1. U.S. DOT ANALYSIS OF COMPOSITE HYDROGEN STORAGE CYLINDERS UNDER TRANSIENT THERMAL LOADS J. Hu, S. Sundararaman and K. Chandrashekhara Department of Mechanical and Aerospace Engineering University of Missouri – Rolla William Chernicoff US Department of Transportation US Department of Transportation Washington, DC 20509

2. U.S. DOT Outline Background Finite Element Model Resin Reaction Model Failure Criterion Temperature Dependent Material Model Sub-laminate Model Results Conclusion

3. U.S. DOT Background Composite Cylinder Wall The inner liner of the cylinder serves as a hydrogen gas permeation barrier The inner liner of the cylinder serves as a hydrogen gas permeation barrier A filament-wound, carbon/epoxy composite laminate provides the desired pressure load bearing capacity A filament-wound, carbon/epoxy composite laminate provides the desired pressure load bearing capacity A glass/epoxy layer provides impact and damage resistance A glass/epoxy layer provides impact and damage resistance Carbon/Epoxy Aluminum liner Glass/Epoxy Major loading bearing component Filament wound Composite Storage Cylinder

4. U.S. DOT Gas filling process Environmental temperature change Exposure to fire Thermal loading Pressure loading (Settled) 34.5 MPa to 70 MPa Hydrogen storage cylinders Bonfire test Background (Contd.)

5. U.S. DOT Finite Element Model The finite element equation for a double curved composite shell where is mass matrix is stiffness matrix is mechanical force loading is thermal force loading  22 11 R2R2 R1R1 Displacement field for a doubly curved shell

6. U.S. DOT Finite Element Model (Contd.) The heat conduction equation can be expressed as where and are thermal conductivity, specific heat and density respectively and are surface heat flux and heat due to resin reaction and flow. Finite element model for transient thermo-mechanical analysis can be written as

7. U.S. DOT Implementation Scheme Thermal loading Mechanical loading Failure theory Initialization Compute stress and temperature Compute material modulus, density, and thermal conductivity Material strength Resin reaction model Density Failure type Stress Failure type Strength Pressure Temperature Reaction heat Heat flux

8. U.S. DOT Resin Reaction Model Reaction kinetic equation (Arrhenius’s law) is: - Pre-exponential factor - Density - Gas constant - Activation energy - Temperature where - Time

9. U.S. DOT Resin Reaction Model (Contd.) Gas mass flux at any spatial location - Wall thickness of composite - Distance from hot face Heat of resin decomposition and gas mass flux can be written as where - Specific heat of gas - Specific heat of composite - Ambient temperature - Heat of decomposition

10. U.S. DOT Resin Reaction Model (Contd.) Parameters of resin reaction model used in present study PropertyValues Pre-exponential factor (A) 500.0 Activation energy (E A ) 6.05×10 4 J/mol Gas constant (R) 8.314 J/mol/K Specific heat of gas (C pg ) 2386.5 J/Kg/K Specific heat of composite (C p ) 1066.0 J/Kg/K Heat of decomposition (Q) 3.5×10 5 J/Kg Ambient temperature (T ∞ ) 20 ° C

11. U.S. DOT Failure Criterion Hashin’s criterion (for progressive failure model) Matrix tensile or shear cracking Matrix compressive or shear cracking where are longitudinal tensile strength, longitudinal compressive strength, transverse tensile strength, transverse compressive strength and shear strength of unidirectional ply respectively. For a two-dimensional analysis with transverse shear deformation, is taken as zero.

