Abstract:
A method for leak-before-rupture assessment including using a failure assessment diagram (FAD) assessment curve from a crack initiation based FAD analysis to analyze a crack in a material; and using a ductile tearing analysis in conjunction with the FAD assessment curve to detect a crack exhibiting at least one of ductile tearing stability and tearing instability prone to rupture during growth of the crack.

Description:
BACKGROUND OF THE INVENTION  
       [0001]     This invention relates to a method for detecting a leak before rupture, and more particularly, relates to a method for detecting a leak before rupture using a tearing instability approach in pipeline applications.  
         [0002]     Cracks or crack fields can initiate and grow in a pipeline by stress corrosion cracking, fatigue, or corrosion fatigue. The pipeline leaks if one of the cracks penetrates through the wall. The prompt detection of the leak can serve as an early warning and remedial actions can be taken to avoid a subsequent catastrophic failure. It is practically important, therefore, to develop analysis methods that predict conditions for a “leak-before-rupture”.  
         [0003]     The first incident of external stress corrosion cracking (SCC) on natural gas pipelines occurred in the mid 1960&#39;s and hundreds of failures have occurred since that time. Stress corrosion cracking (SCC) is the formation of brittle cracks in a normally sound material through the simultaneous action of a tensile stress and a corrosive environment.  
         [0004]     Evaluation of leak-before-rupture for crack containing pipelines is an area that needs to be addressed for integrity assessment. Currently, fracture mechanics based industry standards, such as API 579-2000, provide detailed procedures for leak-before-rupture assessment using a Level II or III Failure Assessment Diagram (FAD) analysis. Since these procedures only predict crack initiation rather than a catastrophic failure for materials that exhibit stable crack growth by ductile tearing, the results are inconsistent with leak incidents observed in the field.  
         [0005]     The criteria for a leak before rupture require that (1) the largest initial crack size left in the structure (e.g., pipeline wall) will not lead to fracture during the life of the component and (2) the largest length of a through-wall crack is less than that which catastrophic rupture will occur for all applicable load cases using either a Level II or Level III FAD assessment method. However, the FAD procedures for critical size analysis, i.e., the largest acceptable crack size, in API 579 is not consistent with crack initiation criteria in references such as, I. Milne, R. A. Ainsworth, A. R. Dowling and A. T. Stewart: “Assessment of integrity of structures containing defects”, CEGB report R/H/R6-Revision 3, 1986; and M. Janssen, J. Zuidema and R. J. H. Wanhill: “Elastic-Plastic fracture mechanics”, Fracture Mechanics, Part III, Chapter 8, pp.198-203, Delft University Press (2002).  
         [0006]     FAD procedures in API 579 for critical size analysis is more appropriate when material failure is expected to be either brittle or is preceded by only a limited amount of ductile tearing. For materials exhibiting significantly ductile tearing prior to failure, prediction of leak or rupture conditions is conservative and does not provide consistent results with field observed “leak-before rupture” incidents. This is because the resulting increase in toughness involved during crack growth is not taken into account in the analysis.  
         [0007]     Accordingly, there is a need for a method for detecting a leak before rupture that accounts for the contribution of significant ductile tearing that provides a more accurate prediction by taking into account an of increase in the material fracture toughness involved during crack growth by a ductile tearing mechanism.  
       BRIEF DESCRIPTION OF THE INVENTION  
       [0008]     The above discussed and other drawbacks and deficiencies are overcome or alleviated in a method of detecting a leak-before-rupture using a ductile tearing and tearing instability approach in pipeline applications.  
         [0009]     In an exemplary embodiment, a method for leak-before-rupture assessment including using a failure assessment diagram (FAD) assessment curve from a crack initiation based FAD analysis to analyze a crack in a material; and using a ductile tearing analysis in conjunction with the FAD assessment curve to detect a crack exhibiting at least one of ductile tearing stability and tearing instability prone to rupture during growth of the crack.  
         [0010]     In another embodiment, a method to detect leak-before-rupture cracks in a pipeline material that exhibits stable crack growth by ductile tearing includes using a failure assessment diagram (FAD) assessment curve from a crack initiation based FAD analysis to analyze a crack in a material; and using a ductile tearing analysis in conjunction with the FAD assessment curve to detect a crack exhibiting at least one of ductile tearing stability and tearing instability prone to rupture during growth of the crack, wherein the ductile tearing analysis takes into account an increase in a material fracture toughness during the crack growth.  
         [0011]     The above-discussed and other features and advantages of the present invention will be appreciated and understood by those skilled in the art from the following detailed description and drawings. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0012]     Referring now to the drawings wherein like elements are numbered alike in the several Figures:  
