Colin Madew

Continuing Development of a Simplified Method to Account for the Interaction of Primary and Secondary Stresses

The R6 defect assessment procedure, used commonly in the UK nuclear industry to assess the significance of defects in structures, uses the Failure Assessment Diagram to evaluate limiting parameters whilst accounting for the effects of plasticity. The interaction of primary and secondary stress is accounted for within R6 through the use of the ρ, or an equivalent V, term. ‘Look-up’ tables are provided in order to evaluate parameters required to derive the ρ or V terms. In some circumstances, the current methodology has been shown to be excessively conservative and the use of the ‘look-up’ tables is somewhat complex and cumbersome anyway. Previous work has shown that an Alternative Method derived from the Time-Dependent Failure Assessment Diagram approach of the R5 high temperature procedure could potentially be considered. This has since been further modified and termed the Simplified Method. This Simplified Method has the benefit of being less conservative than the current R6 method and of not requiring ρ (or V) factors, and hence not requiring the use of the ‘Look-up’ tables. This paper presents the Simplified Method through comparisons within an extended range of Finite Element Analyses upon both an axial and circumferentially cracked pipe and a centre cracked plate. In addition to the use of the Simplified Method, further work is presented in order to include both out of plane primary and secondary stresses when determining the combined reference stress. A full range of crack opening and out of plane forces, as well as a full range of thermally induced secondary stresses, have been included to provide a broad basis upon which to compare the different methods investigated. Through comparing the full range of cases, some of the assumptions made within the R6 procedure have been reassessed. This has led to an average characteristic length, a, being defined to account for differences in loading type and in and out of plane ratios. However, within this paper further positive evidence for the use of the Simplified Method has been demonstrated.Copyright

Extension of the Simplified Method for the Interaction of Primary and Secondary Stresses

The R6 defect assessment procedure, used commonly in the UK nuclear industry to assess the significance of defects in structures, uses the Failure Assessment Diagram to evaluate limiting parameters whilst accounting for the effects of plasticity. The interaction of primary and secondary stress is accounted for within R6 through the use of the ρ, or an equivalent V, term. Previous work has developed an alternate method to that in R6 and has been termed the “Simplified Method”. This Simplified Method has the benefit of being less conservative than the current R6 method and of not requiring ρ (or V factors, and hence not requiring the use of the ‘Look-up’ tables. This paper builds upon the work presented previously and considers the reduction in displacement controlled secondary stress through primary stress induced plasticity by proposing a new function, g(), which is based upon an Option 2 failure assessment curve. Comparisons are also made upon a range of cracked geometries using both the current R6 Method and the derived Simplified Method including g(). The comparisons are made upon both a thermally induced bending stress and a weld residual stresses obtained from a detailed weld simulation. The range of cases provided is to further validate the method and provide strong evidence not only for different geometries but also for realistic residual stress fields. The application of the Simplified Method to the thermally induced bending stress field show improved estimated of KJ over the R6 Method and provide added value to both the Simplified Method and g(). Application to the weld residual stress field shows potential non-conservatism (of both the R6 and Simplified Method) and potential reasons are discussed.© 2009 ASME

An Analysis of the Roles of J and Q in the Assessment of Fracture for Quasi-Statically Extending Cracks in Residual Stress Fields

It is well known that the crack tip stress and strain fields for a crack in an elastic-plastic body depend on the crack tip contour integral J, the Q-stress, and the elastic-plastic properties of the material. This dependence is the fundamental basis of conventional two-parameter J-Q fracture mechanics assessments. It is normally assumed that the crack is created in an unstressed body, or else is inserted concurrently into an existing non-zero stress and strain field such that the crack tip fields build up monotonically and dominate at the crack tip. In such cases, the crack may be regarded as stationary and the J-Q procedure is valid provided that care is taken to calculate J and Q properly when initial stress and/or strains exist. When a crack is introduced progressively and quasi-statically into a component, the location of the crack tip will move along a distinct path. If the component contains residual stress and this is of a significant size along the crack tip path, a re-distribution of the residual stress will occur as the crack tip moves. Specifically, the stress field ahead of the crack tip will unload as the crack tip advances so that non-proportional loading will occur behind the advancing crack tip. In elastic-plastic materials, a wake of plasticity will usually be deposited in the material behind the moving or growing crack tip. Similar effects will also occur when a stationary crack extends due to critical or sub-critical processes. The presence of a plastic wake alters the stress and strain fields at the crack tip so that they do not generally match the fields of a stationary crack. Moreover, J and Q may not describe the stress and strain fields, invalidating the use of the fracture mechanics procedure for such cases. In this paper, a Finite Element analysis of J and Q is carried out for a quasi-statically extending crack inserted in a strip of elastic-plastic material containing an initial residual stress field. Care is taken to model the crack tip conditions appropriately as the crack extends and J is determined using the JEDI post-processing program which can allow for the effects of initial plastic strains and non-proportional loading. An assessment is made of the crack tip field and the likelihood of further extension or fracture is made using local approach models. The analysis considers both cleavage and ductile fracture. The extent of the relationship between J and Q and the crack tip fields is established and the validity of the J-Q procedure to such cases is discussed. The paper considers whether the procedure is conservative when J and Q are determined from an analysis of a stationary crack of the same size inserted into the same initial field.Copyright

