Net-section Collapse Research Articles

Ductile Tearing or Plastic Collapse?

Abstract Ductile fracture is characterized by a large amount of deformation. Two mechanisms may lead to ductile failure: local tearing may appear in front of a stress concentration region like a crack front or large geometry changes in a weak part of the structure can induce global collapse of the structure. For large cracks such as those considered in Leak Before Break studies, tearing analyses and net-section collapse criteria have been used. The present paper examines the link between these two mechanisms for a through-wall cracked pipe under bending and concludes that the transition from ductile tearing to collapse depends not only on material properties but also on geometrical parameters. The reference stress approach is a promising approach for predicting the transition, provided the transferability issue of j-resistance curve has been solved.

Limit Load Solution for Thin-Walled Cylinder with Circumferential Crack under Combined Internal Pressure, Axial Force, Bending Moment and Torsion Moment

T his research aims to establish the limit load solution for thin-walled cylinder with circumferential crack under combined internal pressure, axial force, bending moment and torsion moment. The solution is derived based on the net-section collapse principle and the von Mises yield criterion. The material considered in this work is assumed to be elastic-perfectly plastic. The solutions obtained from this work are compared with the results from the finite element models. The comparison shows that the equations established from NSC analysis provide acceptable results for the case of cracked cylinder under combined axial force and bending moment. For the case of cylinder subjected to internal pressure or torsional moment, however, these equations can be used to predict the limit load only if np ≤ 0.40 and nT ≤ 0.6 . This is because when the effects of internal pressure or torsional moment are included, the distribution of stresses on the crack plane at the yielding does not correspond to the NSC principal.

A simplified formula for calculating the limit load of cracked offshore wind turbine monopile under bending

A simplified methodology is proposed for calculating the plastic collapse (limit) bending moment load of a pipe with a circumferential flaw with an emphasis on its application for use in the assessment of cracked offshore wind turbine monopile using failure assessment diagrams. The proposed methodology is based on the theory of net section collapse (NSC) but differs from existing approaches in that it does not need idealisation and categorisation of the crack before assessment. The proposed methodology is validated against results presented in literature and also finite element analysis results. Although it is possible to obtain limit loads using FE analysis, this is computationally expensive and time consuming. The proposed approach allows for near-instantaneous calculation of limit load for any arbitrary crack configuration and loading direction. This is a significant development for the analysis of offshore wind turbine monopiles as it allows the suitability of the cracked structure to be assessed in pseudo-real time.

A unified theoretical solution of plastic limit load for the thin-walled pipeline with an incomplete welding defect

In this work, a unified theoretical solution of plastic limit load for thin-walled pipeline with an incomplete welding defect is proposed by the Net Section Collapse (NSC) criteria. The plastic limit torque of the thin-walled pipeline with an incomplete circumferential welding defect is calculated by the sand pile analogy method. The unified theoretical solutions of plastic limit loads for the pressure pipeline with a circumferential welding defect under combined tension, torsion and bending moment are deduced, and the influences of circumferential length and defect position on the plastic limit loads are discussed. The comparison with the finite element (FE) results show that the theoretical plastic limit loads of the pressured circumferentially defective pipeline based on the extended NSC criteria are reliable. The study can provide an important theoretical basis to establish the safety evaluations towards the pressure pipelines with incomplete welding defects.

Reference stress solutions for plates with embedded off-set elliptical cracks under combined biaxial forces and cross-thickness bending

The reference stress solutions for plates with embedded off-set elliptical cracks under combined biaxial forces and cross-thickness bending are derived based on the Mises yield criterion and net-section collapse principle. The newly developed reference stress solutions are compared with the reference stresses of plates with embedded rectangular cracks evaluated using the available limit load solutions. The developed reference stress solutions have been used to predict J via the reference stress J scheme. Elastic-plastic 3-D finite element (FE) analyses are used to calculate J values along the crack front and the results are compared with the reference stress predictions. The results show that the estimated J values based on the reference stress method with the reference stress solutions developed in this paper are very close to the FE J values, but the predictions may be non-conservative. However, the non-conservatism could be removed by simply applying a constant factor less than 1 to the reference stress solutions when they are used in the reference stress J scheme.

Applicability of Net-Section Collapse Load Approach to Multiple-Cracked Pipe Assessment: Numerical Study

In this paper, applicability of net-section collapse load approach to circumferential multiple-cracked pipe assessment is investigated using finite element (FE) damage analysis. The FE damage analysis based on the stress-modified fracture strain model is validated against limited fracture test data of two circumferential surface-cracked pipes. Then, the systematic parametric study is performed using the FE damage analysis for symmetrical and asymmetrical surface-cracked pipes. It is found that predictions using the net-section collapse load approach tend to be more accurate with increasing the distance between two symmetrical cracks. For asymmetrical cracks, it is found that the deeper crack plays a more important role and that the existing net-section collapse load expression can be potentially nonconservative. Idealization to symmetrical cracks based on the deeper crack is proposed.

