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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Ab Initio Molecular Dynamics Insights into Stress Corrosion Cracking and Dissolution of Metal Oxides

Oxide phases such as α-Fe2O3 (hematite) and α-Al2O3 (corundum) are highly insoluble in water; however, subcritical crack growth has been observed in humidity nonetheless. Chemically induced bond breaking at the crack tip appears unlikely due to sterically hindered molecular transport. The molecular mechanics of a crack in corundum with a reactive force field reveal minimal lattice trapping, leading to bond breaking before sufficient space opens for water transport. To address this, we model a pre-built blunt crack with space for H2O molecule adsorption at the tip and show that it reduces fracture toughness by lowering the critical J-integral. Then, we explore stress-enhanced dissolution to understand the mechanism of crack tip blunting in the oxide/water system. Density functional theory combined with metadynamics was employed to describe atomic dissolution from flat hematite and corundum surfaces in pure water. Strain accelerates dissolution, stabilizing intermediate states with broken bonds before full atom detachment, while the free energy profile of unstrained surfaces is almost monotonic. The atomistic calculations provided input for a kinetic model, predicting the shape evolution of a blunt crack tip, which displays three distinct regimes: (i) dissolution primarily away from the tip, (ii) enhanced blunting near but not at the apex, and (iii) sharpening near the apex. The transition between regimes occurs at a low strain, highlighting the critical role of water in the subcritical crack growth of oxide scales, with dissolution as the fundamental microscopic mechanism behind this process.

Chemistry↗
DOE OSTI2020

Performance degradation due to anodic failure mechanisms in lithium-ion batteries

Here, we report a mechano-chemical model for anodic degradation during fast-charging of nickel-manganese-cobalt (NMC)/graphite (C) cell due to SEI growth, lithium plating/stripping, dead lithium storage, and film fracture of composite SEI and plated lithium film. Degradation of the battery is analyzed for a range of charging rates from 1 to 6 C-rates, and the influence of plating mechanisms – lithium plating and dead lithium deposition and recovery during stripping – on the film resistance of the anode are accounted for in the model. Dynamic evolution of the interfacial properties is modeled using rule-of-mixture approach. Model predictions of plating associated stress fields are used to compute critical energy release rate for film cracking. The results indicate an increased tendency of fracture for thinner SEI film with lithium plating at higher charging rates. The process of reforming the cracked film absorbs a significant portion of the electrode current thereby reducing the cell capacity and plating efficiency. The mechano-chemical model provides an extensive analytical framework for understanding the synergistic coupling of anodic degradation mechanisms, prognosticating conditions of SEI failure, and evaluating the capacity fade and efficiency of lithium-ion battery.

25 ENERGY STORAGE↗
DOE OSTI2021

Upscaling Reactive Transport and Clogging in Shale Microcracks by Deep Learning

Fracture networks in shales exhibit multiscale features. A rock system may contain a few main fractures and thousands of microcracks, whose length and aperture are orders of magnitude smaller than the former. It is computationally prohibitive to resolve all the fractures explicitly for such multiscale fracture networks. One traditional approach is to model the small-scale features (e.g., microcracks in shales) as an effective medium. Although this fracture-matrix conceptualization significantly reduces the problem complexity, there are classes of physical processes that cannot be accurately upscaled by effective medium approximations, e.g., microcrack clogging during mineral reactions. Here, we employ deep learning in place of effective medium theory to upscale physical processes in small-scale features. Specifically, we consider reactive transport in a fracture-microcrack network where microcracks can be clogged by precipitation. A deep learning multiscale algorithm is developed, in which the microcracks are upscaled as a wall boundary condition of the main fractures. The wall boundary condition is constructed by recurrent neural networks, which take concentration histories as input and predict the solute transport from main fractures to microcracks. The deep learning multiscale algorithm is firstly employed in specific scenarios, then a general model is developed which can work under various conditions. The new approach is validated against fully resolved simulations and an analytical solution, providing a reliable and efficient solution for problems that cannot be upscaled by effective medium models.

