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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 325 records · Page 18

Induced seismicity potential based on probabilistic geomechanics for the San Juan Basin CarbonSAFE project

Although geologic carbon sequestration projects have yet to induce — or may never induce — a damaging earthquake, experiences from other deep injection industries such as hydraulic fracturing, enhanced geothermal systems, and saltwater disposal suggest that effective quantitative seismic risk assessment is necessary for deep saline carbon capture and sequestration (CCS) projects. One such imminent CCS project is the San Juan Basin CarbonSAFE Phase III program. We use Monte Carlo probabilistic geomechanical analyses combined with observations of the geologic and operational parameters of the San Juan Basin site and suggest that this project is of low-induced seismic risk. The primary analysis is split into four sections. First, we assess the literature for faults and past seismicity, and at least five faulting scenarios are directly relevant. Second, we develop and calibrate an integrated earth model for the project site. Third, we perform Monte Carlo simulations that consider reasonable uncertainties of the geomechanical parameters. Of five tested faulting scenarios, only one presents high Coulomb failure functions, but fourth, we determine the risk to be low based on the combined lack of historical seismicity, the geologic framework of the faulting scenario, and the presence of saltwater injection at the same depth as the proposed supercritical carbon dioxide injection. The most sensitive parameters in the geomechanical calculations are the fault dip and the coefficient of friction. The least sensitive are the fault strike and the orientation of the maximum horizontal principal stress.

58 GEOSCIENCES↗

Water-induced surface ordering facilitating the microcutting of ductile metals

Metal cutting is a crucial process in modern manufacturing. Enhancing the machinability of metals can significantly improve their production efficiency and surface integrity. Coating surface-active media (SAM) on the free surface of the metals before cutting is an easy method to improve machinability, which usually pertains to the category of the renowned Rehbinder effect. However, the existing SAM is usually hazardous and complex materials. Besides, the effect of SAM on the local structure of the metal surface remains unclear. In this study, water is employed as a simple yet often overlooked SAM in the microcutting of copper. Using water as SAM also allows the employment of X-ray absorption fine structure spectroscopy (XAFS) to study the local structure of copper with and without water coating. Results show that water coating on the free surface of copper can significantly reduce the cutting force and chip thickness, and improve the surface finish. Interestingly, removing the water coating enables the recovery of the cutting force, demonstrating a reversible effect. Based on the XAFS results and molecular dynamics simulation, a water-induced surface ordering mechanism is proposed to explain the findings from the microcutting experiments. This mechanism suggests that water molecules can induce surface ordering in copper, resulting in reduced surface energy and fracture toughness of copper, thus enhancing machinability. In conclusion, this work provides valuable insights into the comprehension of the Rehbinder effect and shows that picometer-scale modifications of the surface atom arrangement can considerably alter the deformation mode of metals, paving the way for the development of new manufacturing processes.

36 MATERIALS SCIENCE↗

Finite element analysis of the end notched flexure specimen for measuring Mode II fracture toughness

The paper presents a finite element analysis of the end-notched flexure (ENF) test specimen for Mode II interlaminar fracture testing of composite materials. Virtual crack closure and compliance techniques employed to calculate strain energy release rates from linear elastic two-dimensional analysis indicate that the ENF specimen is a pure Mode II fracture test within the constraints of small deflection theory. Furthermore, the ENF fracture specimen is shown to be relatively insensitive to process-induced cracks, offset from the laminate midplane. Frictional effects are investigated by including the contact problem in the finite element model. A parametric study investigating the influence of delamination length, span, thickness, and material properties assessed the accuracy of beam theory expressions for compliance and strain energy release rate, GII. Finite element results indicate that data reduction schemes based upon beam theory underestimate GII by approximately 20-40 percent for typical unidirectional graphite fiber composite test specimen geometries. Consequently, an improved data reduction scheme is proposed.