         [0013]      FIG. 1  is a graph of stress versus crack length illustrating slow crack growth in a plane stress condition for ductile materials;  
         [0014]      FIG. 2  is a typical R-curve illustrating conditions for crack extension initiation and tearing instability (rupture);  
         [0015]      FIG. 3  is a graph of J app  versus crack extension length illustrating a J-R curve in conjunction with various driving forces;  
         [0016]      FIG. 4  is a typical material J-R curve illustrating eight assessment points;  
         [0017]      FIG. 5  is a failure assessment diagram (FAD) for a ductile tearing and tearing instability analysis using J mat  derived from the J-R curve of  FIG. 4  in accordance with an exemplary embodiment;  
         [0018]      FIG. 6  is another failure assessment diagram (FAD) for a ductile tearing and tearing instability analysis illustrating stable crack growth as in  FIG. 5 , no crack growth, and ductile instability in accordance with an exemplary embodiment;  
         [0019]      FIG. 7  is a level III assessment diagram showing critical crack sizes at a pressure of 896 psi (MAOP) in a 16 inch O.D. X-52 pipeline;  
         [0020]      FIG. 8  is an actual J-R curve of a section cut out from the 16 inch O.D. pipeline in accordance with an exemplary embodiment;  
         [0021]      FIG. 9  is a FAD for ductile tearing analysis of different lengths of through-wall cracks in the 16 inch O.D. pipeline at MAOP 896 psi;  
         [0022]      FIG. 10  is a FAD level III analysis for ductile tearing of different lengths of through-wall cracks in a 26 inch O.D. pipeline at MAOP 832 psi; and  
         [0023]      FIG. 11  is a FAD level III analysis for ductile tearing of different lengths of deep SSC cracks (i.e., 90% wt) of a colony in a X52 pipeline. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0024]     The acceptance criteria for a crack-containing structure in accordance with the API 579 assessment procedures and associated assessment procedures, such as, R6 and BS 7910, is analyzed against the initiation of crack extension rather than crack instability (rupture). Since ductile materials in a plane stress loading condition (e.g., thin wall for linepipe ferrite steels on the upper shelf of a ductile-brittle transition curve) often exhibit extensive plastic deformation prior to rupture, the assessment methodology in such a case can be extremely conservative and may not be appropriate for predicting actual failure conditions like leak-before-rupture.  
         [0025]     To develop a tearing instability model for leak-before-rupture assessment, the ductile tearing and tearing instability process is reviewed. This process is graphically illustrated in  FIG. 1 , where a crack with an initial length a o  begins to extend at a i  (e.g., initiation of crack growth) at a certain stress σ i . If the stress is maintained at σ i , no further crack growth occurs at this stress because G=R where G is the driving force and R is the material resistance to crack extension. A slight increase in the stress is then required for an additional crack extension, however, the crack remains stable because a new balance of G=R is established again after the increment of stress. While this process continues, stable crack growth proceeds in a region  10  between a first stress curve  12  and a second stress curve  14  accompanied with increasing stress until a critical combination of stress σ c  and crack length a c  is reached at the second curve  14 . At this point, instability of crack growth occurs. The first curve  12  represents stress for initiation of crack extension σ i , while second curve  14  represents critical stress σ c  for rupture instability tearing. The region  10  between first an second curves represents a stable slow crack growth ductile tearing region.  
         [0026]     The ductile tearing and tearing instability process may be more clearly described using an R-curve concept referring to  FIG. 2 . A material resistance to crack extension is depicted as a rising curve  16 , i.e., R-curve, with a vertical segment  18  corresponding to a no crack extension at a low stress level (i.e., low driving force G). The driving force G for crack extension is depicted as straight lines  20  and  22  (i.e., G-lines G σi  and G c ) through the origin of the coordinates. At a stress level of σ i , crack extension initiates, as indicated by an intersection point  24  of the G σi  line  20  and the R-curve  16 . At this stress level, further crack extension cannot occur because G σi  line  20  is inside R-curve  16 , i.e., G σi &lt;R. Further extension can occur only when G σ  becomes slightly higher than R i  following the R-curve, and the stable growth condition is maintained at each increment of G σ . This slow crack growth by ductile tearing proceeds stably until σ c  and a c  are reached at an intersection point  26  of the G c  line  22  and R-curve  16 . Beyond this point  26 , G σ  becomes greater that R, as indicated by the G c  line  22 , and instable tearing (i.e., rupture) occurs.  
         [0027]     Therefore, the conditions for instable tearing are expressed as:  
                 G   σ     &gt;     R   σ       ⁢     
     ⁢   and           (   1   )                   ∂     G   σ         ∂   a       &gt;       ∂     R   σ         ∂   a               (   2   )             
 
