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Statistical Distributions for Mesh Independent Solutions in ALEGRA

The representation of material heterogeneity (also referred to as "spatial variation") plays a key role in the material failure simulation method used in ALEGRA. ALEGRA is an arbitrary Lagrangian-Eulerian shock and multiphysics code developed at Sandia National Laboratories and contains several methods for incorporating spatial variation into simulations. A desirable property of a spatial variation method is that it should produce consistent stochastic behavior regardless of the mesh used (a property referred to as "mesh independence"). However, mesh dependence has been reported using the Weibull distribution with ALEGRA's spatial variation method. This report describes efforts towards providing additional insight into both the theory and numerical experiments investigating such mesh dependence. In particular, we have implemented a discrete minimum order statistic model with properties that are theoretically mesh independent.

36 MATERIALS SCIENCE↗

Determination of Turboprop Reduction Gearbox System Fatigue Life and Reliability

Two computational models to determine the fatigue life and reliability of a commercial turboprop gearbox are compared with each other and with field data. These models are (1) Monte Carlo simulation of randomly selected lives of individual bearings and gears comprising the system and (2) two-parameter Weibull distribution function for bearings and gears comprising the system using strict-series system reliability to combine the calculated individual component lives in the gearbox. The Monte Carlo simulation included the virtual testing of 744,450 gearboxes. Two sets of field data were obtained from 64 gearboxes that were first-run to removal for cause, were refurbished and placed back in service, and then were second-run until removal for cause. A series of equations were empirically developed from the Monte Carlo simulation to determine the statistical variation in predicted life and Weibull slope as a function of the number of gearboxes failed. The resultant L(sub 10) life from the field data was 5,627 hr. From strict-series system reliability, the predicted L(sub 10) life was 774 hr. From the Monte Carlo simulation, the median value for the L(sub 10) gearbox lives equaled 757 hr. Half of the gearbox L(sub 10) lives will be less than this value and the other half more. The resultant L(sub 10) life of the second-run (refurbished) gearboxes was 1,334 hr. The apparent load-life exponent p for the roller bearings is 5.2. Were the bearing lives to be recalculated with a load-life exponent p equal to 5.2, the predicted L(sub 10) life of the gearbox would be equal to the actual life obtained in the field. The component failure distribution of the gearbox from the Monte Carlo simulation was nearly identical to that using the strict-series system reliability analysis, proving the compatibility of these methods.

Zaretsky, Erwin V.↗

Initial ASME code rule analysis on Simple and Full assessment

ASME & ASTM codes present simple and full assessment methodologies to qualify nuclear grade graphite components. This report explains the theory behind the statistical portion of the codes and describes the issues discussed in a 2020 workshop in the simple assessment, as well as the full assessment. The methodology for the full assessment was developed by Hindley []. He used a validation methodology to match the experimental average failure load of test specimens from several geometries to the calculated 50% POF load to tune the grouping criteria parameters based on an RMSE penalty function. The grouping criteria consists of a minimum volume to satisfy the weakest link theory of the Weibull distribution and a minimum stress range parameter. Hindley’s work found a minimum link volume of 10 times the grain size and a stress range parameter of 7% [satisfy the validation requirements. Several studies found that the link volume of 10 times the grain size was not satisfactory for the volume grouping criteria for graphite grades with fine grains. ASME 2021 code adopted a new volume grouping criteria based on fracture toughness for calculation of the process zone volume. However, errors were found in the ASME 2021 code process zone volume equation and the question is now open as to what volume grouping criteria is satisfactory. This report presents results from sensitivity studies that were done to evaluate the volume grouping criteria effect on the full assessment POF. This report also presents results from sensitivity studies on other aspects of the code that affect the POF, the mesh size and the choice of the Weibull threshold parameter. All three sensitivity studies: the volume grouping criteria, the mesh size, and the threshold parameter choice are found to affect the component qualification decision for components of structural reliability class 1 (SRC-1). The sensitivity analysis results are presented in the body of the report for NBG-18, which is the same grade of graphite as Hindley used in his thesis. Results from NBG-17, IG-110, 2114, and PCEA are presented in the Appendix. For NBG-18, it was found that increasing the threshold increases the POF, finer meshes result in higher POFs, and that smaller link volume requirements lead to higher POFs (which is inconsistent with Hindley’s findings). This report proposes a new validation study similar to Hindley’s []. The purpose of the new validation study is to tune the threshold, mesh size and grouping criteria based on results from multiple grades of graphite, including finer grain graphites T220 (1-3 microns) and NG-CT-50 (5 microns). The test specimens will be broken at 3 labs, such that we can measure between lab measurement variability, with at least 5 test specimens per lab such that the within lab uncertainty can also be measured. Hindley’s validation method tried matching the average experimental load with the median. The future study will attempt to match failures at lower percentiles, which would be closer to the SRC POF limit. We are currently looking into what geometries make sense and the best method to measure multi-axial stress states. These design decisions are still being set.

