Strain-based Fracture Mechanics Analysis of Pipelines

Transcription

1 Proceedings of ICASI International Conference on Advances in Structural Integrit Jul 4-7, 2004, Indian Institute of Science, Bangalore, India ICASI/XX-XXX Strain-based Fracture Mechanics Analsis of Pipelines Jaadevan K. R. a, Østb E. b and Thaulow C. a,* a Department of Engineering Design and materials, The Norwegian Universit of Science and Technolog, b Sintef Material Technolog, Department of Fracture Mechanics and Material Testing, Trondheim, Norwa. * christian.thaulow@ntnu.no ABSTRACT High internal pressure combined with bending/tension, accompanied b large plastic strains, along with the potential flaws in girth welds makes the structural integrit of pipelines a formidable challenge. The existing procedures for the fracture assessment of pipelines are based on simplified analtical methods, and derived for a load-based approach. Hence, application to surface cracked pipes under large deformation is doubtful. The aim of this paper is to explore the applicabilit of a strain-based fracture mechanics approach for pipelines independent of the remote loading conditions. The evolution of CTOD of a pipeline segment with an external/internal circumferential surface crack is examined under tensile loading as well as bending. Detailed three-dimensional elastic-plastic finite element simulations are performed. The effects of ovalisation of pipes under bending on the fracture response are also addressed. The results show a significant effect of the out-of-plane stress due to ovalisation on the crack-driving force relations. However, the stud suggests that the tension results can be used as a reasonabl conservative estimate for more realistic loading situations in pipelines. Kewords: Line-pipes, Surface cracks, Strain-based approach, Biaxial loading, Limit design, Offshore pipelines, Fracture assessment, Structural integrit. INTRODUCTION In several situations, pipes can be subjected to ver large plastic strains up to the order of 3%. The extreme loading conditions (high internal pressure combined with bending/tension) and the potential defects (such as, flaws in girth welds, damage due to corrosion, etc.) further make the fracture assessment of pipelines a formidable challenge. Toda s design practice for offshore pipelines are commonl dictated b the local buckling/collapse limit state. Recent research pushed the allowable strain limits on the compression side to quite large values, up to the order of 3% []. On the other hand, the permissible strain based on fracture on the tension side is still ver restricted. Current codes and standards (for example, BS 790: 999 [2]) for fractures assessment are generall formulated for load-controlled situations. In these loadbased approaches, loading well above the ield is usuall restricted. However, there are several situations where the pipeline is subjected to displacement controlled loading well into the plastic regime. Hence, for the fracture assessment in pipelines, a strain-based approach [3] is advocated. However, these procedures [3] are still based on the existing crack-driving force equations which are limited to small plastic strains, and hence, application in structures subjected to large plastic deformation is doubtful [4]. Hence, an accurate and simple strainbased fracture assessment procedure for offshore pipelines with the objective of possible further enhancement in deformation capacit on the tension side is highl desirable. The J-integral (energ release rate) and crack-tip opening displacement (CTOD) are the most viable fracture parameters for characteriing initiation of crack growth, stable crack growth and subsequent instabilit in ductile materials [5]. This suggests that fracture

2 parameters like J and/or CTOD can be convenientl used to assess the fracture behavior of line-pipe steels. Several studies [6, 7] are reported in the literature concerning fracture assessment of cracks in pipes. Most of these studies focused attention on the nuclear industr, where safet is the major concern, leading to conservative estimates. Further, approximations such as small-strain response, simple loading conditions and crack geometries are inherent in these analtical procedures. Moreover, the biaxial loading effects are accounted for onl b an equivalent tensile load. Hence, although the analtical methods look attractive, the accurac of these procedures in the large plastic strain regime and under complex loading conditions is doubtful [4]. The three-dimensional (3-D) finite element simulations are apparentl necessar to provide accurate results for the fracture