Life Prediction Methodology for Ceramic Matrix Composites

Transcription

1 Life Prediction Methodology for Ceramic Matrix Composites Scott Case and Howard Halverson Materials Response Group Department of Engineering Science and Mechanics Virginia Tech

2 Outline: Micromechanics based life prediction Single mechanism models Multiple mechanism models Phenomenological (residual strength) based life prediction Multi-level modeling Structural analysis (finite element integration)

3 Example of Single Mechanism Model: Assume that crack growth is the mechanism for fiber failure at elevated temperatures. Crack growth is dictated by the Paris Law da dt β = AK K = Yσ t a, b g So with time the strength of an individual fiber is L NM HG I K J z O QP bg F β t b g β 2 2 β 2 β σ t = σ i AY KIc σ app t dt Iyengar & Curtin (1997) 1 β 2

4 Single Mechanism Results: Simulation results are compared to the results of an analytical expression Stress (MPa) Lifetime (hr)

5 Multiple Mechanism Models: Analytic solutions are difficult to obtain Simulation approach readily combines multiple mechanisms Example slow crack growth interfacial asperity creep

6 Multiple Mechanism Result: Shear stress degradation Residual Strength (GPa) Combined Slow crack growth Time (hours)

7 Remaining Strength Predictions: Track remaining strength during the fatigue process Define a scalar failure function based upon tensor strength and stresses; use this failure function for calculations May include the effects of changing loading conditions May be directly validated experimentally, unlike Miner s rule Stress or Strength S ult S a 1 Ν 1 Residual Strength Life Curve Cycles

8 Remaining Strength Predictions: Track remaining strength during the fatigue process Define a scalar failure function based upon tensor strength and stresses; use this failure function for calculations May include the effects of changing loading conditions May be directly validated experimentally, unlike Miner s rule Stress or Strength S ult S a 2 Residual Strength Life Curve Cycles Ν 2

9 Remaining Strength Predictions: Track remaining strength during the fatigue process Define a scalar failure function based upon tensor strength and stresses; use this failure function for calculations May include the effects of changing loading conditions May be directly validated experimentally, unlike Miner s rule Stress or Strength S ult S1 r S a 1 S a 2 Residual Strength n 1 n 2 Life Curve Ν 1 Cycles Ν 2

10 Remaining Strength Predictions: Track remaining strength during the fatigue process Define a scalar failure function based upon tensor strength and stresses; use this failure function for calculations May include the effects of changing loading conditions May be directly validated experimentally, unlike Miner s rule Stress or Strength S ult S1 r S a 1 S a 2 Ν 1 Residual Strength Miner s rule Cycles Ν 2

11 Approach for Variable Loading with Rupture and Fatigue Acting: Divide each step of loading into time increments Treat each increment as a stress rupture problem (constant applied stress and temperature) Reduce residual strength due to time dependent damage accumulation Refine number of intervals until residual strength converges Input next load level Check for load reversal. If load reversal, increment by 1/2 cycle and reduce residual strength due to fatigue damage accumulation n = F HG 1 Fr 1 Fa I KJ 1 j N R S L N M T n + 1/ 2 Fr = b1 Fa2g N j O Q P L N M n N O Q P j U V W af af σ ij ttt, ë ij, T d 1 ij 1 t, σ, T 1 d 0 t T at 0, σij, i 0 t, σ, T d 3 i 3 ij 3 i d t 4 4, σij, T 4 d t 5 i 5, σij, T 5 i

12 Implementation: CCLife Program Begin with matrix stiffness reduction as a function of time and stress level Use a simple stress model (2-D, laminate level) to calculate failure function as a function of time, stress, and temperature Fit stress rupture data Use incremental approach previously presented to sum influence of changing stresses (rupture influence) Adaptively refine increments until residual strength converges to some prescribed tolerance Account for cyclical loading by counting reversals and reducing remaining strength

13 Stiffness Reduction Data for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : 1.0 E/E MPa 103 MPa 134 MPa 173 MPa 207 MPa Fatigue Cycles

14 Stress Rupture Data for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : 1.0 Normalized Applied Stress C Experimental, 1100 C 982 C Experimental, 982 C Time to rupture (s)

15 Stress Rupture Data for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : 1.8x x x10 6 Time to rupture (s) 1.2x x x x x x x Temperature ( oc)

16 Fatigue Data for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : Normalized Stress CCLife 2.0 Data ,000 10,000,000 Cycles

17 Residual Strength Data for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : 1.2 Interrupted Fatigue Test Results R=-1 σ max = 15 ksi 1.0 Normalized Remaining Strength, Normalized Failure Function Normalized Remaining Strength Normalized Failure Function Normalized Experimental Remaining Strength Fatigue Cycles

18 Residual Strength Data for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : 1.2 Interrupted Fatigue Test Results R=-1 σ max = 13 ksi 1.0 Normalized Remaining Strength, Normalized Failure Function Normalized Remaining Strength 0.2 Normalized Failure Function Normalized Experimental Remaining Strength Fatigue Cycles

19 Residual Strength Data for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : 1.2 Interrupted Fatigue Test Results R=-1 σ max = 10 ksi 1.0 Normalized Remaining Strength, Normalized Failure Function Normalized Remaining Strength Normalized Failure Function Normalized Experimental Remaining Strength Fatigue Cycles

20 Validation: Mission loading profile d t 1 1, ëij, T 1 i af af ë ij t, Tt d t 2 2, ëij, T 2 i ë ij, T d at 0 t T Time 0, σij, i 0 t3, ëij, T d 3 3 i

21 Validation: Mission loading profile Normalized Stress CCLife 2.0 Data ,000 3,000 Cycles

22 All results for Nicalon/ E-SiC 2-D Woven Composite [0/90] 2s : Predicted Repetitions to Failure [Predicted time to Rupture (s)] C Rupture 982 C Rupture 700 C Rupture 982 C Rupture 982 C Mission Loading 1100C 0.5 Hz Fatigue 1100C Trapezoidal 1100C Trapezoidal 950C Rupture 950 C Spike & Hold Experimental Repetitions to Failure [Experimental time to Rupture (s)]

23 Integration with FEA: 1.0 Z X Y Normalized Stress Predicted Lifetime Experimental Lifetime F 278 F Cycles to Failure

24 Idea: Use Micromechanical Model Results as Input to Residual Strength Model Why? Micromechanical models (particularly simulations) tend to be computationally intensive, but they can include details of material behavior Residual strength approaches are normally empirically based which casts doubts on their applicability for general conditions

25 Multiple Mechanism Result: Shear stress degradation Residual Strength (GPa) Combined Slow crack growth Time (hours)

26 Conclusions: Micromechanical models, while powerful for modeling material behavior, are somewhat limited Inputs are often difficult to obtain Computationally intensive Residual strength (and other phenomenological approaches) Simpler to implement Details of material behavior are obscured Possible means of exploiting strengths of both approaches has been examined