36 MATERIALS SCIENCE↗

Seawater sea-sand engineered/strain-hardening cementitious composites (ECC/SHCC): Assessment and modeling of crack characteristics

Highlights: • A probabilistic model was proposed to model the crack width evolution of SS-ECC at different strain levels. • The Weibull distribution fit the crack width distribution better than the log-normal distribution. • A 5-D representation was proposed to assess the SS-ECC by considering both cracking and mechanical performance. • Larger sea-sand size and lower fiber dosage led to larger crack widths in SS-ECC under the same tensile strain. • 18-mm PE fiber led to larger crack widths in SS-ECC at strain >2%, due to a large fraction of fiber rupture. Seawater sea-sand Engineered Cementitious Composites (SS-ECC) is a new version of ECC for marine constructions facing the scarcity of freshwater and river/manufactured sand. This study aims to assess and model the crack characteristics of SS-ECC, which are critical for its applications with non-corrosive reinforcements. The influence of sea-sand size, fiber length and fiber dosage on the crack characteristics of SS-ECC was explored. A five-dimensional representation was proposed to assess the overall performance of SS-ECC, by comprehensively considering both the crack characteristics (i.e., crack width and its variation) and the mechanical properties (i.e., compressive and tensile properties). A probabilistic model was also proposed to describe the stochastic nature and evolution of crack width, and it can be used to estimate the critical tensile strain on SS-ECC for a given crack-width limit and cumulative probability. The findings and proposed methods can facilitate the design of SS-ECC in marine and coastal structures.

36 MATERIALS SCIENCE↗

A time-dependent chloride diffusion model for predicting initial corrosion time of reinforced concrete with slag addition

The effect of granulated blast furnace slag (GBFS) addition on the threshold chloride concentration (TCC) for rebar corrosion was investigated. A modified diffusion model, coupled with a time-dependent effective diffusion coefficient and surface chloride concentration, was proposed to predict the chloride profile. The corrosion initiation time was estimated based on the model predictions and the measured TCC. The results indicate that adding GBFS decreases the TCC by lowering the pH value of the pore solution. The evolution of corrosion potential and current density is found to obey a 3-parameter Weibull distribution. MIP tests show that adding GBFS contributes to refinement of pore structure by decreasing the fraction of large capillary pores. The time-dependent model exhibits good predictive strength and helps understand how GBFS addition delays the corrosion initiation by retarding the chloride diffusion, though a lower TCC is obtained.

36 MATERIALS SCIENCE↗

Investigation of 3D printed lightweight hybrid composites via theoretical modeling and machine learning

Hybrid composites combine two or more different fillers to achieve multifunctional or advanced material properties, such as lightweight and enhanced mechanical properties. The properties of the composites significantly depend on their microstructures, which can be tailored via advanced 3D printing processes. Understanding the process-structure-property relationships is critical to enable the design and engineering of novel hybrid composites for applications in aerospace, automotive, and protective coatings. Here, for this work, we develop 3D printable and lightweight hybrid composites and leverage the conventional design of experiments, a theoretical hybrid model, and an image-driven machine learning (ML) method to investigate their mechanical behaviors. The hybrid composites are formulated with elastomer matrix, microfillers, and thin-shell particles, enabling a significant degree of design freedom of microstructures with densities and mechanical properties varying up to 70% and 91%, respectively. Our statistical analysis indicates that the 3D printing path direction and the microfibers fraction are dominating process parameters with contribution percentages of 45.3% and 57.7% on the specific stiffness and strength, respectively. A hybrid mechanics model is developed based on a simple Weibull distribution function and classical single-filler models to effectively capture the variations in mechanical properties, however, it overestimates the values due to its statistical constraints and idealization of experimental uncertainty. The image-driven ML model leverages the microscale images directly without losing the structural details, shows more accurate predictions with experimental data, and has 48.6% lower root mean square error than the theoretical model.

