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Compatibility of molten plutonium with wrought and additively manufactured metal crucibles

Understanding plutonium’s interaction with metals is crucial for optimizing pyrochemical operations, nuclear fuel containment, and various actinide processing techniques. Traditionally, tantalum crucibles are employed for plutonium processing due to their high durability, excellent temperature stability, and low solubility in plutonium. However, tantalum faces challenges such as plutonium wetting and diffusion, making surface coatings particularly important for crucibles in pyrochemical applications to enhance corrosion resistance against plutonium. Tantalum is also expensive and difficult to machine, prompting the need for advanced manufacturing techniques to address these challenges. Here, in this work, we investigate the interaction of Pu with tantalum and titanium crucibles fabricated using both traditional machining methods and laser powder bed fusion (LPBF) additive manufacturing (AM). LPBF-AM is an advanced technique that allows for the creation of complex geometries from traditionally difficult-to-machine metals by using a high-powered laser to build parts. Previous studies of conventional manufactured tantalum have utilized oxidation and carburization of the surface to mitigate plutonium wetting; however, no studies of surface modified LPBF-AM material have been undertaken. These studies are crucial, given the typical differences in the grain structure between conventional and LPBF-AM materials. All crucibles underwent differential scanning calorimetry to confirm the melting of plutonium. Subsequently, the crucibles were sectioned and mounted in epoxy for microstructural analysis using optical microscopy and scanning electron microscopy. This investigation, comparing the performance of wrought vs AM metal crucibles, provides a basis for future tooling applications in actinide processing techniques and can address the challenges associated with traditional machining, particularly in pyrochemical applications.

Actinides

Development of Stable Solid Oxide Electrolysis Cells for Low-Cost Hydrogen Production

The project objective was to demonstrate a solid oxide cell-based steam electrolysis stack that exhibits robustness, reliability, endurance, hydrogen purity, and produces hydrogen at elevated pressure of 2 to 3 bar. Innovative materials and processing methods were evaluated to improve degradation characteristics. Performance improvement focused on nearly all layers involved in the cell and stack assembly. Primary attention was paid to zirconia-ceria interface resistance control via sintering optimization and decrease in degradation from the oxygen electrode by evaluating low strontium (Sr) or Sr-free composition for both the oxygen electrode and current collection layer. Stack robustness was addressed by validating redox tolerance of fuel electrode, confirming capability of cells to survive repeated thermal cycles, studying the effect of pressure on performance and degradation, evaluating the effect of contamination on fuel and oxygen electrode performance and degradation, and identifying mitigation strategies to improve performance. The characterization included evaluation of electrochemical performance and stability followed by microstructural analysis. At the cell level, performance and stability improvements were achieved by incorporating a Sr-free oxygen electrode and a denser oxygen electrode barrier layer. At the stack level, pressurized operation reduces demand on first stage compression, the redox tolerant fuel electrode mitigates risk from service interruptions, and improvements to interconnect coating alleviate chromium (Cr) contamination effects. The denser barrier layer was achieved by adding a sintering aid to the samaria-doped ceria (SDC) composition that reduced sintering temperature by 150 °C. The resulting density was on par with the baseline SDC barrier layer density and the lower sintering temperature resulted in less resistive phase formation during sintering. Button cell tests did not demonstrate a change in performance when exposed to silicon (Si) or manganese (Mn) impurities to the fuel electrode and Cr impurity to the oxygen electrode. More detailed study however is warranted. The project addressed SOEC performance and stability at the cell and stack levels through a systematic approach to known sources of degradation that were combined and tested in three stack tests using an electrolyte supported cell design to allow for evaluation of a variety of fuel and oxygen electrode compositions. STK-82 and STK-83 had identical compositions. STK-100 incorporated the best materials and processing variables developed under this and concurrent projects, and was tested at elevated pressure in steam electrolysis. • STK-82 recovered performance after redox and thermal cycling, demonstrating the robustness of the stack and seals. It exhibited stable performance in testing for 500 hours in SOEC mode, followed by 300 hours of cycling between SOEC and SOFC tests. Degradation during SOEC operation was 1.8 %/ 1,000 hours. • STK-83 generated hydrogen at >80% steam conversion, and oxygen above 98.5 % purity during pressurized operation. Both hydrogen and oxygen were generated at 3 barg pressure without the use of a pressure vessel. In addition to balanced pressure, electrolysis operation at 1 bar differential pressure across anode and cathode was also demonstrated to substantial the robustness of the cell and seal. • STK-100 measured at initial ambient pressure conditions showed an area specific resistance of 1.1 ohm-cm 2 , and STK-83 had 1.3 ohm-cm 2 .