Local and Global Reference Stress for Circumferential Irregular-Shaped Defects in Pipes

Numerical procedures for calculation of reference stresses for pipelines with circumferential defects, based on simulation of global and local ultimate plastic states, are proposed. There are some peculiarities of proposed procedures. First, the schematic analysis of the deformation process of pipe with surface defects is suggested, based on which two critical cases have been specified: Global (the net-section-collapse (NSC) criterion) and local, which are applicable for a very wide surface defect and for a sharp crack, respectively. The global solution also describes behavior of through-wall defects. Second, within the framework of the available NSC criterion the unified algorithm for determination of reference stresses (global solution) for irregular-shaped circumferential defects under multifactor loading (internal pressure, axial force, bending moment) is proposed. Third, according to the local modeling, the restricted capability to resist plastic deformations is takes into account by inserting of artificial symmetrical defect. The unified procedure for calculation of reference stresses (local solution) for pipe with irregular-shaped circumferential defects under multifactor loading is developed. Finally, the results obtained from the proposed solutions are compared with the ones from full-scale burst tests.

Uncertainty analysis for the net-section-collapse failure criterion of circumferentially cracked cylinders for multiple arbitrary-shaped circumferential cracks

In this manuscript, a generalized net-section-collapse (NSC) failure criterion of circumferentially cracked pipes with multiple arbitrary-shaped cracks is presented. This generalized NSC formulation is capable of predicting the NSC moment of a pipe with multiple arbitrary-shaped cracks distributed around the circumference of the pipe, regardless of whether they are distributed symmetrically or not. The case in which internal cracks straddle the compressive zone is accounted for in the present formulation. Closed form solutions are provided for the maximum moments of pipes containing multiple cracks with idealized shapes, namely constant depth, semi-elliptical and parabolic crack profiles. Through a series of examples, the results show the effectiveness and accuracy of the method. Using this method, quantification of the effect of the crack profile uncertainty on the maximum bending moment sustained by a cracked pipe is evaluated. It is demonstrated that while the uncertainty associated with the surface roughness of the crack profile has little to no effect on the maximum bending moment, irregular shape profiles have, not surprisingly, a large effect on the estimation of the maximum bending moment. In fact, it is mathematically shown that the uncertainty associated with the maximum bending moment is proportional to the magnitude of the crack profile uncertainty and inversely proportional to the square root of the uncertainty sampling size (i.e. surface roughness vs. irregular crack profile).

Global limit load solutions for thick-walled cylinders with circumferential cracks under combined internal pressure, axial force and bending moment – Part I: Theoretical solutions

Global limit load solutions for thick-walled cylinders with circumferential internal/external surface and through-wall defects under combined positive/negative axial force, positive/negative global bending moment and internal pressure are derived based on the von Mises yield criterion and the net-section collapse principle. Solutions for cases both with/without considering crack face contact when all or part of the crack is located inside the compressive stress zone are obtained. For some limiting cases, the solutions are compared with available solutions and with some published finite element (FE) data, showing good agreement. Systematic validation of the solutions using a wide range of elastic–perfectly plastic 3-D FE data is described in part II.

A Global Limit Load Solution for Plates With Embedded Off-Set Elliptical Cracks Under Combined Tension and Bending

A global limit load solution is derived in this paper for embedded off-set elliptical cracks in a plate under combined tension and bending, based on the net-section collapse principle. The new limit load solution is validated using 3D elastic-perfectly plastic finite element (FE) limit analyses. The results show that the limit load solution developed in this paper is conservative and close to the elastic-perfectly-plastic FE results. The global limit load solution is then compared with the limit load solution based on the rectangular crack assumption, showing that the difference between the two solutions is negligible as the ratio of crack length to the plate width is less than 0.25. However, the difference may become significant when the ratio approaches one.

Design of a (mini) wide plate specimen for strain-based weld integrity assessment

Wide plate tension tests are commonly executed to investigate the integrity of defective weldsunder a uniaxial load. The specimen can be flat or curved, depending on the geometry from which it hasbeen extracted (plate or pipe). Despite its usefulness, the design of the (curved) wide plate test is still notstandardized up-to-date. This paper compares two specimen designs with a different length-to-width ratiothrough finite element analysis, using a design-of-experiments approach to account for different influentialfactors. The results reveal significant differences between the interpretation of tests with net sectioncollapse and gross section collapse, promoted by weld strength overmatch. Further, both investigateddesigns tend to provide similar estimates of failure mode, strain capacity and crack driving force. Hence,the shorter specimen is considered an acceptable alternative to the slightly more representative longerspecimen.

