No abstract

Deterministic Fracture Mechanics (DFM) assessments of structural components (e.g. pressure vessels and piping used in the nuclear industry) containing defects can usually be carried out using the R6 procedure. The aim of such an assessment is to demonstrate that there are sufficient safety margins on the applied loads, defect size and fracture toughness for the safe continual operation of the component. To ensure a conservative assessment is made, a lower-bound fracture toughness, and upper-bound defect sizes and applied loads are used. In some cases, this approach will be too conservative and will provide insufficient safety margins. Probabilistic Fracture Mechanics (PFM) allow a way forward in such cases by allowing for the inherent scatter in material properties, defect size and applied loads explicitly. Basic Monte Carlo Methods (MCM) allow an estimate of the probability of failure to be calculated by carrying out a large number of fracture mechanics assessments, each using a random sample of the different random variables (loads, defect size, fracture toughness etc). The probability of failure is obtained by counting the proportion of simulations which lead to assessment points that lie outside the R6 failure assessment curve. This approach can give good results for probabilities greater than 10−5. However, for smaller probabilities, the calculation may be inefficient and a very large number of assessments may be necessary to obtain an accurate result, which may be prohibitive. Engineering Reliability Methods (ERM), such as the First Order Reliability method (FORM) and the Second Order Reliability Method (SORM), can be used to estimate the probability of failure in such cases, but these methods can be difficult to implement, do not always give the correct result, and are not always robust enough for general use. Advanced Monte Carlo Methods (AMCM) combine the two approaches to provide an accurate and efficient calculation of probability of failure in all cases. These methods aim to carry out Importance Sampling so that only assessment points that lie close to or outside the failure assessment curve are calculated. Two methods are described in this paper: (1) orthogonal sampling, and (2) spherical sampling. The power behind these methods is demonstrated by carrying out calculations of probability of failure for semi-elliptical, surface breaking, circumferential cracks in the inside of a pressure vessel. The results are compared with the results of Basic Monte Carlo and Engineering Reliability calculations. The calculations use the R6 assessment procedure.

The prediction of residual stresses in ferritic welds using finite element techniques requires materials properties to describe the thermal, tensile, cyclic and phase transformation behaviour that the material undergoes during welding and also during creep as the effect of post weld heat treatment is also of interest. Ferritic steels will transform at a temperature above about 850°C to austenite. As the steel is cooled, a further phase transformation in the structure occurs. The precise structure formed depends on the detailed chemical make-up of the steel and on the rate at which it is cooled. On slow cooling from above 850°C a pearlite-ferrite microstructure is formed. On more rapid cooling, other microstructures, particularly bainite at intermediate cooling rates and martensite at the highest cooling rates are formed. Predicting the phase on cooling requires a Continuous Cooling Transformation diagram that is suitable for welding thermal cycles and reflects the time spent above the austenitisation threshold which influences the austenitic grain size formed and subsequently the phase of material on cooling. Material properties for a SA508 Grade 3 steel and a low carbon SD3 filler metal have been generated and fitted to constitutive models that are available in the finite element codes ABAQUS and SYSWELD. The choice of hardening model and its associated parameters have been evaluated on the basis of the observed cyclic behaviour in materials testing. Validation of these models has then been carried out by finite element simulations of welded mock-ups which have been measured using neutron diffraction. These include an autogenous weld beam and groove weld specimens containing up to eight weld passes. The rationale for using these simple specimens has been to: • Validate the capability of the model to predict the correct phase transformation behaviour and resulting stresses. • Account for the different behaviour of the parent and filler material. • To develop the capability for representing the material cyclic behaviour. On the basis of these simulations recommendations have been made on the material models (and their parameters) that may be used for the finite element simulation of the welding process.