58 GEOSCIENCES↗
DOE OSTI2020

Numerical study of the effect of propped surface area and fracture conductivity on shale gas production: Application for multi-size proppant pumping schedule design

Hydraulic fracturing is a technique extensively used in the oil and gas industry, where water, proppant (sand) and additives are injected into unconventional reservoirs to enhance the recovery of shale hydrocarbon. Although some previous studies have developed pumping schedules that maximize gas production for a single-size proppant, there are very few studies that consider the effect of varying proppant diameters across pumping stages on shale gas production. Motivated by this, we carried out an extensive sensitivity analysis to determine the effect of different proppant diameters on the average fracture conductivity (FC), average propped surface area (PSA) and cumulative shale gas production volume. We found out that the cumulative shale gas production volume depends on both the average PSA and average FC. We also found out that small-diameter proppant resulted in higher average PSA and lower average FC, whereas large-diameter proppant resulted in lower average PSA and higher average FC. Hence, we designed a multi-size proppant pumping schedule considering both of these parameters into account for simultaneously propagating multiple fractures to maximize shale gas production from unconventional reservoirs. Since the size of injected proppant particles determines the average PSA and average FC for the propped hydraulic fractures, we developed a novel framework called Sequentially Interlinked Modeling Structure (SIMS) to predict the average PSA, average FC and cumulative shale gas production volume at the end of 10 years for a given pumping schedule. Then, we used this SIMS framework to obtain a multi-size proppant pumping schedule that maximizes shale gas production. In closing, we demonstrated that the obtained pumping schedule gives a cumulative shale gas production volume greater than the values obtained from the existing pumping schedules.

03 NATURAL GAS↗
DOE OSTI2022

Experimental results of conductive inserts to reduce nuclear fuel temperature during nuclear volumetric heating

Advanced fuel designs that incorporate thinner fuel UO2 pellets interspaced by high thermal conductivity inserts have been proposed, with the primary goals of reducing peak centerline temperatures and temperature gradients across fuel pellets and enhancing heat transfer from the fuel to the coolant. An initial series of experiments has been performed on this design, including laboratory experiments and a series of experiments using the Idaho National Laboratory (INL) Transient Reactor Test (TREAT) Facility, the latter of which compared thermal gradient driven fracture of standard pellet designs with that in the proposed advanced fuel design. Although reducing fracture is not the primary objective of the new fuel design, the lower thermal gradients are expected to reduce fracture, so it can serve as an indicator of the thermal behavior of this fuel in the reactor. The in-reactor tests were conducted at multiple linear heat generation rates and confirm the expected result that fracture in both the standard and advanced fuel pellets occurs during the first ramp to power in standard light-water reactor conditions. Post-irradiation examination of the experiment material was performed and included quantification of the extent of fracture in the fuel pellets. It was found that the advanced-design pellets reduce the extent of fracture in a statistically significant way. This confirms the expected behavior predicted by two-dimensional axisymmetric models of this experiment. Here in this study is an important first experimental confirmation of the efficacy of the proposed inserts for achieving their desired effect on the thermal behavior of the fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Evaluation of Mechanistic and Empirical Models against Existing FFRD and LOCA Experimental Databases

The desire of the nuclear industry to improve the economics of existing nuclear power plants has necessitated research into the potential of a phenomenon known as fuel fragmentation, relocation, and dispersal (FFRD). This phenomenon is possible during a loss-of-coolant accident (LOCA) at relatively high burnup. The Nuclear Energy Advanced Modeling and Simulation program has been developing simulation capabilities for FFRD and LOCA in the BISON fuel performance code for multiple years. This year, the effort has been focused on evaluating new lower length scale informed pulverization thresholds as well as updating and adding new empirical models for various phenomena. Models added or updated this year include a preliminary transient fission gas release model, new high-temperature Zircaloy creep models, a Zircaloy rupture opening area model, and a temperature-dependent emissivity during radiation from the fuel rod to the surrounding atmosphere. The models are verified through implementation tests to demonstrate code correctness after addition to BISON. The models are then assessed against a subset of the existing BISON validation suite for LOCA and FFRD cases. Two new cases, Studsvik Rods 192 and 193, have been added. The results indicate that the inclusion of a bubble pressure evolution model in the bubbles in the high-burnup structure has the largest impact compared to the 3D fracture criterion on reducing the calculated amount of pulverized fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Cracking in first ramp to power of standard versus high thermal conductivity UO2 pellets via internal nuclear heating