         [0028]     For ductile materials in plane stress conditions, it is now generally accepted by those skilled in the pertinent art that the J-integral and the Crack Opening Displacement (COD) approaches provide a proper description of elastic-plastic fracture behavior, which usually involves stable crack growth. In this disclosure, only the J-integral approach is employed. The J-integral is widely accepted as a measure of elastic-plastic fracture toughness of engineering alloys. The driving force for crack extension and the material resistance to crack growth are expressed as J app  and J mat , respectively.  
         [0029]     Referring now to  FIG. 3 , the R-curve  16  of  FIG. 2  is now established in terms of J mat  versus crack length extension (a) in a J-R curve  30 , and the driving force for crack extension is expressed as J app . The tearing instability criteria are then expressed as:  
                 J   app     &gt;     J   mat       ⁢     
     ⁢   and           (   3   )                   ∂     J   app         ∂   a       &gt;       ∂     J   mat         ∂   a               (   4   )             
 
         [0030]     The above approach then serves as the basis for developing a criterion for leak-before-rupture assessment discussed more fully below.  
         [0031]     The FAD curve based on R6, API 579, or BS7910 and associated procedures is widely used to assess the acceptance of crack-like features present in structures. If the assessment point is disposed outside the safe region of the FAD based on the crack initiation criterion, the crack is not acceptable. However, this does not always indicate a failure condition. For materials that exhibit stable crack growth by ductile tearing, the fracture toughness increases with crack growth. Similar to equations (3) and (4) above for tearing instability, the crack will remain stable as long as:  
               J   app     ≤       J   mat     ⁢           ⁢   and   ⁢           ⁢       ∂     J   app         ∂   a         ≤       ∂     J   mat         ∂   a               (   5   )             
 
         [0032]     To demonstrate how a crack remains stable, a ductile tearing analysis is performed by calculating Lr and Kr for a range of postulated crack extensions, Δa, starting from the initial crack length a o , where Kr is K r , a ratio of applied J-integral to material fracture toughness 
 
√{square root over (J app /J mat )}
 
 Referring now to  FIGS. 5 and 6 , the x-axis of FAD  36  is defined as the stress ratio L r , (or, plastic collapse ratio), which is a ratio of reference stress σ ref  (a function of applied stress and crack size) to yield strength 
 
σ ref /σ y  
 
         [0033]     The J mat  is derived from the material&#39;s J resistance (J-R) curve of  FIG. 4  for a crack growth increment Δa. J app  is calculated based on the applied load and the shape of the structure and crack geometry. Under constant load and temperature conditions, and for a single crack, an initial assessment point  38  is initially outside of the FAD  36  in  FIG. 5 . As a result of crack extension, both 
 
√{square root over (J app )} and √{square root over (J mat )}
 
 will increase. However, as long as inequality of equation (5) holds, K r  will decrease. At the same time, L r  will increase somewhat as a result of crack growth, therefore, the locus of assessment points  40  in the FAD  36  will be directed roughly downwards, see Curve AB, from the point  38  corresponding to an initial crack length a o , in  FIG. 5 . 
 
