G. Graham Chell

Probabilistic methods for Design Assessment of Reliability with Inspection (DARWIN)

Conventional rotor life prediction methodologies are based on nominal conditions that do not account for material and manufacturing anomalies that can degrade the structural integrity of high energy rotors. In order to account for these anomalies, an industry committee recommended adoption of a probabilistic damage tolerance approach to supplement the current safe life methodology. The DARWIN computer program computes the probability-of-fracture as a function of flight cycles, considering random defect occurrence and location, random inspection schedules, and several other random variables. This study focuses on the probabilistic fatigue analysis methodology developed and implemented in DARWIN Version 3.2. The computational efficiency and accuracy of this computer program is illustrated for several realistic rotor models provided by aircraft engine manufacturers. It is shown that the life approximation function (LAF) and importance sampling (IS) methods significantly reduce computation time (nearly two orders of magnitude) compared to the Monte Carlo method.

A Probabilistically-Based Damage Tolerance Analysis Computer Program for Hard Alpha Anomalies in Titanium Rotors

A probabilistically-based damage tolerance analysis computer program for engine rotors has been developed under Federal Aviation Administration (FAA) funding to augment the traditional safe-life approach. The computer program, in its current form, is designed to quantify the risk of rotor failure due to fatigue cracks initiated at hard alpha anomalies in titanium. The software, DARWIN (Design Assessment of Reliability With Inspection), integrates a graphical user interface, finite element stress analysis results, fracture-mechanics-based life assessment for low-cycle fatigue, material anomaly data, probability of anomaly detection, and inspection schedules to determine the probability-of-fracture of a rotor disk as a function of operating cycles with and without inspections. The program also indicates the relative likelihood of failure of the disk regions. Work is underway to enhance the software to handle anomalies in cast/wrought and powder nickel disks, and manufacturing and maintenance-induced surface anomalies in all disk materials. *Funded under FAA Grant 95-G-04

A practical methodology for elastic-plastic fatigue crack growth

A practical methodology is being developed to characterize elastic-plastic fatigue crack growth (EPFCG) behavior. The methodology will be implemented in engineering software for crack growth analysis and life prediction of advanced reusable aerospace propulsion systems. The correlating parameter upon which the methodology is based is the range of the J-integral, ΔJ. Existing J solutions are summarized, and robust methods for developing new J solutions under various loading configurations are introduced and validated. Some practical crack growth algorithms required to translate a J calculation into a quantitative prediction of EPFCG life are highlighted. Crack closure plays a significant role in the engineering characterization of EPFCG rates, and simple algorithms to estimate closure stresses are described. Other algorithms address the tearing-fatigue interaction near final instability and the estimation of required material properties. Early results from experimental verification tests are reported.

Application of Advanced Probabilistic Fracture Mechanics to Life Evaluation of Turbine Rotor Blade Attachments

This paper describes the application of an advanced probabilistic fracture mechanics computational algorithm with inspection simulation to the probabilistic life assessment of a turbine blade attachment, sometimes referred to as a steeple or fir tree. The life of the steeple is limited by high cycle fatigue. The methodology utilized combines structural finite element analysis, stochastic fatigue crack growth, and crack inspection and repair. The resulting information provides the engineer with an assessment of the probability of failure of the structure as a function of operating time and the effect of the inspection procedure. This information can form the basis of inspection planning and retirement-for-cause decisions.

Application of Reference Stress and Probabilistic Methodologies to Assessing Creep Crack Growth

This paper describes the application of the reference stress approach and probabilistic methods to the determination of creep crack growth based on the time-dependent fracture mechanics parameter, C(t), where t is time. This parameter is defined as the simple sum of a transient component, C(t → 0), which is applicable to short times and a steady-state component, C*. The reference stress approach enables a relatively simple expression for C* to be derived. A scheme is developed that optimizes the fit of the reference stress approach to published computed solutions for J p , the fully plastic component of the J-integral. The optimization scheme involves the derivation of an engineering parameter, V. An expression for C* is readily derived from an expression for J p by invoking the creep-plastic analogy. Values of V are derived from the analysis of 189 sets of computed solutions. These values are statistically analyzed and used to derive a distribution function describing the uncertainty in V. This function is used together with distribution functions for other random variables (such as the creep strain rate coefficient and crack growth law coefficient) in example probabilistic analyses of flaws in welded internally pressurized pipes operating in the creep regime. Probability sensitivity factors are generated as part of the probabilistic analyses.

