be developed to perform thermo-mehanial analysis of storage ylinders. Optimization of design variables suh as, ylinder size, type of liner, fiber orientation, thikness of the various layers, and loation of the pressure relief devie will be performed. 7. Key Words Hydrogen storage ylinder, finite element analysis, pressure/thermal relief devies 8. Distribution Statement No restritions. his doument is available to the publi through the National ehnial Information Servie, Springfield, Virginia Seurity Classifiation (of this report). Seurity Classifiation (of this page). No. Of Pages. Prie unlassified Form DO F 7.7 (8-7) unlassified 3

4 FINAL REPOR UMR - UNIVERSIY RANSPORAION CENER ADVANCED MAERIALS AND NON-DESRUCIVE ESING ECHNOLOGIES Sequential #: R7 Projet itle: UC/ransportation Fuel Researh and Development-Modeling of Composite Hydrogen Storage Cylinders Using Finite Element Analysis Prinipal Investigator: K. Chandrashekhara, Professor, Department of Mehanial and Aerospae Engineering Projet Duration: 5//6-/3/6 Amount: Not shown Projet Summary: Safe installation and operation of lightweight omposite hydrogen storage ylinders are of primary onern. ypially, the inner liner of the ylinder is made with a high moleular weight polymer or aluminum that serves as a hydrogen gas permeation barrier. A filament-wound, arbon/epoxy omposite laminate plaed over the liner provides the desired pressure load bearing apaity. In many urrent designs, a glass/epoxy layer or other material is plaed over the arbon/epoxy laminate to provide impat and damage resistane. hese ylinders also have pressure/thermal relief devies that are ativated in ase of an emergeny. he diffiulty in aurately analyzing the behavior of a filament wound omposite storage ylinder derives form the ontinually varying orientation of the fibers. Most of the analysis reported in filament wound omposite ylinders is based on simplifying assumptions and does not aount for omplexities like thermo-mehanial behavior and highly orthotropi nature of the material. In the present work, a omprehensive finite element simulation tool for the design of hydrogen storage ylinder system is developed. he strutural response of the ylinder is analyzed using laminated shell theory aounting for transverse shear deformation and geometri nonlinearity. A omposite failure model is used to predit the maximum burst pressure. Results for various thermo-mehanial loading ases are presented. Introdution: Composite high-pressure ylinders (CHC s) have potential appliation as hydrogen storage systems in automotives and transportation systems due to their light weight, simpliity of the storage and low ost for storage and transport of hydrogen gas. ypially, a omposite high-pressure ylinder is made with a high moleular weight polymer or aluminum liner that serves as a hydrogen gas permeation barrier. A filamentwound, arbon/epoxy omposite laminate over-wrapped outside of the liner provides the desired pressure load bearing apaity. he ylinder is apable of sustaining pressures of

5 5 psi or higher by taking advantage of high modulus, high strength and low speifi weight of modern high performane omposite. In addition, the maturation of filament winding manufaturing proess further lowers the prie to pratial and ommon usage in mass transportation systems. o design omposite high-pressure ylinders with the most possible safety, reliability and minimum weight onsiderations, the behavior of omposite strutures under various mehanial and thermal loadings need to be well understood. Compared to pure mehanial loading, fewer studies have been onduted on CHC s subjeted to thermal loads and ombined thermo-mehanial loads. In the present study, a thermo-mehanial finite element model has been developed for the analysis of hydrogen storage ylinders. he omposite lamina wrap of hydrogen CHC typially onsists of helial laminated layers and hoop laminated layers. Both these layers along with an aluminum liner are onsidered for the analysis (Figure ). During servie, hydrogen CHC s unavoidably experiene various thermal loadings ombined with high pressure. o aount for environmental temperature variation, uniform temperature loadings ranging from 5 C to 4 C are onsidered for the analysis. During the gas filling proess, the inner temperature an inrease to around C. Hene, non-uniform thermal loadings have also been onsidered. he variation of material properties with temperature is signifiant for most omposites. A temperature dependent material model has been developed and implemented in ommerial finite element ode ABAQUS, using user subroutines. A laminated shell theory aounting for out-of-plane shear strains and geometri nonlinearity is used for the analysis. Shear Deformable Shell heory: he major loading bearing omponent of hydrogen storage ylinders is the arbon/epoxy omposite shell wrapped around the ylinder liner (shown in Figure ). he omposite shell experienes not only in-plane deformation but also out-of-plane shear strains. he doubly urved shell theory aounting for out of plane shear deformations and geometri nonlinearity is used for the analysis of omposite hydrogen storage ylinders. A multilayered doubly urved shell is shown in Figure 3. he urved oordinated system { ξ, ξ, ζ } is used in spae desription. he oordinates ξ and ξ speify the position on the middle surfae, while ζ measures the distane, along the outward normal, from the mid-surfae to arbitrary point on the shell. he displaement field an be written as: ζ u( ξ, ξ, ζ ) = ( + ) u o ( ξ, ξ ) + ζ φ( ξ, ξ ) R (.a) ζ v( ξ, ξ, ζ ) = ( + ) vo ( ξ, ξ ) + ζ φ( ξ, ξ ) R (.b) w ( ξ, ξ, ζ ) = w o ( ξ, ξ ) (.) he non-linear strain-displaement relations based on Sanders s shell theory an be given as:

