Reliability of welded structures - the next step
TWI Bulletin, November/December 2001
John Wintle is Consultant Engineer for structural integrity and is a leader in the development of reliability engineering at TWI.
TWI has recognised the increasing application of statistics and probability by industry to assess the reliability of welded structures. Design, manufacturing and plant integrity management decisions are moving away from lower bound deterministic approaches and towards decisions based on the balance of probabilities and risk. As John Wintle reports, TWI is supporting this trend by meeting industry's requirement for new statistical methods and applications to structural integrity problems.
The development of new methods and applications has been driven by the requirements of TWI's Industrial Members, both individually and collectively. As part of its service to members, TWI's programme of generic core research has been developing reliability based technology to meet their needs. In addition, TWI has been undertaking reliability research within Group Sponsored Projects and for individual members on a single client basis, and is also participating actively in collaborative research supported by the European Commission.
Reliability of welded structures has been a central theme of the 1998-2000 Core Research Programme (CRP). Specific topics included were:
- An introduction to risk based inspection
- Probability of fatigue crack initiation and growth
- Frequency and size distribution of welding defects
- Appraisal of statistical inspection strategies and inspection updating
- Probabilistic modelling of HAZ hydrogen cracks in C-Mn steels
Other reliability related topics addressed in group, single client and collaborative projects have included:
- Statistical fracture toughness estimation
- Reliability of pressure vessels subject to low temperature transients
- Probability of stress corrosion cracks
- Statistical extrapolation of thickness measurements for pipelines
- Best practice for risk based inspection
Within the confines of this article, it is possible to describe only a few of these projects. For more details, the reader is referred to the relevant TWI member reports and publications.
Probabilistic fatigue
This project was driven by the need to derive acceptance criteria for fabrication defects in welds of steel catenary risers. These are the big pipes that transmit oil from the sea bed terminal to the surface production and storage vessel. They need to be of high integrity. Any leakage of oil would damage the sea environment and production. The welds are loaded by the changing motions and currents of the sea and are susceptible to fatigue.
Riser pipes are welded one to another on a barge at sea. For economic reasons, there is a need to optimise the level of manufacturing quality in the welding (acceptable defect size) against a specified probability of achieving a given design life without leakage failure. The probability of achieving the design life must take account of the variability of the fatigue properties of the material and the loading spectrum during service due to wave and current motions, and depends on the initial size of welding defect allowable.
Within a fatigue crack growth analysis where there is variable amplitude loading, the distribution of stress ranges is important, both for overcoming the threshold required for crack growth and with respect to the increment of growth. Small stress ranges early in life may be below the threshold and produce less growth than later in life when the crack is larger. Dealing with the threshold in combination with variable amplitude loading is difficult when the stress spectrum is not a standard distribution.
TWI has solved this problem and developed a numerical procedure for dealing with the threshold effect under non-standard variable amplitude loading. This has been incorporated within a commercial reliability analysis software system for determining the probability of failure. The threshold stress intensity was input as a known value, and distributions for fatigue crack growth parameters were derived from test data.
The model was applied to steel catenary risers to determine the probability of an initial defect growing to a final height of half wall thickness in a 100 year design life. Typical results for three initial aspect ratios are shown in Fig.1. Taking a bounding approach (a/c = 0.2), the results show that an initial defect of height 3mm would have an annual probability of 10 -5 of failing the pipe at the end of a 100 year design life.
Fig.1. Variation of failure probability with initial flaw height for 100 year design life (flaw height at failure assumed to be 50% wall thickness)
Sensitivity studies have assessed the effect of the threshold stress intensity on the probability of failure. Figure 2 shows that the effect of the threshold can be very significant and reduce the probability by several orders of magnitude. As a whole, the analysis suggests that much larger sizes of fabrication defects could be accepted with tolerable risk than would have been the case from a deterministic analysis.
Fig.2. Effect of crack growth threshold ( ΔK th) on failure probability
Statistics in inspection
TWI has recently assessed the condition of corroding pipework on a North Sea oil platform to determine when replacement might be necessary. Large parts of the pipework were inaccessible. It was therefore necessary to estimate the minimum thickness of the inaccessible parts by extrapolating the distribution of a sample of thickness measurements made using an ultrasonic mapping technique over the accessible area.
Taken as a whole, the raw thickness data did not fit any common distribution with an acceptable degree of correlation. Therefore, the possibility of fitting an extreme value distribution to the minima of the thicknesses measured within sub-divided areas was investigated. The accessible area of the pipe was divided into a rectangular grid, and the minimum thickness of the measurements within each of these areas determined.
The grid size was chosen such that the thickness minima of adjacent areas were weakly correlated. It was found that a grid area of 0.03m 2 resulted in a satisfactory correlation, and from this an extreme value distribution function was fitted, Fig.3. Once the extreme value distribution function of minimum thicknesses was determined for the accessible region, the distribution over the inaccessible areas of the pipework was established by extrapolation.
Fig.3. Extreme value probability plot of minimum thickness data
The extrapolation assumes that the standard deviation σ of thickness minima within the accessible and inaccessible areas is the same. However, the mean of thickness minima within the inaccessible area is decreased according to µ A= µ a - σ log e M, where M = A/a, A is the inaccessible area, and a is the area of each grid square. Hence the minimum thickness in the inaccessible area could be estimated with the required probability. This example shows how extreme value statistics provides a powerful tool for extrapolating thickness measurements made over accessible areas of a component to estimate the thickness in uninspectable parts.