EfficientJ-Based Failure Assessment Diagrams for Engineering Critical Assessments of Circumferentially Cracked Pipes Subjected to Axial Force, Pressure, and Bending

Engineering critical assessments (ECAs) of cracked pipes increasingly involve situations of high strains (e.g., reeling and ratcheting fatigue), multiple loads (combined bending, axial forces, and internal pressure), and multi-axial stressing (due to pressure). In this paper, some of the implications of these loading conditions on ECAs are investigated by generating BS 7910 Level 3C Failure Assessment Diagrams (FADs) from the results of a large matrix of finite element analysis (FEA) J computations for circumferentially cracked pipes. The Level 3C (J-based) FADs (which provide the most accurate FAD approach to ECAs) are compared with the corresponding and more widely employed (but less accurate) Level 2B (material dependent) FADs in order to assess the accuracy of the latter. Use of FEA J solutions in a Level 3C FAD ensures that the effects of material behavior, load type, crack type, crack geometry, and pipe geometry are accurately captured whereas a Level 2B FAD only attempts to accurately capture the effects of material stress-strain behavior. It is demonstrated that under some circumstances a Level 2B assessment will result in non-conservative results compared to the corresponding Level 3C assessment. The current comparison between Levels 3C and 2B addresses the mechanics involved in these approaches and does not take into account the possible differing treatments of material property uncertainties on ECAs within the two approaches. Based on the current results, an efficient J formulation is described that facilitates the practical implementation of a J-based ECA. The novel approach used is based on determining material dependent shift factors that transform Level 3C FADs derived from the fully plastic components of J solutions into Level 3C FADs that represent J behaviors in the linear elastic and fully plastic regimes, and the transition region in-between. This new J formulation treats combined axial forces, pressure, and bending when applied proportionally or non-proportionally and forms the basis of the monotonic and cyclic crack tip driving forces employed in the program FlawPRO. This program performs comprehensive conventional and high strain J-based ECAs that involve reeling, arbitrary strain cycling, ratcheting fatigue, and ductile tearing that are equivalent to a Level 3C FAD approach.Copyright

Full-Scale Validation of a Flaw Assessment Methodology for Welded and Reeled Pipes

Pre-existing weld flaws in pipes subjected to high strains resulting from reeling installation may extend by combined ductile tearing and low-cycle fatigue (LCF). The increase in flaw sizes from this process will reduce the flaw tolerances of reeled pipes subjected to subsequent service high-cycle fatigue (HCF) exposure compared to the tolerances determined ignoring the reeling process. This paper describes a flaw assessment methodology that includes the synergy between ductile tearing and LCF flaw growth due to reeling. The methodology utilizes the Level 3C (J-based) failure assessment diagram (FAD) approach of BS 7910 to explicitly account for the effects of flaw and pipe geometries, as well as material stress-strain behavior, on the crack tip driving force, J. The Level 3C FADs used herein are derived from and validated against the results of a matrix of J-based finite element analyses (FEA) of pipes. They have been incorporated into the computer program FlawPRO™ developed for the offshore industry that enables a comprehensive engineering critical assessment (ECA) for flawed reeled pipes to be performed. The methodology incorporated into FlawPRO is validated against the results of full-scale tests on reeled pipes containing weld flaws subjected to a variety of reeling scenarios. The validation includes investigations into the effects on predicted flaw growth of using J-resistance curves measured on SENB and SENT specimens and of assuming strain versus load controlled reeling. The best agreement with the flaw extensions measured in the full-scale tests is obtained when an SENT J-R curve is used together with assuming reeling occurs under strain controlled conditions. It is concluded that the reeling methodology in FlawPRO is successfully validated by the full-scale test results.Copyright