08 HYDROGEN

Robust Solar Receivers Using MAX Phase Materials

This work was supported by the U.S. Department of Energy’s Office of Energy Efficiency and Renewable Energy under the Solar Energy Technologies Office Award Number 35928. The objective of the proposed effort was to develop and optimize additive manufacturing technologies for low-cost fabrication of high-temperature receivers using MAX phase-based materials (Ti 3 SiC 2 and Ti 3 AlC 2 ). MAX phase materials are a group of ternary metal carbides and nitrides where M stands for an early transition metal element, A is a group 13–16 element, and X is C and/or N. In Phase 1, the binder jetting additive manufacturing process was used to synthesize and characterize the Ti 3 SiC 2 MAX phase material. The typical process involved first producing a TiC preform using binder jetting followed by infiltration of the preform with silicon melt to form Ti 3 SiC 2 in situ. The reaction-infiltrated samples showed formation of MAX phase in the sample core; however, the surface showed cracking. Various process conditions—cooling rates, hold times, Si proportion, etc.—were varied to minimize the surface cracking. The fabricated MAX phase core was characterized by microstructure analysis and evaluations of mechanical properties such as hardness and thermal shock. In Phase 2, the focus included fabrication of Ti 3 SiC 2 MAX phase materials by spark plasma sintering (SPS) and synthesis of Ti 3 AlC 2 MAX phase materials by the Al melt infiltration process. It is expected that Al infiltration will not cause sample cracking, since Al does not expand during solidification. In addition, other processing approaches were investigated to fabricate the MAX phase materials, such as SPS with a graphite bedding approach for producing short-length Ti 3 AlC 2 MAX phase tubes for demonstration of prototypical Concentrating Solar Power receiver tubes. Fabricated samples underwent thermo-mechanical testing to validate the materials for the solar receiver application at temperatures >1000°C. In Phase 3, the effort focused on the development and optimization of the Ti-Al-C MAX phase composite material using the Al melt infiltration approach. We started with optimization of precursor powders and making preform structures by either pressing them in a die or using the binder jetting additive manufacturing process followed by Al melt infiltration. In addition, we investigated the formation of preform structures by cold isostatic pressing followed by Al melt infiltration for making Ti-Al-C MAX phase composite. Thermo-mechanical characterizations, such as creep, strength, and thermal shock, were conducted to establish the structures’ performance.

36 MATERIALS SCIENCE

Additive Manufacturing of Fe-based Alloys for Nuclear Reactor Environments

This report is a Milestone 2 deliverable in FY2025, under work package MT-25AN090211 to support research and qualification activities supported by the Advanced Materials and Manufacturing Technologies (AMMT) program. It provides an update on the work done on the laser based additive manufacturing of steels for nuclear applications, conducted collaboratively by Argonne National Laboratory and Pacific Northwestern National Laboratory. Building upon FY23 and FY24 efforts, the focus of FY25 includes continued optimization of process parameters for the alloys: A709 & G92. The work package also includes fabricating test samples to conduct a thorough microstructural analysis and perform preliminary mechanical testing. The major accomplishments of this work package are summarized below, applicable to both Laser Powder Bed Fusion (LPBF) processes conducted at Argonne National Laboratory and Laser Powder Directed Energy Deposition (LP-DED) processes conducted at Pacific Northwest National Laboratory.

22 GENERAL STUDIES OF NUCLEAR REACTORS

Boride-based Ceramic Super-high Temperature Thermocouples in Harsh Environments (Final Scientific/Technical Report)

