AN INTEGRATED APPROACH TO MODELING AND MITIGATING SOFC FAILURE - PowerPoint PPT Presentation

AN INTEGRATED APPROACH TO MODELING AND MITIGATING SOFC FAILURE Andrei Fedorov, Comas Haynes, Jianmin Qu Georgia Institute of Technology DE-AC26-02NT41571 Program Managers: Travis Shultz National Energy Technology Laboratory

Outline • First Order Failure Criteria for SOFC PEN Structure • Creep Modeling of YSZ/Ni Cermet • Fracture Mechanics Analysis Tool • Thermal Transient Modeling

First Order Failure Criteria for SOFC PEN Structure • Objectives • Local Failure Criteria – Failure Modes – Strength Failure Criteria – Fracture Failure Criteria • Global Failure Criteria • Analyses for Various Crack Cases • Conclusion

Objectives Develop first-order failure criteria to be used for the initial design, material selection and optimization against thermomechanical failure of the PEN structure in high temperature SOFCs.

Failure Modes Material Characteristics • Static Strength • Fracture Toughness • Fatigue Strength Does a material contain flaws above certain threshold value? No -> Failure is strength- controlled Yes -> Failure is fracture toughness-controlled

Strength-Based Failure Theory Failure occurs when σ = σ σ σ = σ f ( , , ) 1 2 3 f where σ = σ σ σ Effective Stress f ( , , ) 1 2 3 σ σ σ , , Principle Stresses 1 2 3 σ Material Strength f

Fracture-Based Failure Theory Fracture occurs when ⎛ ⎞ − ν 2 2 1 K = + + = 2 2 ⎜ III ⎟ G K K G − ν I II c ⎝ ⎠ E 1 where Energy Release Rate G K K K Stress Intensity Factors I II III G c Fracture Toughness

YSZ Electrolyte σ = σ Maximum Normal Stress Criterion f { } σ = σ σ σ = σ σ σ f ( , , ) max , , 1 2 3 1 2 3 σ = 100 ~ 300 MPa f ⎛ ⎞ − ν 2 2 1 K = + + = 2 2 ⎜ III ⎟ Fracture Criterion G K K G − ν I II c ⎝ ⎠ E 1 G = 2 ฀ 7.8 13.7 J m c

YSZ/Ni Cermet σ = σ Von Mises Criterion (elevated temp) f ( ) ( ) ( ) 2 2 2 σ = σ − σ + σ − σ + σ − σ + τ + τ + τ 2 2 2 2 2 2 x y y z z x xy yz zx σ = σ Maximum Normal Stress Criterion f { } σ = σ σ σ = σ σ σ f ( , , ) max , , 1 2 3 1 2 3

⎡ ⎤ E ( ) σ = σ + − − Ni ⎢ ⎥ V 1 V V − ν f YSZ YSZ YSZ Void ⎣ ⎦ E (1 ) YSZ Ni σ = 100 ~ 300MPa = YSZ tensile strength YSZ E = Ni Young's modulus Ni = YSZ Young's modulus E YSZ ν = Ni Poisson's ratio Ni V = YSZ Volume fraction YSZ V = Void Volume fraction Void

Fracture Curvature Criterion R ρ c Global Failure Criteria < Stack Assembly ρ 1/ R ρ = W Warpage Warpage Criterion c W L < W Processing

Implementation � Based on material/geometry parameters to compute W c and ρ c � Measure W or ρ of each cell after sintering � Compare the measured W with W c or ρ with ρ c ρ = 1/ R L W R

Crack Types A – crack in the cathode B – crack in the anode C – delamination crack between the cathode and electrolyte D – delamination crack between the anode and the electrolyte E – blister crack on the anode/electrolyte interface F – crack in the electrolyte A A A A h c h c G G cathode cathode cathode cathode E E C C h e h e F F E E electrolyte electrolyte electrolyte electrolyte D D F F anode anode anode anode h a h a B B L L

