Crack Tip Opening Displacement Estimation Research Articles

Numerical investigation of CTOD estimation methods for laser welds

This paper proposes an estimation method for crack tip opening displacement (CTOD) in laser welds. The theoretical model for CTOD estimation developed by Dugdale and Bilby et al. (DBCS model) was used for laser-welded plates. The yield stress of the laser weld metal and narrow hard zone width affected the CTOD, and the correction of yield stress by using the DBCS model to obtain a suitable CTOD estimation was investigated. To apply the DBCS model to CTOD estimation for laser welds, an equivalent yield stress concept was proposed. The equivalent yield stress was affected by the strength mismatch ratio and hard zone width, because the yield stress of the laser weld metal decreases with the constraint loss caused by the plastic deformation that occurred in the base metal. The predicted CTOD from the value of applied load obtained using the proposed estimation method agrees well with experimental critical CTODs for laser welds of both 780 and 520 MPa class structural steel.

Formulation of CTOD design curve considering the yield to tensile ratio

The Crack Tip Opening Displacement (CTOD) design curve approach is one of the fracture assessment procedures for estimating CTOD as an elastic-plastic fracture driving force, and is used for the assessment of flaws in welded structures. The Japan Welding Engineering Society (JWES) has produced a semi-empirical CTOD design curve, where CTOD is calculated from the local strain acting on the assumed crack, the crack size and the yield strain of the material. CTOD should be estimated by using all the factors influencing the crack driving force in the welded joint, but the yield to tensile ratio, Y/T, which relates to strain hardening behavior, is not used for the CTOD design curve. On the other hand, the new CTOD calculation formula adopted by the JWES CTOD fracture toughness testing standard uses Y/T, and derived CTOD values from the formula are affected by Y/T. Consequently, there is a mismatch in CTOD calculation between the fracture driving force of welded structures and the fracture toughness of standard specimens. In this study, Y/T was considered for formulating a new CTOD design curve. CTOD estimated by the new design curve was compared with CTOD obtained by the finite element analysis of a corner boxing fillet welded joint. The new CTOD design curve contributes to a good CTOD estimation for different Y/T welded joint models.

Nonlinear elastic–plastic stress investigation for two interacting 3‐D cracks in offshore pipelines

AbstractUnder continuous loading conditions, small closely distanced cracks can grow and coalesce into a large one that may subsequently pose a threat to the integrity and safety of structures. Although many research works were carried out for predicting fatigue growth of multiple cracks, few papers focusing on nonlinear elastic–plastic analysis of multiple cracks' fracture behaviours can be referred to. In this study, 3‐D elastic–plastic investigation has been performed on fracture behaviours of two collinear cracks located in offshore pipelines. The influences of the cracks configuration, the separation distance and internal pressure of the pipeline on the crack behaviours are investigated. On the basis of the numerical results, a new strain‐based crack tip opening displacement estimation method is proposed for assessing the fracture behaviour of flawed pipelines with two interacting collinear cracks.

Strain-based CTOD estimation formulations for fracture assessment of offshore pipelines subjected to large plastic deformation

The extreme loading conditions, i.e. the large plastic bending combined with high internal pressure, and the potential cracks or flaws in the welds pose tremendous challenges to the structural integrity for offshore pipelines. In this paper, the fracture response of offshore pipeline with semi-elliptical surface crack under large plastic deformation is analyzed through 3-dimensional finite element simulations. Extensive parametric studies are performed to investigate the influences of the crack geometry, strain hardening coefficient and internal pressure on the evolutions of crack tip opening displacement (CTOD). Furthermore, by virtue of response surface methodology, the new strain-based CTOD estimation formulations are proposed to assess the fracture behavior of flawed pipelines subjected to pure bending load as well as biaxial load, respectively.

