Introduction

History indicates that failures are commonly the result of locally reduced resistance coupled with a defect subject to nominally the same loading due to pressure, with fracture and plastic collapse being the two most prevalent mechanisms of failure. If the steel’s toughness (fracture resistance) suffices then initially sharp defects blunt, with the limit pressure then controlled by the ultimate strength of the steel. Otherwise the initially sharp defects grow through-wall under fracture control. Regardless of the mechanism, the outcome is a leak or a rupture.

This QR segment provides insight into the mechanisms that underlie collapse- and fracture-controlled failures. Collapse-controlled failures are characterized as ductile response, whereas fracture controlled failures exhibit limited plastic flow, which diminishes notionally to zero for fully brittle fracture. The significant conceptual differences in ductile versus brittle failures are manifest in the macro-appearance of such failures due to pressure loading. This is illustrated in the set of images below, which to the left shows typical axial ductile failures contrasted with the sinusoidal cracking paths that are typical of brittle axial failures shown to the right. Also shown are the corresponding fracture surfaces more or less to the same scale.

Typical Macro-Fracture Features

It is apparent that ductile axial failures present two different characteristic ‘looks’ – both of which involve an axial component of cracking. The upper image shows a split that in this case arrested without ‘ring-off’, wherein the crack path turns and begins to run with a circumferential component. Such splits are typical of long-seam failures, but this cracking also occurs in the pipe body well remote to the long seam. The lower image shows ductile axial failure that has developed as a flap. The abutting edges along the path of ductile propagation lie at about 45° to the pipe surface in thinner-walled pipes (i.e., higher diameter to thickness ratio), with the failure occurring by void nucleation, growth, and coalescence. The origin for these ductile failures typically lies within the bulge formed as failure localizes due to the progression of through-wall collapse. Experience indicates that flap opening failure is more common for tougher steels. Both of these failures occurred in liquid (crude) pipelines such that the driving force to sustain axial cracking decayed almost immediately. Had these pipelines been transporting compressible or certain other fluids the circumstances associated with these splits were such that they would have extended axially for at least several joints.

The images to the right illustrate several traits typical of axial propagating brittle fractures, with other usual traits being less evident. This failure occurred in gas-transmission service at ~65% of SMYS, being initiated through a corrosion defect whose length over which through-wall collapse occurred was in excess of the critical length for unstable axial propagation. It is apparent from this image that such brittle failures occur with limited energy dissipation, and track sinusoidal paths. The fact that the pipe in many places retains its curvature prior to failure indicates that brittle failures occur with limited energy dissipation remote to the fracture. It is also apparent that such brittle cracking involves multiple cracks that create ‘shards’ of pipe, with the shadows evident along the right margin of the image showing the characteristic sinusoidal cracking path. The stored energy and its release-rate is very high in such events – sufficiently so to eject the pipe and shards from the ditch and throw them well outside the pipeline’s RoW. Where the propagation is brittle, such failures lie on a crack plane that is 90° to the pipe wall, with little associated through-wall thinning. Cracking occurs via cleavage in such a way to produce chevrons that point back to the origin, which when well-formed can be visible to the unaided eye. The figure in the lower right shows typical chevrons.

The Micro-Mechanics of Failure – Plastic Collapse

Collapse-controlled failure occurs when the net-section resisting the loadings develops stresses that approach the ultimate failure stress for the steel involved, which is termed the ultimate tensile stress (UTS). The strain hardening capacity for the steel involved also is a factor [1]. When this occurs the most highly stressed areas begin to form voids, which grow as the stress continues to increase. As voids cannot sustain load, as they form the net-section resisting the loadings decreases, with this process of void nucleation and growth being fueled by the ever decreasing net-section, which is accompanied by necking that further reduces the net-section. Eventually the voids coalesce across a plane through the net-section, which for thin-walled pipes occurs on a shear plane. The outcome is as the images below depict.