12. U.S. DOT Failure criterion (Contd.) Fiber tensile failure Fiber compressive failure

13. U.S. DOT Failure criterion (Contd.) Material degradation parameters considered are (S. C. Tan, 1991): Matrix tensile or shear cracking: and where Matrix compressive or shear cracking: and where Fiber tensile failure: where Fiber compressive failure: where

14. U.S. DOT Temperature Dependent Material Model Mechanical and thermal properties of fiber reinforced composites vary significantly with temperature. Hyperbolic tan (tanh) function (A. G. Gibson et. al., 2006) is used to fit the test data for temperature dependent material model. where, P(T) - temperature dependent material property P U - the unrelaxed (low temperature) value of that property P R - the relaxed (high temperature) value of that property k - constant describing the breath of the distribution T - temperature T g - mechanically determined glass transition temperature C - constant

15. U.S. DOT Temperature Dependent Material Model (Contd.) Curve fitting test data for transverse and shear moduli

16. U.S. DOT Temperature Dependent Material Model (Contd.) Longitudinal modulus and strength Longitudinal directionPUPU PRPR KCTg ( o C) Modulus (GPa)133.351110.00641100 Strength (MPa) Tensile133.351110.00641070/127100 Compressive133.3510.70.01501070/127100 Transverse modulus and strength Transverse directionPUPU PRPR KCTg ( o C) Modulus (GPa)9.1350.10.0221100 Strength (MPa) Tensile9.1350.10.02240/8.7100 Compressive9.1350.10.022170/8.7100 Shear modulus and strength Shear propertiesPUPU PRPR KCTg ( o C) Modulus (GPa)4.5150.0450.021100 Strength (MPa)4.5150.0450.0270/4.3100 The curve fitting parameters for carbon/epoxy are:

17. U.S. DOT Temperature (  °C) 0207095120170 C p (KJ/Kg/°C)0.80.861.081.281.41.5 Temperature Dependent Material Model (Contd.) Experimental thermal data for carbon/epoxy (G. Kalogiannakis et. al., 2004 ): Temperature (  °C) 20406080100120140  1 (10 -6 / °C) 1.470.970.770.811.091.612.37  2 (10 -6 / °C) 29.229.533.240.050.263.680.4 Longitudinal Thermal Conductivity K 11 = 6.5 W/m/°C Transverse Thermal Conductivity K 22 = 0.65 W/m/°CK 33 = 0.65 W/m/°C

18. U.S. DOT E 1 (GPa)E 2 (GPa)G 12 = G 13 (GPa)G 23 (GPa) 12  1 (1/°C)  2 (1/°C) 55167.65.00.286.3 x 10 -6 32 x 10 -6 Strengths (MPa) 16206904014060 Temperature Dependent Material Model (Contd.) Mechanical properties of S-glass/epoxy Mechanical and thermal properties of Aluminum 6061-T6 Elastic Modulus, E Poisson’s ratio, Poisson’s ratio, Yield strength,  y  (1/°C) 70 GPa 0.33 455 MPa 24.3 x 10 -6 Density Heat capacity Heat conductivity 2700 Kg/m 3 1000 J/g/K 250 W/m/K As thermal conductivity and specific heat of glass/epoxy are very close to those of carbon/epoxy, the same values are taken for glass/epoxy.

19. U.S. DOT Sublaminate Model  Each sublaminate consists of several lamina

20. U.S. DOT Sublaminate Model (Contd.) Sublaminate homogenization: In-plane strains and the interlaminar stresses through the thickness are constant. The lamina stress-strain relationship is: where are sub matrices of global stiffness matrix Partially inverting equation (1) and averaging the in-plane stresses and interlaminar strains: the terms in are constant through the laminate (1) (2) where and is the thickness of each lamina is the total thickness of the sublaminate

21. U.S. DOT Sublaminate Model (Contd.) Partially inverting Eq. (2), yields Equivalent stiffness of the homogenized sublaminate is Equivalent engineering properties can be retrieved by inverting Eq. (4) (3) (4)

22. U.S. DOT Results To evaluate the heat transfer model with resin reaction, a simple case is compared with the results available in literature. Hot face Cold face Cold face temperature variation with time is plotted and compared for a composite panel heated at hot face

23. U.S. DOT Results (Contd.) Modeling  1/8 of cylinder (diameter 0.44 m) is modeled in ABAQUS  A fine mesh is used at the heat source (diameter 0.06 m )  Symmetric boundary conditions are applied Thermal Load  75,000 Watt/m 2 flux acts on the center circle to simulate the localized fire attack Mechanical Load  Internal pressure is applied on the cylinder Model mesh Boundary conditions

