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DOE OSTI2021

Damage development in neutron-irradiated concrete in a test reactor: Hygro-thermal and mechanical simulations

This paper reports the development of a 3D mesoscale hygro-thermal-mechanical simulation approach to predict damage in concrete irradiated in a test reactor. This framework, developed in MOOSE, considers the effects of elevated temperature, moisture content, and high neutron fluence (energy threshold, E > 0.1 MeV) on the mortar and aggregates separately. The first-stage simulation implements hygro-thermal analysis to determine the temperature and RH inside the specimen as a function of imposed radiation energy. These are used as inputs to the second stage, which considers radiation-induced volumetric expansion (RIVE) of aggregates, and creep, shrinkage, and stress-strain response of mortar to predict the expansion, stresses, and damage in specimens made using different coarse aggregates and subjected to different irradiation times. The irradiation time-dependent damage in the mortar is expressed using an isotropic damage parameter. This multi-physics model serves as a predictive tool for damage quantification in concrete due to neutron irradiation.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Viscoelastic Material Characterization and Modeling of Photovoltaic Module Packaging Materials for Direct Finite-Element Method Input

Numerical tools, such as the finite-element method, are increasingly used to design and evaluate the photovoltaic (PV) modules, providing for the reduction of development time and improved performance and reliability. However, high-fidelity material models are necessary to accurately model the complex structural behavior of the involved packaging materials. A common simplification used in recent years is to model the polymer materials (i.e., encapsulant and backsheet) as linear elastic, which will lead to inaccurate results. Therefore, in this work, we present a thorough characterization of the time- and temperature-dependent mechanical response of predominant PV module encapsulant and backsheet materials. Based on this material characterization, we developed and experimentally validated generalized Maxwell models to describe each material's viscoelastic response. In addition, we included measurements of the coefficient of thermal expansion and presented all material models in such a fashion for direct input into commercial finite-element method modeling software.

FEM↗

DOE OSTI2025

Temperature and Strain Sensing Characteristics of a 128° YX-Cut LiNbO 3 Rayleigh-Mode SAW Sensor From Room to Cryogenic Temperatures

Accurate, passive, and wireless monitoring of cryogenic hardware is essential for high-energy physics, space propulsion, and biomedical instrumentation. Here, this study quantifies the coupled temperature-strain behavior of Rayleigh-mode surface acoustic-wave (SAW) delay-line sensors fabricated on 128° YX-cut LiNbO 3 . A nonlinear finite element (FE) model incorporating Varshni-based elastic constants, higher-order thermal expansion, and temperature-dependent piezo- and dielectric coefficients was developed and validated experimentally between 280K and 80K. Free-standing (first test condition) and bonded/wired (second test condition) devices exhibited indistinguishable thermal responses; the average temperature coefficient of delay (TCD) in the critical cryogenic range from 130K down to 80K differed by only 0.15 ppm/K (0.32%), confirming that bonding-induced stress is negligible. Over 280-80K the measured TCD was 61.77 ppm/K, while the FE model predicted an equivalent temperature coefficient of frequency (TCF) of −62.74 ppm/K with an overall coefficient of determination R2 = 0.998. In the critical cryogenic interval 130-80K the TCD fell to 47.66 ppm/K, indicating improved thermal stability at low temperature. Controlled loading (0-300 με) revealed a strain coefficient of delay (SCD) that rises from 0.53 ± 0.02 ppm/με at 300K to 1.05 ± 0.02 ppm/με at 80K. This modest sensitivity confirms that, for temperature sensing, strain is a second-order perturbation above 135K but must be compensated at deeper cryogenic levels. Overall, this work establishes a predictive multiphysics model together with repeatable wired measurements that confirm the suitability of SAW sensors for temperature and strain monitoring in extreme cryogenic environments, while also providing a baseline for future wireless implementations.