Advanced fuel designs that incorporate thinner fuel UO2 pellets interspaced by high thermal conductivity inserts have been proposed, with the primary goals of reducing peak centerline temperatures and temperature gradients across fuel pellets and enhancing heat transfer from the fuel to the coolant. An initial series of experiments has been performed on this design, including laboratory experiments and a series of experiments using the Idaho National Laboratory (INL) Transient Reactor Test (TREAT) Facility, the latter of which compared thermal gradient driven fracture of standard pellet designs with that in the proposed advanced fuel design. Although reducing fracture is not the primary objective of the new fuel design, the lower thermal gradients are expected to reduce fracture, so it can serve as an indicator of the thermal behavior of this fuel in the reactor. The in-reactor tests were conducted at multiple linear heat generation rates and confirm the expected result that fracture in both the standard and advanced fuel pellets occurs during the first ramp to power in standard light-water reactor conditions. Post-irradiation examination of the experiment material was performed and included quantification of the extent of fracture in the fuel pellets. It was found that the advanced-design pellets reduce the extent of fracture in a statistically significant way. This confirms the expected behavior predicted by two-dimensional axisymmetric models of this experiment. This study is an important first experimental confirmation of the efficacy of the proposed inserts for achieving their desired effect on the thermal behavior of the fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

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↗
DOE OSTI2020

Non-Destructive Imaging of a Liquid Moving Through Porous Media Using a Computer Tomography Scanner

The most common approach used by modelers to describe movement of liquids through a porous solid, such as cement, sediment, or glass, is to assume a uniform flow rate, such as a Darcy Flux or a diffusion constant. However, this convenient simplification is problematic because in many cases it ignors the presence of fractures and macropores, which commonly dominate water flow and contaminant transport. For this reason, it is common that such modeling results do not reflect the multi-modal flow detected in laboratory and field studies. The objective of this seedling study was to develop a new capability for SRNL to track liquid moving through micro- (matrix-) and macro-flow using an X-ray Computed Topography (CT) Scanner. 4-dimensional anamated renditions were created that permited quantifying traditional matrix flow and macropore flow. These animations were modelled using a public domain software, HYDRUS 1-D, describing one dimension, dual-porosity and dual-permeability processes. This new capability provides a proof of concept for reducing model uncertainty applicable to waste disposal risk calculations, environmental remediation, and waste form development when describing the movement of liquids as they pass through glass, cement, fractured rock, or soil.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

Characterizing the Influence of Fracture Density on Network Scale Transport

The topology of natural fracture networks is inherently linked to the structure of the fluid velocity field and transport therein. Here we study the impact of network density on flow and transport behaviors. We stochastically generate fracture networks of varying density and simulate flow and transport with a discrete fracture network model, which fully resolves network topology at the fracture scale. We study conservative solute trajectories with Lagrangian particle tracking and find that as fracture density decreases, solute channelization to large local fractures increases, thereby reducing plume spreading. Furthermore, in sparse networks mean particle travel distance increases and local network features, such as velocity zones where flow is counter to the primary pressure gradient, become increasingly important for transport. As the network density increases, network statistics homogenize and such local features have a reduced impact. We quantify local topological influence on transport behavior with an effective tortuosity parameter, which measures the ratio of total advective distance to linear distance at the fracture scale; large tortuosity values are correlated to slow-velocity regions. Additionally, these large tortuosity, slow-velocity regions delay downstream transport and enhance tailing on particle breakthrough curves. Finally, we predict transport with an upscaled, Bernoulli spatial Markov random walk model and parameterize local topological influences with a novel tortuosity parameter. Furthermore, Bernoulli model predictions improve when sampling from a tortuosity distribution, as opposed to a fixed value as has previously been done, suggesting that local network topological features must be carefully considered in upscaled modeling efforts of fracture network systems.