In Core Research work, TWI has investigated the benefits and limitations of sample inspections for the detection of flaws. Sample inspection is useful in detecting the presence or absence of multiple flaws when the objective is to detect a general change in the condition during service or determine the general quality of fabrication. If 'm' flaws are randomly distributed, the amount of sample inspection can be determined in order that one or more flaws are detected with a prescribed level of probability, Fig.4.
Fig.4. Probability of detecting at least one of 'm' randomly distributed flaws in a sample inspection of proportion 'p' of the total weld
Baysian probability theory has been applied to evaluate the benefit of inspection measurements to increase confidence held in prior estimates of the corrosion rate. Figure 5 shows the results of some example calculations. It can be seen that there was a 50% prior confidence ( eg based on published data) of a corrosion rate between 0 and 10mpy. When this is apparently confirmed by thickness measurements from an inspection with 70% reliability, the confidence that the corrosion rate actually lies between 0 and 10mpy increases to 81%! Conversely, the chances that the corrosion rate is actually higher, lying in the ranges of 10 to 20 and 20 to 40mpy, decrease from 30 and 20% to 15 and 5% respectively.
Fig.5. Confidence that the corrosion rate is within given ranges before and after inspection
Probability of welding flaws
A method for determining the probability of heat affected zone (HAZ) hydrogen cracking from welding C-Mn steels has been developed in TWI core research. Hydrogen cracking depends on whether the hardness of the HAZ produced by welding exceeds the critical hardness for cracking of the material. In practice, it is not possible to predict exact values for the produced and critical hardnesses, and they can only be described by statistical distributions derived from experimental test data.
Heat input, thickness and preheat control the cooling rate, which, with composition (carbon equivalent), can be used to predict the HAZ hardness. Comparisons of such predictions with experimental hardness data have shown that the HAZ hardness produced is a normal distribution with mean corresponding to the predicted hardness and a standard distribution of 28HV.
The critical hardness for cracking is a function of the hydrogen level. Using welding trials data generated at TWI, a distribution of the critical hardness was determined for a number of standard ranges of hydrogen level. For example, range B (10-15ml hydrogen per 100g deposited weld metal) produced a normal distribution with a mean hardness of 382HV and a standard deviation of 34HV.
From this data, TWI has developed a model to determine the probability of HAZ hydrogen cracking. The probability of cracking was determined from the overlap between the produced hardness and critical hardness distributions, using commercially available software, Fig.6. The model has been applied to bounding conditions for the avoidance of hydrogen cracking within codes and standards and shown to predict probabilities close to 1 in 200. It also predicts probabilities of between 0.15 and 0.5 for conditions where cracking actually occurred.
Fig.6. Distribution of critical hardness for HAZ hydrogen cracking with hardness distribution produced by welding
The model is useful both as a predictive and retrospective tool for fabrication and inspection. In fabrication, it enables the tolerance of the welding procedure to variations in heat input and preheat to be determined. For inspection, it enables the welds with the highest probability of HAZ hydrogen cracking to be identified.
TWI has also carried out a general review of methods and data for determining frequency and size distribution of welding flaws in steel fabrications. As well as being a means to assess welding quality, such data can also be used to determine the probability of failure. Analysis of defect data from non-destructive testing of welded fabrications has its limitations, and there is increasing interest in statistically modelling the flaw formation process and in systems based on expert opinion.
Risk based inspection
The trend within the petrochemical and other industries towards the planning of plant inspection on the basis of the risk of failure led TWI to provide an introduction to the principles of RBI within a Members research report. In parallel, the UK Health and Safety Executive commissioned TWI to prepare a report of best practice for the application of RBI to pressure systems and hazardous installations. These reports deal with the process and management of RBI, and provide an audit tool and case studies.
Risk based inspection involves the application of information obtained from a risk analysis of the likelihood and consequences of failure to determine the scope, frequency and nature of future inspection necessary to prevent danger. The process evaluates the information that is available about an item of equipment, together with evidence of favourable operating experience and potential deterioration and hazards. A suitable inspection plan is then developed to address the risks at the appropriate time.
In addition to examining the principles and best practices for risk based inspection, TWI has also made a significant product investment in developing a software tool to assist its application. The software Riskwise TM, and its derivatives Pipewise TM and Tankwise TM, provide a means for users to identify and prioritise the risks from different items of equipment with a view to determining inspection intervals. Riskwise TM is on trial in the petrochemical and power industries in Europe, the Middle East and USA.
Future directions
The demand from designers and operators for probabilistic solutions to structural integrity problems is likely to continue. Areas for development will include limit load design, which is already being proposed for subsea pipelines and non-critical applications. There will need to be greater emphasis on statistical modelling of loading and the environmental factors affecting structural integrity. The impact of human factors within plant design and operation and the role of the manufacturing supply chain influencing equipment reliability are new areas of research.
Methods for determining the probability of fatigue and fracture have been developed, but more emphasis is needed on the quality of the materials and flaw data needed to support such assessments. Flaw frequency and size distributions in welded structures will continue to be of interest, and will require a greater degree of modelling of the fundamental factors of welding including the human element.
In order to determine the value of inspection, there will continue to be a requirement to understand and quantify the factors that can influence the probability of detection and sizing error, and to obtain probability of detection data for selected NDT techniques under different conditions. The interaction with human factors is also key where decisions are made by the judgement of an individual inspector.
Within these and other fields, TWI is likely to continue work on the reliability of welded structures for the foreseeable future.