25 ENERGY STORAGE↗

DOE OSTI2021

Performance Improvements for the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. Griffin includes a variety of deterministic radiation transport solvers for fixed source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. A code assessment performed in FY-20 identified two significant issues with the transport solvers in Griffin: first, the primary heterogeneous SN (discrete ordinates) transport solver based on continuous finite element methods required significant mesh refinement and higher memory usage compared to solvers based on the method of characteristic for equivalent accuracy. Second, the homogeneous PN (spherical harmonics expansion) transport solver did not adequately support polynomial refinement, which is a feature usually required for problems with spatial homogenization and pronounced streaming, typical in fast or gas-cooled reactor systems. To address the first issue, the development effort focused on the more promising discontinuous finite element method (DFEM)-based SN transport solver in Griffin. The addition of an asynchronous parallel transport sweeper and coarse mesh finite difference (CMFD) acceleration have rendered a superior heterogeneous SN transport capability for multiphysics problems that requires far less computing resources in terms of both CPU time and memory usage. This is demonstrated with typical thermal- and fast-spectrum reactor benchmark problems, including 2D Transient Reactor Test, 3D Advanced Burner Test Reactor (ABTR), and 2D and 3D Empire microreactor. For the second issue, the development effort focused on a new transport solver based on the hybrid finite element PN method (HFEM-PN), equivalent to the variational nodal method, as well as a new diffusion solver based on HFEM-Diffusion. This solver is intended for homogenized domains with multiphysics coupling (i.e., supports mesh displacement, seamless temperature feedback, etc.). Initial calculations with the HFEM-Diffusion implementation show very good parallel efficiency for the residual evaluations with the 2D ABTR benchmark. A future development effort will be centered on further improvements to the CMFD, HFEM-PN, and DFEM diffusion solvers to ensure Griffin meets performance and software quality assurance requirements for advanced reactor design and analysis.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2020

Technical Performance of Refractory Liners for Molten Chloride Salt Thermal Energy Storage Systems

A chloride-based molten-salt system that uses a ternary blend of MgCl2/KCl/NaCl is investigated to provide higher temperature thermal energy storage capability. Despite higher thermal stability, molten chlorides present several unique challenges, including the design of internal refractory-ceramic liners to prevent the corrosion and thermal stress of alloy tank shells. This work discusses issues and potential solutions related to containment of molten chloride salt, specifically the optimization of the refractory material at the molten salt interface (hot face). The down-selected hot face candidate limits permeation of salt through the material and forms a highly stable secondary surface phase in equilibrium with the molten salt. A mortar is created using the corrosion resistant hot face brick. Brick and mortar composite are subjected to mechanical stress/strain analysis, in order to calculate composite material properties and better inform thermomechanical models. The U.S. Department of Energy Generation 3 (DOE Gen3) program seeks to develop higher efficiency CSP plants that can provide cost-competitive, flexible power in the U.S. electric grid. The proposed Gen3 Liquid Pathway CSP plant closely resembles the configuration of current nitrate salt power towers with two-tank storage (Gen2). The differences between Gen2 and Gen3 include the types of compatible materials used in salt storage tank construction. Stainless steel loses strength at Gen3 temperatures, and although nickel superalloys would be capable of withstanding sustained high temperatures, these materials are prohibitively expensive at scale. Uninsulated tank shells also pose a significant risk as common steels are highly susceptible to chemical attack from molten chloride salt. To address these concerns, refractory-ceramic based containment materials are proposed to line the inside of the hot and cold storage tanks. In doing so, stainless or carbon steel shells may be used in construction depending on the level of insulation provided. The composition of the internal liner requires careful consideration to maximize the efficacy of multiple parameters including corrosion resistance, strength at operating temperature, durability, and cost. This is particularly true for the material at the interface with the salt, known as the "hot face", which is responsible for protecting the insulating layers between the tank shell and the hot face brick layer. The molten salt in this system is superheated over 300 °C above its freeze temperature. Therefore, unlike other industrial processes which use refractory-lined vessels, it is not expected that a freeze plane will develop in the hot face. Therefore, the hot face must be designed to withstand chemical corrosion and inhibit permeation of molten salt into the insulating layers. A down selection was performed to identify a hot face candidate best equipped to maintain thermal, mechanical, and chemical integrity when exposed to molten salt over extended periods of time. Long-duration chemical capability experiments were conducted with the down selected hot face refractory fully immersed in molten chloride salt for up to 3000 hours. The average salt penetration does not exceed 100 microns. When extrapolated to 20 and 30 years of continuous exposure, the expected salt penetration depth is approximately 2.0 mm and 2.9 mm, respectively. A magnesium-rich secondary phases develops at the salt/refractory interface. X-ray diffraction identifies the material as forsterite (Mg2SiO4), which is reported to form synthetically in molten chloride salt solutions. These results suggest the selected hot face will adequately inhibit salt permeation. While there is optimism that the hot face brick will inhibit salt permeation, mortar joints are typically the weakest point of a refractory brick liner. From a thermochemical perspective, differing thermal expansion coefficients may result in the mortar and brick to grow independent of each other, creating gaps through which molten salt can penetrate. To address this issue, NREL has developed an in-house mortar composed of the down selected hot face brick that has been shown to be compatible with the salt. Compressive stress/strain analyses have been performed on the brick/ mortar composites to generate stress/strain curves. Modulus of elasticity and Poisson's ratio of the composite may be calculated from the stress/strain curves, in order to provide more representative data to finite element mechanical models for accurate approximation of stress on the tank shell and the amount of thermal expansion expected within the tank liner.

