Line-spring Finite Element Research Articles

Response of Surface Cracks in Tubular Members During Global Buckling and Instability

Beam-columns in compression are subject to potential buckling. If the axial load is combined with a global bending moment, member instability may occur. One situation where this can occur is for pipelines on the seabed, where thermal strains induce significant compression in the pipeline due to constrained expansion. This may lead to upheaval buckling or snaking. In this condition one should also assess how a weld defect in the buckle zone will evolve. If the crack is located on the compressive side of the cross section, the crack remains closed. If the crack is located on the side where beam bending eventually leads to tension, fracture may develop. This has not been studied sufficiently in the past, and is the topic of the present paper. Here the interesting case of initial compression, with closure of the crack, is followed by a transition to tension and opening of the crack when the transverse displacement increases in the post-buckling regime. Simple cases of tubular beam-columns with surface cracks are investigated for cracks growing in a ductile manner. The simulations are based on shell and linespring finite elements.

CYCLIC PLASTICITY MODELLING FOR ANDES THIN SHELL AND LINE-SPRING FINITE ELEMENTS

This paper presents a proposed methodology to account for cyclic plastic response of the thin shell ANDES and line-spring finite elements. A through thickness integration scheme is employed for the shell element and stress resultant plasticity is used for the line-spring element. A simplified contact formulation to account for crack closure in the line-spring element is also presented. Numerical comparisons between the proposed models and detailed 3D analyses (pipes) are carried out and presented herein. A comparison between the present implementation and large scale experiment of a surface cracked pipe subjected to large cyclic plastic strains is also presented. The purpose of the presented implementation is to account for cyclic loading in pipeline technology where significant amount of plasticity in the loading cycles occurs.

Failure Assessment Diagrams of Semi-Elliptical Surface Crack with Constraint Effect

For accurate failure assessment, a second parameter like T-stress describing the constraint is needed in addition to the single parameter J-integral. In this work, selecting the structures of surface-cracked plate and pipe, we perform line-spring finite element modeling, and accompanying elastic-plastic finite element analyses. We then present a framework, which includes the constraint effects in the R6 FAD approach for failure assessment of cracked-structures.

Failure Assessment Diagrams of Semi-Elliptical Surface Crack with Constraint Effect

For accurate failure assessment, a second parameter like T-stress describing the constraint is needed in addition to the single parameter J-integral. In this work, selecting the structures of surface-cracked plate and pipe, we perform line-spring finite element modeling, and accompanying elastic-plastic finite element analyses. We then present a framework, which includes the constraint effects in the R6 FAD approach for failure assessment of cracked-structures.

Two-parameter fracture mechanics and circumferential crack growth in surface cracked pipelines using line-spring elements

A procedure for constraint correction of crack growth resistance curves for single edge notched specimens and for pipe geometries is presented. The procedure is based on FE models with the combination of shell- and line-spring finite elements. Crack tip opening displacement and T-stress are employed, and ductile crack growth is accounted for. Experimental crack growth resistance curves are obtained for both single edge notched tension- and bending-specimens for different crack depths to cover significantly different constraint levels. To account for different constraint levels, a method to scale the resistance curve using the T-stress is implemented. The analyses include ductile crack growth in both the circumferential and thickness directions. The effect of circumferential crack growth with biaxial loading is also presented. The results from the line-spring model are compared with detailed 3D-models for verification of the implementation of circumferential crack growth. The importance of including crack growth in circumferential direction is discussed based on numerical parametric studies. A measure to quantify the importance of circumferential crack growth is proposed.

Constraint of Semi-Elliptical Surface Cracks in T and L-Joints

Critical defects in pressure vessels and pipes are generally found in the form of a semielliptical surface crack, and the analysis of which is consequently an important issue in engineering fracture mechanics. Furthermore, in addition to the traditional single parameter K or J-integral, the second parameter like T-stress should be measured to quantify the constraint effect. In this work, the validity of the line-spring model is investigated by comparing line-spring J-T solutions to the reference 3D finite element J-T solutions. A full 3D-mesh generating program for semi-elliptical surface cracks is employed to provide such reference 3D solutions. Then some structural characteristics of the surface-cracked T and L-joints are studied by mixed mode line-spring finite element. Negative T-stresses observed in T and L-joints indicate the necessity of J-T two parameter approach for analyses of surface-cracked T and L-joints.

