Finding a fatigue crack in a Swiss watch: Fatigue cracking kinetics and detectability in miniaturized PH13-8Mo shafts
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Finfrock, Christopher Barret [Sandia National Labo↗
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ASSESSING CRACK GROWTH MODELS FOR CHLORIDE-INDUCED STRESS CORROSION CRACKING IN STAINLESS-STEEL CANISTERS
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Mendoza, Hector [Sandia National Laboratories (SNL↗
Threshold fatigue crack growth evaluation & fatigue crack growth predictions.
Abstract not provided.
Ronevich, Joseph Allen↗
Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past
The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.
42 ENGINEERING↗
Complex Dependence of Calcite Crack Kinetics on Salinity: The Role of DLVO and Hydration Forces
Abstract Subcritical crack growth (SCG) plays an important role in many geological processes such as delayed earth rupture and rock weathering. The complex dependency of SCG on the in‐crack fluid chemistry, however, is still poorly understood. In this study, we utilize the newly developed surface force‐based fracture theory (SFFT) to elucidate the relative contributions of surface forces and solute transport to the crack growth kinetics of calcite in NaCl solutions. Expanding on Barenblatt's cohesive crack model, SFFT introduces an effective stress intensity at the crack tip that encompasses all the relevant intermolecular forces across the crack in addition to the external far‐field stresses. The nonlinear system of equations portraying the crack opening profile, the solute distribution in a propagating crack, and the crack growth velocity are numerically solved via an implicit scheme. After carefully calibrating the model for calcite‐water systems, the SFFT is used to predict the SCG response of calcite at different NaCl concentrations, based on various hypotheses. These predictions are then compared to existing SCG data from the literature. We demonstrate that the experimentally observed variation of SCG rate with NaCl concentration cannot be explained solely by DLVO forces (electrostatic and Van der Waals interactions). This can be remediated by introducing an exponentially decaying hydration force with a nonlinear, nonmonotonic dependence on NaCl concentration. Furthermore, we demonstrate that accounting for both diffusive and advective transport of ions is important in explaining the absence of a stage‐II SCG response for calcite in electrolyte solutions. Plain Language Summary Subcritical crack growth (SCG) refers to the slow propagation of cracks in materials under a stress below the threshold for catastrophic failure. SCG is a key process in many geological events, for example, delayed earth ruptures and rock weathering. New initiatives such as underground CO 2 and H 2 storage in carbonate reservoirs further call for better understanding of SCG in carbonate minerals subjected to varying fluid chemistry. This study examines the SCG of calcite, a key mineral found in carbonate rocks, intergranular cement in sandstones, and filling material in mineral veins and faults, determining their deformation and strength. A mathematical model is developed to describe how the crack opens and propagates, how solutes (like salts) distribute within the crack, and how the crack surfaces interact with each other. We used the model to predict calcite SCG in water at different salt concentrations and compared it with experimental data. Our results revealed that the hydration force is the dominating factor in determining the complex, non‐linear dependency of SCG on salinity. We also found that both the movement of ions by diffusion and by bulk water flow are crucial for explaining the SCG rates, especially when the cracks grow quickly. Key Points Surface Force‐Based Fracture Theory predicts the complex subcritical crack growth patterns of calcite crystals immersed in NaCl solutions Results highlight the dominant role of hydration forces in altering the fracture behavior of calcite compared to VdW and electric double‐layer forces Advective solute transport explains the absence of stages‐II and ‐III subcritical crack growth responses in solid‐liquid systems
DLVO↗
Cracking Behavior of Irradiated Ex-Plant Materials