41 EE - Solar Energy Technologies Office (EE-4S)↗

DOE OSTI2024

Griffin: A MOOSE-based reactor physics application for multiphysics simulation of advanced nuclear reactors

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor physics application for multiphysics simulations of advanced reactor designs jointly developed by Idaho National Laboratory and Argonne National Laboratory. This paper summarizes the motivation, significance, architecture, design, and features of Griffin. Griffin offers flexible and extensible features to address the challenges associated with advanced reactor designs. These features range from fundamental particle transport to specific reactor physics tasks. The features cover a wide range including on-the-fly and traditional two-step cross-section generation methods, steady-state and transient transport solvers suitable for both heterogeneous and homogeneous models, high-fidelity depletion where thousands of isotopes can be tracked and low-fidelity depletion characterized by burnup, etc. The most fundamental aspect that sets Griffin apart from other reactor analysis codes is that it is developed based on the MOOSE framework. A modular development approach is strongly enforced, with multiphysics being an essential element considered since the beginning of Griffin’s development. Griffin links various MOOSE physics modules and couples to other MOOSE-based applications and non-MOOSE-based applications for multiphyiscs simulations. Griffin includes three modules: ISOXML for preparing and managing multigroup cross sections, radiation transport for solving the neutron transport equation, and reactor analysis for user-oriented reactor physics analysis functionalities. Griffin uses various finite element methods for spatial discretization, multigroup approximation for energy discretization and discrete ordinates method, spherical harmonics expansion method, and diffusion approximation for streaming direction discretization to solve the neutron transport equation. Griffin’s flexibility is evidenced through Griffin’s various applications to fast reactor, high-temperature reactor, pebble bed reactor, molten salt reactor, and microreactor designs. Griffin development follows the software quality assurance procedure for MOOSE-based applications and with software requirements consistent with the ASME NQA-1 standard. Griffin has been adopted into the reactor analysis system for the U.S. NRC and is in use at U.S. companies, universities and national laboratories.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Time domain probabilistic seismic risk analysis using ground motion prediction equations of Fourier amplitude spectra

Modeling of Fourier amplitude spectra (FAS) of seismic motions has gained much attention in engineering seismology. In the past few years, several ground motion prediction equations (GMPEs) and inter-frequency correlation structure of FAS have been established. Due to many preferable characteristics of FAS, probabilistic seismic hazard/risk analysis is rapidly changing from ergodic, spectrum acceleration Sa(T 0 )-based approach to non-ergodic, site-specific, FAS-based approach. This paper presents time domain intrusive framework for probabilistic seismic risk analysis using GMPE of FAS. Herein, methodology for time domain stochastic ground motion modeling based on GMPEs of FAS is presented in some detail. The simulated uncertain motions are modeled as a random process and represented by polynomial chaos Karhunen-Loève expansion. The random process excitations are further propagated into the uncertain structural system using Galerkin stochastic finite element method (SFEM). Probabilistic evolution of structural response is solved, and such solution is used to develop seismic risk for any damage state. The presented framework is illustrated through seismic risk analysis of a four-story building subjected to possible earthquakes from two strike slip faults. The influences of the epistemic uncertainties in source stress drop Δσ and site attenuation κ0 on seismic risk are investigated. The need for non-ergodic seismic risk analysis with source-specific and site specific characterizations is emphasized.

58 GEOSCIENCES↗

DOE OSTI2024

A mesoscale 3D model of irradiated concrete informed via a 2.5 U-Net semantic segmentation

The concrete biological shield in light-water reactors is exposed to neutron and gamma irradiation, which deteriorates the concrete’s mechanical properties in the long term. To assess the irradiation-induced damage, predictive mechanical models are developed and used in parallel with the characterization of irradiated concrete samples. Realistic 3D simulation domains can drastically improve a model’s prediction. In this work, we utilized x-ray computed tomography (XCT) data of a concrete specimen to reconstruct its 3D microstructure. The XCT data shows low contrast between the concrete’s aggregates and cement paste, resulting in poor image segmentation when using traditional unsupervised techniques. To address this issue, we developed and trained a 2.5D U-Net model on only 24 pre-labeled XCT layers to segment 651 layers of the XCT data. The overall F1-score of the model is approximately 96%. Then, we created a 3D finite element (FE) mesh based on the stack of segmented images. The FE model contains radiation-induced expansion, damage, and creep. The constitutive equations are adapted to each phase (aggregates and cement paste). Here, we simulated the effects of neutron irradiation in the concrete specimen as well as the specimen’s mechanical response to uniaxial compression. Finally, model validation was performed using experimental data on similar concrete specimens in the literature.

