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DOE OSTI2024

Development of Graphite Thermal and Mechanical Modeling Capabilities in Grizzly

Nuclear-grade graphites are used extensively in the core designs of multiple types of advanced nuclear reactors. In the reactor environment, graphite is exposed over long durations to extreme conditions, including high temperatures, radiation and potentially molten salt and oxygen. Exposure to these conditions can cause several degradation mechanisms in graphite, including nonuniform volumetric strains induced by irradiation and thermal expansion, which lead to stresses that can compromise the performance of graphite components. Evaluating component integrity, predicting component performance over the reactor lifetime, and developing design standards all require robust tools for predicting fracture initiation and propagation in graphite structural components in nuclear reactors. This report documents progress in an ongoing effort to develop modeling and simulation tools in the Grizzly code for predicting the performance of graphite exposed to reactor conditions. Recent developments include a set of thermal and mechanical models that now include the IG-110, NBG-18, and H-451 graphite grades. Improvements have also been made to a nonlinear damaged plasticity model applicable to predicting damage under tension and compression to quasibrittle materials, including graphite. In addition, enhancements have been made to the extended finite element method implementation targeted at simulating graphite fracture. These include new capabilities for crack nucleation in the interior of a solid body, improved treatment of crack nucleation on free surfaces, and more robust modeling approaches for crack growth approaching free surfaces or other cracks.

36 MATERIALS SCIENCE↗

NASA NTRS1986

Grain boundary oxidation and its effects on high temperature fatigue life

Fatigue lives at elevated temperatures are often shortened by creep and/or oxidation. Creep causes grain boundary void nucleation and grain boundary cavitation. Grain boundary voids and cavities will accelerate fatigue crack nucleation and propagation, and thereby shorten fatigue life. The functional relationships between the damage rate of fatigue crack nucleation and propagation and the kinetic process of oxygen diffusion depend on the detailed physical processes. The kinetics of grain boundary oxidation penetration was investigated. The statistical distribution of grain boundary penetration depth was analyzed. Its effect on high temperature fatigue life are discussed. A model of intermittent micro-ruptures of grain boundary oxide was proposed for high temperature fatigue crack growth. The details of these studies are reported.

Liu, H. W.↗

NASA NTRS1997

Probabilistic Mesomechanical Fatigue Model

A probabilistic mesomechanical fatigue life model is proposed to link the microstructural material heterogeneities to the statistical scatter in the macrostructural response. The macrostructure is modeled as an ensemble of microelements. Cracks nucleation within the microelements and grow from the microelements to final fracture. Variations of the microelement properties are defined using statistical parameters. A micromechanical slip band decohesion model is used to determine the crack nucleation life and size. A crack tip opening displacement model is used to determine the small crack growth life and size. Paris law is used to determine the long crack growth life. The models are combined in a Monte Carlo simulation to determine the statistical distribution of total fatigue life for the macrostructure. The modeled response is compared to trends in experimental observations from the literature.

Tryon, Robert G.↗

DOE OSTI2019

An anisotropic damage model based on dislocation-mediated nucleation of cracks under high-rate compression

In this report, we developed a thermodynamically-consistent, rate-dependent micromechanics model for brittle damage nucleated by dislocation plasticity applicable for large deformations. Dislocation substructure evolution was used to inform a nucleation criterion for a microcrack. Under global compression, the sliding of a microcrack induces formation of wing cracks. Effective stress drives dynamic growth of these cracks under a 3D stress state, resulting in an anisotropic material stiffness. The model was also advanced to predict grain size dependence of a polycrystalline solid. Internal variables were constrained based on the laws of thermodynamics. Material constants were calibrated for polycrystalline beryllium to demonstrate the applicability of the model to simulate dynamic failure under compression. We demonstrate the versatility of the model to capture brittle to ductile transition governed by temperature and strain rate. The predictive capability of the model to simulate failure stress and failure strain is compared with dynamic and quasistatic data on beryllium.

36 MATERIALS SCIENCE↗

NASA NTRS1978

Tensile and creep properties of the experimental oxide dispersion strengthened iron-base sheet alloy MA-956E at 1365 K

A study of the 1365 K tensile properties, creep characteristics and residual room temperature properties after creep testing of the experimental oxide dispersion strengthened iron-base alloy MA-956E (Fe-20Cr-4.5Al-0.5Ti-0.5Y2O3) was conducted. The 1365 K tensile properties, particularly ductility, are strongly dependent on strain rate. It appears that MA-956E does not easily undergo slow plastic deformation. Rather than deform under creep loading conditions, the alloy apparently fails by a crack nucleation and growth mechanism. Fortunately, there appears to be a threshold stress below which crack nucleation and/or growth does not occur.

