Strength of casing and tubing: Difference between revisions

All the pipe-strength equations previously given are based on a uniaxial stress state (i.e., a state in which only one of the three principal stresses is nonzero). This idealized situation never occurs in oilfield applications because pipe in a wellbore is always subjected to combined loading conditions. The fundamental basis of casing design is that if stresses in the pipe wall exceed the [[Glossary:Yield_strength|yield strength]] of the material, a failure condition exists. Hence, the yield strength is a measure of the maximum allowable stress. To evaluate the pipe strength under combined loading conditions, the uniaxial yield strength is compared to the yielding condition. Perhaps the most widely accepted yielding criterion is based on the maximum distortion energy theory, which is known as the Huber-Hencky-Mises yield condition or simply the von Mises stress, triaxal stress, or equivalent stress.<ref name="r3">Crandall, S.H. and Dahl, N.C. 1959. An Introduction to the Mechanics of Solids. New York City: McGraw-Hill Book Company.</ref> Triaxial stress (equivalent stress) is not a true stress. It is a theoretical value that allows a generalized three-dimensional (3D) stress state to be compared with a uniaxial failure criterion (the yield strength). In other words, if the triaxial stress exceeds the yield strength, a yield failure is indicated. The triaxial safety factor is the ratio of the material<nowiki>’</nowiki>s yield strength to the triaxial stress. The yielding criterion is stated as [[File:Vol2 page 0295 eq 001.png|RTENOTITLE]]....................(9) where

. For any ''p''_''i'' and ''p''_''o'' combination, the sum of the tangential and radial stresses is constant at all points in the casing wall. Substituting '''Eq. 10''' and '''Eq. 11''' into '''Eq. 9,''' after rearrangements, yields [[File:Vol2 page 0296 eq 001.png|RTENOTITLE]]....................(12) in which [[File:Vol2 page 0296 eq 002.png|RTENOTITLE]]

σ_''r'' and setting the triaxial stress equal to the yield strength results in the next equation of an ellipse. [[File:Vol2 page 0296 eq 004.png|RTENOTITLE]]....................(13) This is the biaxial criterion used in API ''Bull. 5C3, Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties'',<ref name="r1">API Bull. 5C3, Bulletin for Formulas and Calculations for Casing, Tubing, Drillpipe, and Line Pipe Properties, fourth edition. 1985. Dallas: API.</ref> to account for the effect of tension on collapse. [[File:Vol2 page 0296 eq 005.png|RTENOTITLE]]....................(14)