Further Studies to Evaluate Crack Opening Areas for Through-Wall Cracks in the Vicinity of Welded Attachments

A paper was presented at the 2009 ASME PVP Conference on evaluating, by finite element techniques, crack opening area (COA) and stress intensity factor, KI , values for through-wall cracks located in the region where an attachment is welded to a plate geometry. Both membrane and bend loads were considered. In addition, based on the stress profile in the un-cracked complex geometry over the region where the cracks would be introduced, COA and KI values were evaluated for the same crack sizes located in a simple plate geometry. This enabled information to be established on the conservatism, or otherwise, of using simple plate solutions to evaluate COA and KI for cracks in the complex geometry. The present paper reports on further studies that have been undertaken to investigate the effect on the previous COA and KI results of considering (i) large displacement theory which may be important for combined membrane and bend loading, and (ii) contact elements in the finite element models since in the previous studies, the mesh was allowed to “overlap on itself” when crack closure was evident due to compressive stresses during bend loading.Copyright

“First Estimate” Plastic Collapse Solutions for Flat and Torispherical Ended Pressure Vessels Subjected to Extensive Corrosion Wall Thinning

Plants in safety-critical industries comprise of a number of different components, including various sizes of pressure vessels, and their integrity is often paramount to the safe running of the plant. In many cases these vessels can contain highly corrosive liquids, which, over time can lead to a degree of thinning in the vessel walls. With corrosion wall-thinning come a number of issues, including a reduced plastic collapse load of the vessel and possible fatigue initiation from corrosion pits. Since failure of these vessels could lead to catastrophic failure and the escape of highly corrosive material, the assessment and maintenance of these vessels is of high importance.Current Fitness for Service Codes and Standards provide guidance on the assessment of cylinders and pipes with localized wall thinning and general corrosion, with respect to plastic collapse. This guidance, however, is not currently applicable to components with geometric discontinuities (the pressure vessel base-wall junction).This paper follows a preceding paper presented at the ASME PVP Conference 2010 which derived “First Estimate” plastic collapse solutions for flat-based, corroded, pressure vessels. These solutions have been expanded through further finite element studies to accommodate the estimation of plastic collapse in tori-spherical headed pressure vessels subjected to extensive corrosion wall-thinning. Results from this study are presented in graphical form to enable a quick and efficient first estimate of the effect of wall thinning on the collapse pressure to be attained.© 2012 ASME

R6 V, Vg and RSE-M Estimates of Experimental Failure for Combined Loading

Engineering components which are considered in safety case assessments contain either real or hypothetical crack-like defects that experience combinations of primary and secondary stresses during service. A number of assessment procedures contain simplified numerical approaches to detail the interaction of these stresses under in-service or fault conditions including the R6 procedure used in the UK and the RSE-M Appendix 5.4 (RSE-M) assessment code adopted in France.The R6 procedure and RSE-M approaches are shown to be relatively similar for cases which do not contain secondary loading but differ when treating secondary stresses. It is generally accepted that the R6 procedure in terms of ρ or V is conservative compared to finite element analyses and plant experience; which has driven the development of a new formalism of the R6 V factor, Vg. This new formalism is seen to be more aligned to the RSE-M approach but differs in some cases.The aim of this paper is twofold: 1) to demonstrate the main divergence between the procedures, and 2) to provide experimental comparison between the R6 V, the newly formalised Vg, and the RSE-M approaches under test cases within literature that contain combined primary and secondary loading.© 2012 ASME