The cracking behavior of reactor core internal materials is a key factor for the long-term safety and availability of light water reactors. Subject to high-temperature coolant, thermal and mechanical loading, and neutron irradiation, reactor core internal materials are susceptible to several degradation mechanisms during power operation. To understand the long-term effects of neutron irradiation, irradiated materials harvested from a decommissioned reactor were studied for their cracking susceptibility and fracture resistance. Small compact-tension specimens were machined from different locations on the baffle plates with irradiation doses ranging from 0.06 to 48.5 dpa. Crack growth rate and fracture toughness J-resistance (J-R) curve tests were performed on these specimens in a simulated light water reactor environment, and the fracture morphologies of the tested samples were examined with a scanning electron microscope. All samples behaved similarly under cyclic loading, and no deteriorated corrosion-fatigue behavior was observed in the test environments. Under constant load, no elevated cracking susceptibility was observed either in these samples at low stress intensity factors. However, a rapid cracking behavior featuring very high crack growth rates was observed in several high-dose samples. This rapid crack growth behavior was activated when the applied stress intensity factor, K, was sufficiently high. Once activated, the rapid crack growth remained steady even when the K was lowered to the pre-activation level and stopped only when the K was reduced drastically. Yet, the rapid crack growth could be re-activated repeatedly in these samples by raising the K above the initial activation level. This rapid cracking response may be related to the severe irradiation embrittlement experienced by these samples. The J-R curve tests performed with these samples showed a significant decline in fracture toughness with increasing neutron irradiation. Local cracking at the crack tip facilitated by the severe irradiation embrittlement of this material may be responsible for the rapid crack growth behavior demonstrated by this decommissioned material.
36 MATERIALS SCIENCE↗
Characterization of Lab-Grown Cracks for Aerosol Transmission Testing
Motivation: Determine the length and opening of two lab-grown cracks, designated as LT-14 and LT-28, representative of stress corrosion cracks in spent nuclear fuel dry storage casks to supplement future testing of gas and aerosol transport. Problem: The extreme aspect ratio of the crack length to opening requires that imaging occurs in stages with the results merged before final analysis. Method: High magnification (1500x) optical images of both sides of the two plates were acquired. 20x stitched images with LSCM were acquired, fully stitched along the length, and leveled with newly developed PLATES Method in MATLAB®. Conclusion for LT-14: Side 1 is 47.25 mm long and has 366 separate crack features with an average length of 23.50 µm and an average opening of 8.27 µm. Side 2 is 69.44 mm long and has 550 separate crack features with an average length of 81.63 µm and an average opening of 67.70 µm. Conclusion for LT-28: Side 1 is 71.95 mm long and has 1,127 separate crack features with an average length of 42.27 µm and an average opening of 10.31 µm. Side 2 is 74.88 mm long and has 520 separate crack features with an average length of 98.13 µm and an average opening of 14.99 µm. The adjacent crack on side 1 is 18.95 mm long and has 37 separate crack features with an average length of 17.46 µm and an average opening of 10.42 µm. The adjacent crack on side 2 is 26.40 mm long and has 55 separate crack features with an average length of 87.26 µm and an average opening of 48.29 µm. Each adjacent crack is approximately 26 mm from the main crack.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Automatic Crack Segmentation and Feature Extraction in Electroluminescence Images of Solar Modules
The effect of cracks in solar cells on the long-term degradation of photovoltaic (PV) modules remains to be determined. To investigate this effect in future studies, it is necessary to quantitatively describe the crack features (e.g., length) and correlate them with module power loss. Electroluminescence (EL) imaging is a common technique for identifying cracks. However, it is currently challenging and time-consuming to identify cracks in a large number of EL images and quantify complex crack features by human inspection. This article introduces a fast semantic segmentation method (~0.18 s/cell) to automatically segment cracks from EL images and algorithms to extract crack features. Here we fine-tuned a UNet neural network model using pretrained VGG16 as the encoder and obtained an average F1 score of 0.875 and an intersection over union score of 0.782 on the testing set. With cracks and busbars segmented, we developed algorithms for extracting crack features, including the crack-isolated area, the brightness inside the isolated area, and the crack length. We also developed an automatic preprocessing tool for cropping individual cell images from EL images of PV modules (~0.72 s/module). Our codes are published as open-source an software, and our annotated dataset composed of various types of cells is published as a benchmark for crack segmentation in EL images.