6 o o εx= εx + ζ κx ; εy = εy + ζ κ γ γ + ζ κ ; γ γ ; γ γ () o o o xy = xy xy yz = yz xz = xz y where ε and κ are defined as: j γ j ε = u w + + w ; = φ o o o o x κ x α ξ R α ξ α ξ o v w w o φ ε y = + + ; κ y = α ξ R α ξ α ξ v u w w = + + ; w v γ yz = + φ - α ξ α ξ αα ξ ξ α ξ R o wo uo γ xz = + φ - α ξ R o o o o o xy κ o o o φ φ v u = - ; dx = αdξ ; dy = αdξ R R o o xy = + - o - α ξ α ξ α ξ α ξ (3) In Eq. (3), u and v are the displaements in the diretion of the tangents to the oordinate lines ξ andξ, respetively, w is the displaement in the diretion of the outward normal and φ and φ are the rotations. he stress-strain relation, aounting for thermal effets, in the shell oordinates for a k th layer an be expressed as: σx Q Q Q6 εx αx σ y Q Q Q6 εy αy τxy = Q6 Q6 Q66 γ xy αxy τ yz Q44 Q 45 γ yz τxz Q Q γ k k xz k (4) where Qij are the transformed elasti oeffiients, is the given temperature distribution, α, α, α are the thermal expansion oeffiients in the shell oordinates. ( ) x y xy he laminate onstitutive equations an be obtained by integrating Eq. (4) over the thikness, and is written as:

7 Nx A A A6 B B B6 ε x N x N y A A A6 B B B 6 ε y Ny N xy A6 A6 A66 B6 B6 B 66 γxy Nxy Qxz A44 A45 γxz = - Q yz A45 A55 γyz M x B B B6 D D D6 κ x Mx My B B B6 D D D6 κ y My M xy B6 B6 B66 D6 D6 D 66 κ xy M xy (5) where N and M are thermal stress and moment resultants h / ( ij ij ij ) ij ( ) (,,,6) A B D = Q z z dz h / h/ ij h/ i j ij i j = (6.a) A = KKQdz( i, j = 4,5) (6.b) Nx, M x Q Q Q6 α x h / Ny, M y Q Q Q = 6 α (, ) h / y z dz (6.) Nxy, M xy Q6 Q6 Q 66 α xy where K is shear orretion fator. Following the standard finite element proedure, the generalized displaements in any element are given by u u v v N w = w ψ i (7) i= φ φ φ φ i where N is the number of nodes in the element and ψ i are the interpolation funtions. Substituting Eq. (7) in Eq. (3), the strains an be expressed as ε = B Δ ; κ = B Δ ; γ = B Δ (8) 3 he finite element equation is written as where { } { } { } Δ = + K e e F e F e (9)