An electromotive force (emf) can be generated along a temperature gradient between the cold end and hot end of a thermoelectric material, termed the Seebeck effect. Based on the Seebeck effect, metallic alloys have been extensively employed to detect temperatures for centuries, named thermocouples. However, commercially available thermocouple alloys suffer from limitations, such as oxidation, chemical degradation, and poor long-term stability under high-temperature harsh environments. This DOE-funded project aimed to develop high-temperature, chemically tolerant thermocouples suitable for operation in extreme environments relevant to semiconducting thermoelectric materials. The research focused on boride-based semiconducting thermoelectric compounds as candidates for next-generation thermocouples with enhanced oxidation resistance, chemical stability, and thermal robustness under conditions representative of charcoal-fired electricity facilities. During the funded years, boride materials were synthesized using an arc-plasma technique under ambient air and argon atmospheres, enabling scalable and cost-effective production compared with conventional boride fabrication methods. The synthesized borides were processed into nanostructured powders, followed by consolidation into dense bulk materials using a spark plasma sintering (SPS) bottom-up approach. Comprehensive characterization was performed, including microstructural analysis, electrical transport measurements, and optical and thermal property evaluation. Both p-type and n-type boride electric legs were fabricated and integrated into boride-based thermocouples. The thermal and irradiation stabilities of the boride nanomaterials and bulk thermoelectric materials were systematically evaluated to assess suitability for long-term operation in harsh environments. Additionally, 12 students were broadly hands-on trained spanning the full research workflow, including word processing and technical editing (e.g., LATEX for manuscript and poster preparation), data collection and analysis (using Python and related libraries and hardware interfaces), sample preparation (including arc-plasma synthesis and spark plasma sintering), and advanced characterization techniques (such as X-ray diffraction, UV–vis spectroscopy, electron microscopy, differential thermal analysis (DTA), and Seebeck coefficient measurements, etc). Overall, this project demonstrated the feasibility of boride-based thermoelectric materials as durable high-temperature thermocouples, providing a promising pathway toward robust temperature sensing technologies aligned with DOE energy infrastructure and extreme-environment monitoring needs.

20 FOSSIL-FUELED POWER PLANTS

Material Characterization Report of FFTF MFF 5 Fuel Element

This report was written as part of the TerraPower Cooperative Research and Development Agreement No. 11-CR-19 with Idaho National Laboratory. TerraPower provided the funding. An as-fabricated fuel element from the Fast Flux Test Facility MFF-5 experiment was sectioned and analyzed for material properties. Results reported include phase characterization, microstructural analysis, density, microhardness, and chemical composition.

11 - NUCLEAR FUEL CYCLE AND FUEL MATERIALS

Study of the production of some superconducting and magnetic materials by solidification in the drop tube and drop tower

A systematic study on the relationship between the microstructure and physical properties of several superconducting materials prepared by solidification in low gravity was conducted. Further study of the materials, such as the applications of hydrostatic pressure which is known to be an effective mean to vary the electronic structure of materials, in conjunction with the detailed microstructure analysis of the samples was also performed to better understand the low gravity effects on the enhancement of the electronic properties. Results of the studies on the directionally solidified AlInSn alloys processed in the KC-135 aircraft and immiscible GaBi alloy prepared during free fall in the Marshall Space Flight Center Drop Tower are presented.

Wu, M. K.

Microstructural and magnetic characterization of rapidly solidified and annealed Pt-Co-B alloys

Significant increases in intrinsic coercivity (Hic) of Pt-Co alloys have been obtained by the addition of boron and the application of rapid solidification processing. After rapid solidification by double anvil splat quenching with subsequent annealing at 650 C for 30 min, an alloy of Pt42Co45B13 exhibits an Hic as high as 14 kOe. Annealing of the Pt-Co-B influences the L1(0) superlattice structure and grain size of the matrix, the crystal structure and size of Co-boride precipitate, and the distribution of magnetic domain walls. A microstructural analysis shows that the maximum H(ic) occurs when Co borides, having the Co3B structure, are within the single magnetic domain size. The magnetic hardening mechanism in Pt-Co-B is believed to be a combination of inhibited magnetic domain nucleation and difficult reverse magnetic domain growth caused by the interaction of the magnetically anisotropic Co borides with the L1(0) Pt-Co matrix.

Qiu, N.

