An extended finite element method (XFEM) coupled with a Monte Carlo approach is proposed to quantify the uncertainty in the homogenized effective elastic properties of multiphase materials. The methodology allows for an arbitrary number, aspect ratio, location and orientation of elliptic inclusions within a matrix, without the need for fine meshes in the vicinity of tightly packed inclusions and especially without the need to remesh for every different generated realization of the microstructure. Moreover, the number of degrees of freedom in the enriched elements is dynamically reallocated for each Monte Carlo sample run based on the given volume fraction. The main advantage of the proposed XFEM-based methodology is a major reduction in the computational effort in extensive Monte Carlo simulations compared with the standard FEM approach. Monte Carlo and XFEM appear to work extremely efficiently together. The Monte Carlo approach allows for the modeling of the size, aspect ratios, orientations, and spatial distribution of the elliptical inclusions as random variables with any prescribed probability distributions. Numerical results are presented and the uncertainty of the homogenized elastic properties is discussed. Copyright © 2011 John Wiley & Sons, Ltd.

Uncertainty quantification in homogenization of heterogeneous microstructures modeled by XFEM

Mechanical performance of three oxide/oxide ceramic matrix composites (CMCs) based on Nextel 610 fibers and SiOC, alumina, and mullite/SiOC matrices respectively, is evaluated herein. Tensile strength and stiffness of all materials decreased at 1000 °C and 1200 °C, probably because of degradation of fiber properties beyond 1000 °C. Microstructural changes in the composites during exposure at 1000 °C and 1200 °C for 50 h reduce their flexural strength, fracture toughness and work of fracture. A literature review regarding mechanical properties of several oxide/oxide CMCs revealed lower influence of fiber properties on composite strength compared with elastic modulus. The tested composites exhibit comparable stiffness and strength but higher fracture toughness compared with average values determined from a literature review. Considering CMCs with different compositions, we observed an interesting linear trend between strength and fracture toughness. The validity of the linear relationship between fracture strength and flexural toughness for CMCs is discussed.

Assessment of three oxide/oxide ceramic matrix composites: Mechanical performance and effects of heat treatments

We review the development of virtual tests for high-temperature ceramic matrix composites with textile reinforcement. Success hinges on understanding the relationship between the microstructure of continuous-fiber composites, including its stochastic variability, and the evolution of damage events leading to failure. The virtual tests combine advanced experiments and theories to address physical, mathematical, and engineering aspects of material definition and failure prediction. Key new experiments include surface image correlation methods and synchrotron-based, micrometer-resolution 3D imaging, both executed at temperatures exceeding 1,500°C. Computational methods include new probabilistic algorithms for generating stochastic virtual specimens, as well as a new augmented finite element method that deals efficiently with arbitrary systems of crack initiation, bifurcation, and coalescence in heterogeneous materials. Conceptual advances include the use of topology to characterize stochastic microstructures. We discuss the challenge of predicting the probability of an extreme failure event in a computationally tractable manner while retaining the necessary physical detail.

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Stochastic Virtual Tests for High-Temperature Ceramic Matrix Composites

The operating temperatures of surfaces in the hot sections of gas turbines are of great practical importance, but are often very hard to measure. Thermal indicating paints offer one possible and practical way, but they have many disadvantages. A novel concept for the utilisation of phosphorescent coatings as thermal history sensors was proposed by Feist et al. [1] in 2007. These phosphor coatings undergo irreversible changes when exposed to high temperatures that affect their photoluminescent properties and are a function of both the temperature and duration of exposure. If care is taken to ensure steady state conditions during exposure, subsequent off-line analysis of emission in the laboratory can reveal the temperature experienced by the coating. In this paper, an investigation of the amorphous-to-crystalline change of Y 2 SiO 5 :Tb is reported and used to provide a proof of concept for a phosphorescent thermal history sensor. Phosphor powder was calcined at different temperatures and for different periods, and characterised using photoluminescence spectroscopy. A calibration curve was generated and shows that this phosphor is suitable for temperature measurements over a temperature range from 600  ° C to at least 1000  ° C. With more advanced signal processing routines it is anticipated that the dynamic range might be extended to 1400  ° C. Such routines and other materials/physical processes are the subject of on-going research in the area at Imperial College and Southside Thermal Sciences.

Phosphorescent thermal history sensors

The degradation of SiC-based ceramic matrix composites (CMCs) in conditions typical of gas turbine engine operation proceeds via the stress-rupture of fiber bundles. The degradation is accelerated when oxygen and water invade the composite through matrix microcracks and react with fiber coatings and the fibers themselves. We review micromechanical models of the main rate-determining phenomena involved, including the the diffusion of gases and reaction products through matrix microcracks, oxidation of SiC (in both matrix and fibers) leading to the loss of stiffness and strength in exposed fibers, the formation of oxide scale on SiC fiber and along matrix crack surfaces that cause the partial closure of microcracks, and the concomitant and synergistic loss of BN fiber coatings. The micromechanical models could be formulated as time-dependent coupled differential equations in time, which must be solved dynamically, e.g., as an iterated user-defined material element, within a finite element simulation. A paradigm is thus established for incorporating the time-dependent evolution of local material properties according to the local environmental and stress conditions that exist within a material, in a simulation of the damage evolution of a composite component. We exemplify the calibration of typical micromechanical degradation models using thermodynamic data for the oxidation and/or volatilization of BN and SiC by oxygen and water, mechanical test data for the rate of stress-rupture of SiC fibers, and kinetic data for the processes involved in gas permeation through microcracks. We discuss approaches for validating computational simulations that include the micromechanical models of environmental degradation. A special challenge is achieving validated predictions of trends with temperature, which are expected to vary in a complex manner during use..