8 ( ) e { Δ } = {{} u {} v { w} { φ} { φ} } { F e } = ( B N + B M ) d( Area) e { F } = ( B N + B M ) d( Area) e K = B AB+ B BB + BBB+ BDB + B3SB3 d( Area) For any given mehanial and temperature loadings, Eq. (9) an be assembled and solved to determine displaements and stresses. Composite Failure Model: Failure in omposites is a ompliated phenomenon and usually involves proesses suh as fiber break, matrix raking, de-bonding of the fiber and matrix, and fiber bulking. In order to relate these failure modes to some evaluable physial quantities (stress, strain or energy), a onsiderable number of failure theories for omposite have been proposed. However, only the most ommon and well tested theories are appliable in failure predition. sai-wu failure theory is a simplifiation of Gol denblat and Kapnov s generalized failure theory for anisotropi materials. It was originally developed to predit the failure of filamentary omposite materials and experimentally verified by many authors. sai-wu failure riterion is used here for omposite failure evaluation. aking as fiber diretion and and 3 as transverse diretions, the sai-wu failure riterion an be expressed as: I F = F σ + F σ + F σ + F σ F σ + F σ F σ 44 3 Fσ σ <. () he oeffiients in Eq. () are defined as: or F F = X + t X, F = Y + t Y, F =, X tx F =, F 44 =, F 55 =, F 66 =, YY S S S t biax σ biax Xt X Yt Y Xt X YY t 3 = σ + + σ F = f FF ( f ) 3 biax where, X t and X are tensile and ompressive stress strength along fiber diretion, Yt and Y are tensile and ompressive stress strength in transverse fiber diretion, S 3, S 3 and S are the maximum shear strength in orresponding planes, σ biax is the equi-biaxial stress at failure and f is an experiene oeffiient.

9 Material Properties: Carbon fiber reinfored omposites are widely used as strutural materials in lightweight hydrogen storage beause of their high speifi strengths, moduli, and design flexibilities. However, mehanial and thermal properties of fiber reinfored omposites vary signifiantly with temperature. As the arbon/epoxy laminate arries the pressure loading from the hydrogen gas, the effet of temperature on its material properties an not be ignored. he moduli and thermal expansion oeffiients are dependent on temperature. For HFG CU5 arbon/epoxy, the temperature dependent material properties and are given by: E = (GPa) (5 C < < 4 C) E = (GPa) (5 C < < 4 C) G = (GPa) (5 C < < 4 C) () υ = (5 C < < 4 C) α = ( ) x -6 (3 C < < 3 C) α = ( ) x -6 (3 C < < 3 C) Furthermore, G 3 is taken as G and G 3 is assumed as.7 G. he ultimate strengths of arbon/epoxy do not hange muh with temperature and are assumed to be onstant and are listed in able. he material properties for glass/epoxy are listed in able. he outer most glass/epoxy layer is only used for protetion of the load bearing arbon/epoxy lamina. Hene temperature dependent material properties are not used for the glass/epoxy layers. Properties of innermost aluminum liner are listed in able 3. Numerial Simulation: he storage ylinder onsidered for the analysis has an inner diameter R in =.44 m and outer diameter R out =.47 m (Figure 3). he wall onsists of innermost liner, arbon/epoxy laminate (helial and hoop) and an outermost protetion glass/epoxy layer. he thikness of the liner is.5 mm. he helial and hoop laminates have a total thikness of 8 mm and protetive glass/epoxy layer is mm thik. In the present work, the total thikness of helial and hoop laminates do not hange, but the thikness ratio (thikness of helial laminates over hoop laminates) varies. he optimized thikness ratio an be obtained by identifying the maximum burst pressure while thikness ratio varies in a range of. to.. With the ombined onsideration of manufaturing apability and the possible higher burst pressure, the winding angle (the angle between fiber and axial diretion or diretion 3 in helial layer) usually fall in a span ranging from to 3. o over this range, three ases with different winding angles, and 3 respetively are onsidered in this study. he lay up of helial lamina is hosen as [θ /-θ ] 6s (θ=, and 3 ). In hoop layer, fiber diretion is ideally supposed to be 9. he lamina is oriented as [89 /-89 ] 6s for manufaturing possibility. he fiber diretion in protetion layer is taken as [45 /-45 ] ross ply. For eah ase, the temperatures for uniform thermal loading are taken as 5 C, 5 C, 75 C, C, C

