On the Interaction of Non-Coplanar Embedded Crack With Surface Crack in 3D Using FE and Multi-Level Sub-Structuring

The interaction and coalescence of multiple cracks may significantly affect the designed lives of aging pressure vessel structures. Knowledge of the growth behavior of interacting cracks is still limited. In this paper, a novel sub-modeling meshing algorithm is used in three-dimensional linear finite element analysis to investigate the interaction between two identical, non-coplanar, semi-elliptical cracks. One of these cracks is modeled as a surface crack while the other is modeled as an embedded crack under a weld toe. Both interacting cracks are assumed to be in an infinite plate subjected to a remote tension loading condition. The energy release rates (G) and the Stress Intensity Factors (SIF’s) for these cracks are calculated along the interacting crack-front. And, a parametric study involving the variation of the relative horizontal separation distance between the two interacting cracks is carried out for a specific crack depth to plate thickness ratio, a/t, of 0.2. The crack shape aspect ratio, a/c, is also varied in this study within a range that extend between 1.0 and 0.33. An empirical formula is derived that relates the effects of the relative positions of these cracks to their SIFs.

The Application of Reliability-Based Design Factors in Stress Corrosion Cracking Evaluations

First-order reliability methodology (FORM) is used to develop reliability-based design factors for deterministic analyses of stress corrosion cracking. The basic elements of FORM as applied to structural reliability problems are reviewed and then employed specifically to stress corrosion cracking evaluations. Failure due to stress corrosion cracking is defined as crack initiation followed by crack growth to a critical depth. The stress corrosion cracking process is thus represented in terms of a crack initiation time model and a crack growth rate model, with the crack growth rate integrated from the initiation time to the time at which the crack grows to its critical depth. Both models are described by log-normal statistical distribution functions. A procedure is developed to evaluate design factors that are applied to the mean values of the crack initiation time and the crack growth rate for specified temperature and stress conditions. The design factors, which depend on the standard deviations of the statistical distributions, are related to a target reliability, which is inversely related to an acceptable probability of failure. The design factors are not fixed, but are evaluated on a case-to-case basis for each application. The use of these design factors in a deterministic analysis assures that the target reliability will be attained and the corresponding acceptable probability of failure will not be exceeded. An example problem illustrates use of this procedure.

The Impact of an Improved Flaw Model on a Pressurized Thermal Shock Evaluation

The current regulations for pressurized thermal shock (PTS) were derived from computational models that were developed in the early-mid 1980s. The computational models utilized in the 1980s conservatively postulated that all fabrication flaws in reactor pressure vessels (RPVs) were inner-surface breaking flaws. It was recognized at that time that flaw-related data had the greatest level of uncertainty of the inputs required for the probabilistic-based PTS evaluations. To reduce this uncertainty, the United States Nuclear Regulatory Commission (USNRC) has in the past few years supported research at Pacific Northwest National Laboratory (PNNL) to perform extensive nondestructive and destructive examination of actual RPV materials. Such measurements have been used to characterize the number, size, and location of flaws in various types of welds and the base metal used to fabricate RPVs. The USNRC initiated a comprehensive project in 1999 to re-evaluate the current PTS regulations. The objective of the PTS Re-evaluation program has been to incorporate advancements and refinements in relevant technologies (associated with the physics of PTS events) that have been developed since the current regulations were derived. There have been significant improvements in the computational models for thermal hydraulics, probabilistic risk assessment (PRA), human reliability analysis (HRA), materials embrittlement effects on fracture toughness, and fracture mechanics methodology. However, the single largest advancement has been the development of a technical basis for the characterization of fabrication-induced flaws. The USNRC PTS-Revaluation program is ongoing and is expected to be completed in 2002. As part of the PTS Re-evaluation program, the updated risk-informed computational methodology as implemented into the FAVOR (Fracture Analysis of Vessels: Oak Ridge) computer code, including the improved PNNL flaw characterization, was recently applied to a domestic commercial pressurized water reactor (PWR). The objective of this paper is to apply the same updated computational methodology to the same PWR, except utilizing the 1980s flaw model, to isolate the impact of the improved PNNL flaw characterization on the PTS analysis results. For this particular PWR, the improved PNNL flaw characterization significantly reduced the frequency of RPV failure, i.e., by between one and two orders of magnitude.