Long discontinuous fiber composite structure: Forming and structural mechanics

Cost effective composite structure has motivated the investigation of several new approaches to develop composite structure from innovative material forms. Among the promising new approaches is the conversion of planar sheet to components of complex curvature through sheet forming or stretch forming. In both cases, the potential for material stretch in the fiber direction appears to offer a clear advantage in formability over continuous fiber systems. In the present study, the authors have established a framework which allows the simulation of the anisotropic mechanisms of deformation of long discontinuous fiber laminates wherein the matrix phase is a viscous fluid. The initial study focuses upon the establishment of micromechanics models for prediction of the effective anisotropic viscosities of the oriented fiber assembly in a viscous matrix. Next, the developed constitutive relation is employed through an analogy with incompressible elasticity to exercise the finite element technique for determination of local fiber orientation and laminate thickness after forming. Results are presented for the stretch bending of a curved beam from an arbitrary composite laminate and the bulging of a clamped sheet. Structural analyses are conducted to determine the effect of microstructure on the performance of curved beams manufactured from long discontinuous fiber composites. For the purposes of this study, several curved beams with ideal and non-ideal microstructures are compared for response under pure bending. Material parameters are determined from a separate microstructural analysis.

Pipes, R. B.

Solidification kinetics and metastable phase formation in binary Ti-Al

Electromagnetic levitation was used to solidify near-equiatomic alloys of Ti-Al at various bulk undercoolings. Detailed thermal histories were acquired during experiments using optical pyrometry with sampling rates as fast as 500 KHz. Solidification and other high-temperature transformation pathways were deduced from the thermal data and microstructural analysis. Recalescence rise times were employed to determine semiquantitative primary solidification kinetics for the different phases. Primary beta solidification was observed at compositions well into the equilibrium alpha regime; this is presented as part of a near-equiatomic nucleation domain diagram that shows the primary solidification phase that results for each combination of nucleation temperature and composition. Solidification kinetics are faster for primary beta than they are for primary alpha. For undercoolings less than about 150 K, the primary solidification kinetics are about an order of magnitude slower for gamma than for alpha.

Anderson, C. D.

Thermal Stability of Hi-Nicalon SiC Fiber in Nitrogen and Silicon Environments

The room temperature tensile strength of uncoated and two types of pyrolytic boron nitride coated (PBN and Si-rich PBN) Hi-Nicalon SiC fibers was determined after 1 to 400 hr heat treatments to 1800 C under N2 pressures of 0.1, 2, and 4 MPa, and under 0.1 Mpa argon and vacuum environments. In addition, strength stability of both uncoated and coated fibers embedded in silicon powder and exposed to 0.1 MPa N2 for 24 hrs at temperatures to 1400 C was investigated. The uncoated and both types of BN coated fibers exposed to N2 for 1 hr showed noticeable strength degradation above 1400 C and 1600 C, respectively. The strength degradation appeared independent of nitrogen pressure, time of heat treatment, and surface coatings. TEM microstructural analysis suggests that flaws created due to SiC grain growth are responsible for the strength degradation. In contact with silicon powder, the uncoated and both types of PBN coated fibers degrade rapidly above 1350 C.

Bhatt, R. T.

Parabolic aircraft solidification experiments

A number of solidification experiments have been utilized throughout the Materials Processing in Space Program to provide an experimental environment which minimizes variables in solidification experiments. Two techniques of interest are directional solidification and isothermal casting. Because of the wide-spread use of these experimental techniques in space-based research, several MSAD experiments have been manifested for space flight. In addition to the microstructural analysis for interpretation of the experimental results from previous work with parabolic flights, it has become apparent that a better understanding of the phenomena occurring during solidification can be better understood if direct visualization of the solidification interface were possible. Our university has performed in several experimental studies such as this in recent years. The most recent was in visualizing the effect of convective flow phenomena on the KC-135 and prior to that were several successive contracts to perform directional solidification and isothermal casting experiments on the KC-135. Included in this work was the modification and utilization of the Convective Flow Analyzer (CFA), the Aircraft Isothermal Casting Furnace (ICF), and the Three-Zone Directional Solidification Furnace. These studies have contributed heavily to the mission of the Microgravity Science and Applications' Materials Science Program.

Workman, Gary L.

Failure Mechanisms During Isothermal Fatigue of SiC/Ti-24Al-11Nb Composites

Failure mechanisms during isothermal fatigue of unidirectional SiC/Ti-24Al-11Nb (at.%) composites have been determined by microstructural analysis of samples from tests interrupted prior to the end of life and from tests conducted to failure. Specimens from three regions of life were examined based on the maximum strain from a fatigue life diagram: Region 1 (high strain), Region 2 (mid-strain) and Region 3 (low strain). Crack lengths were also measured from interrupted samples and compared based on temperature (23-815 C), region of life and numbers of cycles. Region 1 was controlled by fiber-dominated failure. A transition zone was observed between Regions 1 and 2 due to competition between failure mechanisms. Failure in Region 2 was generally described as surface-initiated cracking with varying amounts of fiber bridging. However, the specific descriptions of crack propagation through the fibers and matrix varied with strain and temperature over this broad region. Region 3 exhibited endurance behaviour at 23 C with no cracking after lO(exp 6) cycles. However at 425 C, surface-initiated cracking was observed after 10(exp 6) cycles with fractured fibers in the crack wake. If endurance behaviour exists for conditions of isothermal fatigue in air at temperatures of greater than or equal to 425 C, it may only be found at very low strains and at greater than 10(exp 6) cycles.