Whittenberger, J. D.↗

DOE OSTI2022

A phase-field model of quasi-brittle fracture for pressurized cracks: Application to UO 2 high-burnup microstructure fragmentation

Here, in this paper, we present a phase-field model of quasi-brittle fracture with pressurized cracks, with dedicated applications for polycrystalline materials. The model is formulated as a minimization problem within the variational framework. The external work done by pressure on the crack surfaces is included in the objective function. Several careful modeling choices lead to a regularization-length-independent critical strength. The model is constructed to give a softening response with an underlying linear traction-separation law. The pressure-dependent softening response and the regularization of the prescribed pressure are demonstrated with a (quasi) one-dimensional numerical analysis. In a two-dimensional numerical analysis under plane strain assumptions, the critical stress corresponding to crack propagation (as predicted by our quasi-brittle fracture model) is compared with linear elastic fracture mechanics (LEFM) analytical solutions. Our model is further utilized to simulate fission-gas-induced fragmentation of the UO 2 high-burnup structure (HBS). Simulation results show that pressurized bubbles can cause crack nucleation and propagation, and that the bubble size and the surrounding external pressure affect the critical pressure corresponding to crack nucleation. Simulations of a partial HBS at different recrystallization stages show that different grain structures (due to recrystallization) also influence crack paths and fragmentation morphology.

36 MATERIALS SCIENCE↗

NASA NTRS2008

Multiscale Modeling of Damage Processes in Aluminum Alloys: Grain-Scale Mechanisms

This paper has two goals related to the development of a physically-grounded methodology for modeling the initial stages of fatigue crack growth in an aluminum alloy. The aluminum alloy, AA 7075-T651, is susceptible to fatigue cracking that nucleates from cracked second phase iron-bearing particles. Thus, the first goal of the paper is to validate an existing framework for the prediction of the conditions under which the particles crack. The observed statistics of particle cracking (defined as incubation for this alloy) must be accurately predicted to simulate the stochastic nature of microstructurally small fatigue crack (MSFC) formation. Also, only by simulating incubation of damage in a statistically accurate manner can subsequent stages of crack growth be accurately predicted. To maintain fidelity and computational efficiency, a filtering procedure was developed to eliminate particles that were unlikely to crack. The particle filter considers the distributions of particle sizes and shapes, grain texture, and the configuration of the surrounding grains. This filter helps substantially reduce the number of particles that need to be included in the microstructural models and forms the basis of the future work on the subsequent stages of MSFC, crack nucleation and microstructurally small crack propagation. A physics-based approach to simulating fracture should ultimately begin at nanometer length scale, in which atomistic simulation is used to predict the fundamental damage mechanisms of MSFC. These mechanisms include dislocation formation and interaction, interstitial void formation, and atomic diffusion. However, atomistic simulations quickly become computationally intractable as the system size increases, especially when directly linking to the already large microstructural models. Therefore, the second goal of this paper is to propose a method that will incorporate atomistic simulation and small-scale experimental characterization into the existing multiscale framework. At the microscale, the nanoscale mechanics are represented within cohesive zones where appropriate, i.e. where the mechanics observed at the nanoscale can be represented as occurring on a plane such as at grain boundaries or slip planes at a crack front. Important advancements that are yet to be made include: 1. an increased fidelity in cohesive zone modeling; 2. a means to understand how atomistic simulation scales with time; 3. a new experimental methodology for generating empirical models for CZMs and emerging materials; and 4. a validation of simulations of the damage processes at the nano-micro scale. With ever-increasing computer power, the long-term ability to employ atomistic simulation for the prognosis of structural components will not be limited by computation power, but by our lack of knowledge in incorporating atomistic models into simulations of MSFC into a multiscale framework.

Hochhalter, J. D.↗

DOE OSTI2023

A robust interface finite element formulation for modeling brittle material failure problems

Abstract Failure of many brittle materials and structures can be modeled using interface‐oriented finite elements combined with intrinsic cohesive zone models. The discontinuous Galerkin (DG) finite element method provides an innovative framework for modeling brittle crack propagation with zero‐thickness interface elements, which can accommodate extrinsic cohesive laws to avoid the artificial compliance required in intrinsic cohesive models. However, robust formulations and implementations of DG methods are critical in alleviating the well‐known convergence issues for both crack nucleation and propagation with reduced instability. This paper presents a robust interface element formulation by modifying the incomplete interior penalty Galerkin (IIPG) method, which successfully avoids the initial element interface penetration across elements that occurs prior to crack nucleation, and thereby greatly reduces the instability issue as cracks open. We further verified and validated our implementation by using a bar tension test and a beam fracturing benchmark. The robustness of our proposed interface element method was demonstrated by a micromechanics fiber/matrix debonding problem with 64 fibers embedded in a bulk matrix.