Two-parameter fracture assessment of surface cracked cylindrical shells during collapse

The present study addresses the use of CTOD and T-stress in fracture assessments of surface cracked shell structures. A new software is developed for this purpose, denoted LINK pipe. It is based on a combination of a quadrilateral assumed natural deviatoric strain thin shell finite element and an improved linespring finite element. Plasticity is accounted for using stress resultants. A power law hardening model is used for shell and linespring materials. A co-rotational formulation is employed to represent nonlinear geometry effects. With this, one can carry out nonlinear fracture mechanics assessments in structures that show instabilities due buckling (local/global), ovalisation and large rigid body motion. Many constraint-measuring parameters have been proposed, with the Q-parameter or the T-stress being the most popular ones. Solid finite element meshing for complex structures such as pipes containing semi-elliptical surface cracks in order to compute Q is at present not a feasible approach. However, shell structures are most conveniently meshed with shell finite elements, and the linespring finite element is a natural way of accounting for surface cracks. The T-stress is readily obtained from the linespring membrane force and bending moment along the surface crack. In this study we present a new approach to analyse cracked shell structures subjected to large geometric changes. By numerical examples it is shown how geometric instabilities and fracture compete as governing failure mode.

Numerical investigation of ductile tearing in surface cracked pipes using line-springs

Accurate prediction of crack-driving force equations is important in any pipeline fracture assessment program. In highly ductile materials, such as pipeline steel, a considerable amount of stable crack growth can be tolerated before the failure of the structure. The existing methods use simplified analytical procedures to account for ductile tearing, and they often result in conservative critical crack sizes. Further, none of the published numerical tools for modelling crack growth is suitable for engineering applications. This work describes a simple method for simulating through-thickness ductile tearing in surface cracked pipes, using line-spring finite elements. The crack growth resistance curve is used to advance the crack front. The line-spring results are verified using crack growth simulations employing the Gurson damage model. Finally, a detailed parametric study is carried out to examine the effect of ductile tearing on crack driving force relationships in circumferentially surface cracked pipes. The results demonstrate that considering ductile tearing is important in fracture assessment procedures for pipelines.

Thin shell and surface crack finite elements for simulation of combined failure modes

In this study we present a new approach to analyse cracked shell structures subjected to large geometric changes. It is based on a combination of a rectangular assumed natural deviatoric strain thin shell finite element and an improved linespring finite element. Plasticity is accounted for using stress resultants. A power law hardening model is used for shell and linespring material. A co-rotational formulation is employed to represent nonlinear geometry effects. With this, one can carry out nonlinear fracture mechanics assessments in structures that show instabilities due buckling (local/global), ovalisation and large rigid body motion. By numerical examples it is shown how geometric instabilities and fracture compete as governing failure mode.

Closed form line spring yield surfaces for deep and shallow cracks: formulation and numerical performance

The line-spring finite element is a versatile numerical tool for performing engineering fracture mechanics analysis of surface cracked shells. The accuracy of the line-spring finite element solution for deep/medium-sized cracks has shown to be higher than the accuracy for the shallow-sized ones. Proper treatment of shallow cracks is important because they are the ones most frequently encountered in engineering practice. Accurate yield surfaces of plane-strain single edge-cracked specimens having shallow, as well as deep, cracks are developed here in order to improve the overall performance of the line-spring element. The yield surface is represented by equations that automatically satisfy the convexity requirement and that fit the result of limit load analyses. The present study addresses, furthermore, the performance of the backward Euler return algorithm for one of the accurate yield surface formulated here, by means of iso-error maps.

Efficient fracture assessment of pipelines. A constraint-corrected SENT specimen approach

Reeling has proven to be an efficient and cost effective method for offshore pipelaying. During the reeling process the pipe undergoes deformation that can strain the material by 1–2%. The existing failure assessment methods often turn out to be too conservative to allow such a strain level in the structure. The amount of conservatism can be significantly reduced by using a new failure assessment approach developed by SINTEF. This approach depends on finite element calculations for establishing the non-linear fracture mechanics parameters and the stress and strain distributions in the pipe. The present study addresses the performance of shell and line spring finite elements as a cost effective tool for performing such numerical calculations.

Constraint of Semi-elliptical Surface Cracks in T and L-joints

Critical defects in pressure vessels and pipes are generally found in the form of a semi-elliptical surface crack, and the analysis of which is consequently an important problem in engineering fracture mechanics. Furthermore, in addition to the traditional single parameter K or J-integral, the second parameter like T-stress should be measured to quantify the constraint effect. In this work, the validity of the line-spring finite element is investigated by comparing line-spring J-T solutions to the reference 3D finite element J-T solutions. A full 3D-mesh generating program for semi-elliptical surface cracks is employed to provide such reference 3D solutions. Then some structural characteristics of the surface-cracked T and L-joints are studied by mixed mode line-spring finite element. Negative T-stresses observed in T and L-joints indicate the necessity of J-T two parameter approach for analyses of surface-cracked T and L-joints.

Failure Assessment Diagrams of Semi-Elliptical Surface Crack with Constraint Effect

In recent years, the subject of remaining life assessment has drawn considerable attention in the power generation industry. In power generation systems a variety of structural components, such as steam pipes, turbine rotors, and superheater headers, typically operate at high temperatures and high pressures. Thus a life prediction methodology accounting for fracture and rupture is increasingly needed for these components. For accurate failure assessment, in addition to the single parameter such as K or J-integral used in traditional fracture mechanics, the second parameter like T-stress describing the constraint is needed. The most critical defects in such structures are generally found in the form of semi-elliptical surface cracks in the welded piping-joints. In this work, selecting the structures of surface-cracked plate and straight pipe, we first perform line-spring finite element modeling, and accompanying elastic-plastic finite element analyses. We then present a framework for including constraint effects (T-stress effects) in the R6 failure assessment diagram approach for fracture assessment.

