Peter J. Budden

Plastic loads for 90° thick-walled elbows under combined pressure and bending:

This paper extends plastic load solutions proposed by the authors for 90° thin-walled elbows, to thick-walled elbows, based on three-dimensional finite element analyses using the large geometry change option. For loading, internal pressure, in-plane, and out-of-plane bending, as well as combined pressure and bending, are considered. As no experimental data are available for thick-walled elbows, the proposed solutions are indirectly validated by comparing thin-walled solutions with exiting experimental data.

Plastic limit loads for thick-walled branch junctions

This technical note extends the validity of limit load solutions for thin-walled branch junctions, previously proposed by the current author, to thick-walled cases. It is achieved simply by re-normalizing the thin-wall expressions by the limit loads of thick-walled tubes instead of those of thin-walled tubes. Comparison with finite element results shows overall good agreement.

Plastic limit loads for piping branch junctions under out-of-plane bending

This paper presents approximate closed-form plastic limit load solutions for branch junctions under out-of-plane bending and under combined pressure and out-of-plane bending, based on three-dimensional finite element limit analyses for an elastic-perfectly plastic material. When bending is applied to the branch pipe, the plastic limit loads for out-of-plane bending are shown to be lower than those for in-plane bending. However, for bending to the run pipe, the opposite trend is found. For combined pressure and out-of-plane bending, either the circular interaction or the parabolic interaction rule can be used, depending on the bending location and the branch geometry. Comparison with published experimental plastic limit load data shows that the predictions agree relatively well with the test data.

Limit load solutions of plates with extended surface cracks under combined biaxial forces and cross-thickness bending

Lower bound limit load solutions for extended surface cracks in plates with free ends (pin-loaded) under combined biaxial positive/negative force/stress and positive/negative through-thickness bending are developed based on the lower bound limit load theorem and both Tresca and Mises criteria. An existing Mises limit load solution for extended surface cracks in plates with fixed ends under combined biaxial tension and positive moment is extended to general solutions for combined biaxial positive/negative force/stress and positive/negative through-thickness bending moment. Corresponding reference stress expressions are also derived and presented.

Estimation of the V-Factor for Circumferentially Cracked Pipes Under Combined Thermal and Mechanical Stresses Using a Strain-Based Failure Assessment Diagram

This paper presents finite element solutions for elastic-plastic J for circumferentially cracked pipes under combined mechanical and thermal loads in terms of the V/Vo factor used within a strain-based failure assessment diagram. In this study, 3-dimensional finite element analyses are conducted to calculate the V-factor under combined mechanical and thermal load. It is found that estimation of V/Vo is sensitive to the method used for its evaluation. For larger thermal stresses, currently proposed estimation methods are overly conservative.Copyright

Development of Test Guidance for Single Edge Notch Bend Fracture Toughness Specimens Containing Notches Instead of Fatigue Pre-Cracks

Structural integrity assessment codes such as R6 and BS7910 provide guidance on the assessment of flaws that are assumed to be infinitely sharp. In many cases, such as fatigue cracks, this assumption is appropriate, however it can be pessimistic for flaws that do not have sharp tips such as lack of fusion, porosity or mechanical damage. Several methods have been proposed in the literature to quantify the additional margins that may be present for non-sharp defects compared to the margins that would be calculated if the defect were assumed to be a sharp crack. A common feature of these methods is the need to understand how the effective toughness, characterised using the J-integral for a notch, varies with notch acuity. No comprehensive guidance currently exists for obtaining J experimentally from specimens containing notches, hence the typical approach is to use equations intended for pre-cracked specimens to calculate J for notched specimens.This paper presents a comprehensive set of test guidance for calculating J from Single Edge Notch Bend (SENB) fracture toughness specimens containing notches instead of fatigue pre-cracks. This has been achieved using 3D Finite Element Analyses to quantify the accuracy of formulae intended for pre-cracked specimens in fracture toughness testing standards ASTM E1820, BS7448-1 and ESIS P2-92 when applied to specimens containing notches. The paper quantifies the accuracy of these equations for notched SENB specimens and identifies the conditions under which the equations can lead to inaccurate measurement of J for notched specimens.Copyright