J and CTOD estimation formulas for C(T) fracture specimens including effects of weld strength overmatch

This work focuses on an evaluation procedure to determine the elastic–plastic J-integral and Crack Tip Opening Displacement (CTOD) fracture toughness based upon the η-method for C(T) fracture specimens made of homogeneous and welded steels. The primary objective of this investigation is to enlarge on previous developments of J and CTOD estimation procedures for this crack configuration while, at the same time, addressing effects of strength mismatch on the plastic η-factors. The present analyses enable the introduction of a larger set of factors η for a wide range of crack sizes (as measured by the a/W-ratio) and material properties, including different levels of weld strength mismatch, applicable to pipeline and pressure vessel steels. Very detailed non-linear finite element analyses for plane-strain and 3-D models of C(T) fracture specimens with centerline-cracked welds provide the evolution of load with increased load-line and crack mouth opening displacement required for the estimation procedure. Overall, the present study, when taken together with previous investigations, provides a fairly extensive body of results to determine parameters J and CTOD for different materials using C(T) specimens with varying overmatch conditions.

Difference between ASTM E1290 and BS 7448 CTOD Estimation Procedures

Since the British Standards Institution (BSI) standardized BS 5762 in 1979, a popular way of calculating the Crack Tip Opening Displacement (CTOD) has been the use of the plastic hinge model with an assumed rotational centre. The American Society for Testing and Materials (ASTM) previously accepted the plastic hinge model and standardized E1290 in 1989. However, ASTM revised E1290 in 2002, and has proposed a fracture parameter conversion from the J-integral to CTOD. These two different CTOD calculations probably lead to confusion for Fitness-for-Service (FFS). The Fracture Toughness Study Committee of the Japan Welding Engineering Society (JWES) organized a working group, and the effects of CTOD testing methodology on CTOD values were investigated. In this paper, the results of CTOD round-robin tests in the working group are summarized, and the difference between the critical CTOD values obtained by ASTM E1290–02 and those by BS 7448, which involves the plastic hinge model, is described.

WES2805における溶接継手止端部き裂のCTOD評価に用いる応力集中とひずみの計算

WES 2805, a Japanese fitness-for-service procedure, proposes a crack tip opening displacement (CTOD) design curve for the brittle fracture assessment of welded joints, where the local strain acting on the cracked region, ε, is calculated using the stress concentration factor, Kt, and ε is converted to CTOD. However, in WES 2805, Kt, is shown as a few constants that depend on the ratio of crack depth, α, to the welded joint thickness, t, and the constants can be excessively conservative. In this study, the relation between Kt and the stress intensity magnification factor, Mk, was theoretically indicated, and the utility of Mk in the design curve was investigated for three kinds of welded joints. In addition, the local average strain by area was calculated by finite element analysis, and was used for the design curve instead of ε. It was demonstrated that constant Kt was sometimes excessively high and Mk was helpful in modifying Kt. Moreover, the local average strain by area contributes to good CTOD estimation, especially for a toe crack in a load-carrying fillet welded cruciform joint.

Reference Stress Approximations for J and COD of Circumferential Through-Wall Cracked Pipes

Reference stress approximations for the J integral and crack tip opening displacement (COD) for circumferential through-wall cracked pipes under tension and under bending are reported. The proposed J estimation equation is fully compatible with the existing reference stress based J estimation, currently embedded in the R6 assessment procedure, but involves a slightly different definition of the reference stress, using an optimised reference load instead of the limit load. This modification enhances the accuracy of the J estimation for circumferentially cracked pipes. Confidence in the proposed equation is gained from the significantly reduced hardening dependence of the plastic influence functions in the GE/EPRI method. The proposed COD estimation equation includes two further modifications. One is the use of a power-law fit to the plastic portion of the stress strain data, instead of the use of the actual stress strain data. In this context, a robust estimation equation for the strain hardening index is given. The other modification is to the plasticity correction term in contained yielding. A lower bound COD estimation equation is also given, similar to the R6 option 1 Jestimation curve, which is suitable when only limited tensile properties are available. The resulting estimation equations are simple to use. Comparisons with experimental pipe test data show that the proposed COD estimation equations provide overall good agreement, which gives confidence in applying them to Leak-before-Break (LBB) analyses.

Crack tip opening displacement estimation formulae for C(T) specimens

Improved formulae for estimating crack tip opening displacement (CTOD) from test records of compact tension (C(T)) specimens are developed. Two-dimensional, plane strain, finite element analyses of 1T C(T) specimens are made for normalized crack depths, a/ W, of 0.40–0.70 using Ramberg–Osgood material behavior with strain hardening coefficients n=5, 10, and 20. Finite element predictions of J, CTOD, crack mouth opening displacement (CMOD) and load are used to obtain proportionality constants relating the area under the load–CMOD pl curve to J pl, and J to CTOD in terms of a/ W and n. Improvements in CTOD estimates of 25% over existing estimation methods are obtained. Correction factors for displacements measured on the specimen front face instead of the load line are also examined.