response of surface cracked pipes. Shimanuki and Inoue [8] conducted an assessment of brittle fracture in girth-weld joints of pipelines subjected to combined loading conditions. The concluded that for the X80 line-pipe steel, the fracture resistance is secured onl within the elastic region. Considering the importance of the scenario, a detailed numerical and experimental program has been initiated in the Fracture Control project at SINTEF, Norwa [9]. In tune with the existing guidelines [], a strain-based design procedure from a fracture mechanics view point is envisaged in this project. The ultimate goal of the project is to establish safet levels based on reliabilit approaches for the limitstate design of offshore pipelines. Recentl, the authors [4, 0] carried out a detailed investigation to derive the crack-driving force equations for cracked pipes under tensile and bend loading. We observed that for both tension and bending, a simple linear CTOD-strain relationship can be approximated up to moderatel large plastic strain levels. The slope of this curve depends strongl on the crack depth, crack length, internal pressure and the material properties. This stud aims at exploring the applicabilit of the strain-based fracture mechanics approach for pipelines independent of the remote loading conditions. The evolution of CTOD of a line-pipe segment with an external/internal circumferential part-through surface crack is investigated under tensile loading as well as bending. Three-dimensional elastic-plastic finite element simulations are performed using the ABAQUS finite element code []. The effects of ovalisation on crackdriving force relations are also addressed. The results suggest that the tensile loading of external cracked pipes can be used to establish strain-based fracture assessment procedures for pipelines. 2. NUMERICAL DETAILS The details of the pipe geometr considered in this work are shown in Fig.. An external/internal surface cracked straight pipe with outer diameter, D=400 mm and wall thickness, t=20 mm, is chosen. The crack is assumed to be of uniform depth, a, along the circumferential crack length, 2c, with an end-radius equal to the crack depth (Fig. ). The details of the crack are similar for external (Fig. ) and internal (Fig. (c)) configurations. A crack length ratio, c/πr=0. (R being D/2) is chosen for the simulations. Two different crack depth to thickness ratios of a/t=0. and 0.2 are considered. Some analses with an uncracked pipe are also conducted for comparison. The total length, 2L of the pipe segment is taken to be six times the outer diameter. The details of the mesh emploed in this stud have been reported b Jaadevan et al. [4]. Considering the smmetr, onl one-quarter of the pipe is modeled. A blunt crack front is explicitl modeled with a radius of 25 microns. Smmetr boundar conditions (see Fig. ) are prescribed on the top and bottom edges of the pipe model as well as at nodes on the mid-section of the pipe, excluding crack face nodes. The different loading situations investigated in this stud are displaed in Figs. 2-(d). In the tension case (Figs. 2 and ), the pipe is loaded b specifing the axial displacement for the end-nodes. For the bending (Figs. 2(c) and (d)), a set of multi-point constraint (MPC) relations is used to prescribe rotation at the uncracked end of the pipe. These MPC s constrain the deformation of the end-plane to remain in its plane. t r = a a 2c 2L s a Figure. Geometr of the pipe with an external circumferential surface flaw. Details of the surface crack. (c) An internal surface crack. t x D (c)

3 F F P M F pr M P the crack front [4]. Recentl, the authors have demonstrated that the axial strain on the top surface and at a length of D from the mid-length of the pipe can be used for deriving strain-based fracture mechanics relations up to moderatel deep cracks [4, 0]. These values of the D global strain and mid-section CTOD are used to present the results. (c) (d) 3. RESULTS AND DISCUSSION Figure 2. The different loading situations analed in this stud. Pure tensile loading, pure bending and (c) biaxial loading under tension and (c) bending. The effect of biaxial loading under tension and bending (Figs. 2 and (d)) is also investigated. For both the biaxial loading cases, pressure load was applied in one step on the inner surface of the pipe as a distributed load, and then the axial/rotational displacement for tension/bending was prescribed graduall. For the bending with internal pressure, an end-load (F pr in Fig. 2(d)) was also applied in one step as a concentrated force at the end along with the pressure load. This