The image to the left above shows fine coalesced micro-voids, with the particles that served as their initiators visible at this scale in some cases. This patch accounts for about 100 microns (or about 0.004 inch) of crack advance. The middle image above illustrates the process of micro-void initiation and growth, along with some segments over which coalescence has occurred. Micro-void nucleation here is focused below what begins as a vee-tipped notch that has blunted and undergoing stable tearing as void coalescence occurs. Regarding the schematic, beginning at the top it illustrates the sequence from sharp notch through blunting, and then void nucleation and coalescence, in a process simply termed micro-void coalescence (MVC). Coalescence leads to transgranular (TG, or across the grains[1]) cracking that typically is planar unless other factors like geometry come into play. The extent of the effects of associated plastic deformation develops in proportion to the uniform strain capacity of the steel involved.

The Micro-Mechanics of Failure – Fracture

Fracture-controlled failure can occur either in a ductile mode or in a brittle mode, or in a mixed mode, depending on whether the service temperature is above or below the ductile-to-brittle transition temperature (DBTT). Ductile failures tend to occur along a shear plane such that shear-area (SA) serves as a measure of ductility. One-hundred percent SA (%SA) reflects fully ductile response whereas zero %SA reflects fully brittle response. Predominantly ductile response is evident above ~85 %SA such that service at temperatures above the 85 %SA DBTT the mode of cracking is predominantly ductile. The QR Code Failure Mechanisms and Pipeline Properties outlines testing methods that are used to quantify the DBTT, and to quantify the corresponding toughness. Toughness is considered herein, in a later subsection.

The underlying micro-mechanism of ductile fracture is as it was for collapse-controlled failure – that is MVC. And as for collapse controlled failures, blunting first occurs the extent to which depends on the toughness, where after TG cracking ensues. As noted above, such crack paths are generally planar unless the geometry and/or other factors affect the cracking directions. Brittle fracture can occur in a fully brittle mode, or it can occur in a mixed mode that couples the brittle and ductile modes. Brittle fracture occurs at a micro-scale by cleavage or quasi-cleavage, which looks much like cleavage except for the presence of MVC scattered within the cleavage fields. Brittle fracture can occur on a TG path, as was the case for collapse-controlled failures. Brittle fracture also can occur along an intergranular (IG) path – where the cracking runs between the grains along the grain boundaries – as opposed to across the grains. Distinguishing between cleavage and quasi-cleavage both of which occur by TG cracking is by the presence of localized ductile response within the otherwise cleavage-dominated fracture surface. Secondary cracking out of plane to the quasi-cleavage also can occur. The images below illustrate features that are characteristic of brittle fracture. The image to the left shows TG brittle fracture that in this case occurs via cleavage. The image to right shows IG brittle fracture wherein anodic dissolution has occurred along the grain boundaries creating the fracture surface. To the right-side of each of the fracture surfaces is an image that characterizes a cross-section through a typical cracking path. It is apparent that the IG path is a zig-zag path as the cracking direction turns with each grain encountered. In contrast, while the TG path also shows change in cracking direction, there are long runs of planar cracking between such changes.

Whether TG or IG, such brittle cracking involves little to no evidence of plastic flow, is highly reflective if untarnished, and tends to be planar. As evident above, such cracking can be fragmented or stepped.

Effects of Collapse and Fracture Control on Failure Pressure

Background. This section presents the results of simulations of defect initiation and growth in pipelines to illustrate defect sizes that fail as pressure increases, and identify conditions that promote the transition from plastic-collapse-controlled failure to fracture-controlled failure. The simulations were made with Release 4.5 of the pipeline axial flaw failure criterion (PAFFC), which has been broadly proven for applications involving isolated defects [2, 3]. PAFFC is a software-based model that combines the PRCI ductile flaw growth model (DFGM) [4] with a collapse model of the form developed to predict failure in blunt metal loss (such as corrosion) [5]. PAFFC determines the hoop stress at failure for each of these limit states and outputs the lesser of these as a function defect size at failure, specifically for axially oriented defects.

As indicated above, PAFFC develops accurate predictions of failing defect sizes as well as for the transition from leak to rupture based on axially stable versus unstable response. This has been shown for a range of defect lengths in pipe diameters from 8 inches (203 mm) through 42 inches (1067 mm) and grades ranging from X42 through X65, for failures in the body of the pipe as well as in ERW long seams [3]. Its accuracy also has been demonstrated in a blind round-robin comparison of such models, and through recent full-scale testing of higher toughness steels in grades through X80 [3], as well as the full-scale testing done for the PRCI by Battelle in the late 1960s [6]. PAFFC does not include any embedded factors of safety, leaving the choice of an appropriate safety margin to be selected and applied on a case-specific basis.