Gillespie, J. W., Jr.↗

TBS (Trabecular Bone Score) Expands Understanding of Spaceflight Effects on the Lumbar Spine of Long Duration Astronauts

Background: Bone loss due to long-duration spaceflight has been characterized by both DXA and QCT serial scans. It is unclear if these spaceflight-induced changes in bone mineral density and structure result in increased fracture incidence. NASA astronauts currently fly on 5-6-month missions on the International Space Station (ISS) and at least one 12-month mission is planned. While NASA has measured areal BMD (by DXA) and volumetric BMD (by QCT), and has estimated hip strength (by finite element models of QCT data, no method has yet been used to examine bone microarchitecture from lumbar spine (LS). DXA scans are routinely performed pre- and post-flight on all ISS astronauts to follow BMD changes associated with space flight. Trabecular Bone Score (TBS) is a relatively new method that measures grey-scale-level texture information extracted from lumbar spine DXA images and correlates with 3D parameters of bone micro-architecture. We evaluated the ability of LS TBS to discriminate changes in astronauts who have flown on ISS missions and to determine if TBS can provide additional information compared to DXA. Methods: LS (L1-4) DXA scans from 51 astronauts (mean age, 47 +/- 4) were divided into 3 groups based on the exercise regimes performed while onboard the ISS. Pre-ARED (exercise using a load-limited resistive exercise device, <300lb), ARED (exercise with a high-load resistive exercise device, up to 600lb) and a Bisphos group (ARED exercise and a 70-mg alendronate tablet once a week before and during flight, starting 17 days before launch). DXA scans were performed and analyzed on a Hologic Discovery W using the same technician for the pre- and postflight scans. LSC for the LS in our laboratory is 0.025 g/cm2. TBS was performed at the Mercy Hospital, Cincinnati, Ohio on a similar Hologic computer. TBS precision was calculated from 16 comparable test subjects (0.0XX g/cm2). Data were preliminary analyzed using a paired, 2-tailed t-test for the difference between pre- and postflight means.

Sibonga, Jean D.↗

On surface energy and the continuum thermodynamics of brittle fracture

When a separating body is viewed as a nonequilibrium thermodynamic process, the full thermodynamic nature of the surface energy induced by crack propagation becomes apparent. Within such a general framework it is no longer possible to view the surface energy as a material constant. For the self-propagating crack the induced surface energy is shown to depend explicitly on the square of the crack propagation speed. It is also shown that a separating body produces entropy even though the mechanical response of the solid may be elastic. The introduction of surface quantities such as surface energy into the continuum description of the fracture process forces a major departure from the mechanics appropriate to the nonseparating body. Local equations of balance are no longer obtainable as derived consequences of postulated global balance equations. They must instead be imposed as separate additional postulates.

Eftis, J.↗

Some recent theoretical and experimental developments in fracture mechanics

Recent theoretical and experimental developments in four distinct areas of fracture mechanics research are described. These are as follows: experimental comparisons of different nonlinear fracture toughness measures, including the nonlinear energy, R curve, COD and J integral methods; the singular elastic crack-tip stress and displacement equations and the validity of the proposition of their general adequacy as indicated, for example, by the biaxially loaded infinite sheet with a flat crack; the thermodynamic nature of surface energy induced by propagating cracks in relation to a general continuum thermodynamic description of brittle fracture; and analytical and experimental aspects of Mode II fracture, with experimental data for certain aluminum, steel and titanium alloys.

Liebowitz, H.↗

Simulation of hardened cement degradation and estimation of uncertainty in predicted failure times with peridynamics

Modeling the degradation of cement-based infrastructure due to aqueous environmental conditions continues to be a challenge. In order to develop a capability to predict concrete infrastructure failure due to chemical degradation, here we created a chemomechanical model of the effects of long-term water exposure on cement paste. The model couples the mechanical static equilibrium balance with reactive–diffusive transport and incorporates fracture and failure via peridynamics (a meshless simulation method). The model includes fundamental aspects of degradation of ordinary Portland cement (OPC) paste, including the observed softening, reduced toughness, and shrinkage of the cement paste, and increased reactivity and transport with water induced degradation. This version of the model focuses on the first stage of cement paste decalcification, the dissolution of portlandite. Given unknowns in the cement paste degradation process and the cost of uncertainty quantification (UQ), we adopt a minimally complex model in two dimensions (2D) in order to perform sensitivity analysis and UQ. We calibrate the model to existing experimental data using simulations of common tests such as flexure, compression and diffusion. Then we calculate the global sensitivity and uncertainty of predicted failure times based on variation of eleven unique and fundamental material properties. We observed particularly strong sensitivities to the diffusion coefficient, the reaction rate, and the shrinkage with degradation. Also, the predicted time of first fracture is highly correlated with the time to total failure in compression, which implies fracture can indicate impending degradation induced failure; however, the distributions of the two events overlap so the lead time may be minimal. Extension of the model to include the multiple reactions that describe complete degradation, viscous relaxation, post-peak load mechanisms, and to three dimensions to explore the interactions of complex fracture patterns evoked by more realistic geometry is straightforward and ongoing.