J-Based Failure Assessment Diagrams for Axially Cracked Pipes Under Pressure

This paper describes the results of performing a comprehensive matrix of J-based finite element analyses (FEA) of external and internal surface axial cracks in pressurized pipes. The computations were performed for a range of stress-strain behaviors and pipe sizes typical of gas and liquid transmission pipelines. The J results for the deepest and surface points on flaws are presented in the form of failure assessment curves (FACs) plotted on failure assessment diagrams (FADs). The FACs are consistent with the Level 3C and material specific Level 2B FADs used in BS 7910. Yield pressures derived from the FEA results are used to evaluate the FAD parameter Lr (= pressure/yield pressure) for the Level 3C FACs. This choice of yield pressures facilitates the collapse of the Level 3C FACs in the fully plastic region of the FAD onto material specific curves relatively independent of geometric features. The Level 3C FACs generated from the FEA J results show a strong dependence on crack size in the elastic-plastic part of the FADs, particularly for long flaws. In these cases, the Level 3C FACs fall inside the corresponding material specific FACs derived according to Level 2B procedures. The reason for this is thought related to the development of local and global yield mechanisms and the incorporation in Level 3C FACs of geometry dependencies which are ignored in Level 2B. It is concluded that the Level 2B procedures may not always be conservative for long deep axial flaws in pressurized pipes when used in conjunction with accurate (e.g. determined from FEA) global yield pressures. Similarly, account has to be taken of the transition from local to global yielding in J estimation schemes that are formulated as the sum of elastic and plastic components if these are not to be non-conservative in the transition from elastic to fully plastic behavior. A method is suggested for incorporating the local to global yielding transition in J estimation schemes that also reduces the geometry dependence of Level 3C FADs to facilitate their representation by approximately material specific (Level 2B-type) FADs applicable to axially flawed pipelines.Copyright

Evaluation of Welding Flaws Under Ratcheting Fatigue

Hydrocarbon-carrying lines can be subjected to cyclic loads superimposed on monotonically increasing mean strains well into the plastic domain, resulting in tearing and tearing fatigue of initial welding flaws. This combined demand is referred to here as ratcheting fatigue. Examples of these loads are frost-heave in pipelines and thermal cycling of flowlines. This paper presents the experimental verification of a fracture mechanics model of monotonic and cyclic crack extension under ratcheting fatigue loads and its calibration to small-scale tests. The model is an extension of one currently used to predict tearing and tear-fatigue due to reeling. Crack driving forces (J-solutions) under load- and displacement-control conditions were derived and used with the model to predict test results. A total of 24 single-edge notched bend (SEN-B) specimens, taken from a welded riser, were tested for crack extension under combined monotonic and cyclic loads. Comparisons of predicted to measured fatigue crack-growth rates, and alternatively cyclic J-R curves, provide quantitative and qualitative validation of the model. However, calibration to large–scale tests are needed before the model can be used for design. ExxonMobil has already completed the first set of large-scale pipe tests under ratcheting fatigue loading, including internal pressure.Copyright

Nonlinear Harmonic Monitoring of Gouged Dents in Pipeline Specimens Under Cyclic Loading

The only in-line inspection technology commercially available for quantitative evaluation of gouged dents is the geometry pig which cannot discriminate between gouged and smooth dents and has no sensitivity to re-rounded dents. Southwest Research Institute® (SwRI®), has been funded by the US Pipeline and Hazardous Materials Safety Administration (PHMSA) and the Gas Research Institute (GRI) through the Pipeline Research Council International (PRCI), to determine the capability of the nonlinear harmonic (NLH) method to characterize the severity of gouged dents, including those that have been re-rounded by internal pressure. This paper describes the NLH method and presents a summary of results from previous work involving burst tests of gouged dents in 24” pipe as a precursor to the current work that involves experiments with four pressure chambers made from 12-inch line pipe under cyclic pressure changes. In each case, internal scanner hardware, driven from outside the pipe, deployed NLH probes against the pipe inner surface, the gouges being on the outer surface. Analysis of the mapped NLH signals on the inner pipe surface revealed residual strain patterns in the pipe and the strain anomalies produced by gouging. The strain anomalies clearly indicated the presence of the gouges on the outside surface, even when they had re-rounded. The signal maps also indicated the length and width of the gouges whereas the signal strength indicated the residual depth. Data are presented showing that the NLH method is capable of ranking the severity of pipeline gouged dents and their propensity for failure under cyclic loading.© 2006 ASME