         [0034]      FIGS. 5 and 6  also show that an assessment point  42  eventually drops below the assessment curve  36  as a result of ductile tearing and thus crack extension would eventually stop indicated by the nonfilled assessment points under FAD  36  in  FIG. 6 . For these cracks, even though they initiate outside the assessment curve  36  and exhibit some degeree of stable crack extension, the cracks do not result in failure by rupture at the operating pressure, implying that the crack is stable and acceptable in terms of failure by rupture even though a certain amount of crack increment has occurred.  
         [0035]     On the basis of above analysis, two situations are recognized with respect to Curve AB: First, if the crack in  FIG. 5  is a through-wall crack, a leak is expected because the assessment points eventually dropped below the assessment curve  36 , indicating that the crack is stable and will not cause rupture even though the assessment point  38  is initially outside the FAD assessement curve  36 . Second, if the crack is a surface crack, the crack may penetrate through the wall at a constant applied load, resulting in a leak due to stable crack extension if the crack is relatively deep and the crack extension is predominantly in the through-wall direction.  
         [0036]     Referring now to  FIG. 6 , two more examples are illustrated for completeness of analysis. Curve CD is disposed entirely below the assessnment curve  36  and thus, no crack extension occurs at the applied load. Curve EF initiates above curve  36  and then becomes tangent to the assessment curve  36  at tangent point  46 , which means that the load level for this particular crack is the limiting case. Any load greater than this load would result in a catastrophic failure. On the contrary, any load smaller than this load the assessment point  46  would eventually drop below the assessment curve  36  as a result of ductile tearing and crack growth would stop. The crack would leak if the crack was or had become a through-wall crack instead of rupturing.  
         [0037]     It will be recognized that the above analysis considers ductile tearing due to application of a certain load only. It is assumed that no form of subcritical crack growth is involved during the tearing. If these crack growth mechanisms cannot be excluded, this analysis should only be applied to overload conditions. Obviously, subcritical crack growth under normal operating pressure should be taken into account to estimate the crack size after a certain service time and should be used for life cycle calculation based on subcritical crack growth rate and the critical size estimated from tearing instability based analysis.  
         [0038]     Furthermore, it is evident that a J-R relationship should be establised experimentally for the material containing crack-like features at the assessment temperature for performing tearing instability analysis.  
         [0039]     Two field examples are presented below to validate the effectiveness of the tearing instability appproach for leak-before-rupture assessment described above. First, a small leak was found in a joint of a 16 inch O.D. pipeline due to a through-wall SCC crack. The 16-inch O.D. pipeline was manufactured in 1961 from API 5LGrade X-52 steel, and was designed for and operates at a Maximum Allowable Operating Pressure (MAOP) of 896 psi. Second, a through-wall crack was found during a recent excavation in a 26-inch O.D. pipeline manufactured in 1956 from API 5L Grade X-52 steel, and operated at a MAOP of 832 psi.  
         [0040]     FAD analysis and tearing instability assessment were then performed to estimate the critical crack size for the initiation of crack extension and leak-before-rupture. Assessments assumed that the cracks were single isolated cracks, i.e., no interactions between cracks in the crack field were considered. Prior to assessment, the material&#39;s true stress-strain curve, J mat , and J-R curve were measured in accordance with ASTM standards E646, E833 and E1820 in order to perform high level FAD (material specific Method D) and tearing instability assessment.  
         [0041]      FIG. 7  shows the level III method-D assessment results (referred to API 579), indicating that through-wall cracks with a size larger than 2 inches are outside of the assessment curve  100  and not acceptable for service based on the crack initiation criteria.  
         [0042]     Tearing instability assessment showed, however, that through-wall cracks with a size smaller than 6.5 inches long would not result in catastrophic failure.  FIG. 8  illustrates the measured J-R curve  110  and  FIG. 9  illustrates a FAD ductile tearing analysis  112 . In actuality, field examination found a small leak in 2001 and subsequent examination determined the size of the crack associated with the leak to be a 2.2-inch through-wall crack.  