3D printing↗

Degradation in interfacial shear strength of carbon fiber/ vinyl ester composites due to long-term exposure to seawater using push-out tests

Here, in this study, single fiber (~7-μm diameter) push-out tests are conducted to evaluate hygrothermal effects on the interfacial shear strength (IFSS) of carbon fiber/vinyl ester (CF/VE) composites. Hygrothermal conditioning is achieved by saturating samples in simulated seawater at 40 °C for two years. An investigation has been conducted on the preparation, validity, and interpretation of the push-out test results. First, the authors present a polishing methodology that results in thin films of CF/VE composites in the thickness range of 15–120 μm and produces an average 41.2% drop in IFSS due to long-term hygrothermal exposure. Using scanning electron microscopy (SEM), we show that during the push-out tests, the failure initiates locally at the zone of minimum bond strength at the bottom (away from the indenter), then propagates along the length of the interface. The influence of radial tensile stresses originating due to bending is found to be negligible. Using the SEM imaging of the pushed-out fibers, we validate the failure of the interface to be the primary source of failure. The associated results are found to depend on the thickness of the interface. We then reevaluate the results using the Weibull distribution, knowing that the failure mechanism is analogous to the weakest link theory. The results show a 25.5% drop in the IFSS of the CFVE composite, measured at an infinitesimal scale due to long-term to hygrothermal conditioning at 40 °C. A significant drop in IFSS was observed after reheating above glass transition temperature (T g ) and cooling.

36 MATERIALS SCIENCE↗

Reliability comparisons between additively manufactured and conventional SiC–Si ceramic composites

Abstract An additively manufactured reaction‐bonded silicon carbide ceramic composite is fabricated using a bimodal powder feedstock and the binder‐jetting printing technique. On fabricating, the ceramic is investigated to report its composition, mechanical, and thermal properties at room temperature and high temperatures (up to 750). The ceramic has a density of 2.76 g/cc, and shows a hardness of 21.74 GPa, and a flexure strength of 207.5 MPa at room temperature. The mechanical property of flexure strength is used to estimate its failure probability under applied stress, using a Weibull distribution. The mechanical properties and failure probabilities are compared with those of conventionally fabricated reaction‐bonded silicon carbide ceramics reported in the literature. These ceramics were fabricated using methods such as slip‐casting, compacting, and tape‐casting. The comparison is used to elucidate the advantages and areas of improvement of the present additive manufacturing technique for reaction‐bonded ceramics.

14 SOLAR ENERGY↗

Mechanical and Thermophysical Properties of 3D-Printed SiC-FY20

In the Transformational Challenge Reactor (TCR), the fuel blocks consist of an additively-manufactured silicon carbide (SiC) matrix and uranium nitride tristructural isotropic (UN TRISO) fuel particles, which are stacked to form fuel columns. The SiC matrix is manufactured using binderjet 3D printing followed by loading the TRISO fuel particles and the chemical vapor infiltration (CVI) process. Because the fuel matrix is a primary component of the TCR core and its response to mechanical and thermal loads during operation is one of the most influential factors on the integrity of TCR core, testing and evaluation have focused on producing mechanical and thermophysical properties data for the binderjet/CVI SiC. Mechanical and thermophysical properties were measured from various types of specimens printed for two or three orientations, which included equibiaxial flexural failure strength, elastic constants, thermal diffusivity and conductivity, density, and the coefficient of thermal expansion. Flexural failure strength datasets showed similar Weibull distributions regardless of sample variants including different orientations. The mean failure strengths of the 3D-printed SiC variants were in the range of 286–306 MPa, which are 22–27% lower than that of the CVD SiC. Thermophysical test results showed that specific heat and thermal expansion are not sensitive to the build directions of SiC samples, while thermal diffusivity is highly dependent on the build direction and can be correlated to the anisotropic character of the 3D-printed SiC. This report also includes discussions on the uniaxial tensile properties of the as-printed SiC before CVI and on ongoing efforts for irradiation effects studies.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Initial development of a high temperature life prediction method directly accounting for variability in material properties