Max. Allowable Warpage G c = fracture toughness ⎛ ⎞ W G L = c c ⎜ ⎟ Y h e = electrolyte thickness ⎝ ⎠ L h E h E e = modulus of electrolyte e e e − 1/ 2 ⎡ ⎤ C rack A 1 / 2 2 ⎛ ⎞ ⎛ ⎞ ∆ α 2 ⎛ ⎞ 3 h E a ⎢ ⎥ = + − ⎜ ⎟ ⎜ ⎟ 2 2 ⎜ ⎟ Y t − ν ⎝ 4 ⎠ 2 ⎢ ⎥ ⎝ 16 H E ⎠ ⎝ Q (1 ) ⎠ 2 ⎣ ⎦ 3 3 − 1 / 2 1/ 2 ⎛ ⎞ ⎛ ⎞ ∆ α C rack C 3 2 h E c F 4 h ( ) F = − + − 2 2 ⎜ 2 2 ⎟ ⎜ 3 2 3 2 1 ⎟ Y Q Q 1 3 ⎝ ⎠ ⎝ ⎠ 16 16 h c 3 3 − 1/ 2 ⎡ ⎤ C rack D 1 / 2 2 ⎛ ⎞ ⎛ ⎞ ∆ α − 2 ⎛ ⎞ 3 h h h = ⎢ + ⎥ ⎜ 2 ⎟ ⎜ ⎟ 1 3 ⎜ ⎟ Y π − ν ⎢ ⎝ ⎠ ⎥ ⎝ ⎠ ⎝ ⎠ 16 aE Q (1 ) 2 ⎣ ⎦ 2 2 − 1/ 2 1 / 2 ⎛ ⎞ ⎛ ⎞ ∆ α C rack E 2 3 h E c F 4 h ( ) F − − = ρ + 2 2 2 ⎜ 2 2 ⎟ ⎜ ce 2 ce 1 ⎟ Y Q Q 1 3 ⎝ ⎠ 16 h ⎝ 16 h c ⎠ 2 ce ce ⎛ ⎞ C rack F 2 Q h h E 1 P P = + 2 2 2 ⎜ 1 2 ⎟ Y ∆ α ⎝ ⎠ 4 P G 1 c

Implementation Definition of Variables: Material Properties Needed: � See our monthly report or � Elastic moduli e-mail � Coefficient of thermal jianmin.qu@me.gatech.ed expansion u � Fracture toughness Basic Assumptions: Other Parameters needed: � Linear elastic fracture � Layer thickness mechanics � Warpage (curvature) Implementation: � A FORTRAN code

Materials Properties CTE(10 -6 / o C) Young’s Poisson’s Thickness µ Modulus (GPa) Ratio ( m ) Cathode 90 0.3 11.7 75 Electrolyte 200 0.3 10.8 15 Anode 96 0.3 11.2 500 Considering sintering process, the set of materials in table will result in – tensile stress in cathode; – compressive stress in electrolyte; – compressive stress in anode;

Average Stress in Cathode Average in-Plane Stress in 800 o C 20 o C 800 o C 800 o C 20 o C 60 cooling NiO reduction cooling heating 50 40 the PEN Layers 30 Stress (MPa) 20 10 0 0 20 40 60 80 100 -10 -20 • Stress free at 800 o C Cathode -30 -40 Time • No-creep Average Stress in Electrolyte 800 o C 20 o C 800 o C 800 o C 20 o C • NiO reduction results in 0.1% NiO reduction cooling cooling heating 20 vol. shrinkage -20 Stress (MPa) -60 -100 A A -140 Electrolyte -180 0 20 40 60 80 100 h c G cathode cathode E Time C Average Stress in Anode h e E F electrolyte electrolyte D 800 o C 20 o C 800 o C 800 o C 20 o C F cooling NiO reduction cooling heating anode 8 anode 6 h a 4 Stress (MPa) 2 0 0 20 40 60 80 100 -2 Anode -4 B -6 L Time