36 MATERIALS SCIENCE↗

Project Methods to Enhance Wellbore Cement Integrity with Microbially-Induced Calcite Precipitation (MICP) (Final Scientific/Technical Report)

The goal of this project was to develop improved methods for sealing compromised wellbore cement in leaking oil and gas wells, thereby reducing the risk of unwanted upward fluid migration. Novel methods for improving wellbore integrity, such as microbially induced calcite precipitation (MICP), can reduce leakage potential, improve the safety of fossil fuel extraction, improve the public perception of hydraulic fracturing, and promote environmentally-prudent unconventional oil and gas development. Microbes, with the urease enzyme, can catalyze the chemical reaction of urea hydrolysis to induce the precipitation of calcium carbonate which can be used as a cementitious material to seal leakage pathways. In this project, methods to promote robust bio-composite cementitious materials were designed and tested in the laboratory. Scale-up of those methods were tested in meso-scale reactor systems and in field applications. In this report, in Section One, we describe laboratory efforts to develop injection strategies to promote precipitation in wellbore analogs and determine the strength of the bio-composite cements as compared to fine cement. In Section Two, we describe the efforts to scale up the work and study the use of materials that can be used in field application, for example exploring the use of calcium chloride ice melt or urea fertilizer as source chemicals. In Section Three, the three field trials (methods and results) performed as part of the project are described and summarized. At the end of the report is a comprehensive summary and conclusion section which highlights the key findings of the project. The work performed during this project significantly advanced the technology readiness level (TRL) of the MICP wellbore sealing strategy.

02 PETROLEUM↗

Methods to Enhance Wellbore Cement Integrity with Microbially-Induced Calcite Precipitation (MICP) (Final Scientific/ Technical Report)

The goal of this project was to develop improved methods for sealing compromised wellbore cement in leaking oil and gas wells, thereby reducing the risk of unwanted upward fluid migration. Novel methods for improving wellbore integrity, such as microbially induced calcite precipitation (MICP), can reduce leakage potential, improve the safety of fossil fuel extraction, improve the public perception of hydraulic fracturing, and promote environmentally-prudent unconventional oil and gas development. Microbes, with the urease enzyme, can catalyze the chemical reaction of urea hydrolysis to induce the precipitation of calcium carbonate which can be used as a cementitious material to seal leakage pathways. In this project, methods to promote robust bio-composite cementitious materials were designed and tested in the laboratory. Scale-up of those methods were tested in meso-scale reactor systems and in field applications. In this report, in Section One, we describe laboratory efforts to develop injection strategies to promote precipitation in wellbore analogs and determine the strength of the bio-composite cements as compared to fine cement. In Section Two, we describe the efforts to scale up the work and study the use of materials that can be used in field application, for example exploring the use of calcium chloride ice melt or urea fertilizer as source chemicals. In Section Three, the three field trials (methods and results) performed as part of the project are described and summarized. At the end of the report is a comprehensive summary and conclusion section which highlights the key findings of the project. The work performed during this project significantly advanced the technology readiness level (TRL) of the MICP wellbore sealing strategy.

