Statistical Analysis of Coiled Tubing Fatigue Data

Abstract

Abstract To study the influence of surface defects on the fatigue life of coiled tubing (CT), an extensive database has been developed. Samples of CT were tested by cycling at a fixed bending radius in a fatigue testing fixture at constant internal pressure until failure occurs. Data have been generated using samples with a wide range of defect geometries. The results have been used to develop an analytical model that explicitly considers the measured geometry along with the influence of high and low internal pressures. This model is based on a damage parameter that correlates defect severity with fatigue life reduction. Unfortunately, scatter plagues fatigue data and variability in the small defect dimensions can exacerbate this scatter. When CT fatigue data are plotted in terms of a damage parameter versus life, average behavior is usually revealed in terms of "bands" of data with varying widths. Correlations based on curves through the middle of those bands can be considered estimates of "mean" life. Alternatively, such life estimates can be considered to exhibit "50%" survival. In other words, half the samples should fail before their predicted life and the other half should survive longer. To account for scatter and assure that a higher percentage of cases exceed the predicted life, users typically retire tubing when estimated fatigue lives reach a value corresponding to about 80% of their estimated life. However, statistically based techniques are available to make life predictions of higher survival percentages with specific confidence levels. Effectively, estimated life curves based on these approaches pass through the bottom of the scatter band exhibited by fatigue test results, rather than through the middle of the band, such that a higher percentage of samples can be expected to exceed their estimated life. This leads to a safe design limit, extracted from available data that can be used with a specific degree of confidence. This paper describes a procedure to estimate the life of CT with a surface defect. The predicted life should be exceeded by a particular percentage of all cases in the field, and this assertion can be stated with a specific confidence. One-sided lower tolerance interval or bound curves are constructed for different CT materials, since users are primarily concerned with the minimum safe fatigue life value. Example design curves are presented to make statistically valid life predictions that should be exceeded by 90, 95 or 99% of the samples, with 90, 95 and 99% confidence levels, respectively. The data used to define these predictions show that defects are more damaging in low pressure situations than they are in high pressure cases, in terms of percentage life reduction. Introduction Over the past several years, an ongoing research effort [1] has focused on the generation of an extensive database of CT fatigue results. These data have been generated with the intent of assessing the influence of surface defects of known geometries on CT under cyclic bending. To assess the influence of "defects" on a particular grade of CT, a large number of tests are required. Not only is it necessary to assess a wide range of defect geometries, but for one particular defect geometry the other parameters that influence fatigue must also be examined. These include tubing diameter, wall thickness, bending radius, and internal pressure.