Plastic limit load analysis for pressure pipe with incomplete welding defects based on the extended Net Section Collapse Criteria

With von Mises yield criterion, the loading range of Net Section Collapse (NSC) Criteria is extended from combined tension and bending loadings to combined bending, torsion and internal pressure loadings. A new theoretical analyzing method of plastic limit load for pressure pipe with incomplete welding defects based on the extended NSC Criteria is presented and the correlative formulas are deduced, the influences of pipe curvature, circumferential length and depth of incomplete welding defects on the plastic limit load of pressure pipe are considered as well in this method. Meanwhile, according to the orthogonal experimental design method, the plastic limit loads are calculated by the finite element method and compared with the theoretical values. The results show that the expressions of plastic limit load of pressure pipe with incomplete welding defects under bending, torsion and internal pressure based on extended NSC criteria are reliable. The study provides an important theoretical basis for the establishment of safety assessment measure towards pressure pipe with incomplete welding defects.

Improved Prediction Method for Estimating Notch Elastic-Plastic Strain

Notch stress-strain conversion (NSSC) rules are widely used to estimate nonlinear and history-dependent stress-strain behavior of the notch components or structures. This paper focuses on the estimation of stress and strain using the conventional NSSC rules and linear elastic analysis by considering the entire relaxation locus of the component during inelastic action. On the basis of local effects, net-section collapse, and reference stress, a simple method for estimating inelastic strain in the vicinity of stress concentrations is proposed. The accuracy of the method is compared with elastic-plastic finite element analysis for several notch configurations exhibiting two-dimensional and three-dimensional effects.

Modified expression for predicting the bending resistance of a locally corroded pipeline and its experimental verification

In practical service, transmitted pipelines may suffer from corrosion, which affects the safety of the component. For an engineering pipeline subjected to local corrosion, the pipe wall becomes thinner locally, and the bending load bearing capacity is inevitably reduced. Therefore, proper prediction of the bending resistance of a pipeline with locally corroded defects is very significant with respect to the safety assessement of a servicing pipeline. In the present paper, the effect of the length of local thinning in a pipe in the longitudinal direction is considered. A modification to the net-section collapse failure (NSC) criterion is then proposed. 3-point bending experiments for J55 pipe with artificially machined local thinning on the outer-surface of the pipe are conducted to verify the modified expression. Comparison of the predictions of the modified NSC with the experimental data indicates that the modified expression can predict the general variation tendency of the normalized bending resistance (M/M0) with the relative longitudinal defect lenght ( $$(L/\sqrt {Rt} )$$ ). However, discrepancy between the theoretical prediction and experimental data is apparent for a small relative longitudinal defect leght ( $$L/\sqrt {Rt} \sim 1$$ to 3). This discrepancy might result from the stress concentration effect, which has not been considered in the model.

Limit load solutions for thin-walled cylinders with circumferential cracks under combined internal pressure, axial tension and bending

Limit load solutions for thin-walled cylinders with circumferential cracks under combined axial tension, bending and pressure are developed, considering the effect of pressure-induced hoop stress via the Mises yield criterion. The new solutions cover thin-walled cylinders with constant-depth or semi-elliptical surface cracks and through-wall cracks. The predictions of the new Mises-based limit load equation agree very well with elastic-perfectly plastic finite element results. However, net-section collapse equations, which ignore the hoop stress in the cylinder, tend to over-estimate the limit load when internal pressure is dominant. The solution for constant-depth cracks without crack closure is proposed for inclusion in fitness-for-purpose assessment procedures for constant-depth or semi-elliptical surface cracks and through-wall cracks.

Modified expression for estimating the limit bending moment of local corroded pipeline

During service, engineering pipelines may suffer from corrosion, which may affect the safety of the component. For an engineering pipeline subjected to local corrosion, the wall becomes thinner locally and the bending load bearing capacity reduces. Therefore, the evaluation of the bending limit moment for a pipeline with such locally corroded damage is important for assuring safety. In this paper, taking the local thinning length of a pipe in the longitudinal direction into consideration the net-section collapse failure (NSC) criterion, proposed by Kanninen et al., is modified. The limit moment estimated from the modified NSC expression for the local wall-thinning pipe under pure bending is compared with those from 3D elastic–plastic finite element computation. The results show that the modified expression could reflect the longitudinal size effect of the local corrosion, and the estimated results agree with those of the finite element method; the limit moment of the pipe is affected not only by the width of the defect but also by the longitudinal length of the defect. When the relative longitudinal length of the defect (L/ Rt ) exceeds some critical value (around 1.5), the results from the net-section collapse criterion (NSC) are in reasonable agreement with the results from both the finite element method and the modified expression. Therefore, the NSC formula could be employed to assess the limit load-carrying capability for locally corroded pipe with relatively long defects under bending, while for relatively short defects, the modified expression and FEM give reasonable results compared to the conservative NSC.

