OMAE Fracture Control Offshore Pipelines - Advantages of using direct calculations in fracture assessments of pipelines

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1 Proceedings of OMAE th International Conference on Offshore Mechanics and Arctic Engineering (OMAE 2005) June 12-16, 2005, Halkidiki, Greece OMAE Fracture Control Offshore Pipelines - Advantages of using direct calculations in fracture assessments of pipelines Christian Thaulow Norwegian University of Science and Technology, N-7491 Trondheim, Norway christian.thaulow@ntnu.no Bjørn Skallerud Norwegian University of Science and Technology, Trondheim, Norway K R Jayadevan Government Engineering College, Thrissur, Kerala,India Espen Berg Norwegian University of Science and Technology, Trondheim, Norway ABSTRACT Surface cracks pose major challenges for the structural integrity of pipelines. In fracture assessment programs the use of constraint parameters, such as the T-stress, along with K, J or CTOD are important to account for the limitations of singleparameter fracture mechanics. However, the three-dimensional nature of surface cracks precludes detailed 3-D finite element modeling for routine calculations. Here line-spring/shellelement models are demonstrated to be an efficient and reasonably accurate tool for constraint estimation even under large deformation levels when general yielding prevails in the pipe. Envisaging the potential use of this procedure in fracture analysis of pipelines, a new software, LINKpipe, has been developed. The program has been developed as a part of the Joint Industry project Fracture Control Offshore Pipelines. The objective of this project is to study the behaviour of defected girth welds in pipelines subject to construction and operational loads ever experienced before. The calculations have been performed in close cooperation with the project participants; see presentations of project-colleagues at OMAE 2005: Bruschi et al (2005), Østby (2005), Nyhus et al (2005) and Sandvik et al (2005). In this paper the line-spring calculations are compared with 3-D FE calculations and computations according to BS A pipe geometry, with OD=400mm, was selected for the comparisons. The line-spring calculations were close to the 3-D calculations, while BS7910 was very conservative for long cracks and unconservative for short cracks. In highly ductile materials, such as pipeline steels, considerably amount of stable crack growth can be tolerated prior to the final failure of the structure. A simple method for simulating ductile tearing in surface cracked pipes with the line-spring model has been developed. A detailed parametric study has been performed to examine the effect of ductile tearing for pipes loaded in tensile, bending and with internal pressure. A significant reduction in deformation capacity from the stationary case is noticed. As the crack depth increases, the effect of ductile tearing becomes more important. And under biaxial loading a significant reduction of the deformation capacity is found as the internal pressure is increased. The development of the line-spring methodology paves the way for a transition from to-days rule-based design to direct calculations. 1 Copyright #### by ASME

2 INTRODUCTION Surface cracks are common in girth-welded pipes and pose major challenges in structural integrity assessments. The use of high strength steels, which provides cost savings, however, increase the importance of fracture mechanics in the design of pipelines. The constraint parameters, namely Q-parameter and T- stress along with K, J or CTOD are proposed in the literature to account for the limitations of single parameter fracture mechanics, Thaulow et al (2004a). Among these, the T-stress is more popular because it can be computed rather easily from the elastic finite element analysis. However, for surface-cracked pipes, 3-D finite element modeling becomes too cumbersome to employ for routine calculations. On the other hand, the knowledge of constraint estimates for surface cracked pipes is important in the fracture assessment of pipelines. Hence, an efficient and accurate procedure for the computation of fracture parameters, such as K, J, CTOD and T-stress, directly from the structural finite element models is highly desired. Line-spring finite element, proposed initially by Rice and Levy (1972) and later extended by Lee and Parks (1995), provides an alternative, simple approach to model surface cracks. Attractive features of this method are that it facilitates the computation of the T-stress and ductile tearing, rather easily. Recently, incorporating this line-spring technology, a new software, LINKpipe tailor made for pipeline applications, has been developed using a co-rotated kinematic description of shell- and line-spring elements, LINKpipe (2004). Numerical aspects and implementation of LINKpipe are described by Skallerud et al (2004). Recently, Jayadevan et al (2005a) have verified the accuracy and the usefulness of the line-spring method and published a compendium of normalized stress intensity factors and T-stresses for surface cracked pipes. In this paper the application of line-spring/shell model for the fracture assessment of surface cracked pipes is explored. First, the line-spring results are validated by finite element simulations and the constraint loss under large deformations in SENT specimens are examined. The linespring calculations of CTOD vs. strain are then compared with computations according to BS Finally, the application of LINKpipe to investigate the effect of ductile tearing in pipes is presented. the stress intensity factor, K, and the crack driving force, CTOD or J, may be calculated. The details of the pipe geometry considered in this work are shown in Fig. 2. An external surface cracked straight pipe with outer diameter, D and wall thickness, t, 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. Figure 1. (a) 2-D shell model with line-springs representing the surface cracked pipe shown in Fig. 2. (b) The compliances at any point along the line-spring are obtained from corresponding SEN bar in plane strain. Constraint evolution In the line-spring model, the surface cracked pipe is represented by a 2-D shell structure with a through slit. The additional compliance introduced by replacing the part-through flaw with a through-slit is accounted by line-springs, as schematically illustrated in Fig. 1. The local compliance of a spring connecting one point of the slit to the corresponding point on the other side is calculated based on known solutions of single edge notch (SEN) specimens under plane strain conditions. Thus knowing the local compliance of a spring, which depends on the depth of the surface crack at that point, Figure 2. (a) Geometry of the pipe with an external circumferential surface flaw. (b) Details of the surface crack. 2 Copyright #### by ASME