R6 V and Proposed Vg Plasticity Correction Terms for Combined Loading Applied to Experiments

Engineering components may contain small crack-like defects that experience combinations of primary and secondary stresses during service. A new formalism of the R6 V factor, Vg, has been introduced over previous years to quantify the influence of plasticity interaction under combined primary and secondary loading based upon such defects within a large range of finite element analyses.The aim of this paper is provide experimental validation to the Vg approach such that it satisfies validation requirements for potential inclusion to R6. Estimates of failure from implementing Vg, as well as the R6 V approach, to experiments available from literature are presented. These experiments include plate tests subjected to weld residual stresses, cylinders subjected to thermal shock conditions and pre-compressed laboratory specimens. This range of specimens covers those considered in validation of the existing approaches in R6 and some more recent experiments.When applying the existing R6 V and the Vg plasticity interaction parameters the accuracy of the methods diverges with increasing plasticity; with the Vg approach providing the more accurate result at intermediate and high levels of Lr (i.e. beyond Lr = 0.7). However, since both the existing R6 and the Vg plasticity interaction parameters are conservative the experiments provide useful validation to both methods.© 2012 ASME

Provisional Results for an Experimental Investigation Into the Effect of Combined Primary and Secondary Stresses When Considering the Approaches of R6 and the Recently Developed g() Method

Engineering components, particularly those containing weldments, may contain small crack-like defects that experience combinations of primary and secondary stresses during service. A new function, g(), has been introduced previously to quantify the influence of plasticity interaction under combined primary and secondary loading on a components crack driving force. This paper compares g() with experiments performed to consider g() over a range of plasticity values. This experimental programme was performed on scalloped notch three point bend specimens that had experienced a pre-compression to induce a residual stress field before being tested to failure over a range of temperatures (−150, −90 and −50 °C). Samples which did not undergo a pre-compression were also tested to provide an estimate of the materials fracture toughness at the temperature in question. Through analysing the experimental results it is clear that further material characterisation is required. This paper, therefore, only presents the initial results at this stage. However, as a pessimistic interpretation of the results has been made, and since both the existing R6 and the g() plasticity interaction parameters are acceptable, the experiments provide useful validation to both methods.Copyright

The Evaluation of Crack Opening Areas for Through-Wall Cracks in the Vicinity of Pipe Branch Connections

A number of papers have been presented at previous ASME PVP conferences, which have evaluated the crack opening areas (COA) and stress intensity factors (K), using elastic finite element analysis techniques, for through-wall cracks in a region where an attachment is welded to a plate. This was a simplified geometry aimed at representing a more complicated geometry of a pipe-branch connection. A number of analyses were considered and conclusions made on the estimation of COA and K using simple handbook solutions. More recently the analyses included the application of nonlinear geometry and the addition of crack face contact when applying bending loads. This paper is a continuation of these previous studies, assessing through-wall cracks in a more realistic pipe-branch connection geometry. The calculated COA and K values for the more complex geometry are compared to values from pipe models with no branch connections, in a similar manner to that applied in the previous work on the simplified plate geometry. Judgments are made on the conservatism, or otherwise, of the estimated COA and K for the more complex geometry solutions compared to the simple geometry solutions.Copyright

Assessment of Lower Regions of Pressure Vessels Subjected to Corrosion Wall Thinning

Pressure vessels are common components of plant currently in operation within the nuclear industry and elsewhere. Their assessment and maintenance is of paramount importance to the integrity and safe working of the plant. Often these pressure vessels contain highly corrosive substances, which over time, cause deterioration in the integrity of the vessel. Current codes and standards such as BS7910, API579 and FITNET provide guidance on the assessment of cylinders and pipes with localised and general corrosion, but to date, no such guidance is available for complete vessels, where the corrosion occurs in the lower region of the vessel, e.g. where the base of a vessel is connected to the vessel wall. This paper investigates the resistance to plastic collapse, from internal pressure loading, of flat based cylindrical pressure vessels, where the base and wall thicknesses are considerably different due to corrosion damage. A ‘First Estimate’ or conservative lower bound collapse pressure solution for such vessels is described. The solution has been derived using axi-symmetric finite element models with varying degrees of general corrosion thinning.Copyright