Symposium 14: Probabilistic Aspects of Fatigue Crack Growth and Fracture: Frameworks, Tools, and Applications

To analyze the integrity of piping components in nuclear power plants (NPPs), the U.S. Nuclear Regulatory Commission (NRC) Office of Nuclear Regulatory Research and the Electric Power Research Institute jointly developed a probabilistic fracture mechanics computer code. The Extremely Low Probability of Rupture (xLPR) code simulates crack initiation and growth from fatigue and stress corrosion cracking (SCC) degradation mechanisms and other aspects of piping component structural integrity. This presentation provides an overview of the NRC staff’s applications of the xLPR code since its public release in 2020 to assist in risk-informed regulatory evaluations of leak-before-break (LBB) analyses for pressurized water reactor piping systems with dissimilar metal welds susceptible to SCC. Potential use of the xLPR code to estimate loss of coolant accident (LOCA) frequencies and to interface with artificial intelligence machine learning (AI/ML) models are also discussed.
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The US NRC and EPRI have developed a probabilistic fracture mechanics code through a memorandum of understanding. The code is called xLPR (extremely low probability of rupture) and can be used to evaluate a variety of structural integrity problems dealing with fatigue and primary water stress corrosion cracking (PWSCC) degradation. The code version 2 is now officially released and has been used by both NRC, EPRI and their contractors to perform a series of studies.
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Planned and unplanned transients in the operation of a nuclear reactor place stresses on the reactor pressure vessel (RPV) that affect its structural integrity. FAVPRO: Fracture Analysis of Vessels - Probabilistic, is a modern, parallel, object-oriented software tool that can provide high-confidence probabilistic assessments of reactor pressure vessel integrity for any population of flaws and any number of transients, with the goal of risk-informing technical and regulatory decision making. FAVPRO is the successor to the NRC’s FAVOR code with higher solution speeds and new features like automated testing and documentation. The updated tool also includes new embrittlement models and other improvements to align with new fracture mechanics standards.
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Aero-engine turbine disks are safety-relevant components which are operated under high thermal and mechanical stress conditions. The aim of this work is to present part of a fracture mechanics-based probabilistic assessment procedure under development which aims at calculating the critical rotational speed of the turbine disk based on the numerical-analytical solutions and regulations for the failure probability. In particular, the rim-peeling failure mode is considered as case study. A semi-circular surface crack is modelled at the most stressed region at the diaphragm of a turbine disk. In order to design a lab representative specimen, beside the crack driving force, expressed in terms of J-integral, also the constraint to plastic deformation e.g., stress triaxiality, at the crack-tip must be similar for the same crack in the specimen and in the disk. The analytical solutions to calculate the crack driving force for the lab representative specimen are used for the Monte Carlo simulations, the result of which has been assessed in the form of a Failure Assessment Diagram (FAD). The results of the probabilistic structural integrity assessment show good agreement between Monte Carlo simulations and certification values for the disk in terms of expected failure mode and value of the critical speed.
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The fatigue crack growth rate exhibits apparent self-similarity as it grows as a power of the stress intensity factor (the Paris–Erdogan law). We have studied the fatigue crack growth in two aluminum alloys (Al-1050 and Al-5005) using optical methods and found that the crack tip advances in an intermittent way, characterized by a power-law distribution of crack tip jump sizes. The exponent of the distribution is around two – higher than what is usually observed in avalanching systems – and there is a cutoff that increases with increasing crack velocity. If the generally accepted one-to-one correspondence between the crack tip advancement per cycle and the fatigue striation lines on the fracture surface holds, one should expect a similar distribution for the striation line spacings. We have performed post-mortem fractography using scanning electron microscopy and, by automatically tracking the striation spacings, we indeed see a similar power-law distribution with a cutoff and an exponent around two.
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While the advance of experimental and computer modeling techniques has continued to push mechanistic understanding and predictive modeling capabilities forward, the capability to generate fatigue data has been almost stagnant. Fatigue engineering and research efforts often operate in a data starved modality (considering the highly stochastic nature of fatigue failures). This impedes attempts to effectively use modern machine and statistical learning tools for fatigue performance prediction, both within standard prognosis frameworks, and integrated computational materials engineering (ICME) frameworks.
This presentation will report on our exploration for opportunities to improve the throughput of fatigue testing machines utilizing the expanded design space offered by technological advancement, e.g., computer aided drawing and manufacturing, data acquisition and computer modeling, and robotic automation. Following our review, we will present two concepts for uniaxial high throughput fatigue testing, with the goal of improving fatigue throughput by ~100x while conforming to popular test standards. Our progress towards this goal, and ultimately the prospects for achieving it, will be presented by sharing the results of multiple design-build-test iterations.
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Rather than energy release rate, the proposed framework starts from the energy function itself. Instead of strain energy density, it considers the change in volume-specific free energy density from mechanical deformation. The free energy function must capture strain induced orthotropy, known to be critical for polymers but also important for metals plasticity. To capture strain induced orthotropy, free energy is defined in terms of principal strains and by separating deformation into dilatational and distortional contributions. The separation does not utilize deviatoric strain. Rather, it leverages a new distortional strain definition and the new concept of orthotropic dilataion, enabling clean separation to large strain.

The proposed framework clarifies how a generalized Maxwell model spring-dashpot mechanical analog cleanly interperets the First and Second Laws of Thermodynamics. A transition state theory based nonlinear viscoelastic (NLVE) model is mated to the Maxwell model. Nonlinear Maxwell springs feature an instability in their constitutive law, providing a viscoelastic failure criterion. Embedding the instability into the springs in an NLVE model provides a failure criterion that accommodates complex temperature histories, rate dependence, and self generated heat from cyclic loading.
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