3 Detailed three-dimensional elastic as well as elastic-plastic finite element analyses were carried out to validate the crack driving force and T-stress from LINKpipe. The details of these models are reported by Jayadevan et al. (2004, 2005a). The finite element analyses were made using ABAQUS, with 20- noded isoparamteric three-dimensional solid elements and reduced integration. Unlike the complex 3-D models, the linespring model is rather simple. This model contains 31 shell elements along the length and 30 along the circumferential direction. Twelve line-spring elements are used to model the crack. Figure 3(a) shows the evolution of crack-tip opening displacement (CTOD) with applied moment for a typical surface cracked pipe (a/t=0.2, c/πr=0.1, D/t=20 and n=0.1) subjected to bending. Results predicted from line-spring and 3- D models are presented. First, these results demonstrate that the predictions from line-spring model are in excellent agreement with those from 3-D simulations. Further, Fig. 3(a) illustrates that in both models, CTOD first increases slowly with moment, but after a certain value of moment, CTOD increases exponentially. Finally, the crack ceases to open further when local buckling on opposite side initiates. Error! In order to demonstrate the accuracy of T-stress predictions from the line-spring model, the variation of biaxiality parameter (β=t(πa)1/2/k) along the crack front is displayed in Fig. 3(b). Evolutions of T-stress with CTOD in SENT specimens, predicted by line-spring model are shown in Fig. 4. In this case, the results are presented up to CTOD levels which are only just above the complete ligament yielding. This figure illustrate that the constraint loss increases with decrease in crack depth which is expected, Thaulow et al (2004b). Further, for any CTOD level in Fig. 4, the difference in constraint levels between different specimens remains almost the same. In fact, it has been verified that the biaxiality parameter computed for the same specimens using line-spring/shell model are in good agreement with the literature values. K / σ (πa) 1/2 (a) β = T (πa) 1/2 / K (b) Pipe - Bending a / t = D Link Mid-section s / c Surface Pipe - Tension a / t = D Link Mid-section s / c Surface Figure 3. Comparison between line-spring (LINK pipe) and 3-D FE calculations. (a) Evolution of CTOD with normalised stress intensity factor and (b) variation of biaxiality parameter along the crack front in a surface cracked pipe (a/t=0.2, c/pr=0.1, and D/t=20) tension Error! 3 Copyright #### by ASME