Numerical Examples of Max. Allowable Warpage 10 Crack C is the limiting Crack C a / h = 0.01 Crack D 8 factor, unless crack A is 3 Crack A larger than 5% of the 6 cathode thickness. W (mm) L = 10 cm a / h 3 = 0.05 4 A A h 3 cathode cathode G E C h 2 E F electrolyte electrolyte D 2 F anode anode a / h 3 = 0.1 h 1 0 0 5 10 15 20 B G c (J/m 2 ) L

Statistical Consideration Failure theories have the following form: Failure occurs when Σ > Σ f where Σ is the “ stress ” (e.g., max. normal stress, Mises stress, or SIFs, max. warpage, etc. ) and Σ f is the “ strength ” (e.g., yield strength, fracture toughness, etc.) Both Σ and Σ f can be random variables with certain distributions, such normal distribution, Weibull distribution, etc.

Assume: g ( σ ) = distribution of stress; g f ( σ ) = distribution of strength The probability of failure at a given stress σ is σ ∫ g ( ) x dx f −∞ The probability of failure for a given stress distribution g ( σ ) is ⎡ ⎤ ∞ σ ∫ ∫ = σ σ ( ) ( ) p g g x dx d ⎢ ⎥ ⎣ ⎦ f f −∞ −∞

Example (Normal Distributions) ⎡ ⎤ 2 ⎛ ⎞ σ − σ 1 1 ⎢ ⎥ σ = − ⎜ f ⎟ Strength distribution g ( ) exp ⎜ ⎟ ⎢ ⎥ f π 2 s s 2 ⎝ ⎠ ⎣ ⎦ f f ⎡ ⎤ σ − σ 2 ⎛ ⎞ 1 1 σ = − ⎢ ⎥ ⎜ ⎟ Stress distribution g ( ) exp π ⎝ ⎠ ⎢ ⎥ 2 s s 2 ⎣ ⎦ s = Standard deviation σ = Mean value ∞ ∫ σ σ = g ( ) d 1 −∞ σ σ f ⎡ ⎤ ⎡ ⎤ σ − σ σ − σ 2 ⎛ ⎞ 1 ∞ ∫ = − σ ⎢ ⎥ ⎢ ⎥ f ⎜ ⎟ p Exp Erfc d f π ⎝ ⎠ −∞ ⎢ ⎥ ⎢ ⎥ 2 s 2 s 2 s 2 ⎣ ⎦ ⎣ ⎦ f

Failure Probability σ σ σ = σ s s p f f f f f Factor of Safety Deviation Failure Probability 1.0 any value 0.5 3.8 10 − × 2.0 0.2 2 2.3 10 − × 5.0 0.2 4 7.3 10 − × 10.0 0.2 5 9.2 10 − × 1.5 0.1 3 2.0 10 − × 2.0 0.1 4 1.2 10 − × 3.0 0.1 6 5.7 10 − × 4.0 0.1 8 1.2 10 − × 1.5 0.05 6 7.7 10 − × 2 0.05 13 2.3 10 − × 1.5 0.02 32

= s s f σ σ f 0.1 0.075 p 0.5 f 0.05 0.4 0.025 0 0.3 1 1 s 0.2 2 2 σ f σ 0.1 3 3 f σ 4

Summary - First Order Failure Criteria • Local and global failure criterion were established. These criterion may be easily used to aid the initial design, material selection and optimization of SOFCs. • Using the local failure criteria, the user can predict (estimate) the potential material failure • Using the global failure criteria, the user can predict whether a cell can survive the stacking assembly process

A Numerical Simulation Tool for Fracture Analysis in Solid Oxide Fuel Cells ( ) − ε + ≡ × 1 2 i K = K iK applied stress FL I II Crack Material 1 Material 2 KI KII KIII opening shear out of plane

Significance of SIFs 1. Will the crack grow? 2 1 KK K + = III G ( ) πε µ ic * 2 * E cosh 2 2. In what direction? (What is mode mixity?) − ⎡ ⎤ ε i 1 Im[ K L ] ψ = ⎢ ⎥ tan ε i ⎣ ⎦ Re[ K L ]