03 NATURAL GAS↗

Knowledge of Pest Resistance in SiC/BN/SiC Composites Improved

Ceramic-matrix composites (CMC's) consisting of a silicon carbide matrix reinforced with boron-nitride- (BN-) coated silicon carbide (SiC) fibers are strong contenders for commercial and aerospace applications (in particular, the hot sections of high-performance turbine engines in advanced aircraft and generators). They have very good mechanical properties below approximately 600 C and above approximately 1000 C. Between those temperatures, however, the BN coating oxidizes easily, and the oxidation of the SiC matrix is too sluggish to seal off the composite with a protective layer of silica. In that temperature interval, the preferential oxidation of the BN weakens and embrittles the composite. That phenomenon, referred to as "pest" degradation, is the focus of this work, which aims to identify the causes of and remedies for pesting. Previous work established that pesting in Hi-Nicalon (Nippon Carbon Co., Ltd., Japan)/SiC composites was caused by a layer of free carbon that undermined the oxidation resistance of the BN. New work suggests that composites containing a source of carbon are prone to severe pesting and that those that are free of elemental carbon are resistant pesting. Pest resistance was assessed by exposing machined samples for 100 to 150 hr in an atmospheric burner rig at 600 to 1100 C, followed by a tensile fracture test to measure residual mechanical properties and by characterization of the interphase microstructure. Whether the elemental carbon came from intrinsic or extrinsic sources, its presence induced the tensile strength to drop by over 50 percent in the burner rig, with an even more severe loss of fracture strain. A likely mechanism by which burnoff of the carbon layer exposes the BN to accelerated flank attack by ambient oxidants is shown. The BN is replaced with borosilicates that attack the fiber, and ultimately with silica that embrittles the composites by rigidly bonding components. Thus, the study has shown that pesting can be prevented in SiC/BN/SiC, or at least reduced, by simply excluding free carbon. These studies continue, and plans for future work include investigating the role that carbon may play elsewhere in the interphase region.

Thomas-Ogbuji, Linus U.↗

Techniques for increasing boron fiber fracture strain

Improvement in the strain-to-failure of CVD boron fibers is shown possible by contracting the tungsten boride core region and its inherent flaws. The results of three methods are presented in which etching and thermal processing techniques were employed to achieve core flaw contraction by internal stresses available in the boron sheath. After commercially and treatment induced surface flaws were removed from 203 micrometers (8 mil) fibers, the core flaw was observed to be essentially the only source of fiber fracture. Thus, fiber strain-to-failure was found to improve by an amount equal to the treatment induced contraction on the core flaw. Commercial feasibility considerations suggest as the most cost effective technique that method in which as-produced fibers are given a rapid heat treatment above 700 C. Preliminary results concerning the contraction kinetics and fracture behavior observed are presented and discussed both for high vacuum and argon gas heat treatment environments.

Dicarlo, J. A.↗

Produced water sharing: Improved economics and reduced community impact – A Pennsylvania case study

Here, hydraulic fracturing for oil and gas extraction from unconventional reservoirs is water intensive. Between water sourced for fracturing purposes and water present in rock formations, operators often produce a greater volume of water than oil or gas. Historically, this surplus of produced water has mainly been disposed of via deep injection wells. Rising disposal costs, seasonally limited water availability, and concerns over induced seismicity have incentivized produced water recycling practices, where an operator uses produced water for hydraulic fracturing operations. The logistical challenges associated with produced water recycling have also encouraged operators to adopt ad-hoc water exchange practices, in which competing operators will exchange produced water for mutual cost savings. In this paper, we investigate the potential benefit from systematic produced water exchange among operators in Northeastern Pennsylvania. We leverage PARETO, a free and open-source modeling framework for produced water management optimization, to quantify the benefits of water exchange practices. In an example drawn from FracFocus data, we find that the adoption of systematic water sharing could improve produced water recycling rates from 49.2% to 99%, decreasing operating and trucking costs.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

Magnetic Resonance Imaging (MRI) to Assess Changes to Trabecular Microarchitecture (Trb µArch) of the Hip

