Coiled Tubing Life Prediction
Authors: Avakov V.A. , Foster J.C. , Smith E.J. 
Published: October 2008

ABSTRACT
The paper addresses a recently developed mathematical model for coiled tubing fatigue life prediction. It is shown that the coiled tubing stress-strain condition is unique and is primarily characterized by plane elastic stress state induced by internal pressure and superimposed over extremely high plastic alternating bending strains. The model wm developed using full-scale tubing fatigue tests. In these tests three strength level of coiled tubing material were tested at discrete pressure levels in ranges from O to 7500 psi using two types of gripper blocks: standard semicircle and universal V-shaped. It is revealed that the steady tangential stress component, induced by pressure, affects fatigue life in a nonlinear manner. Conventional failure theories do not work to describe and predict coiled tubing life. Instead, an algorithm based on equivalent strain as a function of principal strains is proposed. Constants of the function are defined in a way to achieve maximum correlation between model predicted life and actual life. Correlation coefficient became as high as 0.973. Fatigue strength of coiled tubing material is expressed in terms of low-cycle S-N (strain versus life) fatigue line. This line is defined by reference point and slope. Fatigue life scatter is defined by lognormal distribution and its variation coefficient (standard deviation in terms of mean) is 0.11. That is, the test results are in close agreement with the model prediction. Cumulative damage is expressed using Miner's rule and equivalent strain. Nonlinear equivalent strain respectively leads towards nonlinear cumulative damage expression.

PROBLEM STATEMENT
Design in fatigue is a relatively simple problem when a detail is subjected to a uniaxial stress state with steady stress cycle components. For high-cycle fatigue of ductile metals under multiaxial stress state, the Tresca criteria (maximum shear stress failure theory) and von Mises criteria (distortion energy failure theory) are the most popular. But in low-cycle fatigue, these simple theories are unable to correlate the experimental results. For instance, G.Z. Libertine [1] notes that the von Mises criterion cannot allow for the effect of hydrostatic pressure. According to M.W. Brown and K.J. Miller [2], this situation has led to many criteria being suggested for correlating low-cycle, multiaxial fatigue, but no single criterion has been shown to have universal applicability. For example, M. Liddle and K.J. Miller [3] have tested tubes of 1% Cr-Mo-V steel in combined tension and torsion, for lives between 200 and 5000 cycles. Tests were controlled between constant strain limits, The authors were unable to correlate the results satisfactorily with a single criterion. As an alternative, they presented a series of constant life contours on a graph of maximum plastic shear strain range against the total tensile strain range, which is normal to the maximum shear plane. D. L. McDiarmid [4] ran a comprehensive series of tests on thin-walled tubes of an aluminum alloy subjected to repeated internal pressurization and axial load.