The Effect of Axial Load on Casing Collapse
Authors: Pattillo P.D. , Huang N.C. 
Published: December 2007

Summary
This paper presents a unified treatment of the effect of axial load on casing collapse wherein no a priori assumptions regarding the failure mode of the casing need be made. Rather, the specific mode of failure (elastic buckling, plastic buckling, or ultimate strength failure) appears as a natural consequence of the analysis. This study of casing collapse is based on an analysis of an infinitely long, thin, cylindrical shell. Guidelines concerning the anticipated degree of error from the thin shell approximation are included in the Appendix. The two major sections of the paper are devoted toan introduction to the governing equations, followed by a discussion of their relation to expressions used by previous authors, andcomparison of the derived expressions with experimental data.
Comments regarding the determination of various constants introduced in the analysis also are included.

Introduction
The variety of mechanical failure modes that the body of an oilwell casing joint can undergo can be subdivided into two areas-failure modes related to the inherent strength of the casing steel (burst or axial yield) and failure modes related to structural instability (column buckling or collapse). Indeed, casing failure in either of these categories depends on the geometry of the casing and the ultimate strength of the casing steel. However, in the case of stability failures (particularly collapse), one normally tries to avoid the initiation of instability with the understanding that buckling, and not the postbuckled behavior, represents the point at which the casing loses its intended design integrity. In this paper, the topic is the prediction of the onset of cross-sectional collapse of casing subjected to axial tension. In the following discussion, the axial load may or may not be zero. However, even for nonzero axial loads, the primary concern is the cross-sectional integrity of the casing. So-called "stretch" failures from excessive axial load in the presence of little or no external pressure are ignored.

Basic Equations
Under the action of axial tension and external pressure, a tube cross section can fail in three possible modes -elastic collapse, plastic collapse, or failure caused by exceeding the ultimate strength of the material. For any given combination of material properties and tube geometry, it is necessary to determine the critical conditions for all three failure modes. Actual failure of the tube (i.e. both the load at which the tube collapses and the mode of failure characterizing the collapse) is governed by the failure mode corresponding to the smallest failure load. Failure of a tube by elastic collapse may be determined from
(1)
where equivalent external pressure p and mean diameter D' are introduced in the Appendix. Notice that PCE is independent of axial load. Tube failure by ultimate strength may be approximated by an expression such as Eq. A-6 in the Appendix, or Pcu may be determined numerically from the equations for a thick cylinder. The collapse equations for both elastic collapse and ultimate strength failure modes present no major analytical difficulties and are capable of predicting their respective failure modes with an acceptable degree of accuracy. Unfortunately, most oil well casing, either in the presence or absence of axial load, fails by plastic collapse. The primary complicating factor in analyzing plastic collapse, even in the absence of axial loading, is that one must have available a description of the uniaxial stress-strain curve of the tube material.
JPT
P. 159^