2.5D U-Net↗

DOE OSTI2020

Simulation of the Fast Reactor Fuel Assembly Duct-Bowing Reactivity Effect Using Monte Carlo Neutron Transport and Finite Element Analysis

This paper discusses a new method of simulating the fuel assembly duct-bowing reactivity coefficient for EBR-II run 138B. Quantification of the fuel assembly duct-bowing reactivity effect in liquid metal–cooled fast reactors has been a persistent problem since they were first designed and operated. Simulation of the duct-bowing reactivity effect is difficult because the level of detail required to simulate the effect has exceeded most modeling capabilities. The new method outlined in this paper utilizes the finite element analysis code ANSYS to analyze the thermal and structural components. Here, the displacement of the fuel assembly duct due to thermal expansion and mechanical interaction was calculated by ANSYS using recorded EBR-II run 138B temperature and power boundary value data. The displacement values were incorporated into to a Monte Carlo model of EBR-II run 138B and keff was calculated. Multiple Monte Carlo calculations were performed with duct displacement values corresponding to different reactor temperatures. Using the calculated keff values associated with the different duct displacement results allowed calculation of the duct-bowing reactivity coefficient. The duct-bowing reactivity coefficient was calculated to be –14.5 × 10 –4 $/°C/ ± 4.4%.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2021

Topological Assembly of a Deployable Hoberman Flight Ring from DNA

Deployable geometries are finite auxetic structures that preserve their overall shapes during expansion and contraction. The topological behaviors emerge from intricately arranged elements and their connections. Despite the considerable utility of such configurations in nature and in engineering, deployable nanostructures have never been demonstrated. In this paper, a deployable flight ring, a simplified planar structure of Hoberman sphere is shown, using DNA origami. The DNA flight ring consists of topologically assembled six triangles in two layers that can slide against each other, thereby switching between two distinct (open and closed) states. The origami topology is a trefoil knot, and its auxetic reconfiguration results in negative Poisson’s ratios. This work shows the feasibility of deployable nanostructures, providing a versatile platform for topological studies and opening new opportunities for bioengineering.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2022

A New Perspective of Post-Weld Baking Effect on Al-Steel Resistance Spot Weld Properties through Machine Learning and Finite Element Modeling

The root cause of post-weld baking on the mechanical performance of Al-steel dissimilar resistance spot welds (RSWs) has been determined by machine learning (ML) and finite element modeling (FEM) in this study. A deep neural network (DNN) model was constructed to associate the spot weld performance with the joint attributes, stacking materials, and other conditions, using a comprehensive experimental dataset. The DNN model positively identified that the post-weld baking reduces the joint performance, and the extent of degradation depends on the thickness of stacking materials. A three-dimensional finite element (FE) model was then used to investigate the root cause and the mechanism of the baking effect. It revealed that the formation of high thermal stresses during baking, from the mismatch of thermal expansion between steel and Al alloy, causes damage and cracking of the brittle intermetallic compound (IMC) formed at the interface of the weld nugget during welding. This in turn reduces the joint performance by promoting undesirable interfacial fracture when the welds were subjected to externally applied loads. The FEM model further revealed that increase in structural stiffness, because of increase in steel sheet thickness, reduces the thermal stresses at the interface caused by the thermal expansion mismatch and consequently lessens the detrimental effect of post-weld baking on the joint performance.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Convergent laser beam shapes: Unveiling the dynamics of Laser-induced elastic waves in composite materials

Overcoming the low signal-to-noise ratio (SNR) in laser ultrasonic testing of composite materials remains a significant challenge. Current efforts focus on enhancing SNR by inserting more energy into the material through temporal and/or spatial modulation of the laser beam. However, potential SNR improvements through wave convergence and wave energy manipulation have been overlooked. This paper addresses this gap by demonstrating the convergence of different wave types to a designated point and by showing the feasibility of directing absorbed laser energy into a specific wave type through spatial modulation of the laser beam. To achieve this, mathematical expressions for the convergent laser beams are derived. Various laser beam profiles are then introduced to the thermoelastic equations and solved using the finite element method. The sample under investigation is a transversely isotropic unidirectional carbon fiber reinforced plastic, characterized by anisotropic thermal expansion coefficients and thermal conductivities. Results reveal pronounced convergence of the intended wave type at the center due to laser beam shaping. This study showcases the ability to direct absorbed laser energy toward a specific wave type through spatial modulation of the laser beam and highlights the role of material anisotropy in energy focusing.