Liu, Ruijie↗

NASA NTRS1994

Fatigue life until small cracks in aircraft structures: Durability and damage tolerance

Crack initiation in notched elements occurs very early in the fatigue life. This is also true for riveted lap joints, an important fatigue critical element of a pressurized fuselage structure. Crack nucleation in a riveted lap joint can occur at different locations, depending on the riveting operation. It can occur at the edge of the rivet hole, at a small distance away from the hole, but still with subsequent crack growth through the hole, and ahead of the hole with a crack no longer passing through the hole. Moreover, crack nucleation can occur in the top row at the countersunk holes (outer sheet) or in the bottom row at the non-countersunk holes. Fractographic evidence is shown. The initial growth of the small cracks occurs as an (invisible) part through crack. As a consequence, predictions on the crack initiation life are problematic. After a though crack is present, the major part of the fatigue life has been consumed. There is still an apparent lack of empirical data on crack growth and residual strength of riveted lap joints, five years after the Aloha accident. Such data are very much necessary for further developments of prediction models. Some test results are presented.

Schijve, J.↗

NASA NTRS1972

Ductile-brittle transition of thoriated chromium.

Unalloyed chromium and chromium containing approximately 3 wt % ThO2 were prepared from powder produced by a chemical vapor deposition process. When rolled to sheet and tested in tension, it was found that the thoriated material had a lower ductile-to-brittle transition temperature (DBTT) than unalloyed chromium. This ductilizing was evident both in the as-rolled condition and after the materials had been annealed for 1 hour at 1200 C. The improved ductility in thoriated chromium may be associated with several possible mechanisms: (1) particles may disperse slip, such that critical stress or strain concentrations for crack nucleation are more difficult to achieve; (2) particles may act as dislocation sources, thus providing mobile dislocations in this normally source-poor material, in a manner similar to prestraining; and (3) particles in grain boundaries may help to transmit slip across the boundaries, thus relieving stress concentrations and inhibiting crack nucleation.

Wilcox, B. A.↗

DOE OSTI2019

Direct measurements of slip irreversibility in a nickel-based superalloy using high resolution digital image correlation

Fatigue crack nucleation in crystalline materials typically develops due to highly localized cyclic slip. During a fatigue cycle, reverse slip differs locally from slip in the forward direction particularly in precipitate-containing materials such as superalloys. In this paper we report the first direct measurements of irreversibility at the scale of individual slip bands by high-resolution digital image correlation (DIC) in a polycrystalline nickel-based superalloy. Quantitative measurements of the slip irreversibility are challenging for regions of material that have a size that captures the microstructure and its variability. High spatial resolution at the nanometer scale during experimental measurements is needed to observe slip localization during deformation. Moreover, large fields are also needed to obtain the material response over statistically representative populations of microstructural configurations. Recently, high resolution scanning electron microscope (SEM) digital image correlation (DIC) has been extended for quantitative analysis of discontinuities induced by slip events using the Heaviside-DIC method. Therefore, this novel method provides quantitative measurements of slip localization at the specimen surface. In this paper, the Heaviside-DIC method is used to measure slip irreversibility and plastic strain accumulation in a nickel-based superalloy. The method detects bands with high levels of irreversibility early in cycling that ultimately form fatigue cracks upon further cycling. The local microstructural configurations that induce large amounts of plasticity and slip irreversibility are correlated to crack nucleation locations.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Four-dimensional microstructurally small fatigue crack growth in cyclically loaded nickel superalloy specimen

Here, we nondestructively image a low-solvus high refractory (LSHR) nickel base specimen microstructure during cyclic loading to characterize crack propagation during the microstructurally small crack (MSC) growth regime. Micro-computed tomography (uCT) is used to characterize the material density and identify crack interfaces, while high-energy diffraction microscopy (HEDM) provides snapshots of the microstructural orientation field changes. From these measurements, data are computationally reconstructed and coregistered to describe the specimen’s configuration before load, before crack nucleation, and throughout the crack propagation/loading process. An MSC forms at a FIB-cut notch, which was previously placed to concentrate stress at the center of the specimen gauge, and propagates along a facet parallel to the local {1 1 1} crystallographic plane. Analysis of available crystallographic slip directions and measured point-to-point disorientation axes indicate probable single and coplanar slip activity along FCC octahedral planes within this region. Similar analyses of other crack propagation facets reveal generally slower growth along directions favoring zig-zag cross and codirectional cross slip, which are often disfavored at room temperature.