58 GEOSCIENCES↗
DOE OSTI2024

An integrated experimental–modeling approach to identify key processes for carbon mineralization in fractured mafic and ultramafic rocks

Abstract Controlling atmospheric warming requires immediate reduction of carbon dioxide (CO2) emissions, as well as the active removal and sequestration of CO2 from current point sources. One promising proposed strategy to reduce atmospheric CO2 levels is geologic carbon sequestration (GCS), where CO2 is injected into the subsurface and reacts with the formation to precipitate carbonate minerals. Rapid mineralization has recently been reported for field tests in mafic and ultramafic rocks. However, unlike saline aquifers and depleted oil and gas reservoirs historically considered for GCS, these formations can have extremely low porosities and permeabilities, limiting storage volumes and reactive mineral surfaces to the preexisting fracture network. As a result, coupling between geochemical interactions and the fracture network evolution is a critical component of long-term, sustainable carbon storage. In this paper, we summarize recent advances in integrating experimental and modeling approaches to determine the first-order processes for carbon mineralization in a fractured mafic/ultramafic rock system. We observe the critical role of fracture aperture, flow, and surface characteristics in controlling the quantity, identity, and morphology of secondary precipitates and present where the influence of these factors can be reflected in newly developed thermo-hydro-mechanical–chemical models. Our findings provide a roadmap for future work on carbon mineralization, as we present the most important system components and key challenges that we are overcoming to enable GCS in mafic and ultramafic rocks.

58 GEOSCIENCES↗
DOE OSTI2024

Altered post-fracture systemic bone loss in a mouse model of osteocyte dysfunction

Femur fracture leads to loss of bone at uninjured skeletal sites, which may increase risk of subsequent fracture. Osteocytes, the most abundant bone cells, can directly resorb bone matrix and regulate osteoclast and osteoblast activity, but their role in systemic bone loss after fracture remains poorly understood. In this study we used a transgenic (TG+) mouse model that overexpresses human B-cell lymphoma 2 (BCL-2) in osteoblasts and osteocytes. This causes enhanced osteoblast proliferation, followed by disruption in lacunar-canalicular connectivity and massive osteocyte death by 10 wk of age. We hypothesized that reduced viable osteocyte density would decrease the magnitude of systemic bone loss after femur fracture, reduce perilacunar remodeling, and alter callus formation. Bone remodeling was assessed using serum biomarkers of bone formation and resorption at 5 d post-fracture. We used micro-computed tomography, high resolution x-ray microscopy, mechanical testing, and Raman spectroscopy to quantify the magnitude of systemic bone loss, as well as changes in osteocyte lacunar volume, bone strength, and bone composition 2 wk post-fracture. Fracture was associated with a reduction in circulating markers of bone resorption in non-transgenic (TG-) animals. TG+ mice exhibited high bone mass in the limbs, greater cortical elastic modulus and reduced post-yield displacement. After fracture, TG+ mice lost less trabecular bone than TG- mice, but conversely TG+ mice exhibited trends toward a lower yield point and reduced femoral cortical thickness after fracture, though these were not statistically significant. Lacunar density was greater in TG+ mice, but fracture did not alter lacunar volume in TG+ or TG- mice. These findings suggest that osteocytes potentially play a significant role in the post-traumatic systemic response to fracture, though the effects differ between trabecular and cortical bone.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Modeling active nematics via the nematic locking principle

Active nematic systems consist of rod-like internally driven subunits that interact with one another to form large-scale coherent flows. They are important examples of far-from-equilibrium fluids, which exhibit a wealth of nonlinear behavior. This includes active turbulence, in which topological defects in the nematic order braid around one another in a chaotic fashion. One of the most studied examples of active nematics consists of a dense two-dimensional layer of microtubules, crosslinked by kinesin molecular motors that inject extensile deformations into the fluid. Though numerous theoretical studies have modeled microtubule-based active nematics, no consensus has emerged on how to fully and quantitatively capture the features of the experimental system. Here, to better understand the theoretical foundations for modeling this system, we propose a fundamental principle we call the nematic locking principle—individual microtubules cannot rotate without all neighboring microtubules also rotating. Physically, this is justified by the high density of the microtubules, their elongated nature, and their corresponding steric interactions. We assert that the nematic locking principle holds throughout the majority of the material, but breaks down in the neighborhood of topological defects and other regions of low density. We derive the most general nematic transport equation consistent with this principle and also derive the most general term that violates it, introducing fracturing into the material. We then examine the standard Beris–Edwards approach, commonly used to model this system, and show that it violates the nematic locking principle throughout the majority of the material due to fracturing. We then propose a modification to the Beris–Edwards model that enforces nematic locking nearly everywhere. This modification shuts off fracturing except in regions where the order parameter (a proxy for density) is reduced. In these regions fracturing is turned on. The resulting simulations in turn show strong nematic locking throughout the bulk of the material, with narrow bands of fracturing, consistent with experimental observation. One additional advantage of enforcing nematic locking is that nontrivial stationary state solutions, common in Beris–Edwards simulations but not seen in experiments, are eliminated.