Failure pressure is presented as a fraction of the pressure to cause yielding in the pipe wall subjected to parametric variations in Grade, and toughness quantified here in terms of the full-size (area-equivalent, FSE) Charpy vee-notch (CVN) energy. Recognizing that failing defect sizes and shapes can be expressed in normalized terms for a wide range of pipe diameters and wall thickness [3], only select cases need be considered. Failing sizes have been calculated for unflawed pipes, as well as pipes with axial surface-connected cracking for depths up to 90 percent of the wall thickness and lengths up to 15 inches (381 mm). As becomes evident later the toughness of steels has evolved significantly since the 1950s with the present results considered representative of steels produced from the 1950s into the 1970s.

Results. Failing crack-sizes as a function of pressure were characterized in terms of length, L, and depth, d, normalized by the wall thickness, t, in figures identified hereafter by number as 1 through 4. Figures 1 and 4 present extremes in toughness – 180 ft-lb (244 J) and 10 ft-lb (13.6 J) – with two intermediate values considered between these extremes. These figures present the failure boundaries for sharp defects in the same 30-inch (762-mm) diameter grade X52 (358 MPa) line pipe, with a 0.312-inch (7.9-mm) thick wall. The y-axis as noted above presents the failure stress (or pressure) normalized by SMYS (or the pressure corresponding to SMYS). The x-axis presents the defect length, L, with defect depth being represented by contours of constant d/t.

Trends in Collapse versus Fracture Control. Trends that reflect plastic collapse control of failure for sharp defects are smooth and continuous, and are spaced uniformly as a function of normalized defect depth, with the trend for all depths being independent of toughness. Such response reflects the dependence of failure pressure on the net-section resisting the pressure. This behavior is evident for all situations where the toughness suffices to ensure plastic collapse’ with the effects of toughness on the failure pressure becoming evident as toughness decreases. Such differences are marginally evident in comparing the failure boundaries in Figure 1 that reflects a toughness of 180 ft-lb (244 J) FSE CVP, which suffices for collapse control, to those in Figure 2, which reflects 75 ft-lb (102 J). This comparison indicates that all failure boundaries therein are comparable to those in Figure 1, except for d/t = 0.60 for the longer lengths. The area in this figure where this break in nested response occurs is encircled by a dashed boundary. For such long cracks, the limit-state failure pressure is simply determined by the UTS and the net thickness, which is fixed by the depth of the defect relative to the wall thickness. For shorter cracks, the length of the crack also is a factor, which is obvious in reference to the defect-free limit state where the limit state has a constant value for all defect lengths.

Figure 1

 

Figure 2

 

Figure 3

Figure 4

It is evident in this context that the smooth, continuous, uniformly spaced appearance of failure boundaries for sharp defects evident in Figure 1 is lost where toughness controls. This is clearly evident by contrasting the trends evident in Figure 1 for the very tough steel to those in Figures 3 and 4, which respectively reflect toughness values of 30 ft-lb (40 J) and 10 ft-lb (13.6 J) FSE CVP. It is apparent that the scope of crack sizes failing under toughness control expands as the toughness decreases. At 30 ft-lb (40 J) FSE CVN most intermediate-depth defects experience fracture controlled failure at the longer lengths as is apparent by inspection of Figure 3. But, when the toughness falls to 10 ft-lb (13.6 J) it is apparent from Figure 4 that all depths quantified therein experience fracture-controlled failure. In comparing those failure boundaries to those in Figure 1 it is also evident that the transition to fracture control can shift the relative locations of adjacent failure boundaries, which significantly reduces both the length and depth available for stable growth at a given pressure.

What is Toughness ?

The discussion above made frequent reference to “toughness” without defining it, or considering the options to quantify toughness and fracture resistance, with these aspects addressed next. Further details can be found in textbooks such as References 7 and 8, or with a pipeline focus in Reference 6.