36 MATERIALS SCIENCE↗

DOE OSTI2023

The Influence of Nominal Composition on the Microstructure, Tensile Properties, and Weldability of Cast Monel Alloys

Cast Monel alloys are used in many industrial applications that require a combination of good mechanical properties and excellent resistance to corrosion. Despite relative widespread use, there has been limited prior research investigating the fundamental composition–structure–property relationships. Here in this work, microstructural characterization, thermal analysis, electron probe microanalysis, tensile testing, and Varestraint testing were used to assess the effects of variations in nominal composition on the solidification path, microstructure, mechanical properties, and solidification cracking susceptibility of cast Monel alloys. It was found that Si segregation caused the formation of silicides at the end of solidification in grades containing at least 3 wt pct Si. While increases to Si content led to significant improvements in strengthening due to the precipitation of β 1 -Ni 3 Si, the silicide eutectics acted as crack nucleation sites during tensile loading which severely reduced ductility. The solidification cracking susceptibility of low-Si Monel alloys was found to be relatively low. However, increases to Si concentration and the onset of associated eutectic reactions increased the solidification temperature range and drastically reduced cracking resistance. Increases in the Cu and Mn concentrations were found to reduce the solubility limit of Si in austenite which promoted additional eutectic formation and exacerbated the reductions in ductility and/or weldability.

36 MATERIALS SCIENCE↗

NASA NTRS1975

Fatigue failure of hydrogen embrittled high strength steels

Results of an experimental investigation are presented concerning the fracture behavior of cathodically charged, quenched and tempered martensitic steels under cyclic load conditions. Introduction of H2 by cathodic charging reduced fatigue life by as much as 60%. It is proposed that subsurface transverse fatigue cracks nucleate simultaneously at multiple sites, such as at microcracks, voids, or inclusions. Fatigue crack growth then occurs on planes perpendicular to the major applied stress axis in the presence of the critical combination of applied external stress and hydrogen.

Kim, Y. G.↗

NASA NTRS1989

Characterization of failure processes in tungsten copper composites under fatigue loading conditions

A fractographic and metallographic investigation was performed on specimens of a tungsten fiber reinforced copper matrix composite (9 vol percent), which had experienced fatigue failures at elevated temperatures. Major failure modes and possible failure mechanisms, with an emphasis placed on characterizing fatigue damage accumulation, were determined. Metallography of specimens fatigued under isothermal cyclic loading suggested that fatigue damage initiates in the matrix. Cracks nucleated within the copper matrix at grain boundaries, and they propagated through cavity coalescence. The growing cracks subsequently interacted with the reinforcing tungsten fibers, producing a localized ductile fiber failure. Examinations of interrupted tests before final failure confirmed the suggested fatigue damage processes.

Kim, Yong-Suk↗

NASA NTRS1989

Properties of oxide dispersion strengthened alloys

A contrast is drawn between the behavior of ODS alloys' matrix compositions and that of more conventional alloys. Mechanical property enhancements associated with ODS alloys are accounted for by both the presence of the dispersoids and, in some cases, the smaller size and number of secondary phases. Data obtained for ODS materials to date indicate the presence of three different threshold stresses, due to dislocation-particle interactions, diffusional creep/grain boundary sliding, and, in the case of the MA 956 ODS alloy, crack nucleation and growth processes. It is critical to establish which threshold stress is in effect, since the latter two stresses can result in failure by cracking.

Whittenberger, J. Daniel↗

DOE OSTI2023

Local structural ordering determines the mechanical damage tolerance of amorphous grain boundary complexions

Amorphous grain boundary complexions act as toughening features within a microstructure because they can absorb dislocations more efficiently than traditional grain boundaries. This toughening effect should be a strong function of the local internal structure of the complexion, which has recently been shown to be determined by grain boundary crystallography. To test this hypothesis, molecular dynamics are used here to simulate dislocation absorption and damage nucleation for complexions with different distributions of structural short-range order. Here, the complexion with a more disordered structure away from the dislocation absorption site is actually found to better resist crack nucleation, as damage tolerance requires delocalized deformation and the operation of shear-transformation zones through the complexion thickness. The more damage tolerant complexion accommodates plastic strain efficiently within the entire complexion, providing the key mechanistic insight that local patterning and asymmetry of structural short-range order controls the toughening effect of amorphous complexions.

36 MATERIALS SCIENCE↗

NASA NTRS2005

High-Frequency, High-Temperature Fretting Experiments

Fretting is a structural damage mechanism observed when two nominally clamped surfaces are subjected to an oscillatory loading. A critical location for fretting induced damage has been identified at the blade/disk and blade/damper interfaces of gas turbine engine turbomachinery and space propulsion components. The high-temperature, high-frequency loading environment seen by these components lead to severe stress gradients at the edge-of-contact. These contact stresses drive crack nucleation and propagation in fretting and are very sensitive to the geometry of the contacting bodies, the contact loads, materials, temperature, and contact surface tribology (friction). To diagnose the threat that small and relatively undetectable fretting cracks pose to damage tolerance and structural integrity of in-service components, the objective of this work is to develop a well-characterized experimental fretting rig capable of investigating fretting behavior of advanced aerospace alloys subjected to load and temperature conditions representative of such turbomachinery components.

Matlik, J. F.↗