Brindley, P. K.

Stressed Oxidation of C/SiC Composites

Constant load, stressed oxidation testing was performed on T-300 C/SiC composites with a SiC seal coat. Test conditions included temperatures ranging from 350 C to 1500 C at stresses of 69 MPa and 172 MPa (10 and 25 ksi). The coupon subjected to stressed oxidation at 550 C/69 MPa for 25 hours had a room temperature residual strength one-half that of the as-received coupons. The coupon tested at the higher stress and all coupons tested at higher temperatures failed in less than 25 hr. Microstructural analysis of the fracture surfaces, using SEM (scanning electron microscopy), revealed the formation of reduced cross-sectional fibers with pointed tips. Analysis of composite cross-sections show pathways for oxygen ingress. The discussion will focus on fiber/matrix interphase oxidation and debonding as well as the formation and implications of the fiber tip morphology.

Halbig, Michael C.

Effects of HF Treatments on Tensile Strength of Hi-Nicalon Fibers

Tensile strengths of as-received Hi-Nicalon fibers and those having a dual BN/SiC surface coating, deposited by chemical vapor deposition, have been measured at room temperature. These fibers were also treated with HF for 24 h followed by tensile strength measurements. Strengths of uncoated and BN/SiC coated Hi-Nicalon fibers extracted from celsian matrix composites, by dissolving away the matrix in HF for 24 h, were also determined. The average tensile strength of uncoated Hi-Nicalon was 3.19 +/- 0.73 GPa with a Weibull modulus of 5.41. The Hi-Nicalon/BN/SiC fibers showed an average strength of 3.04 q 0.53 GPa and Weibull modulus of 6.66. After HF treatments, the average strengths of the uncoated and BN/SiC coated Hi-Nicalon fibers were 2.69 +/- 0.67 GPa and 2.80 +/- 0.53 GPa and the Weibull moduli were 4.93 and 5.96, respectively. The BN/SiC coated fibers extracted from the celsian matrix composite exhibited a strength of 2.38 +/- 0.40 GPa and a Weibull modulus of 7.15. The strength of the uncoated Hi-Nicalon fibers in the composite was so severely degraded that they disintegrated into small fragments during extraction with HF. The uncoated fibers probably undergo mechanical surface damage during hot pressing of the composites. Also, the BN layer on the coated fibers acts as a compliant layer which protects the fibers from mechanical damage during composite processing. The elemental composition and thickness of the fiber coatings were deten-nined using scanning Auger analysis. Microstructural analyses of the fibers and the coatings were done by scanning electron microscopy and transmission electron microscopy. Strengths of fibers calculated using average and measured fiber diameters were in good agreement. Thus, the strength of fibers can be evaluated using an average fiber diameter instead of the measured diameter of each filament.

Bansal, Narottam P.

Oxygen Diffusion and Reaction Kinetics in Continuous Fiber Ceramic Matrix Composites

Previous stressed oxidation tests of C/SiC composites at elevated temperatures (350 C to 1500 C) and sustained stresses (69 MPa and 172 MPa) have led to the development of a finite difference cracked matrix model. The times to failure in the samples suggest oxidation occurred in two kinetic regimes defined by the rate controlling mechanisms (i.e. diffusion controlled and reaction controlled kinetics). Microstructural analysis revealed preferential oxidation along as-fabricated, matrix microcracks and also suggested two regimes of oxidation kinetics dependent on the oxidation temperature. Based on experimental results, observation, and theory, a finite difference model was developed. The model simulates the diffusion of oxygen into a matrix crack bridged by carbon fibers. The model facilitates the study of the relative importance of temperature, the reaction rate constant, and the diffusion coefficient on the overall oxidation kinetics.

Halbig, Michael C.