4 CTOD, mm a / t = SENT n = T / σ o (a) Figure 4. Evolution of T-stress with CTOD in SENT specimens for different crack depths. Engineering Critical Assessment To demonstrate the potential for direct calculations, the crack driving force for Engineering Critical Assessments has been calculated for a pipe loaded in tension. CTOD vs. applied strain was calculated according to LINKpipe, 3-D ABAQUS and BS7910 (with the software CrackWise), Fig.5. All parameters were kept constant except for the crack length (2c), varying from 4 to 30% of the circumference. For all cases, LINKpipe is very close to the 3-D calculations, or slightly conservative, while the analytical solutions are varying. The best result is obtained for a crack length of 10%. But the analytical result is unconservative for the short crack and very conservative for the long crack. The result demonstrates the need for direct calculations for the fracture assessment of pipelines. Ductile tearing A ductile crack growth model using line-spring finite element was proposed by Lee and Parks (1998) for fully plastic, quasi-static through-thickness crack growth in surface cracked shell structures. They employed a plane-strain slidingoff and cracking model to obtain the instantaneous crack tip opening angle in terms of the material parameters and the instantaneous slip-line angle and stress triaxiality at the crack tip. However, this approach is not straight forward and it requires determining some model parameters from experiments. A more simplistic approach to propagate the crack in line-spring model is to use the traditional material crack growth resistance curve. This is in accordance with the established use of the resistance curves to account for ductile tearing. Further, the constraint correction of the resistance curve Nyhus et al., (2002) can be easily included (b) (c) Figure 5. CTOD vs. strain for a pipe loaded in tension. Comparison between line-spring (LINKpipe), 3-D and analytical (BS7910/CrackWise) calculations. The crack length varies from (a) 4%, (b) 10% to (c) 30% of the circumference. 4 Copyright #### by ASME

5 in the simulations since the T-stress is readily available from the line-spring element The line-spring results from Fig. 5 are re-plotted in Fig. 6, including the effect of ductile tearing. These results Figure 7. The effect of crack depth on ductile tearing on CTOD vs. strain in surface cracked pipes under tension. Predicted from the crack growth line-spring model. Figure 6. The effect of crack length on ductile tearing on CTOD vs. strain in surface cracked pipes loaded in tension. The predictions are based on the crack growth line-spring model. The stationary line-spring results from Fig.5 are included for comparison. corresponds to a surface cracked pipe with a/t=0.2 and D/t=20 loaded in tension. The CTOD-strain relationship shows that before the initiation of crack growth, only a marginal increase in CTOD with increase in crack length is observed. But after the initiation of ductile tearing, a significant increase in CTOD at any given strain level can be noticed. The effect of crack depth at a constant crack length is displayed in Fig. 7. For the cases with a/t = 0.2 and 0.3, the results from the analyses of the stationary cracks are plotted to provide a direct comparison. The local responses displayed in Fig. 7 show that for any given strain level, the CTOD increases with increase in crack depth. Hence, the crack growth initiates at lower levels of deformation as crack depth increases. Thus, while the ductile tearing in shallowest crack (a/t = 0.1) starts at about 4% strain, the same for the deepest crack (a/t = 0.5) begins at strain levels below the yield strain. Further, as the crack depth increases, the stable crack growth regime gets shortened and unstable tearing starts at lower levels of deformation. Thus, the unstable ductile tearing in the deepest cracked pipe occurs almost just after the initiation, and no stable crack growth is observed in this case. Shown in Fig. 8 are the results obtained from the tensile loading of a surface cracked pipe with additional internal pressure. The magnitude of pressure is marked as the ratio of hoop stress caused by the internal pressure to the initial yield stress. The pressure load was applied first, and then the end displacements were applied gradually, since this loading sequence corresponds to realistic situations. The CTOD responses displayed in Fig. 8 show that with increase in magnitude of hoop stress, the CTOD at any given strain level increases significantly. For stationary cracks, Jayadevan et al. (2004) have verified from the 3D finite element analyses of surface cracked pipes that the biaxial loading strongly enhance the ligament localisation. Also, for the same deformation level, the biaxial loading increases the load carrying capacity of the ligament, which is also reflected in the global load response as shown in Fig. 8(b). This increased local loading for the same strain level leads to more enhanced local deformation, and hence, higher CTOD values under biaxial loading. More importantly, Fig. 8(a) demonstrates that as the magnitude of internal pressure increases, the unstable tearing begins at lower values of deformation level. In other words, the deformation capacity of the cracked pipe is significantly reduced under biaxial loading. This can clearly be seen from the global load responses (Fig. 8(b). 5 Copyright #### by ASME