Alternative RTNDT for Linde 80 Weld Materials

The ASME Boiler and Pressure Vessel Code provides fracture toughness curves of ferritic pressure vessel steels that are indexed by a reference temperature for nil ductility transition (RTNDT). The ASME Code also prescribes how to determine RTNDT. The B&W Owners Group has reactor pressure vessels that were fabricated by Babcock & Wilcox using Linde 80 flux. These vessels have welds called Linde 80 welds. The RTNDT values of the Linde 80 welds are of great interest to the B&W Owners Group. These RTNDT values are used in compliance of the NRC regulations regarding the PTS screening criteria and plant pressure-temperature limits for operation of nuclear power plants. A generic RTNDT value for the Linde 80 welds as a group was established by the NRC, using an average of more than 70 RTNDT values. Emergence of the Master Curve method enabled the industry to revisit the validity issue surrounding RTNDT determination methods. T0 indicates that the dropweight test based TNDT is a better index than Charpy transition temperature based index, at least for the RTNDT of unirradiated Linde 80 welds. An alternative generic RTNDT is presented in this paper using the T0 data obtained by fracture toughness tests in the brittle-to-ductile transition temperature range, in accordance with the ASTM E1921 standard.

Load History Effect on Plastic Collapse in a Single-Edge Notched SUS316 Subjected to a Combined Tension and Bending

This paper is evaluates the effects of load history on the plastic collapse load of stainless steel members with a single-edge notch. It considers, both the tension force due to an internal pressure and the bending moment caused by an earthquake, considered as load cases for a structure. Experimental equipment was specially developed to cope with the indeterminate problems in fracture mechanics. In this experiment, the stress state of a plastic collapse point was assessed using a membrane stress and axial displacement chart as well as a bending stress and deflection angle chart, which is well known as the ligament method. As a result, we successfully developed a new method for assessing plastic collapse under a complex load. We found that a different load history affects the formation of the plastic region and the collapse point position. The effects of load history on the plastic collapse load were not very big.

Fatigue Fracture Behavior of Steel Pipes With a Pre-Crack

The behaviour of fatigue crack propagation of mild steel pipes, each consisting of an inclined semi-elliptical crack, subjected to axial loading was investigated both experimentally and theoretically. The inclined angle of the crack with respect to the axis of loading varied between 0° and 90°. In the present investigation, the gowth of the fatigue crack was monitored using the AC potential drop technique. The Von Mises yield criterion was applied to define the core region, instead of assuming a core region with a constant distance r from the crack lip. The two commonly employed fracture criteria, i.e., the maximum tensile stress and the minimum strain energy density criteria, were modified by adopting Von Mises elasto-plastic boundary. The results obtained using the innproved fracture criteria are, in most cases, in better agreement with test results as compared with those obtained using the commonly employed fracture criteria.

A Contribution to Proof the Component Integrity Taking Into Account the Corrosion-Assisted Crack Growth

The proof of the component integrity is fundamental for a safe and reliable operation of Nuclear Power Plants (NPP). The concept of the Material Testing Institute (MPA) for integrity assessment is based on fracture mechanic analysis which results in detailed regulations for nondestructive examination. This approach has to account for the main damage mechanisms as fatigue and corrosion. This paper focuses on the influence of corrosion-assisted crack growth which strongly depends on corrosion and environmental conditions (e.g. coolant purity). Up to stress intensity of approximately 60 MPa√m for ferritic low-alloy steels in high-purity water (acc. to specification) under constant load conditions the analysis can be based on a crack extension of max. 70 μm for each load cycle. Related to a test duration of 1000 hours this is equivalent to a formally calculated crack growth rate (CGR) of ≤2 · 10 −8 mm/s. For austenitic stainless steels more complex dependences on material, environmental and mechanical parameters exist. Particularly, for stabilized austenitic steels the crack growth rate data base is relatively weak. Under unfavourable environmental conditions in single cases crack growth rates up 6 mm/a have been measured. Based on experimental results an arithmetic mean value of 0.95 mm/a and a median value of 0.6 mm/a have been determined. A further improvement of data base is desirable.

