Cumulative Fatigue Damage of Drill Pipe in Dog-Legs
Authors: Hansford J.E. , Lubinski A. 
Published: December 2007

Abstract
Rotating drill pipe passing through dog-legs suffers fatigue damage due to cyclic bending stresses. Curves of the cumulative fatigue damage incurred in either steel or aluminum drill pipe going through such dog-legs are presented. These curves provide means for properly planning the rate of angle build-up in directionally drilled wells and allow discarding of drill pipe which has been fatigue-damaged in dog-legs.

Introduction
Drill pipe which is subjected to bending as it rotates, experiences a cyclically varying bending stress. If this bending stress is sufficiently large, the drill pipe is fatigue-damaged by each revolution, and ages as fatigue damage accumulates. Drill pipe can be bent intentionally, as in the case of directionally drilled holes, or unintentionally due to undesired changes in hole direction caused by variations in formation properties, weight on bit, etc. These changes in hole direction, whether intentional or unintentional, are called dog-legs. The theoretical limits of dog-legs which are permissible before the drill pipe begins to fatigue can be calculated. However, in wells where the maximum permissible dog-leg is exceeded, the concept of cumulative fatigue damage can be used to estimate damage suffered by the drill pipe. This concept has already been used to estimate the cumulative fatigue damage of drill pipe due to drilling vessel roll. The purpose of this paper is to extend the usage of the cumulative fatigue damage concept to drill pipe in dog-legs, and to draw conclusions which may be beneficial in preventing numerous frustrating and expensive drill pipe failures.

FATIGUE OF STEEL DRILL PIPE IN IDEALIZED GRADUAL AND LONG DOG-LEGS
It is taken for granted that, if necessary, the reader will become familiar with the definitions and concepts which follow by examining the reference cited in each case. For Ref. 1, it will suffice to read only through the section Abrupt Dog-Legs.Concept of the two extreme kinds of idealized dog-legs: gradual and long dog-legs and abrupt dog-legs,Concept of why the bending moment in drill pipe under tension is the largest in the vicinity of the tool joint,Concept of why dog-leg severity which drill pipe can withstand decreases with an increase in tension, andDefinition of the rate of change of over-all hole angle (dog-leg severity).
Figs. 1 and 2 indicate the aging (fraction of life expended) of steel drill pipe passing through a gradual and long dog-leg. Both figures have a left-hand ordinate scale labled Length of Drill Pipe Below Dog-Legs. This scale can be used for cases in which the drill collar weight is applied to the bit and does not contribute to the tension in the drill pipe. It can be used for either 3 1/2-, 4 1/2- or 5-in. drill pipe. This is due to the fact that, if the drill collars do not contribute to the drill pipe tension, then the effect of pipe tension on bending due to a change in pipe size is nearly compensated for by a corresponding change in pipe rigidity. On the other hand, if drill pipe is rotated off bottom, then drill collars contribute to the tension in the drill pipe and this increase in tension is not compensated for. In this case, one of the three right-hand ordinates must be used (the one which corresponds to the correct drill pipe size). In the right-hand ordinates, tension should be understood as the weight in mud of the portion of the drilling string below the dog-leg, minus the weight on bit.
JPT
P. 359ˆ