24. U.S. DOT Results (Contd.)  Sublaminate technique is used to model the composite cylinder wall  The model is implemented in ABQUS FEA code by user subroutine S8RT doubly curved shell element Outer surface Inner surface Dimensions Thickness of aluminum liner: 2.54 mm Thickness of each hoop sublaminate: 5.8 mm Thickness of each helical sublaminate: 3.6 mm Thickness of protection layer (S-glass/epoxy) : 4 mm

25. U.S. DOT Temperature Distribution Temperature of various locations in thickness direction at the heat source Inner surface of sublaminate 1 Outer surface of sublaminate 4 Outer surface of sublaminate 5 Outer surface of sublaminate 6 Outer surface of S-glass/epoxy sublaminate

26. U.S. DOT Temperature Distribution Temperature distribution along the path path

27. U.S. DOT Residual Resin Content Residual resin content varies with time at different locations in thickness direction at the heat source S-glass/epoxy Sublaminate Sublaminate 6 Sublaminate 5 Sublaminate 4 Sublaminate 1

28. U.S. DOT path Density change along path Residual Resin Content

29. U.S. DOT Resin Depletion in Sublaminate 6

30. U.S. DOT Stress Distribution in Liner Stress distribution in liner (1000 second ) path Stress distribution along path

31. U.S. DOT Stress Distribution in Sublaminate 6 (Hoop layer) Longitudinal stress distribution in sublaminate 6 (1000 sec ) path Stress distribution along path Transverse stress distribution in sublaminate 6 (1000 sec ) Shear stress distribution in sublaminate 6 (1000 sec )

32. U.S. DOT Stress Distribution in Sublaminate 5 (Helical Layer) Longitudinal stress distribution in sublaminate 5 (1000 sec ) path Stress distribution along path Transverse stress distribution in sublaminate 5 (1000 sec ) Shear stress distribution in sublaminate 5 (1000 sec )

33. U.S. DOT Composite Cylinder Failure Time = 1 Sec SL1SL2SL3SL4SL5SL6 34.5 MPa000000 48 MPa000000 69 MPa111111 86 MPa111111 Time = 1000 Sec SL1SL2SL3SL4SL5SL6 34.5 MPa001011 48 MPa111111 69 MPa111111 86 MPa222222 SL – sublaminate, 0 – no failure, 1 – matrix failure, 2 – fiber break  For a pressure of 34.5 MPa, no failure occurs due to mechanical load. Matrix failure occurs during fire exposure in the layers close to the heat source (sublaminates 5 and 6).  For a pressure of 48 MPa, no failure occurs due to mechanical load. Matrix failure occurs during fire exposure in the all the layers.  For a pressure of 69 MPa, matrix failure occurs due to mechanical load.  For a pressure of 86 MPa, matrix failure occurs due to mechanical load. Fiber break occurs due to localized heat source.

34. U.S. DOT Matrix Failure Process in Sublamiate 5 (34.5 MPa pressure)

35. U.S. DOT Fiber Break Process in Sublamiate 6 (86 MPa pressure)

36. U.S. DOT Conclusions  A comprehensive finite element model is developed accounting for temperature dependent material properties, resin reaction and progressive failure model.  Under localized fire exposure, the temperature of outermost layer increases rapidly around the heat source, however, the temperature increase in the cylinder inner layers and adjacent area is not significant.  Under localized fire exposure, resin is depleted quickly in the outermost layers and very slowly in inner layers. The resin depleted area may cause fiber breakage during the cool down process which may be a safety concern.  For lower internal pressures, localized fire exposure cause matrix failure in and around the regions of the heat source.  Under high internal pressures, localized fire exposure initiates fiber breakage and may cause overall failure of the cylinder.

37. U.S. DOT Continuing Efforts Continued refinement of the model – evaluation of heat transfer to a PRD and other safety devices Continued refinement of the model – evaluation of heat transfer to a PRD and other safety devices Comparison to physical test Comparison to physical test NHTSA NHTSA Other Other

38. U.S. DOT Thank you K. Chandrashekhara chandra@umr.edu http://www.umr.edu/~chandra/ William Chernicoff william.chernicoff@dot.gov http://hydrogen.dot.gov