Stress-Induced Microcracking and Fracture Characterization for Ultra-High-Temperature Ceramic Matrix Composites at High Temperatures
Abstract
:1. Introduction
2. Temperature-Dependent Models
3. Results and Discussion
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
List of Notations
Notation | Description |
R | Particle radius |
s | Flaw size |
P | Residual stress |
αm,αp | Thermal expansion coefficients of the matrix and particle |
Em,Ep | Young’s modulus of the matrix and particle |
νm,νp | Poisson’s ratio of the matrix and particle |
Ts | Sintering temperature |
Tr | Room temperature |
Tm | Melting temperature |
Radial components of residual stress | |
Tangential components of residual stress | |
Stress intensity factor at the tip of the flaw due to residual stress | |
P(T) | Temperature-dependent residual stress |
T | Current temperature |
αm(T), αp(T) | Temperature-dependent thermal expansion coefficients of the matrix and particle |
Em(T), Ep(T) | Temperature-dependent Young’s modulus of the matrix and particle |
νm(T), νp(T) | Temperature-dependent Poisson’s ratio of the matrix and particle |
Temperature-dependent stress intensity factor at the tip of the flaw due to residual stress | |
Temperature-dependent critical inclusion size for spontaneous microcracking | |
Temperature-dependent critical stress intensity factor for a local failure | |
Temperature-dependent critical stress intensity factor for the extension of a critical flaw | |
Constant | |
Temperature-dependent fracture toughness | |
External stress | |
Stress intensity factor at the tip of the flaw due to applied stress | |
Temperature-dependent stress intensity factor at the tip of the flaw due to both residual stress and applied stress | |
Temperature-dependent critical inclusion size for microcracking under the applications of external stress and residual stress | |
Temperature-dependent fracture strength | |
A | Constant |
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Material Parameters | Values and Expressions |
---|---|
νm | 0.25 |
νp | 0.19 |
Ts (°C) | 1950 |
Tm (°C) | 3049.85 |
T0 (°C) | 25 |
γ(T0) (J⋅m−2) | 12.76 |
Cp(T) (cal/mol) | 15.34 + 2.25 × 10−3 (T + 273.15) − 3.96 × 105 (T + 273.15)−2 |
αm(T) (°C−1) | (2.33 + 0.006 × (T + 273.15) − 0.2 × 10−5 × (T + 273.15)2) × 10−6 |
αp(T) (°C−1) | (−1.8276 + 0.0178(T + 273.15) − 1.5544 × 10−5(T + 273.15)2 + 4.5246 × 10−9 (T + 273.15)3) × 10−6(0 °C ≤ T < 1000 °C) |
αp(T) (°C−1) | 5.0 × 10−6(T ≥ 1000 °C) |
Em(T) (GPa) | |
Ep(T) (GPa) |
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Gu, M.; Wu, C.; Chen, X.; Wan, Y.; Liu, Y.; Zhou, S.; Cai, H.; Jia, B.; Wang, R.; Li, W. Stress-Induced Microcracking and Fracture Characterization for Ultra-High-Temperature Ceramic Matrix Composites at High Temperatures. Materials 2022, 15, 7074. https://doi.org/10.3390/ma15207074
Gu M, Wu C, Chen X, Wan Y, Liu Y, Zhou S, Cai H, Jia B, Wang R, Li W. Stress-Induced Microcracking and Fracture Characterization for Ultra-High-Temperature Ceramic Matrix Composites at High Temperatures. Materials. 2022; 15(20):7074. https://doi.org/10.3390/ma15207074
Chicago/Turabian StyleGu, Mingyu, Chunyan Wu, Xingyu Chen, Yu Wan, Yumeng Liu, Shan Zhou, Hongwei Cai, Bi Jia, Ruzhuan Wang, and Weiguo Li. 2022. "Stress-Induced Microcracking and Fracture Characterization for Ultra-High-Temperature Ceramic Matrix Composites at High Temperatures" Materials 15, no. 20: 7074. https://doi.org/10.3390/ma15207074