Leakage Rates Through Complex Crack Paths Using an ODE Method

The geometry of a crack is a fundamental consideration when calculating leakage rates for Leak-before-Break assessments. Carrying out fluid mechanics calculations does not give any additional benefit if there is not enough information on the crack shape. To address this issue, work is being carried out under the R6 development programme to derive a model that couples fluid mechanics and solid mechanics. The aim is to combine complex crack shapes with relatively simple fluid mechanics models and compare with experimental data. Then, the model can be extended to examine various stress distributions, and give indications as to how conservative are the current models. The model is a development of the one presented in a previous PVP paper (Reference 1), and a special case of isothermal gas flow is considered, where the equations reduce to an Ordinary Differential Equation (ODE). This is solved using a Runge-Kutta integration scheme in MATHCAD. A test case is presented based on the crack geometries considered in experiments, and upon comparison with numerical results; it is clear that choosing the correct crack shape is crucial in obtaining accurate predictions of leak rate. The assumed crack openings are rectangular, diamond or elliptical. In addition to this, weld residual stress profiles are postulated, based on experience of welds in piping components. Comparing the numerical simulations with the simplified DAFTCAT model indicates that the more precise ODE method can reduce conservatism in calculation of leak rates.Copyright

A Comparison of Notch Failure Assessment Diagram Methods for Assessing the Fracture Resistance of Structures Containing Non-Sharp Defects

This paper analyses and compares a range of Notch Failure Assessment Diagram (NFAD) methods for assessing the fracture resistance of structures and components that contain defects with non-sharp tips. As micromechanistic failure criteria for predicting fracture from notch tips have developed, several forms of NFADs have been proposed over the last 20 years with notable developments having been made in the last 10 years. This paper quantifies the differences between four different types of NFAD approach and uses test results from test specimens containing notches of varying acuities to evaluate each approach. The results highlight significant differences in fracture predictions between the different NFAD approaches due to differences in the definition of the NFAD axes, the failure loci, the assumed failure mechanism and the corresponding micromechanistic failure criteria employed by each method.Copyright

Comparison of Probabilistic Fracture Mechanics Evaluations for a Through-Wall Cracked Pipe Under the STYLE Project

One of the large scale mock-up experiments (Mock-Up 2) of the recent STYLE European project was a ductile fracture test carried out on a pipe containing a circumferential through-wall crack located in a repair weld and loaded under four-point bending. This experiment has been used as a basis for undertaking a comparative probabilistic fracture mechanics benchmark study by a number of the organisations participating in STYLE.In launching the benchmark study, the pipe and crack dimensions were specified as fixed values, applied bending stress (moment) was considered as a deterministic variable and three values were taken for weld residual stress (assuming constant membrane values). Tensile and fracture toughness material properties were considered to be random variables and these were specified by log-normal distribution parameter values. In undertaking their evaluations, the participants were asked to evaluate J-integral versus applied bending moment, probability of crack growth initiation versus applied bending moment, probability of net-section collapse versus applied bending moment and carry out various sensitivity analyses.This paper focuses mainly on the contribution to the benchmark study primarily based on the R6 methodology and includes examples of contributions provided using other methods.Copyright

Benchmark Evaluations to Compare R6 Calculations to European Engineering Assessment and Leak-Before-Break Methods Based on STYLE Mock-Up Experiments

As part of the recent STYLE European project, three large scale mock-up experiments (Mock-up 1, Mock-up 2 and Mock-up 3) were performed. The Mock-ups were representative of nuclear power plant locations containing welds or cladding and contained an initial defect, either through-wall or surface breaking, and were loaded under four point bending conditions.Benchmarks based on each of these experiments were launched to investigate current Engineering Assessment Methods (EAMs) and Leak-before-Break (LbB) procedures used throughout Europe and how the application of these methods compare to each other and to the experimental data. Parameters that were specified for the benchmark participants to evaluate included crack opening displacement (COD), critical crack size, limit load, and load vs various amounts of ductile tearing.This paper presents and compares the results of the calculations performed by the participants in the benchmark. It focuses on the AMEC calculations using R6 and draws conclusions regarding its relative conservatism compared with each of the other methods and through comparison with the results of the Mock-up experiments.Copyright