10 and 4 C. For non-uniform temperature loading, the temperature distribution varies linearly aross the thikness (inner to outer) from 5 C to 4 C, 5 C to C, and 75 C to C and inverse. ABAQUS is a reliable finite element ode for solving general solid mehanis, heat transfer and fluid problems. It is widely used by the industry as well as researhers for its flexibility of implementing user defined subroutine and its powerful nonlinear solver. he failure model, the temperature dependent material properties, and fiber orientations are implemented in ABAQUS using user subroutines. aking advantage of symmetry, only /8 th of the hydrogen ylinder is modeled and meshed using ABAQUS/CAE as shown in Figure 4. he omposite shell uses the S4R element whih is based on a doubly urved shell element aounting for transverse shear deformation. Solid brik element C3D8R is used for liner. he model is solved by using ABAQUS/standard solver. he results obtained of eah ase are listed in ables 4 through 6 and seleted results are plotted and disussed. Results and Disussion: hree different winding orientations of the helial layers, and 3 have been onsidered for the analysis. Also, uniform temperature distribution (ylinder inner temperature = ylinder outer temperature), and a variety temperature gradients (ylinder inner temperature < outer temperature, ylinder inner temperature > outer temperature) have also been onsidered for the analysis. Burst pressures as a funtion of thikness ratio for these temperature distributions are presented. Figures 5, 6 and 7 plot the variation of burst pressure as a funtion of thikness ratio (total thikness of helial laminates/total thikness of hoop laminates) for various uniform temperature distributions. It an be seen that with inreasing temperature the burst pressure goes up in eah ase under uniform thermal loading. In non-uniform thermal loading ases (Figures 8 through 3), the burst pressure drops dramatially with inreasing temperature. his may be explained by observing the failure pattern plotted in Figures 4 and 5 for Case (winding angle = ). Figures 4 and 5 plot the failure oeffiients as a funtion of the layer number for a thikness ratio of.75. In Figure 4, it an be seen that with inreasing temperature, the failure oeffiient of layers (based on sai-wu failure) are lose together, whih means the load is more evenly distributed in eah layer. his even load distribution ontributes to the signifiant inrease in burst pressure. For non-uniform thermal loading ases (Figure 5), the failure oeffiients for the various layers are not lose together and have a slope indiating that the applied load is not evenly distributed among the layers (some layers have high stress as ompared to others ausing them to fail first). his explains the dramati drop in burst pressure when non-uniform temperature field in applied. When the ylinder is experiening uniform thermal loading (Figures 5, 6 and 7), there is a peak pressure whih an be found in eah ase. he thikness ratio at the peak pressure is approximately.5 when the winding angle is and.75 in when the winding angle is and 3. With inreasing winding angle, marginal effet of optimized thikness ratio

11 beomes more obvious. he urve around the peak pressure beomes flatter and the optimized thikness ratio is over a wider range. Also, under non-uniform thermal loading when the inner temperature is lower (Figures 8 through ) the optimized thikness ratio shifts muh to the left side. For non-uniform temperature distribution, when the inner temperature is higher, there is no obvious peak pressure (Figures through 3). Axial loading is mainly sustained by the helial layers. When the inner temperature is higher, the axial loading is transferred to the hoop layers beause of the higher thermal expansion of the helial layers. However, the hoop layers annot sustain axial loading (as the reinforement is not along the diretion of the load) and hene a distint peak does no our in the urve. For non uniform thermal loading, when the inner temperature is lower, it an be seen that the failure oeffiient is higher in the inner layers (Figure 5). Hene, when the inner temperature is lower, the inner layers fail first. When the inner temperature is higher, the outer layers fail first as the inner thermal strain is higher than the strain in the outer layers. he outer layers sustain the majority of mehanial loading ausing them to fail first. his is also refleted in Figure 5 with outer layers having higher failure oeffiients. Conlusions: A doubly urved shell model that is apable of treating both thik and thin ylindrial shells with thermal loading is used for the finite element simulation of omposite high pressure storage ylinders. emperature dependent material properties of the load arrying arbon/epoxy layer and geometry nonlinearity are also onsidered in the numerial model. hree typial ases have been onsidered and the analysis is arried out by applying uniform/non-uniform thermal loading and high pressure mehanial loading. sai-wu failure riterion is employed to predit the burst pressure by heking the failure layer by layer. Under uniform thermal loading, a temperature inrease signifiantly inreases maximum burst pressure. Contrastively, the non-uniform thermal loading an ause an uneven load distribution and hene derease the maximum burst pressure. he ratio of thikness of the helial layer to the hoop layer also plays an important role in determining the maximum burst pressure and should be seleted appropriately based on the thermal and mehanial loading onditions. Aknowledgements: he projet is sponsored by the US. Department of ransportation and University ransportation Center. Publiation:. S. Sundararaman, J. Hu, K. Chandrashekhara and W. Chernioff, hermomehanial Analysis of Composite Cylinders for Hydrogen Storage, Proeedings of the SAMPE Conferene, Baltimore, MD, June 3-7, 6 (o appear).