end-load corresponds to that caused b pressure assuming closedends for the pipe. The above loading sequences simulate realistic situations encountered in pipelines. A tpical value of internal pressure (P=20 MPa) that causes a hoop stress (σ h ) equal to 50% of the ield stress (σ o ) is taken in the simulations. The material behaviour is assumed to follow the Mises isotropic power-law hardening behaviour. The following representative values of line-pipe steels are chosen in the simulations. Initial ield stress, σ o = 400 MPa, strain hardening exponent, n = 0.05, Young's modulus, E = 200 GPa and Poisson's ratio, ν = 0.3. The simulations were carried out using ABAQUS []. The effects of large strain and displacement were considered in the analses. Also, the chosen element tpe (ABAQUS tpe C3D20R, []) in the analses accounts for the volumetric locking due to plastic incompressibilit. A detailed mesh sensitivit stud was carried out [4, 0] to arrive at the appropriate finite element model. This stud confirmed that the model emploed can accuratel predict the fracture parameters within reasonable limits. Also, it was found that the chosen length of the pipe model (L = 3D, see Fig. ) is long enough to cause an end-effects on the computed fracture parameters to be negligible [4, 0]. The crack-tip opening displacement (CTOD) values are extracted from the finite element displacements of the nodes which are at the 45 o intercept from the crack front. The maximum CTOD is expected at the mid-section of 3.. Pure tensile/bend loading Figures 3 and show the evolutions of CTOD with strain for a surface cracked pipe (c/πr=0., D/t=20 and n=0.05) with a/t=0. and 0.2, respectivel. In both these figures, the results for internal and external crack configurations under pure tension (Fig. 2) and bending (Fig. 2) are included. CTOD, mm CTOD, mm EC_TEN EC_BEN IC_TEN IC_BEN 0.2 a / t = 0. c / π R = 0. n= EC_TEN EC_BEN IC_TEN IC_BEN a / t = 0.2 c / π R = 0. n= Figure 3. The evolutions of CTOD with strain for external (EC) and internal (IC) surface cracked pipes (c/πr=0., D/t=20 and n=0.05) under tension (TEN) and bending (BEN). a/t=0. and a/t=0.2.

4 The results shown in Fig. 3 in general show that a linear CTOD-strain relationship can be approximated over a large window of deformations. For small strain levels (ε < ε o, the ield strain), ie., when the pipe is globall elastic, the CTOD-strain relationship is quadratic ( Region ). As the plasticit spreads over the pipe, the CTOD-strain variation becomes approximatel linear, and this trend remains up to moderatel large strain levels (ε < 3%) ( Region 2 ). This simple linear relationship between CTOD and strain suggests that a strain-based approach would be more appropriate for surface cracked pipes than a load-based procedure in which the fracture response is too sensitive to load at large plastic strain levels. With further increase in plastic deformation, CTOD increases rapidl with strain ( Region 3 ) for tensile loading of both external and internal cracked pipes. This is more pronounced for a/t=0.2 than a/t=0.. Thus, for a/t=0., the CTOD-strain curve remains linear up to ε=5%, whereas the curve for a/t=0.2 shows a sudden increase in CTOD at about ε=4%. This ma be due to the more enhanced localied deformation and changes in the kinematics near the crack region [4] with increasing crack depth and strain level. It ma further be noted from Figs. 3 and that the CTOD-strain curve for the internal cracked pipe under tension differs marginall from the corresponding external crack. In contrast, under bending, the CTOD values for both (a/t=0. and 0.2) external surface cracked pipes decrease with increase in deformation (see Fig. 3), particularl for ε>%. For the shallow (a/t=0.) internal crack under bending (Fig. 3), the CTOD at large strains is higher than the corresponding tension case. Similar results for a/t=0.2 show that the CTOD for the internal crack under bending is slightl less than the tension case. Also, this curve remains linear up to strains less 5%. The deviation of trends between tension and bending or internal and external cracks is marginal up to strain level of %. These observations ma be attributed to the ovalisation of the pipe under bending, which is displaed in Fig. 4. Figure 4 shows the change in vertical diameter (along -axis, see Fig. ) of the pipe as a function of the global strain. The current diameter extracted from the midlength of the pipe is normalied with the original value. The results corresponding to the two cracked pipes and also for the uncracked pipe are included in Fig. 4. These results illustrate that for