Toughness defined in the context of fracture is a measure of a material’s resistance to the initiation and growth of a crack-like defect. As discussed in related textbooks [7,8] the crack localizes the effect of the imposed load or stress, much the same as a notch causes stress concentration. However, the effect of the crack can be much more severe, as becomes evident from the adjacent schematic.

Two strips with rectangular cross-sections are shown in this figure. That on the left side contains a ‘crack’ whereas that on the right side does not. As indicated in the figure, each is loaded axially and each has a constant nominal width and thickness along their length. The ‘cracked’ sample, denoted A, has a cross-section area remote to the plane of the crack that is much larger than that of the ‘un-cracked’ sample, denoted B. The width of Sample A is (a + b), where, as indicated in the figure, the symbol “a” denotes the depth of the crack, and “b” denotes the width of the remaining (net) section. It is important to note that the width of Sample B is identical to the un-cracked (net) width of Sample A. Thus, the net-width multiplied by the thickness which is termed the net-section is equal for both samples.

In spite of both samples having the same net cross-section area, the limit load of the cracked specimen can be much lower than that of the un-cracked specimen if the material it is made from lacks toughness – the ability to resist cracking. As this illustration shows, the load-carrying capacity of the cracked specimen is determined by its toughness. The larger its toughness, the more load it can carry; conversely the smaller its toughness the lower the load it can sustain.

Key in this context is the observation that when engineering materials lack adequate toughness, it is possible for failure to occur at a load much less than the limit load corresponding to the UTS.

In regard to Figures 3 and 4, consider a long shallow 20% through-wall defect. For the longest length shown, failure at 30 ft-lb (40 J) occurs at a hoop stress of about 117% SMYS – which is well above possible failure in a high-pressure hydrotest. In contrast, at 10 ft-lb (13.6 J) failure is indicated to occur at a hoop stress of about 85% SMYS – and now would fail a 90% hydrotest. The point is that for steels with very low toughness a shallow defect can fail under nominally elastic conditions. As the schematic indicates, the load-carrying capacity is reduced due to the defect that localizes the effect of the imposed load or stress. Lower toughness steel lack the ductility to blunt the sharp crack. Such blunting spreads the localized stress and makes the steel more tolerant of the crack, as occurs with higher-toughness steels.

Toughness can be measured under either quasi-static or dynamic loading rates. Test protocols facilitate measuring toughness in absolute terms, which involves measuring a local change specific to crack response during loading, or where a global metric such as fracture energy is measured. Such aspects are discussed further in the QR segment dealing with Properties. In the simplest situation, toughness is quantified as a function of stress acting perpendicular to the axis of the defect and the defect size. In the worst practical case, the axis of the defect lies along the length of the pipeline. Regardless:

K = S f(a/w)( a)0.5,

wherein the symbol K denotes the linear-elastic fracture mechanics (LEFM) stress intensity factor, a universal measure of crack driving force. The symbol S denotes the remote section stress, f(a/w) is a function that depends on the crack and structural geometries, and “a” is crack length. Handbooks tabulate values of K for a range of crack and idealized structural shapes [e.g., 9], while References 10-12 present values of K of interest in transmission pipeline applications. The QR segment dealing with Defect Assessment presents more related detail.

When the right-hand-side of this expression is measured in the laboratory for a specific material, the corresponding value of K reflects the material’s (fracture) toughness, usually denoted as Kc or KIc. In contrast, when S, the function f(a/w), and the crack length “a” represent the pipeline operating situation, the corresponding value of K represents the crack driving force. The value of S used in this context for pipelines is the MAS, whereas the function f(a/w) and the crack size reflect the minimum defect size that can be reliably detected. This minimum crack or defect size usually includes an allowance for in-service growth. The value of K calculated under these conditions represents the toughness required to avoid cracks becoming unstable in service. This toughness value, if included in the specifications for the line-pipe steel, would ensure detection of defects and cracks prior to their causing a rupture.

Experience indicates that line-pipe steels can exhibit ductility beyond that for which LEFM is valid, for which equations like that above are replaced in the framework of non-linear fracture mechanics (NLFM)[e.g.,2,4]. Such technologies characterize toughness with regard to methods much different that CVN energy. Textbooks dealing with NLFM should be consulted for guidance.