Probabilistic elastic-plastic fracture analysis of circumferentially cracked pipes with finite-length surface flaws

A probabilistic model was developed for predicting elastic-plastic fracture response and reliability of circumferentially cracked pipes with finite-length, constant-depth, internal surface cracks subject to remote bending loads. It involves engineering estimation of energy release rate, J-tearing theory for characterizing ductile fracture, and standard methods of structural reliability theory. The underlying J-estimation model is based on the deformation theory of plasticity, a constitutive law characterized by power law model for stress-strain curve, and an equivalence criterion incorporating reduced thickness analogy for simulating system compliance due to the presence of a crack. New analytical equations were developed to predict J-integral and are shown to be fairly accurate when compared with generally more accurate elastic-plastic finite-element results. Using this J-estimation method, fast probability integrators and simulation methods were formulated to determine the probabilistic characteristics of J. The same methods were used later to predict the probability of crack initiation and net-section collapse as a function of the applied load. Numerical examples are provided to illustrate the proposed methodology. The results show that probabilistic analysis based on net-section collapse (without any margin) may significantly overpredict the reliability of surface-cracked pipes.

Limit moment of local wall thinning in pipe under bending

In engineering practice, pipe containing local wall thinning may be subjected to bending load. The existence of local wall thinning on pipe surface impairs the load-carrying capacity of pipe. In order to maintain the integrity of the pipe containing local wall thinning, it is very important to develop a method to evaluate such a pipe with local wall thinning under bending. In this paper, the limit moment of local wall thinning pipe under pure bending is computed employing 3D elastic–plastic finite element analysis. The results show that the limit moment of pipe is affected not only by the width of defect but also by the longitudinal length of defect. When the longitudinal length of defect overpasses some critical value, the results from net-section collapse criterion (NSC) are in very reasonable agreement with the results from finite element analysis. Therefore, the NSC formula can conservatively be used to assess the limit load-carrying capability of local wall thinning pipe under bending.

Net-section-collapse analysis of circumferentially cracked cylinders—part I: arbitrary-shaped cracks and generalized equations

This is the first in a series of two papers generated from a study on net-section-collapse (NSC) analysis of circumferentially cracked pipes. In this paper (part I), a generalized NSC method is presented to predict the maximum moment of a circumferentially cracked pipe with a variable-depth internal surface crack subject to combined bending and tension (pressure-induced) loads. Two sets of equations were derived. The first set involves the case where the entire crack is subjected to tension, while the second set involves the case where part of the crack is subjected to compression. For the second set, separate equations were derived for both tight (closed) and blunt (open) cracks. In both cases, these equations are based on the static equilibrium of the cracked pipe subject to externally applied bending moment and pipe internal pressure. The generalized method is capable of predicting NSC moment of a pipe with any arbitrary-shaped crack that has symmetry with respect to the bending plane of the pipe. Using this method, the maximum moments of cracked pipes with constant-depth, elliptical, and parabolic cracks were calculated to study the influence of crack shape on a pipe’s load-carrying capacity. Later, the method was applied to analyze two full-scale pipe fracture experiments. The results show that the generalized NSC method can accurately predict experimental moments when the failure mechanism is governed by the limit–load criterion.

Net-section-collapse analysis of circumferentially cracked cylinders—Part II: idealized cracks and closed-form solutions

This paper (Part II), which is the second in a series of two papers, presents new closed-form solutions for net-section-collapse (NSC) analysis of circumferentially cracked pipes for several idealized crack shapes subjected to combined bending and tension (pressure-induced) loads. They are based on further simplifications of generalized NSC equations developed in a parallel study. Analytical solutions were developed for cracks with constant-depth, parabolic, and elliptical shapes. For all three crack shapes, separate equations were developed when the entire crack is subjected to tension and when part of the crack is subjected to compression. For part of the crack subjected to compression, the proposed equations can handle both tight (with crack-closure) and blunt (without crack-closure) cracks. Currently, of the three crack shapes examined in this paper, previous analytical solutions exist only for the constant-depth crack. Hence, they should be useful for pipe fracture analysis involving other crack shapes, such as the elliptical and parabolic cracks. The analytical solutions were validated by numerical analysis based on the generalized NSC equations.