composite materials↗

DOE OSTI2024

ITER ECH Transmission Line System Design and Status

The electron cyclotron (EC) heating & current drive (H&CD) system on ITER provides plasma heating by generating, transmitting, and launching high-intensity, high-frequency (170 GHz) electromagnetic wave energy steerable across the plasma cross-section. The transmission line (TL) subsystem connects the Matching Optics Unit (MOU) on each of the 24 gyrotrons to the 32 feed points in the four upper launchers and the 24 feed points in the equatorial launcher. Each TL must be able to operate at up to 1.2 MW of input power for up to 1 hour pulse lengths. The TL system contains 50 mm water-cooled corrugated waveguide, 90o miter bends, 140o miter bends, polarizer miter bend pairs, switches, expansion units, pumpouts, DC breaks, MOU-TL adapters, Radio Frequency (RF) loads, and isolation shutter valves. A detailed finite element analysis has been used to verify the thermo-mechanical performance of each component. The microwave performance has been analyzed using a 2-D electromagnetic code combined with a Monte Carlo code. This approach allows the impact of manufacturing and installation tolerances to be assessed and optimized to provide a high probability of achieving the system performance requirements. Prototypes of the waveguide and TL components have been fabricated and tested at high-power. Production contracts are now being issued for fabrication and delivery of the waveguide and components to ITER.

Hanson, Gregory↗

DOE OSTI2020

Ultrasonic waves from radial mode excitation of a piezoelectric disc on the surface of an elastic solid

In this work, we discuss the ultrasonic wave propagation characteristics in an isotropic elastic solid due to the radial mode excitation of a piezoelectric disc actuator bonded to its surface. Finite element simulations using coupled electromechanical modeling is employed to investigate the wave propagation behavior. We find that the radial mode vibrations on the surface of the elastic solid generates all the three types of ultrasonic waves: longitudinal, shear, and surface waves. The waves in the solid are comprised of a central lobe and multiple side lobes based on the frequency of the radial mode excitation. The central lobe is predominantly composed of longitudinal waves and the side lobes are composed of shear waves. While the longitudinal waves have a strong central lobe and weak side lobes that are not fully developed, shear waves consists of fully developed side lobes. In addition, we observe that the longitudinal waves have fewer side lobes inside the solid compared to the shear waves. A semi-analytical approach is presented to explain the above observations. The interface traction boundary condition between the piezoelectric disc and the elastic solid is approximated as a truncated 'Bessel' excitation over the area of the piezoelectric disc in contact with the solid. A Fourier–Bessel series expansion technique is used to investigate the wave propagation behavior from the above traction boundary condition. The results obtained explain the observations from the finite element simulations with regard to the number and distribution of side lobes pertaining to the longitudinal and shear waves generated from the radial modes of the piezoelectric disc. The proposed semi-analytical approach is general and can be applied to any arbitrary axisymmetric excitations on the surface of an elastic solid.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗

DOE OSTI2024

Thermal and electric field driven rf breakdown precursor formation on metal surfaces

The phenomenon of electric breakdown poses serious challenges to the design of devices that operate in high electric field environments. Experimental evidence points toward breakdown events that are accompanied by elevated temperatures and dark current spikes, which is attributed to high-asperity nanostructure formation that enhances the local electric field and triggers a runaway process. However, the exact mechanistic origin of such nanostructures under typical macroscopic operational conditions of electric field and magnetic-field-mediated heating remains poorly understood. In this work, we simulate the evolution of a copper surface under the combined action of the electric fields and elevated temperatures. Using a mesoscale curvature-driven surface evolution model, we show how a copper surface can undergo a type of dynamical instability that naturally leads to the formation of sharp asperities in realistic experimental conditions. Exploring the combined effect of fields and temperature rise, we identify the critical regimes that allow for the formation of breakdown precursors. The results show that thermoelastic stresses, while not essential, can significantly lower the critical electric field required for runaway surface instability, which is consistent with experimental observations that thermal effects can increase breakdown rates. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗

DOE OSTI2024

Operator product expansion for radial lattice quantization of 3D ϕ 4 theory

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3D Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the quantum finite elements method to implement radially quantized critical ϕ 4 theory on simplicial lattices approaching R × S 2 . Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions Δ ε and Δ T as well as ratios of the operator product expansion coefficients f σ σ ε and f σ σ T of the first spin-0 and spin-2 primary operators ε and T of the 3D Ising CFT. Published by the American Physical Society 2024

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

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↗