Summary

Analysis indicates that plastic collapse generally controls failure for shallow defects in the pipe body (d/t ≤ 0.15) at wall stresses as high as occur in cross-country service, even for low toughness steels. While shorter defects likewise tend to experience collapse control that can be traced to the reinforcement associated with the surrounding full pipe wall, no lower bound length exists beyond which cracks consistently fail by collapse when lower toughness steels are considered.

The obvious changes in the shapes and nesting of failure boundaries evident in comparing Figures 1 through 4 clearly illustrate the differences between collapse controlled and fracture controlled failure boundaries. It can be seen that fracture control is evident first for longer features with mid-wall depths. Sizes under fracture control spread to shorter crack lengths and initially shallower defects, but eventually all but very deep and quite shallow defects become fracture controlled.

Toughness adequate to support plastic collapse is a key element in pipe-steel design and specification. Fracture control plans should be developed even where propagating failures are not a concern.

References

  1. Zhu, X.K. and Leis, B.N., “Average Shear Stress Yield Criterion and its Application to Plastic Collapse of Pipelines,” International Journal of Pressure Vessels and Piping, Vol. 83, 2006, pp. 663-671.
  2. Leis, B. N. and Eiber, R. J., “Fracture Control Technology for Transmission Pipelines”, PR-003-084506, December, 2014: currently PRCI Member Access only
  3. Leis, B. N., Rudland, D. L., and Eiber, R. J., “Evaluation of the Benefits of Hydrotesting Gas-transmission Pipelines,” PR 3-9523, Pipeline Research Committee International, Catalog No. L51844e, February, 1997.
  4. Leis, B. N., Brust, F. W., and Scott, P. M., “Development and Validation of a Ductile Flaw Growth Analysis for Gas Transmission Line Pipe”, (NG-18 Report No. 193), American Gas Association, A.G.A. Cat. No. L51543, June 1991.
  5. Leis, B.N., and Stephens, D.R., “An Alternative Approach to Assess the Integrity of Corroded Line Pipe — Part I: Current Status, and Part II: Alternative Criterion,” 7th International Offshore and Polar Engineering Conference, Vol. 4, May 1997, pp. 624-634, and pp. 635-641.
  6. Leis, B. N. and Bubenik, T., “Primer on Design to Avoid Failure in Steel Transmission Pipelines,” Gas Research Institute, GRI-00/0229, January 2001.
  7. Hertzberg, R. W., Deformation and Fracture Mechanics of Engineering Materials, John Wiley and Sons, 1976
  8. Broek, D., Elementary Engineering Fracture Mechanics, Noordhoff, 1974.
  9. Tada, H., Paris, P. C., and Irwin, G. R., The Stress Analysis of Cracks Handbook, Del Research Corp., 1977
  10. Stonesifer, R. B., Brust, F. W., and Leis, B. N., “Stress-Intensity Factors for Long Axial Exterior Surface Cracks in Large R/t Pipes”, ASTM STP 1131, American Society for Testing and Materials, Philadelphia, pp 29-45, 1992.
  11. Stonesifer, R. B., Brust, F. W., and Leis, B. N., “Mixed Mode Stress Intensity Factors for Interacting Semi-Elliptical Surface Cracks in a Plate”, Engineering Fracture Mechanics, Vol. 45, No. 3, pp. 357-380, 1993.
  12. Leis, B. N., “Characterization of Axial Flaws in Pipelines, With a Focus on Stress-Corrosion Cracking: NG-18 Report No. 212, American Gas Association, 1997
  1. Grains can be thought of as the microstructural building blocks that nucleate and grow integral to one another as the steel cools to a solid. In the early steels these building blocks typically range in size from about 100 microns (0.004”), whereas for the more recent steels down this size decreases to about 1/20 of that or ~5 microns (0.0002”). Finer grained steels are stronger and generally tougher than their coarser-grained counterparts – all else being equal. The voids nucleate at ‘particles’ within the grains, which can involve either desirable or deleterious constituents, depending on the circumstances.