Containerless, Low-Gravity Undercooling of Ti-Ce Alloys in the MSFC Drop Tube

Previous tests of the classical nucleation theory as applied to liquid-liquid gap miscibility systems found a discrepancy between experiment and theory in the ability to undercool one of the liquids before the L1-L2 separation occurs. To model the initial separation process in a two-phase liquid mixture, different theoretical approaches, such as free-energy gradient and density gradient theories, have been put forth. If there is a large enough interaction between the critical liquid and the crucible, both models predict a wetting temperature (T(sub w)) above which the minority liquid perfectly wets and layers the crucible interface, but only on one side of the immiscibility dome. Materials with compositions on the other side of the dome will have simple surface adsorption by the minority liquid before bulk separation occurs when the coexistence (i.e., binoidal) line in reached. If the interaction between the critical liquid and the crucible were to decrease, T(sub w) would increase, eventually approaching the critical consolute temperature (T(sub cc)). If this situation occurs, then there could be large regions of the miscibility gap where non-perfect wetting conditions prevail resulting in droplets of L1 liquid at the surface having a non-zero contact angle. The resulting bulk structure will then depend on what happens on the surface and the subsequent processing conditions. In the past several decades, many experiments in space have been performed on liquid metal binary immiscible systems for the purpose of determining the effects that different crucibles may have on the wetting and separation process of the liquids. Potard performed experiments that showed different crucible materials could cause the majority phase to preferentially wet the container and thus produce a dispersed microstructure of the minority phase. Several other studies have been performed on immiscibles in a semi-container environment using an emulsion technique. Only one previous study was performed using completely containerless processing of immiscible metals and the results of that investigation are similar to some of the emulsion studies. In all the studies, surface wetting was attributed as the cause for the similar microstructures or the asymmetry in the ability to undercool the liquid below the binoidal on one side of the immiscibility dome. By removing the container completely from the separation process, it was proposed that the loss of the crucible/liquid interaction would produce a large shift in T(sub w) and thus change the wetting characteristics at the surface. By investigating various compositions across the miscibility gap, a change in the type and amount of liquid wetting at the surface of a containerless droplet should change the surface nucleating behavior of the droplet - whether it be the liquid-liquid wetting or the liquid-to-solid transition. Undercooling of the liquid into the metastable region should produce significant differences in the separation process and the microstructure upon solidification. In this study, we attempt to measure these transitions by monitoring the temperature of the sample by optical pyrometry. Microstructural analysis will be made to correlate with the degree of undercooling and the separation mechanisms involved.

Robinson, M. B.

Intermediate Temperature Stress Rupture of Woven SiC Fiber, BN Interphase, SiC Matrix Composites in Air

Tensile stress-rupture experiments were performed on woven Hi-Nicalon reinforced SiC matrix composites with BN interphases in air. Modal acoustic emission (AE) was used to monitor the damage accumulation in the composites during the tests and microstructural analysis was performed to determine the amount of matrix cracking that occurred for each sample. Fiber fractograph), was also performed for individual fiber failures at the specimen fracture surface to determine the strengths at which fibers failed. The rupture strengths were significantly worse than what would have been expected front the inherent degradation of the fibers themselves when subjected to similar rupture conditions. At higher applied stresses the rate of rupture "?as larger than at lower applied stresses. It was observed that the change in rupture rate corresponded to the onset of through-thickness cracking in the composites themselves. The primary cause of the sen,ere degradation was the ease with which fibers would bond to one another at their closest separation distances, less than 100 nanometers, when exposed to the environment. The near fiber-to-fiber contact in the woven tows enabled premature fiber failure over large areas of matrix cracks due to the stress-concentrations created b), fibers bonded to one another after one or a few fibers fail. i.e. the loss of global load sharing. An@, improvement in fiber-to-fiber separation of this composite system should result in improved stress- rupture properties. A model was den,eloped in order to predict the rupture life-time for these composites based on the probabilistic nature of indin,idual fiber failure at temperature. the matrix cracking state during the rupture test, and the rate of oxidation into a matrix crack. Also incorporated into the model were estimates of the stress-concentration that would occur between the outer rim of fibers in a load-bearing bundle and the unbridged region of a matrix crack after Xia et al. For the lower stresses, this source of stress-concentration was the likely cause for initial fiber failure that would trigger catastrophic failure of the composite.

Morscher, Gregory N.