6 Concluding remarks The use of an efficient and accurate line-spring model for fracture assessment of pipelines is studied in this work. Detailed 3-D analysis has been carried out for the verification of the line-spring method. Following are the main conclusions: -Fracture parameters estimated from the line-spring model for surface cracked pipes are in good agreement with those from 3-D simulations -The line-spring model is an efficient and accurate tool for constraint estimation in surface cracked pipes. -The applied CTOD calculated from analytical solutions (BS7910) can be conservative and unconservative, depending on the crack dimensions. -Ductile tearing strongly influences the CTOD-strain relationships in surface cracked pipes. A significant reduction in deformation capacity from the stationary case is noticed when ductile tearing is considered. As crack size increases, the effect of ductile tearing becomes more important. - Under biaxial loading, a pronounced effect of ductile tearing on the crack driving force relationships is noticed. With increase in magnitude of internal pressure, the deformation capacity is reduced significantly (a) ACKNOWLEDGEMENTS The authors gratefully acknowledge the support from the Joint Industry Project Fracture Control Offshore Pipelines. Also K R Jayadevan would like to thank the Norwegian Research Council for the financial support towards his research program REFERENCES Bruschi R., Torselletti E.,Vitali L.,Hauge M and Levold E., 2005.: Fracture Control Offshore Pipelines. Current status of fracture assessment for pipeline limitations and the need for development. OMAE 2005, June 12-16, Halikidiki, Greece. Jayadevan K R, Østby E, Thaulow C., Fracture response of surface cracked pipes under large deformations under tension. Int. J. Press. Vessels Piping, 81, (b) Figure 8. The effect of biaxial loading on ductile tearing in a surface cracked pipe under tension, predicted from the crack growth line-spring model. (a) Variations of CTOD and (b) global load with global strain. Jayadevan, K.R., Thaulow, C., Østby, E., Berg, E., Skallerud, B., Holthe, K., Nyhus, B., 2005a. Structural Integrity of Pipelines: T-stress by line-spring. Fatigue and Fracture of Engineering Materials & Structures (accepted for publication). Jayadevan K R, Berg,E, Thaulow,C.,Østby,E. and Skallerud,B. 2005b Numerical investigation of ductile tearing in surface cracked pipes using line-spring Submitted to Int. J. Solids and Structures 6 Copyright #### by ASME

7 Lee,H. and Parks,D.M Enhanced elastic-plastic line-spring finite element, Int. J. Solids Structures 32, pp Lee, H. and Parks, D. M Line-spring finite element for fully plastic crack growth-i. Formulation and onedimensional results. Int. J. Solids Structures, 35, LINKpipe, Verification manual LINKftr AS, Trondheim, Norway Nyhus, B., Zhang, Z.L., Thaulow, C., Normalisation of material crack resistance curves by the T- stress. In: Proceedings of 14th European Conference on Fracture, 8-13 Sept, 2002, Cracow, Poland. Nyhus B., Østby E., Knagenhjelm H. O., Black S. and Røstadsand P.,2005. Fracture Control Offshore Pipelines Experimental Studies on the Effect of Crack Depth and Asymmetric Geometries on the Ductile Tearing Resistance. OMAE 2005, June 12-16, Halikidiki, Greece. Rice,J.R. and Levy,N., 1972 The part-through surface crack in an elastic plate, J. Appl. Mech. 39, pp Sandvik A., Østby E., Naess A., Sigurdsson G. and Thaulow, C : Fracture Control Probabilistic Fracture Assessment of Circumferentially Surface Cracked Ductile PipelinesUsing Simplified Equations. OMAE 2005, June 12-16, Halikidiki, Greece. Skallerud B, Holthe K and Haugen B., Thin shell and surface crack finite elements for simulation of combined failure modes. Comp. Meth. Appl. Mech. Engng. (accepted for publication). Thaulow C, Østby E, Nyhus B, Zhang Z L and Skallerud B 2004a. Constraint correction of high strength steel: Selection of test specimens and application of direct calculations. Engng. Fract. Mech., 71, Thaulow C, Jayadevan K R, Skallerud B, Holthe K, Berg B, Østby B and Nyhus B., 2004b. Advances in computational procedures for the structural integrity of pipelines. Proc. of Int. Conf. on Advances in Structural Integrity, July 14-17, Indian Institute of Science, Bangalore, India. Østby E.,2005.: Fracture Control New Strain-Based Fracture Mechanics Equations Including the Effects of Biaxial Loading, Mismatch and Misalignment. OMAE 2005, June 12-16, Halikidiki, Greece. 7 Copyright #### by ASME