Mitchell, Kevin A. [Univ. of California, Merced, C↗
DOE OSTI2023

CIEL ∗ Ch color map for visualization and analysis of sea ice motion

The International Commission on Illumination (CIE) designed its color space to be perceptually uniform so that a given numerical change in the color code corresponds to perceived change in color. This color encoding is demon- strated to be advantageous in scientific visualization and analysis of vector fields. The specific application is analysis of ice motion in the Arctic where patterns in smooth monthly-averaged ice motion are seen. Furthermore, fractures occurring in the ice cover result in discontinuities in the ice motion. This vector jump in displacement can also be visualized. We then analyze modeled and observed fractures through the use of a metric on the color space, and image amplitude and phase metrics. Amplitude and phase met- rics arise from image registration that is accomplished by sampling images using space filling curves, thus reducing the image registration problem to the more reliable functional alignment problem. We demonstrate this through an exploration of the metrics to compare model runs to an observed ice crack.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Crack-Free 30% Chromium-Nickel Alloy Welding Products for Nuclear Service

We report prior research in the development of 30% chromium-nickel alloy nuclear welding wires has resulted in the resolution of primary water stress corrosion cracking (PWSCC) and ductility dip cracking (DDC) as well as improvement in solidification cracking (SC) resistance. The resolution of DDC exhibits some Laves phase, which has a negative effect on SC resistance. In this study, the use of an alternate carbide former, tantalum (Ta), in combination with niobium (Nb) was researched. Three heats of recently designed Filler Metal 52MSS-Ta (i.e., HV1648, HV1673A, and VX131WXW) were melted, fabricated, and systematically studied. DDC and SC were evaluated with thermodynamic modeling using the Scheil solidification simulation model, two types of varestraint tests, and strain-to-fracture (STF) testing. The varestraint and STF test results showed an improved SC resistance with reduced Laves phase and concurrent excellent DDC resistance. Optimized compositions with low Laves phase also exhibited high threshold strain values (TSVs) in the STF test. VX131WXW — which contains 2.81 wt-% Ta, 0.6 wt-% Nb, and 6 wt-% iron (Fe) - exhibited a TSV of 24%. Thermo-Calc computed the Laves phase to be 0.24% for VX131WXW compared to 0.06% in HV1673A. This difference in Laves phase resulted in the lower SC resistance of VX131WXW compared to HV1673A when measured with longitudinal varestraint testing. The maximum crack distance for HV1673A was about 0.6 mm while that of heat VX131WXW was about 1.0 mm. The typical diluted weld deposit made with VX131WXW was also resistant to PWSCC due to the chromium content exceeding 24%. These simultaneous results mark progress toward crack-free welds and provide direction for further optimization of Ta-containing filler metals.

30% chromium-nickel alloy↗
DOE OSTI2020

An Improved Fracture Mechanics-Informed Multiscale Thermomechanical Damage Model for Ceramic Matrix Composites

This paper extends recent work done by the authors in modeling length scale-dependent damage behavior of ceramic matrix composites (CMCs) to include effects of local anisotropy introduced by matrix cracking. This model captures scale-dependent damage initiation and propagation behavior of the brittle matrix by employing internal state variable (ISV) theory within a multiscale modeling framework to obtain damaged matrix stress/strain constitutive relationships at each length scale. The damage ISV captures the effects of matrix cracking and growth by using fracture mechanics and the self-consistent scheme to determine the reduced stiffness of the cracked matrix. Matrix cracks, which activate when stress intensity factors near manufacturing induced cavities exceed the fracture toughness of the material, are assumed to be transversely isotropic in the plane of the crack, and matrix anisotropy occurs when the damaged stiffness tensor is rotated from the crack plane to the global axes. The crack progression and temporal evolution of the damage ISV are governed by fracture mechanics and crack growth kinetics. The model effectively captures first matrix cracking, which is the first significant deviation from linear elasticity. The nonlinear predictive capabilities of the material model are demonstrated for monolithic silicon carbide (SiC) and a 2D woven five-harness satin (5HS) carbon fiber SiC matrix (C/SiC) CMC.