12 able. Ultimate strength of arbon/epoxy omposite t t Strength F L F L F F MPa S F L able. Mehanial and thermal properties of S-glass/epoxy G E (GPa) E (GPa) = G 3 G (GPa) 3 (GPa) υ α (/ C) α (/ C) t t S Strength F F L L F F F L MPa able 3. Mehanial and thermal properties of Aluminum 66-6 Elasti Modulus Poisson s ratio Yield strength hermal expansion 7 GPa MPa able 4.a Burst pressure varying with uniform temperature and thikness ratio (Case : winding angle ) able 4.b Burst pressure varying with gradient temperature and thikness ratio (Case : winding angle )

13 able 5.a Burst pressure varying with uniform temperature and thikness ratio (Case : winding angle ) able 5.b Burst pressure varying with gradient temperature and thikness ratio (Case : winding angle ) able 6.a Burst pressure varying with uniform temperature and thikness ratio (Case 3: winding angle 3 ) able 6.b Burst pressure varying with gradient temperature and thikness ratio (Case 3: winding angle 3 )

14 Hoop Lamina Helial Lamina Liner Figure High pressure omposite ylinder Outer S-glass/Epoxy Protetion Layer Inner Strutural Carbon/Epoxy Hoop Laminate Aluminum Liner R in Inner Strutural Carbon/Epoxy Helial Laminate R out Figure Cross-setion of hydrogen storage ylinder ζ ξ ξ R R Figure 3 Doubly urved shell and oordinate system

15 5 45 Burst Pressure (MPa) hikness Ratio Figure 4 Finite element model of hydrogen storage ylinder Figure 5 Uniform thermal loading (Case ) Burst Pressure (MPa) hikness Ratio Burst Pressure (MPa) hikness Ratio Figure 6 Uniform thermal loading (Case ) Figure 7 Uniform thermal loading (Case 3) Burst Pressure (MPa) hikness Ratio Figure 8 Gradient thermal loading with lower inner temperature (Case ) Burst Pressure (MPa) hikness Ratio Figure 9 Gradient thermal loading with lower inner temperature (Case )

16 Burst Pressure (MPa) hikness Ratio Figure Gradient thermal loading with lower inner temperature (Case 3) Burst Pressure (MPa) hikness Ratio Figure Gradient thermal loading with higher inner temperature (Case ) Burst Pressure (MPa) hikness Ratio Figure Gradient thermal loading with higher inner temperature (Case ) Burst Pressure (MPa) hikness Ratio Figure 3 Gradient thermal loading with higher inner temperature (Case 3). hikness Ratio:.75 hikness Ratio:.75 sai-wu Failure Coeffiient Sequene of Layers (from inner to outer) sai-wu Failure Coeffiient Sequene of Layers (from inner to outer) Figure 4 Failure evaluation (ai-wu theory) under uniform thermal loading (Case ) Figure 5 Failure evaluation (ai-wu theory) under non-uniform thermal loading (Case )