strains, ε>%, the crosssection of the pipe ovalises strongl with increase in deformation. Thus, Fig. 4 shows that the vertical diameter decreases b about 25% when the strain level exceeds 5%. For ε<%, the ovalisation of the cross section is marginal. This corroborate with the fact that the CTOD-strain relations under bending and tension are approximatel similar for small strain levels (ε<%). Finall, it is important to note from Fig. 4 that the ovalisation is onl marginall affected b shallow surface cracks. The observed deviation of trends in the CTOD-strain relationships for surface cracked pipes under bending from the tension can be explained based on the effect of out-of-plane stress due to ovalisation on the effective ield stress. This is schematicall illustrated in Fig. 5. The ovalisation of the pipe causes bending stresses in the hoop direction as shown in Fig. 5. These bending stresses are tensile on the tope side of the thickness, whereas the stresses are compressive on the bottom. This indicates that the shear bands of external/internal cracked pipe under bending will be subjected to additional out-of-plane tensile/compressive stresses. Also, the magnitude of the out-of-plane stress near the crack-tip varies with the crack depth. The effect of outof-plane loading on the effective ield stress is schematicall shown in Fig. 5. This figure illustrates that the out-of-plane tensile stress increases the effecting ield stress whereas the compressive stress decreases the ield stress. The above observations from the schematic demonstrate that the ovalisation can cause an apparent material hardening or softening effects on the local cracktip plasticit. This in turn is reflected in the CTOD-strain relationships of cracked pipes under bending. Thus, for the external shallow cracked pipe under bending, the localised material hardening effects give rise to lower values of CTOD compared to the tension case. On the other hand, for the internal cracked pipe (a/t=0.), the material softening increases the CTOD for bending above D/D o c / π R = 0. n = 0.05 Bending At mid-section Uncracked a / t = 0. a / t = Figure 4. Ovalisation of the surface cracked pipes under pure bending, extracted from the mid-length. The result for the uncracked pipe is also included. D D o

5 the tensile loading at large strain levels. As the crack depth increases, the near-tip deformation increases strongl at large strain levels. Further, the magnitude of out-of-plane stress near the tip region also varies with the crack depth. The competing effects of enhanced ligament deformation and ovalisation on CTOD at large strains is reflected in a/t=0.2 (Fig. 3). Thus, under bending, the CTOD-strain curve for the internal crack with a/t=0.2 remains approximatel linear up to ver high strains (ε<5%). Further, this curve falls below the corresponding curve for the tension case. Thus the results demonstrate that shallow internal surface cracks are more critical under pure bending compared to tension. This ma be important in pipelaing operations like reeling. However, the CTOD levels observed for these cracks are small, and ma probabl be of less interest in the design. Further, in realit, some stable crack growth is observed in ductile materials before an catastrophic fracture. As the crack depth increases (Fig. 3), the results show that CTODstrain relationships derived for external surface cracked pipes under tension gives reasonabl conservative estimates for the bending, irrespective of the crack position Biaxial loading C In service, the pipes are subjected to internal pressure along with bending or axial tension. It is expected that the internal pressure gives some stiffening effect which T σ 2 Figure 5. Schematics showing the out-of-plane stresses due to ovalisation and its effect on ield stress. Ligament plasticit will be under additional tensile/compressive out-of-plane stress for external/internal cracks. σ ma counter the ovalisation of the pipe under bending. This is illustrated in Fig. 6 showing the change in vertical diameter at the mid-length of the uncracked pipe under pure bending as well as bending with internal pressure (σ h =0.5σ o ). As seen from this figure, the ovalisation of the pipe becomes negligible when additional internal pressure is applied along with bend loading. This indicates that with internal pressure, the ovalisation effects on the CTOD-strain relationship will also be marginal. This effect of biaxial loading on the crackdriving force relations are presented in Fig. 7. Shown in Fig. 7 are the evolutions of CTOD with strain for a shallow cracked pipe (a/t=0.) under tension and bending