BACKGROUND . Calculated loss rates in trabecular (Trb) volumetric bone mineral density (vBMD), in astronauts after return from 6-month long-duration (LD) spaceflight, are rapid relative to menopause-induced loss rates and could contribute to the observed lack of recovery. Perforations in the Trb bony struts, skeletal fragility and fractures [5] have been associated with the rapid rate of bone loss in women due to menopause. The more rapid loss rate observed in astronauts could be inducing similar, irreversible losses of trabecular connectivity as seen in cadaver studies of female skeletons. These changes are not detectable by DXA technology and would not be discovered in astronauts during scheduled, triennial DXA testing for primary osteoporosis. High-resolution-peripheral quantitative computed tomography (HR-pQCT) of the lower leg have detected losses in Trb vBMD (vBMD) and changes in Trb microarchitecture (µArch) in astronauts immediately following routine 6-month spaceflights and continuing in some individuals for 1 or more years postflight with no signs of recovery. Resolution of these microarchitectural changes by whole body QCT, especially in the deeply embedded hip bone, is prohibitive due to excessive and unsafe radiation exposures. While HR-pQCT has sufficient resolution to study Trb µArch at safe and lower radiation exposure testing is restricted only to the lower leg and wrist. Hence, a technology to detect detrimental changes to Trb µArch in astronauts, especially of the hip, is needed to inform type and timing of countermeasures to irreversible deficits (preflight, inflight and postflight). METHODS . This HRP-funded study (2023-2027) will verify the sensitivity of a protocol for MRI scanning (on a 3T Siemens Vida) to detect changes to hip Trb µArch in persons following spinal cord injury (SCI); skeletal immobilization below the spinal lesion will serve as an analog for non-weight-bearing during spaceflight. The study period has been extended by 1 yr due to delayed Richmond IRB approval in Y1. A 3T MRI protocol will characterize serial changes in hip Trb µArch in SCI patients from time of admission at the Richmond VA Medical Center to their scheduled annual exam 12-months later. SCI patients with age, sex, and physical characteristics like ISS astronauts will be consented. The ability of 3T MRI hip scan to discriminate loss of trabecular connectivity subjects with SCI will be compared to age- and sex-matched ambulatory controls. A comparison between HR-pQCT and MRI measurements at the ankle (distal tibia) of study subjects will also be performed. A modified DXA scan analysis (3D-Shaper) will also be verified as a potential method for monitoring concurrent changes in hip Trb bone over 12-month. SIGNIFICANCE . Deliverables: a surveillance method for assessing for irreversible losses of connectivity and how skeletal changes after LD spaceflight(s) would modify the terrestrial risk of primary osteoporosis.

Spinal Cord Injury↗

Magnetic Resonance Imaging (MRI) to Assess Changes to Trabecular Microarchitecture (Trb µArch) of the Hip

BACKGROUND . Calculated loss rates in trabecular (Trb) volumetric bone mineral density (vBMD), in astronauts after return from 6-month long-duration (LD) spaceflight, are rapid relative to menopause-induced loss rates and could contribute to the observed lack of recovery. Perforations in the Trb bony struts, skeletal fragility and fractures [5] have been associated with the rapid rate of bone loss in women due to menopause. The more rapid loss rate observed in astronauts could be inducing similar, irreversible losses of trabecular connectivity as seen in cadaver studies of female skeletons. These changes are not detectable by DXA technology and would not be discovered in astronauts during scheduled, triennial DXA testing for primary osteoporosis. High-resolution-peripheral quantitative computed tomography (HR-pQCT) of the lower leg have detected losses in Trb vBMD (vBMD) and changes in Trb microarchitecture (µArch) in astronauts immediately following routine 6-month spaceflights and continuing in some individuals for 1 or more years postflight with no signs of recovery. Resolution of these microarchitectural changes by whole body QCT, especially in the deeply embedded hip bone, is prohibitive due to excessive and unsafe radiation exposures. While HR-pQCT has sufficient resolution to study Trb µArch at safe and lower radiation exposure testing is restricted only to the lower leg and wrist. Hence, a technology to detect detrimental changes to Trb µArch in astronauts, especially of the hip, is needed to inform type and timing of countermeasures to irreversible deficits (preflight, inflight and postflight). METHODS . This HRP-funded study (2023-2027) will verify the sensitivity of a protocol for MRI scanning (on a 3T Siemens Vida) to detect changes to hip Trb µArch in persons following spinal cord injury (SCI); skeletal immobilization below the spinal lesion will serve as an analog for non-weight-bearing during spaceflight. The study period has been extended by 1 yr due to delayed Richmond IRB approval in Y1. A 3T MRI protocol will characterize serial changes in hip Trb µArch in SCI patients from time of admission at the Richmond VA Medical Center to their scheduled annual exam 12-months later. SCI patients with age, sex, and physical characteristics like ISS astronauts will be consented. The ability of 3T MRI hip scan to discriminate loss of trabecular connectivity subjects with SCI will be compared to age- and sex-matched ambulatory controls. A comparison between HR-pQCT and MRI measurements at the ankle (distal tibia) of study subjects will also be performed. A modified DXA scan analysis (3D-Shaper) will also be verified as a potential method for monitoring concurrent changes in hip Trb bone over 12-month. SIGNIFICANCE . Deliverables: a surveillance method for assessing for irreversible losses of connectivity and how skeletal changes after LD spaceflight(s) would modify the terrestrial risk of primary osteoporosis.