14 SOLAR ENERGY↗
Evaluation of ceria as a surrogate material for UO 2 in experiments on fuel cracking driven by resistive heating
A variety of normal operation and accident scenarios can generate thermal stresses large enough to cause cracking in light-water reactor (LWR) fuel pellets. Cracking of fuel pellets can lead to reduced heat removal, larger centerline temperatures, and localized stress in cladding all of which impact fuel performance. Furthermore, pellet cracking also contributes to a temperature reduction in the pellet since the pellet fragments tend to move towards the heat sink (cladding), and the heat flow remains predominantly radial despite the presence of cracks. It is important to understand the temperature profile on the pellet before and after cracking to improve cracking models in fuel performance codes However, in-reactor observation and measurement of cracking is very challenging owing to the harsh environment and design of fuel rods. Recently, an experimental pellet cracking test stand was developed for separate effects testing of normal operations and accident temperature conditions, using thermal imaging to capture the pellet surface temperature for evaluation of thermal stresses and optical imaging to capture the evolution of cracking in real time. Cracking experiments were initially performed using ceria (CeO 2 ) as a surrogate fuel material, which is useful for developing and demonstrating the experimental approaches but is also valuable in its own right for cracking model development and validation. A combination of induction and resistance heating was used for volumetric heat generation in the pellet creating a thermal gradient. The material properties of CeO 2 and UO 2 are reviewed and compared for use in model development. Simulations of the experiment were performed to evaluate the behavior of the surrogate (CeO 2 ) fuel in BISON. The measured temperature profiles from BISON models match reasonably well with the observed experiments for the ceria pellets before cracking. The findings from this work will help improve confidence in fracture models used for fuel pellets under similar in-reactor conditions.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
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↗
Nonlinear modeling and performance analysis of cracked beam microgyroscopes
Cracks constitute a common structural defect in microelectromechanical systems that may arise during manufacturing, mechanical fatigue, or shock loading. Areas weakened by cracks increase the flexibility of the microstructure. Furthermore, depending on the crack severity, the increased flexibility can cause dramatic changes in the static and dynamic behaviors of electrically actuated MEMS. In this study, a numerical investigation of the depth and location of multiple edge cracks on the performance of beam microgyroscopes is conducted. Applying the Griffith strain energy release theorem for an edge crack, the vibrational characteristics of microgyroscopes with multiple cracks including the static deflection, natural frequencies, and mode shapes are studied analytically. Then, the differential quadrature method is employed to model the nonlinear dynamic behaviors of the cracked gyroscope system. Cracks initiated along the driving or sensing directions of the microgyroscope are found to have differing effects on its nonlinear dynamic response. This numerical study reveals that the onset of severe single cracks or a series of multiple cracks can significantly affect the sensitivity of the microgyroscope to base rotations and therefore leads to a degradation in the performance of the damaged MEMS sensor. This study also shows that a potential design approach for broadband microgyroscope systems manufactured with cracks can be proposed.
42 ENGINEERING↗
Crack nucleation at forging flaws studied by non-local peridynamics simulations
We present a computational study and framework that allows us to study and understand the crack nucleation process from forging flaws. Forging flaws may be present in large steel rotor components commonly used for rotating power generation equipment including gas turbines, electrical generators, and steam turbines. The service life of these components is often limited by crack nucleation and subsequent growth from such forging flaws, which frequently exhibit themselves as non-metallic oxide inclusions. The fatigue crack growth process can be described by established engineering fracture mechanics methods. However, the initial crack nucleation process from a forging flaw is challenging for traditional engineering methods to quantify as it depends on the details of the flaw, including flaw morphology. We adopt the peridynamics method to describe and study this crack nucleation process. For a specific industrial gas turbine rotor steel, we present how we integrate and fit commonly known base material property data such as elastic properties, yield strength, and S-N curves, as well as fatigue crack growth data into a peridynamic model. The obtained model is then utilized in a series of high-performance two-dimensional peridynamic simulations to study the crack nucleation process from forging flaws for ambient and elevated temperatures in a rectangular simulation cell specimen. The simulations reveal an initial local nucleation at multiple small oxide inclusions followed by micro-crack propagation, arrest, coalescence, and eventual emergence of a dominant micro-crack that governs the crack nucleation process. The dependence on temperature and density of oxide inclusions of both the details of the microscopic processes and cycles to crack nucleation is also observed. The results are compared with fatigue experiments performed with specimens containing forging flaws of the same rotor steel.