along with internal pressure. The results corresponding to internal and external cracks are included. These results illustrates that external cracks under tension with internal pressure are the most critical case for the in-service loading situations. For strain levels ε>%, a noticeable decrease in CTOD is observed even for the internal crack under tension from the corresponding external case. This ma be due to the compressive radial stress on the ligament side of the external cracked pipe. This radial stress ma lead to enhanced ligament deformation, and hence higher CTOD, due to the localised softening effect on the effective ield stress (see Fig. 5. Further, Fig. 7 shows that the bending with pressure load leads to lower levels of CTOD compared to the tension, irrespective of the crack position. This ma be due to the linear bending strain distribution around the circumference of the pipe. D/D o n = 0.05 Uncracked pipe Bending σ h = 0 σ h = 0.5 σ Figure 6. Effect of biaxial loading on ovalisation of the uncracked pipe under bending. D D o

6 CTOD, mm EC_TEN EC_BEN IC_TEN IC_BEN a / t = 0. c / π R = 0. n=0.05 σ h = 0.5 σ Figure 7. The evolutions of CTOD with strain for external (EC) and internal (IC) surface cracked pipe (a/t=0., c/πr=0., D/t=20 and n=0.05) under tension (TEN) and bending (BEN) along with internal pressure (σ h =0.5σ o ). 4. CONCLUSION The crack-driving force relations for the strain-based fracture mechanics assessment of surface cracked pipes have been examined. In particular, the criticalit of the position of the crack and tpe of remote loading has been addressed. The following are the main conclusions from this stud. Without pressure load, higher CTOD values are observed for shallow (a/t<0.) internal surface cracked pipes under bending compared to the corresponding external case or external/internal cracks under tension, particularl for ε>%. However, as the crack depth increases (a/t>0.2), tensile loading of external/internal crack becomes the most critical. Under biaxial loading, CTOD-strain relationships for external surface cracked pipes under tension give reasonabl conservatives estimates for bending. The CTOD values for the internal crack under tension/bending with additional hoop stress are much lower than the corresponding external crack. The ovalisation of the pipe is marginall affected b shallow surface cracks (a/t<0.2). The biaxial loading significantl resists the ovalisation of the pipe. More importantl, the results demonstrate that an external surface cracked pipe under tension can be used to establish the strain-based fracture mechanics procedures for pipelines. ACKNOWLEDGMENTS Authors gratefull acknowledge the support from the Joint Industr Project Fracture Control Offshore Pipelines. Also the second author would like to thank the Norwegian Research Council for the financial assistance towards his research program. REFERENCES. DNV, Rules for submarine pipeline sstems, Det Norske Veritas, Høvik, Norwa, BS 790, Guide on methods for assessing the acceptabilit of flaws in metallic structures, BSI, H. A. Bratfos, Use of strain-based ECA for the assessment of flaws in pipeline girth welds subjected to plastic deformations, Proc. Int. Conf. Application and Evaluation of High Grade Linepipes in Hostile Environments, Yokohoma, Japan, pp , K. R. Jaadevan, E. Østb and C. Thaulow, Fracture response of pipelines subject to large plastic deformation, Int J Pressure Vessels Piping, 2004 (accepted for publication) 5. J. W. Hutchinson, Fundamentals of the phenomenological theor of nonlinear fracture mechanics, J Appl Mech 49, pp , S. Rahman and F. W. Brust, Approximate methods for predicting J-integral of a circumferentiall surface-cracked pipe subject to bending, Int J Fract 85, pp. -30, Y. J. Kim, D. J. Shim, N. S. Huh and Y. J. Kim, Quantification of pressure-induced hoop stress effect on fracture analsis of circumferential through-wall cracked pipes, Engng Fract. Mech 69, pp , H. Shimanuki and T. Inoue, Assessment of brittle fracture in girth weld joint of pipelines subjected to internal pressure and bending load, Int Conf on the Application and Evaluation of High-Grade Linepipes in Hostile Environments, Yokohama, Japan, Project Fracture Control in Offshore pipelines, Sintef Material Technolog, Department of Fracture mechanics and Material Testing, Trondheim, Norwa K. R. Jaadevan, E. Østb and C. Thaulow, Fracture response of pipelines subject to large plastic deformation under bending, Int J Pressure Vessels Piping, 2004 (under review).. ABAQUS, User s Guide and Theoretical Manual, Version 6.3. Hibbitt, Karlsson, & Sorensen, Pawtucket, RI 2003.