         [0043]     Similar assessment was performed on the 26-inch pipeline in the second example. Referring to  FIG. 10 , the ductile tearing analysis suggests that through-wall cracks with a size smaller than 4.9 inches would not cause rupture. The analysis is consistent with the field observation where a through-wall crack was found during excavation. The crack was a 3.6 inches long with part of the crack having penetrated through the wall.  FIG. 10  illustrates the FAD analysis results.  
         [0044]     The above analysis is based on an assumption of a single crack. However, cracks formed by SCC are often characterized as crack colonies or crack fields. Generally, SCC colonies are comprised of various crack sizes with inter-spacings therebetween. Fracture mechanics analysis suggests that failure initiates from one of the worst cracks caused by SCC and then links with others to form a larger crack that finally results in either a leak, rupture, or leak then rupture, depending on crack sizes, crack spacing, loading condition and material properties.  
         [0045]     For example, if there is a very deep SCC crack (e.g., 90% wt) in a colony of SCC in a X52 pipeline, and the crack is longer than the critical size for initiation of extension but smaller than that for rupture in accordance with the FAD level III analysis, then this crack could start to grow by ductile tearing if a favorable loading condition (e.g., operating pressure) is present. The ductile tearing would pre-dominantly occur at the deepest point of the crack where the stress intensity is the highest. The crack could readily penetrate through the remaining wall ligament and result in a leak. Rupture could finally occur as a result of linkage of this newly formed through-wall crack with its adjacent cracks to form a larger crack. Whether rupture occurs or not depends on the size of the linked cracks (for example, more than 4.5 inches long based on tearing instability analysis of  FIG. 11 ) combined with local loading and temperature conditions (i.e. pressure fluctuation induced overload). The time for this transition, however, cannot be easily predicted—it could last for months, or several days, or hours. However, fractographic analysis for this particular case has shown that transition from leak to rupture might last a length of time in order to bring the temperature of the joint (about 15 ft from on either side of the fracture origin) down to the Charpy (CVN) transition temperature.  
         [0046]     For shallow but closely aligned long cracks, (for example, crack depth&lt;60% wt), inter-link of adjacent cracks is the main process for ductile tearing. Therefore, rupture is expected to be the predominant form for most of the failures of these types of cracks based on the tearing instability analysis.  
         [0047]     The above described disclosure provides a leak-before-rupture criterion using a ductile tearing and tearing instability analysis approach. This criterion takes into account the significant ductile tearing and stable crack extension that may occur prior to catastrophic failure. Assessments based on this criterion provide more accurate predictions and are consistent with limited field examinations thus far. Preliminary results using this assessment criterion have shown that the chance for a leak-before-rupture in SCC induced crack-containing pipelines may not be low, for example, cracks with a depth of 90% wt and a length less than 4.5 inches will most likely leak before rupture for qualified X52 grade steel. These findings suggest that in addition to the current widely used “crack initiation based FAD analysis”, a ductile tearing analysis should be used for integrity assessment if leak-before-rupture is a concern. The findings also suggest that the stress alone cannot predict a leak before rupture or vice-versa. A combined stress, material properties, temperature, and crack size determines the critical condition for failure by leak or rupture.  
         [0048]     While the invention has been described with reference to an exemplary embodiment, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the scope of the invention. In addition, many modifications may be made to adapt a particular situation or material to the teachings of the invention without departing from the essential scope thereof. Therefore, it is intended that the invention not be limited to the particular embodiment disclosed as the best mode contemplated for carrying out this invention, but that the invention will include all embodiments falling within the scope of the appended claims.