97 MATHEMATICS AND COMPUTING↗
Separate-Effects Tests for Studying Temperature-Gradient-Driven Cracking in UO 2 Pellets
We report a variety of normal operation and accident scenarios can generate thermal stresses large enough to cause cracking in light-water reactor (LWR) fuel pellets. Cracking of fuel pellets can lead to reduced heat removal, higher centerline temperatures, and localized stress in cladding, all of which impact fuel performance. It is important to experimentally characterize the thermal and mechanical behavior in the pellet before and after cracking to improve cracking models in fuel performance codes. However, in-reactor observation and measurement of cracking is very challenging due to the harsh environment and logistics. Recently, an experimental pellet cracking test stand was developed for separate effects testing of normal operations and accident temperature conditions, using thermal imaging to capture the pellet surface temperature for evaluation of thermal stresses and optical imaging to capture the evolution of cracking in real time. Experiments were performed using depleted uranium dioxide (UO 2 ) pellets, which are useful for collecting data valuable for development and validation of cracking models. A combination of induction and resistance heating was used to create an average temperature gradient of 236°C/cm and 193°C/cm before and after cracking respectively. Characterization of the pellets were done before as well as after cracking. The cracking patterns are somewhat different than those expected in a typical reactor because of the differences in thermal conditions and pellet microstructure. However, if the actual conditions of these experiments are reproduced in computational models, these out-of-pile tests on UO 2 pellets provide relevant data for modeling purposes.
11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
Quantitative analysis of three-dimensional fatigue crack path selection in Mg alloy WE43 using high-energy X-ray diffraction microscopy
Fatigue short-cracks in Mg alloys display complex growth behavior due to high plastic anisotropy and crack path dependence on local microstructural features. In this study, the three-dimensional crystallography of short-crack paths in Mg alloy WE43 was characterized by mapping near-field high-energy X-ray diffraction microscopy (HEDM) reconstructed grain maps to high-resolution X-ray CT reconstructions of the fracture surfaces in the crack initiation and short-crack growth regions of six ultrasonic fatigue specimens. Crack–grain–boundary intersections were analyzed at 81 locations across the six crack paths. The basal intragranular, non-basal intragranular, or intergranular character of short-crack growth following each boundary intersection was correlated to crystallographic and geometric parameters of the trailing and leading grains, three-dimensional grain boundary plane, and advancing crack front. The results indicate that crack paths are dependent on the combined crystallographic and geometric character of the local microstructure, and crack path prediction can be improved by use of dimensionality reduction on subsets of high-linear-correlation microstructural parameters.
36 MATERIALS SCIENCE↗
Residually Stressed Bimaterial Beam Specimen for Measuring Environmentally Assisted Crack Growth
Background: Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip. Objective: Here we present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading. Methods: Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force. Results: The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data. Conclusions: The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.
