A comprehensive software framework has been developed for probabilistic fatigue crack growth (FCG) analysis of safety-critical metallic components. The framework has been implemented in a computer code called DARWIN® (Design Assessment of Reliability With INspection). DARWIN determines the probability of fracture for a component as a function of operating cycles, with and without inspection, by integrating finite element (FE) geometries, stress, and temperature analysis results; fracture mechanics models; material anomaly data; probability of anomaly detection; and uncertain inspection schedules with a user-friendly graphical user interface (GUI). The framework can accommodate anomalies occurring anywhere in the volume of the component (such as material voids or inclusions) or anomalies occurring only on the surface of the component (such as manufacturing or maintenance damage).
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Themes: Probabilistic Aspects of Fatigue Crack Growth and Fracture: Frameworks, Tools, and Applications
PROLOCA 7.1 A PROBABILISTIC FRAMEWORK FOR FATIGUE ANALYSIS OF ALUMINUM AND WELD STEEL STRUCTURES [Keynote]
PROLOCA 7.1 is a probabilistic fracture mechanics (PFM) cods developed for the analysis of damage initiation and growth up to the point of structural failure. The PROLOCA (PRObability of Loss Of Coolant Accident) code was formulated to address nuclear piping and was based on past probabilistic analyses of fatigue in aircraft. These methods were integrated into a code, PROLOCA 2.0 originally developed under NRC contract [1], which was developed for nuclear piping analyses. Since that time, PROLOCA was continually improved under contract to an international team of regulators and operators. In this paper we examine some of the key differences between PROLOCA and other frameworks for fatigue analyses. Examples of the application of PROLOCA to dissimilar metal welds and aircraft damage tolerance are given to demonstrate the extremely low risk of failure with and without inspections and leak detection
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PROBABILISTIC STRUCTURAL INTEGRITY ASSESSMENT OF WELDED JOINTS [Keynote]
The fatigue assessment of welded joints requires several input data, which can be subdivided into three categories: geometry, material and loading. The number of input data depends essentially on the complexity of the models employed and on the level of accuracy of the analysis. It is common practice to use safety factors in design to account for the scatter of the input parameters. Nevertheless, overly-conservative factors lead often to unrealistic estimations of fatigue life. This work presents a fracture mechanics-based model for the structural integrity assessment of welded joints under constant amplitude fatigue loading, in which the local geometry at the weld toe and the fatigue crack growth properties are considered statistically distributed. The approach is validated against a large number of experimental data.
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PROBABILISTIC CRITICAL FLAW SIZE ASSESSMENTS IN THE CIRCUMFERENTIAL WELDS OF LAYERED PRESSURE VESSELS [Keynote]
The National Aeronautics and Space Administration (NASA) operates approximately 300 aging, carbon steel, layered pressure vessels (LPVs) that were designed and manufactured prior to ASME Boiler and Pressure Vessel (B&PV) code requirements. Fitness-for-service assessments and traditional evaluations of these non-code vessels is a challenge due to unique uncertainties that are not present in code vessels, such as missing construction records and the use of proprietary materials in construction. Furthermore, many of the steels used in these non-code vessels are at a risk of cleavage fracture at low temperatures within the operating temperature ranges of the NASA sites where these vessels are installed. Additionally, the stress state in critical regions of the LPVs, such as the longitudinal seam welds and circumferential welds, is uncertain due to weld residual stresses (WRS), geometric discontinuities, and stress concentrations in weld connections. In order to guide non-destructive evaluation (NDE) and assessment of the circumferential welds and account for uncertainties in these non-code LPVs, probabilistic critical initial flaw size (CIFS) and critical crack size (CCS) analyses were performed for eleven locations of interest within the head-to-shell and shell-to-shell circumferential welds of three demonstration LPVs.
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INTERMITTENCY IN FATIGUE CRACK GROWTH AND FATIGUE STRIATIONS
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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TOWARDS HIGH THROUGHPUT FATIGUE CHARACTERIZATION
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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A LOADING HISTORY AGNOSTIC FREE ENERGY BASED FRACTURE CRITERION
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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XLPR: A PROBABILISTIC CODE FOR FATIGUE AND PWSCC ANALYSIS OF WELD IN NUCLEAR POWER PLANT
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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FAVPRO: NRC’S 21ST CENTURY REACTOR PRESSURE VESSEL PROBABILISTIC FRACTURE ANALYSIS TOOL
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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ADAPTIVE MULTIPLE IMPORTANCE SAMPLING FOR STRUCTURAL RISK ASSESSMENT [Keynote]
The USAF Airworthiness Bulletin Risk Identification and Acceptance for Airworthiness Determination defines airworthiness in terms of the probability of aircraft loss per flight hour1 with one important component being the aircraft structure. The probability-of-failure of an aircraft component is challenging to compute due to its small size, typically 10-7 or less. As a result, simplified fracture mechanics models are usually used with a small number of random variables. However, these simplifications may lead to an inaccurate probability-of-failure estimate. To address this issue, an adaptive multiple importance sample method was developed that can compute very low probabilities with significant efficiency. This allows one to consider more realistic fracture mechanics models and a larger number of random variables than has been previously possible. The method is adaptive in that it will adjust to the varying relative importance of the random variables for different applications. Convergence is ensured such that the coefficient of variation is below a user-defined threshold. Results to date show efficiency gains of 5 or 6 orders of magnitude over standard Monte Carlo sampling for typical problems of interest. The methodology will be outlined and demonstrated using aircraft example problems.
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