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Modeling environmentally induced property degradation of SiC/BN/SiC ceramic matrix composites

The oxidation and scale crystallization kinetics of Hi-NicalonTM-S SiC fibers were measured after oxidation in dry air between 700° and 1400°C. Scale thickness, composition, and crystallization were characterized by TEM with EDS, supplemented by SEM and optical microscopy. TEM was used to distinguish oxidation kinetics of amorphous and crystalline scales. Oxidation initially produces an amorphous silica scale that incorporates some carbon. Growth kinetics of the amorphous scale was analyzed using the flat-plate Deal-Grove model. The activation energy for parabolic oxidation was 248 kJ/mol. The scales crystallized to tridymite and cristobalite, starting at 1000°C in under 100 h and 1300°C in under 1 h. Crystallization kinetics had activation energy of 514 kJ/mol with a time growth exponent of 1.5. Crystalline silica nucleated at the scale surface, with more rapid growth parallel to the surface. Crystalline scales cracked from thermal residual stress and phase transformations during cool-down, and during oxidation from tensile hoop growth stress. High growth shear stress was inferred to cause intense dislocation plasticity near the crystalline SiO2–SiC interphase. Crystalline scales were thinner than amorphous scales, except where growth cracks allowed much more rapid oxidation.

Hi‐NicalonTM‐SSiC Fiber Oxidation and Scale Crystallization Kinetics

Nextel™ 610 alumina fiber tows were heat-treated at 1100°C–1500°C for 1 to 100 h in air. Tensile strengths and Weibull moduli were measured for 30 filaments after each heat-treatment. 3-D grain size and orientation distributions were described using oblate ellipsoids. The number of grains in a 1 inch gauge length and grains with the largest major and minor ellipsoid-axes were determined from these distributions. The grain with the largest KEFF for mixed-mode fracture was also determined, using the maximum energy release rate criteria from grain-size and orientation distributions. Grain-size dependence of tensile strength and Weibull modulus was evaluated. Strength had no obvious dependence on grain size for fibers with average major-axes smaller than 0.25 μm. For fibers with larger grains, grain-size dependence may involve flaws originating from clumps of grains, rather than a single grain. Possible relationships between strength and grain-size and other causes of strength degradation after heat-treatment are discussed.

Fiber Strength After Grain Growth in Nextel™ 610 Alumina Fiber

Monazite coatings were deposited on woven cloths and tows of Nextel™ 610 fibers by heterogeneous nucleation and growth using solution precursors. Initial experiments revealed two coating regimes in which monazite was either precipitated both in solution and onto the fiber surfaces or only onto the fiber surfaces depending on the precursor solution concentration and fiber surface area. In both cases, regions of tightly packed fibers within cloth were uncoated. Image analysis of coated fiber cross sections revealed a strong correlation between fiber separation and coating thickness, suggesting that the coating of tightly packed fibers was limited by transport of the reactants in solution to these areas. By adopting a coating procedure in which the tightly packed regions are saturated with reactants before precipitation, more uniform coatings of monazite were obtained throughout the cloth; however, the strength of as-coated and heat-treated fibers was degraded and remains problematic.

Precipitation Coating of Monazite on Woven Ceramic Fibers: I. Feasibility

Woven cloths of Nextel™ 610 and 720 fibers were coated with monazite by precipitation. The cloths were first saturated with concentrated precursor solutions, and then submerged in warm water to initiate precipitation onto the fiber surfaces. Coatings were characterized by scanning electron microscopy, and transmission electron microscopy; thermogravimetric analysis was performed on LaPO4 owders precipitated in solution under the same conditions as the coatings were deposited. Coating thickness distributions were measured and analyzed. Coated fiber strength was measured following heat treatment for 2 h at 1200°C. Processing conditions which retain a substantial fraction of the uncoated fiber strength are identified, and are discussed in the context of current understanding of strength degradation in coated fibers. Strength retention of coated Nextel™ 610 fibers following heat treatment was broadly insensitive to precursor solution chemistry and was more strongly affected by intercoat firings which govern the final coating microstructure. For fixed processing conditions, more strength degradation was observed in Nextel™ 720 due to higher residual stresses in the fiber.

Precipitation Coating of Monazite on Woven Ceramic Fibers: II. Effect of Processing Conditions on Coating Morphology and Strength Retention of Nextel™ 610 and 720 Fibers

Polycrystalline yttrium–aluminum garnet (YAG) fibers are attractive for high-power lasers and for high-temperature structural materials. Processing methods for

Geoff E. Fair

Papers

Hi‐NicalonTM‐SSiC Fiber Oxidation and Scale Crystallization Kinetics

Fiber Strength After Grain Growth in Nextel™ 610 Alumina Fiber

Precipitation Coating of Monazite on Woven Ceramic Fibers: I. Feasibility

Precipitation Coating of Monazite on Woven Ceramic Fibers: II. Effect of Processing Conditions on Coating Morphology and Strength Retention of Nextel™ 610 and 720 Fibers

Development of polycrystalline yttrium aluminum garnet (YAG) fibers