This report presents the initial development of a life prediction method that accounts for the variability of the material properties in Grade 91 steel. We account for material variability by both fitting a variable 3-parameter Weibull distribution to the rupture data of the material and by quantifying the effect that the creep deformation properties have on stresses via a Monte Carlo approach. To ensure a reasonable time frame when applying Monte Carlo to the creep stress, we propose a methodology that models the material as an extremely viscous Stokes flow with a non-Newtonian viscosity, therefore solving the problem in a single step. We use the final probabilistic model for structural failure developed in this document to evaluate a Flat Head Vessel designed with the Section III, Division 5 ASME Boiler Pressure and Vessel Code rules with a 100,000h design life and assess its probability of premature failure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Mechanical and Thermophysical Properties of 3D-Printed SiC before and after Neutron Irradiation – FY21

This report presents the mechanical and thermophysical properties of 3D-printed SiC before and after neutron irradiation that have been evaluated to assess the fuel matrix material for the Transformational Challenge Reactor (TCR). The TCR fuel form consists of an additively-manufactured silicon carbide (SiC) matrix and uranium nitride tristructural isotropic (UN TRISO) fuel particles, which is manufactured through a newly developed processing route combining binderjet 3D printing, TRISO fuel particle loading, and chemical vapor infiltration (CVI). Because the fuel matrix is a primary component of the TCR core and its response to mechanical and thermal loads during operation is one of the most influential factors on the integrity of TCR core, testing and evaluation have focused on producing mechanical and thermophysical properties data for the binderjet/CVI SiC. Baseline mechanical and thermophysical properties were measured from the disk specimens printed for different and sizes orientations, which included equibiaxial flexural failure strength, elastic constants, thermal diffusivity and conductivity, density, and the coefficient of thermal expansion. Flexural failure strength datasets showed similar Weibull distributions regardless of sample variants including different orientations. The mean failure strengths of the 3D-printed SiC variants were in the range of 280–310 MPa, which are slightly lower than that of the chemical vapor deposition (CVD) SiC. Thermophysical test results showed that specific heat and thermal expansion are not sensitive to the build direction of SiC samples, while thermal conductivity is highly dependent on the build direction and can be correlated to the anisotropic character of the 3D-printed SiC. Neutron irradiation tests were carried out on the 3D-printed 6-mm diameter SiC disk specimens. Irradiation was carried to 2.3 dpa over a temperature range of 360–880°C. No significant degradation in strength was observed in SiC after irradiations in various conditions and with different orientations. Anisotropy that had been observed in the thermal conductivity of 3D-printed SiC prior to irradiation vanished after irradiation as the irradiation defect thermal resistivity accumulated in the material. Electron microscopy of the microstructure after neutron irradiation showed distinct defect morphologies in the heterogenous material, but no evidence for irradiation-induced cracking or degradation in the microstructure was observed.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Verification Testing For Solid-Element Material Models 11-19 in DYNA3D/ParaDyn

This technical report documents the creation and implementation of verification tests for solid-element material models 11 through 19 available in DYNA3D/ParaDyn. The verification tests covered all aspects of each material model, except for the Weibull distribution functionality in material models 15 and 19. General test cases were created to verify the elastic and plastic behavior of the material models. Other additional tests were developed to examine the intricacies of each material model. Each test involved the use a kinematic load case and specification of material parameters necessary to activate corresponding features of the material model. The load cases prescribed the full time history of the kinematic motion for the solid elements, and these loads are independent of the material model or element formulation. When possible, closed form solutions were then derived for each verification test in a continuum setting. The DYNA3D simulations for each test were carried out over a unit time interval, t ϵ [0, 1], and the as implemented DYNA3D response was compared to the closed form solutions evaluated at discrete points in time. A relative error measure was determined for each test to justify the proper implementation of the material model. The relative errors comparing the DYNA3D solution to the analytical solution were, in general, on the order of machine precision except where noted. This signifies the proper implementation of solid-element material models 11-19. In the development of these verification tests, six bugs were found and fixed in the source code. Additionally, this work generated eighteen DYNA3D input decks and answer extraction scripts in the DYNA3D/ParaDyn Software Quality Assurance test suite, which are comprised of a total of 285 solid-element tests. Testing for each material model utilizes two input decks and answer extraction scripts, where one focuses on the linear elastic response and the other examines the inelastic and remaining functionalities of the material model. In total, this work added 285 individual verification test problems in the DYNA3D/ParaDyn test suite.