Line-spring finite element for fully plastic crack growth—I. Formulation and one-dimensional results

A line-spring finite element model is developed to resolve fully plastic, quasi-steady, through-thickness crack growth in plane strain single-edge-cracked (SEC) specimens and surface-cracked plate/shell structures. The plane strain sliding-off and cracking model of McClintock et al. (1995) is adopted to obtain the instantaneous crack-tip opening angle (CTOA) in terms of material parameters and the instantaneous slip-line angle and stress triaxiality at the crack-tip. The slip-line angle and crack-tip stress triaxiality are calculated approximately using the least upper bound method of Kim et al. (1996a). Utilizing these approaches, the generalized forces transmitted by the line-spring finite element provide the constraint-dependent CTOA. The increment of crack extension is then determined from the kinematic relation with incremental crack-tip opening displacement through CTOA. Detailed description of the model, as incorporated into the ABAQUS (1993) finite element code in the form of a user-defined element, is given in Part I. Parametric studies in plane strain SEC specimens are carried out to examine the effects of loading type, ductility and strain hardening on plane strain crack extension behavior, and the effects of elastic surroundings on structural stability. Applications of the line-spring model to problems of surface-cracked plate and pipe are presented in Part II (Lee and Parks, 1998).

Line-spring finite element for fully plastic crack growth—II. Surface-cracked plates and pipes

Crack-tip opening angle (CTOA) is generally considered as the most operable fracture descriptor for fully plastic, quasi-steady, extensive crack extension. In Part I, based on the CTOA crack growth criterion, a line-spring finite element model was presented to resolve through-thickness crack growth in plane strain single-edge-cracked specimens and surface-cracked plate/shell structures under fully plastic loading. With constraint-dependent CTOA and some supplemental kinematic relations given, the line-spring model ultimately monitors crack extension from the history of generalized displacements. The model was implemented in the implicit ABAQUS finite element code (1993b) in a user-defined element form. Following the plane strain parametric studies in Part I, we further apply the line-spring model to the problems of surface-cracked plates and pipes in Part II here. Effects of material hardening, configuration and location of the surface crack on the histories of penetration-displacement/pressure are examined in a remotely-stretched plate and a pressurized cylindrical vessel. As the most plausible exercise of a stable crack propagation leading to leak-before-break failure, a circumferentially cracked pipe subject to pure bending is selected. Evolution of CTOA along the crack-front and surface crack enlargement pattern are examined for each case. Experimentally-observed CTOA values for the remotely-stretched plate are interpreted in light of the model prediction.

Enhanced elastic-plastic line-spring finite element

The elastic-plastic line-spring finite element of Parks and White (1982), as implemented in the ABAQUS finite element code (1988b), is modified in several ways for a better evaluation of crack-tip deformation parameters such as K1, J, crack-tip opening displacement and crack-tip stress triaxiality, the last of which is inferred or measured by the so-called T-stress and Q-stress parameters. An effective crack length formulation is introduced to capture the nonlinearity due to contained plane strain crack-tip plastic deformation, the size and orientation of which are known to be sensitive to the sign and magnitude (relative to yield strength) of the T-stress. More accurate yield surfaces, obtained from finite element limit analyses of plane strain single-edge cracked specimens, are employed to more sharply define the behavior of the line-spring model in the fully plastic region. More accurate relationships between incremental plastic crack-tip opening displacement and incremental load point displacement/rotation are also incorporated into the model for shallow crack configurations under fully plastic loading. The modified line-spring model is then applied to surface cracked plate problems having a wide range of crack-tip constraints, and the feasibility of implementing J-T(Q) based two-parameter characterizations of elastic-plastic crack front fields via simplified line-spring elements is examined.

Elastic-Plastic Line-Spring Finite Elements for Surface-Cracked Plates and Shells

The elastic line-spring finite element of Parks, et al. [1], which was incorporated into the ABAQUS© finite element program, is extended to include elastic-plastic response for approximate evaluation of the J-integral in surface-cracked plates or shells. J-analysis of a long axial crack in a pressurized cylinder is performed both with the virtual crack extension method and with a single elastic-plastic line-spring element attached to a 180-deg ring of shell elements constrained to (axial) plane strain. Agreement of the two models is generally good, both in the elastic range (as was noted earlier by Buchalet and Bamford) and in the plastic range. An axially cracked, internally pressurized cylinder containing a semi-elliptical flaw of aspect ratio a/c = 1/3, and of varying maximum relative depths a/t has also been analyzed.