Influence Coefficients to Calculate Stress Intensity Factors for an Elliptical Crack in a Plate

Crack assessment in engineering structures relies first on accurate evaluation of the stress intensity factors. In recent years, a large work has been conducted in France by the Atomic Energy Commission to develop influence coefficients for surface cracks in pipes. However, the problem of embedded cracks in plates (and pipes) which is also of practical importance has not received so much attention. Presently, solutions for elliptical cracks are available either in infinite solid with a polynomial distribution of normal loading or in plate, but restricted to constant or linearly varying tension. This paper presents the work conducted at EDF R&D to obtain influence coefficients for plates containing an elliptical crack with a wide range of the parameters: relative size (2a/t ratio), shape (a/c ratio) and crack eccentricity (2e/t ratio where e is the distance from the center of the ellipse to the plate mid plane). These coefficients were developed through extensive 3D finite element calculations: 200 geometrical configurations were modeled, each containing from 18000 to 26000 nodes. The limiting case of the tunnel crack (a/c = 0) was also analyzed with 2D finite element calculation (50 geometrical configurations). The accuracy of the results was checked by comparison with analytical solutions for infinite solids and, when possible, with solutions for finite-thickness plates (generally loaded in constant tension). These solutions will be introduced in the RSE-M Code that provides rules and requirements for in-service inspection of French PWR components.

Numerical Modeling of Fracture Toughness in RPV Steel Containing Segregated Zones

Segregation zones, called ghost lines, may be present near the inner side of PWR vessel issued from plain ingots of A508 class 3 steel. They are enriched in alloying elements and impurities and may have a significant influence on mechanical properties, in particular on fracture toughness. Toughness values of a compact tension specimen containing segregation zones have been evaluated using a bimaterial model with a 3 D finite element simulation. Two fracture criteria have been tested and the results compared with the French database of RPV steel toughness values. The first model assumes that fracture occurs when the maximum tensile stress ahead of the crack tip reaches a critical value over a critical distance. The second model, which is statistical, is based on Beremin’s theory. The results obtained with both models are compared. It is shown that the critical fracture stress model reproduces with a good accuracy the lower bound of toughness values which were determined in RPV steel. The Beremin model gives an estimate of the scatter in fracture toughness measurements. This model takes also into account a size effect related to the ghost line density present along the crack front.

Detailed Assessment of Fatigue Life: A Critical Review

For the construction, design and operation of technical components and systems the appropriate technical codes and standards provide detailed stress analysis procedures, material data and a design philosophy which guarantees a reliable behaviour of the structural components throughout the specified lifetime. Especially for cyclic stress evaluation the different codes and standards provide different fatigue analyses procedures to be performed considering the various (specified or measured) loading histories (of mechanical and thermal origin) and geometric complexities of the components. In order to fully understand the background of the fatigue analysis included in the codes and standards as well as of the fatigue design curves used as a limiting criteria (to determine the fatigue life usage factor), it is important to understand the history and the methodologies which are available for the design engineers. In the paper the different fatigue analysis procedures in the technical codes and standards (e.g. ASME-III, KAT 3201.2, prEN 13445-18) are discussed in detail. The most important parameters influencing the fatigue analysis, like plastification factor Ke, the correction factors with respect to mean stress, to surface finish, to tempeature, to the environment and to unwelded and welded components are verified on the basis of experimental results. Thus safety margins relevant for the assessment of fatigue life are shown and compared with the safety factors implemented in the different technical codes and standards.