42 ENGINEERING↗

Validation of a Custom Ball-on-Ring Apparatus and Consideration of Common Issues for Use in Further Testing (SULI Deliverables)

Ceramic materials are well-known for their high hardness and strength but are limited in their application due to low toughness and sudden failure. As a potential solution, inspiration can be taken from dental enamel nanostructure, where undulating rods cause cracks to branch or deflect, increasing the energy needed to cause total fracture of a ceramic part. Following the dental enamel structure, a novel ceramic which uses 3D printed Yttria stabilized Zirconia rods in an alumina matrix was developed. To test this bio-inspired ceramic material, a proper testing apparatus needed to be created and tested to verify its accuracy. For this project, a bespoke ball on ring testing apparatus was created and tested using both conventionally sintered alumina disks and purchased alumina disks to validate its accuracy. By comparing the Weibull distribution of rupture strengths measured by the tests to literature values, it was shown that the testing frame had a wide distribution of strength which did not align with literature values on the lower end. Through fractography, it was found that some samples fractured from the contact stress induced by the ball indenter, which could not be used to calculate rupture strength. This fracture was often linked to low stress to failure, which was initiated by a flaw on the surface near the indenter which acted as a stress concentrator. Removal of these samples from the data set increased the accuracy of the reported rupture strength values for the ceramic. Considering the equations for the magnitude of contact and flexural strength, along with observations of initiating flaws, several measures can be taken for testing the bio-inspired composite. These measures include proper polishing of both sides of the sample, reducing sample thickness, and potentially using a softer indenter material.

36 - MATERIALS SCIENCE↗

Estimating Weibull parameters for composite materials.

This paper deals with the statistical analysis of strength and fracture of materials in general, with application to fiber composites. The 'weakest link' model is considered in a fairly general form, and the resulting equations are demonstrated by using a Weibull distribution for flaws. This distribution appears naturally in a variety of problems, and therefore additional attention is devoted to analysis and statistical estimation connected with this distribution. Special working charts are included to facilitate interpretation of observed data and estimation of parameters. Implications of the size effect are considered for various kinds of flaw distributions. The paper describes failure and damage in a fiber-reinforced systems.

Robinson, E. Y.↗

The tensile failure modes of metal-matrix composite materials

The strengths of individual boron fibers extracted from various as-received and thermally fatigued aluminum alloy matrix materials were measured. The results are described in terms of a Weibull distribution, and strengths of composites fabricated from these fibers are calculated in terms of lower and upper bounds. Tests conducted on composite specimens indicated that strengths approaching the upper bounds can be achieved in composites fabricated by normal diffusion bonding techniques. Cyclic temperature changes effectively reduced the strength values toward the lower bounds. It was concluded that this effect resulted from the degradation of the strength of the fiber-matrix bond.

Wright, M. A.↗

Lifetimes of fiber composites under sustained tensile loading

Results are presented for a study intended to summarize lifetime data on several fiber/epoxy composite materials subjected to sustained uniaxial tensile loading, to report preliminary results of an accelerated test method for predicting the life of simple composites, and to describe related work in progress on pressure vessels and other filament-wound structures. The lifetime performance of the tested composites was compared by plotting the percent of ultimate strength (applied fiber stress normalized with respect to fiber failure stress in a composite) versus lifetime. In terms of performance in long-term tensile applications, the tested composites are ranked in the following order: graphite/epoxy, Be wire/epoxy, Aramid/epoxy, and S-glass/epoxy. The accelerated test using temperature and stress to simulate the passage of time proves to be encouraging, at least in the case of the Aramid/epoxy composite. The potential of a statistical analysis based on Weibull distribution analyses or a power law relationship is demonstrated.

Chiao, T. T.↗

Rolling element fatigue testing of gear materials

Rolling element fatigue lives of eleven alloys were evaluated. The eleven alloys studied were three nitriding alloys (Super Nitralloy, Nitralloy 135, and Nitralloy N), four case carburizing alloys (AISI 9310, CBS 600, CBS 1000M and Vasco X-2), and four throughhardening alloys (Vasco Matrix II,AISI W-1, AISI S-2 and AISI O-2). Several different heat treatments and/or melting processes were studied on the three carburizing alloy steels. Metallurgical analyses were made before and after the RC rig tests. Test data were statistically analyzed using the Weibull distribution function. B-10 lives were compared versus VIM-VAR AISI M-50 and carburized VAR AISI 9310, as reference alloys.

Nahm, A. H.↗