36 MATERIALS SCIENCE↗
Fatigue-Crack Detection and Monitoring through the Scattered-Wave Two-Dimensional Cross-Correlation Imaging Method Using Piezoelectric Transducers
Piezoelectric transducers are convenient enablers for generating and receiving Lamb waves for damage detection. Fatigue cracks are one of the most common causes for the failure of metallic structures. Increasing emphasis on the integrity of critical structures creates an urgent need to monitor structures and to detect cracks at an early stage to prevent catastrophic failures. This paper presents a two-dimensional (2D) cross-correlation imaging technique that can not only detect a fatigue crack but can also precisely image the fatigue cracks in metallic structures. The imaging method was based on the cross-correlation algorithm that uses incident waves and the crack-scattered waves of all directions to generate the crack image. Fatigue testing for crack generation was then conducted in both an aluminum plate and a stainless-steel plate. Piezoelectric wafer transducer was used to actuate the interrogating Lamb wave. To obtain the scattered waves as well as the incident waves, a scanning laser Doppler vibrometer was adopted for acquiring time-space multidimensional wavefield, followed with frequency-wavenumber processing. The proof-of-concept study was conducted in an aluminum plate with a hairline fatigue crack. A frequency-wavenumber filtering method was used to obtain the incident wave and the scattered wave wavefields for the cross-correlation imaging. After this, the imaging method was applied to evaluate cracks on a stainless-steel plate generated during fatigue loading tests. The presented imaging method showed successful inspection and quantification results of the crack and its growth.
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Numerical and Analytical Modeling of the Effect of Cracks on the Self-Inductance of a COTS YJ-41003-TC Toroid
COTS inductors and transformers often contain partial cracks whose effect on inductance, a key performance parameter, have not been carefully studied. In this report, the effects of both partial and complete cracks on the self-inductance of a 100 turn square cross section COTS YJ-41003-TC toroid comprised of J Material was comprehensively investigated using both analytically derived closed form expressions and 3D computational techniques employing commercial codes. Both partial (half-penny) and complete (air gap) cracks of 10 and 25 μm were investigated. The crack is defined as the physical distance between two faces of the toroid's magnetic core, such that the surface normal of either face is along the Φ-direction, in alignment with the B-field. For the purposes of validation, two different approaches were incorporated for both the analytical and numerical models. The two analytical methods are comprised of a first principles approach based on the physics of electromagnetics, as well as linear circuit theory. The former directly utilizes the integral form of Maxwell's equations while the latter exploits the interchangeable relationship between electric and magnetic circuits. Validation within the computational scheme is realized through a code-to-code comparison between commercial solvers, COMSOL Multiphysics and CST, with the former employing the Finite Element Method (FEM) and the latter the Finite Difference Time Domain (FDTD) technique. Sound agreement between all four methods (ie., two analytical and two numerical) is observed, with results indicating that only a perturbation in self-inductance occurs for the half-penny cracks, while a substantial reduction takes place for the case of complete cracks. It is important to note that even though a static μ r is applied, representing the linear region of the BH curve (based on manufacturer specifications), the complete crack results still place a lower conservative bound on the inductance. This follows from the fact that even in the case of a half-penny crack, if the magnetic core portion of the crack approaches saturation, the crack begins to behave like an air gap, or complete crack. When an air gap is introduced into a magnetic core, a substantial reduction in inductance can occur due to the significant difference in permeabilities between the two mediums (ie., μ core >> μ air ). The once intact bulk magnetic core of the toroid essentially begins to behave like an air core.
36 MATERIALS SCIENCE↗
Thermal conductivity of crack-containing media: A numerical study
The present study aims to evaluate the effective thermal conduction behavior of crack-containing media through micromechanical modeling. Numerical analyses were performed using the finite element method, first using periodic arrays of elliptical pores and then reducing the elliptical minor axis to reach the crack limit. This parametric approach was seen to be able to capture the effect of discontinuity across the crack face in a straightforward manner. The overall thermal conductivity of the model structures, encompassing a range of crack densities and spatial distributions, was investigated. It was found that, for cracks with mixed orientations, the effective thermal conductivity is insensitive to the actual crack alignment and can be uniquely represented by the crack density. The mixed-orientation periodic crack configurations are also representative of random sizes, orientations, and spatial distributions of cracks, thus exhibiting a high degree of generality. The modeling analyses can also be used to determine simple empirical expressions for two- and three-dimensional media containing random cracks.
36 MATERIALS SCIENCE↗