Skinner, Travis↗
DOE OSTI2020

Grain detachment and transport clogging during mineral dissolution in carbonate rocks with permeable grain boundaries

In this paper, we explore the effect of permeable grain boundaries on carbonate rock dissolution in order to improve our understanding of grain detachment and migration during reactive flow. To do so we investigated the effects of grain size and enhanced reactivity along grain boundaries on global dissolution kinetics. Variations of permeability and porosity were calculated, and exponential relationships were observed in fractured rocks. Our model employed a reactive transport framework based on the Darcy-Brinkman equation to simulate calcite dissolution in carbonate rocks composed of microporous grains and, included fluid transport along grain boundaries. The model includes fluid flow, solute transport by advection–diffusion, heterogeneous reaction between fluid and minerals and grain detachment with subsequent grain transport in macropores. The migration of solid particles due to dissolution was based on cluster analysis and local movement, and the results show that grain detachment can lead to significant decreases in permeability due to the clogging of transport pathways. Microporous media with smaller grain sizes (fine grains in this study) showed a higher average reaction rate than those with coarser grains. In addition, as the overall rates of geochemical processes are commonly affected by the presence of texture heterogeneities such as fractures, a single fracture (macropore) introduced into a microporous matrix composed of permeable grains and grain boundaries was modelled as a large channel connecting the inlet and outlet of the simulation domain. It was found that macropore clogging by grain detachment temporary decreased permeability, lowering the long-term global reaction rates. Lastly, we observed that increases in flow rate can reduce detachment and fracture clogging by reducing local dissolution along grain boundaries.

58 GEOSCIENCES↗
DOE OSTI2026

Subsurface mechanical damage of fused silica glass during grinding by various sub-aperture tools with and without ultrasonics

The subsurface mechanical damage (SSD) depth after grinding fused silica glass with a comprehensive set of sub-aperture fixed abrasive grinding tools [cup, wheel, belt, pad, and rotary face mill (with and without ultrasonics)] and process parameters has been statistically measured using the taper wedge technique and evaluated. Consistent with a previously reported grinding model [J. Non-Cryst. Solids 352, 5601–5617 (2006) Crossref , Materials Science and Technology of Optical Fabrication (Wiley & Sons, 2018)], based on the sliding indentation fracture by sliding particles or asperities where the normal load per particle determines the depth of the fracture (and ultimately the overall SSD depth), the dominant factor controlling SSD depth was found to be the abrasive size regardless of the tool type and process conditions. Compared to full aperture grinding methods, the overall SSD depth was higher using the sub-aperture tools, likely due to the higher effective pressure and higher load per particle distribution. Here, in addition to abrasive size, a significant reduction in SSD depth was achieved by: (1) reducing the load distribution on the abrasive particles via increase in contact area and/or decrease in mechanical loading; (2) using a more compliant host tool medium; and (3) in what we believe is a more novel way, using ultrasonics. Combining low abrasive size, larger contact area, and a compliant host, the 6 µm diamond in a resin matrix (Trizact) on a foam pad led to very low SSD depth (~ 4.6 µm), relatively fast grinding rate (186 mm 3 /h), and little or no figure degradation. This grinding tool/process is an attractive choice for final grind, resulting in significantly reduced polish out (i.e., “grey out”) times. With the rotary face mill tool, the use of ultrasonics consistently led to a SSD depth reduction (ranging from 17%–34%). A new fracture mechanics-based model, to the best of our knowledge, where the relevant normal load is parallel to the feed direction, has been developed to explain how ultrasonics leads to lower SSD depth. The key factors, supported by finite element stress analysis and load measurements, are (1) the initiation of fractures at higher z heights during the tool’s ultrasonic vertical oscillations, thus propagating less deep into workpiece; (2) reduction in load (and therefore reduction in fracture propagation distance) due to smaller tool-workpiece feed direction contact area (again caused by higher heights relative to depth of cut); (3) upward movement of the tool during oscillation leads to fracturing toward the surface instead into the depth; and finally (4) at tool’s lowest point of oscillation cycle, there may not be enough time for the fracture to propagate to its full length.

Optics and optical instruments↗