Jand CTOD Estimation Equations for Shallow Cracks in Single Edge Notch Bend Specimens

AbstractFracture toughness values determined using shallow cracked single edge notch bend. SE(B), specimens of structural thickness are useful for structural integrity assessments. However, testing standards have not yet incorporated formulas that permit evaluation of J and CTOD for shallow cracks from experimentally measured quantities (i.e., load, crack mouth opening displacement (CMOD), and load line displacement (LLD)). Results from two-dimensional plane strain finite element analyses are used to develop J and CTOD estimation strategies appropriate for application to both shallow and deep crack SE(B) specimens. Crack depth to specimen width (a/W) ratios between 0.05 and 0.70 are modeled using Ramberg-Osgood strain hardening exponents (n) between 4 and 50. The estimation formulas divide J and CTOD into small scale yielding (SSY) and large scale yielding (LSY) components. For each case, the SSY component is determined by the linear elastic stress intensity factor. Kf. The formulas differ in evaluation of the LSY component. The techniques considered include: estimating J or CTOD from plastic work based on load line displacement (Apl∣CMOD), from the area under a load versus plastic crack mouth opening displacement diagram (Apl∣CMOD), and from the plastic component of crack mouth opening displacement (CMODpl). Apl∣CMOD provides the most accurate J estimation possible. The finite element results for all conditions investigated fall within 9% of the following formula. J=K2(1−v2)F+ηJ−CBbApl∣CMOD whereηJ−C=3.785−3.101aW+2.018(aW)2 The insensitivity of ηJ−C to strain hardening permits J estimation for any material with equal accuracy. Further, estimating J from CMOD rather than LLD eliminates the need to measure LLD, thus simphfying the test procedure. Alternate estimates of J and CTOD from measured plastic areas have equivalent accuracy to this formula; however, the η coefficients in these equations depend on the strain hardening coefficient. CTOD estimates based on scalar proportionality of CTODlsy, and CMODpl, such as that used in ASTM E 1290, Test Method for Crack-Tip Opening Displacement (CTOD) Fracture Toughness Measurement, are highly inaccurate especially for materials with considerable strain hardening.

CTOD estimates of surface cracked wide plates in bending—III. The wide plate with overmatched welded joint

Applied crack tip opening displacement (CTOD) of the surface cracked wide plate having an overmatched welded joint in bending was estimated by using the Level-3 CTOD methods. Two crack locations, in the weld metal and along the fusion line, were considered. Three dimensional elastic-plastic finite element analyses were also carried out and the estimated value of applied CTOD was compared with the finite element results. The correlations between the local strain in the weld metal and the gross section straining in the parent plate, and their influences on the CTOD estimates by the Level-3 CTOD method, were discussed.

CTOD Estimates of surface cracked wide plates in bending—I. Finite element analysis

Three dimensional elastic-plastic finite element analysis of the surface cracked wide plate in bending was performed. Applied crack tip opening displacement (CTOD) extracted from the finite element nodal displacements showed a good correlation with the experimental results. The crack tip at the bottom of the surface crack was in plane strain accompanied by the high plastic constraint. Applied CTOD was estimated by the WI-CTOD design curve and compared with the finite element results. The conservatism of the CTOD design curve was highly dependent on the definition of applied strain and the crack geometries. For the surface crack with aspect ratio of 0.1, the applied CTOD was underestimated in the large scale yield range.

CTOD estimates of surface cracked wide plates in bending—II. Level-3 CTOD method

The Welding Institute Level-3 crack tip opening displacement (CTOD) method was expanded to be applicable to plane strain (Plane-strain Level-3 CTOD method). The definition of the reference strain is a major source of uncertainty in the application of the Level-3 CTOD method. Two different measures of the reference strain were proposed. Applied CTOD estimates of the surface cracked wide plate in bending were performed using the Level-3 CTOD methods. It was found that the proposed Plane-strain Level-3 CTOD method can provide highly accurate predictions of applied CTOD with a safety factor approximately equal to 1.0 for the surface crack in bending.