Risk Surveillance↗

Microstructure and mechanical properties of friction stir weld performed on neutron-irradiated 304L steel with helium

As nuclear power plants (NPPs) approach or exceed 40–60 years of service, it may become necessary to repair damaged neutron-irradiated components to prolong longevity. However, fusion welding repair of irradiated steels and metallic materials is challenging because of helium-induced cracking. This study used friction stir welding (FSW) to address helium-related issues, such as helium bubble formation and grain boundary cracking. The microstructure, helium-induced degradation, and mechanical properties of a friction stir weld produced on neutron-irradiated 304L stainless steel with approximately 5.2 appm of helium were characterized. The analysis focused on variations in grain size, texture, and the morphology of helium-induced damage in the friction stir weld. Mechanical properties were characterized on the irradiated base metal (BM) and metallurgical zones of the friction stir weld: the stir zone (SZ), the thermo-mechanically affected zone (TMAZ), and the heat affected zone (HAZ). Only minor scattered porosity in the SZ and TMAZ and a few short microcracks (below 20 μm in length) in the TMAZ were observed, indicating limited helium-induced degradation. Tensile tests revealed good mechanical properties and fractography analysis demonstrated predominantly ductile fracture. In conclusion, the results highlight the immediate and substantial benefits of the FSW approach for repairing or joining helium-containing irradiated materials in NPPs.

36 MATERIALS SCIENCE↗

The Linkage Between Electro-Chemical Mechanical Instabilities in Battery Materials

Battery chemistry must be diversified to achieve a sustainable energy landscape by effectively utilizing renewable energy sources. Alkali metal-ion, all-solid-state, metal–air batteries, and multivalent batteries offer unique cost, safety, raw material abundance, energy, and power density solutions. However, realizing these “beyond Li-ion batteries” must uncover their working principles and performance & property relationships. In this aspect, mitigating chemo-mechanical instabilities in the structure and surface of the electrodes plays a crucial role in their performance. Unfortunately, the coupling between electrochemical and mechanical interactions is often poorly understood due to a lack of operando characterization. Here, this review article explains the working principles of curvature measurement and digital image correlation for measuring stress and strain generations in battery materials. We provided specific examples of how these operando mechanical measurements shed light on instabilities in alkali metal ion electrodes, solid electrolytes, Li-O 2 batteries, and aqueous Zn-ion batteries. Operando mechanical measurements offer an effective way to map changes in the physical fingerprint of the battery materials, therefore providing crucial information to elucidate instabilities in battery materials.

25 ENERGY STORAGE↗

A Novel Design of Guiding Stress Wave Propagation

Impact loads can induce a series of undesirable physical phenomena including vibration, acoustical shock, perforation, fracture and fragmentation, etc. The energy associated with the impact loads can lead to severe structure damage and human injuries. A design approach which effectively reduces these negative impacts through shock/stress wave diversion is highly needed. In this paper, a computational model which predicts stress wave propagation by considering different beam geometries and configurations is developed. Additionally, a novel concept of wave guide design which modifies the stress wave propagation path without disturbance is also presented. Furthermore, this design approach is not only useful for material property characterization particularly at intermediate or high strain rates, but also allows stress wave propagation in a desired direction as the shock/impact energy can be redistributed in controllable paths. The numerical results are experimentally verified through a Drop-Hopkinson bar apparatus at Sandia National Laboratories.

36 MATERIALS SCIENCE↗

Factors influencing the thermally-induced strength degradation of B/Al composites

Literature data related to the thermally-induced strength degradation of B/Al composites were examined in the light of fracture theories based on reaction-controlled fiber weakening. Under the assumption of a parabolic time-dependent growth for the interfacial reaction product, a Griffith-type fracture model was found to yield simple equations whose predictions were in good agreement with data for boron fiber average strength and for B/Al axial fracture strain. The only variables in these equations were the time and temperature of the thermal exposure and an empirical factor related to fiber surface smoothness prior to composite consolidation. Such variables as fiber diameter and aluminum alloy composition were found to have little influence. The basic and practical implications of the fracture model equations are discussed.

Dicarlo, J. A.↗