Constraint-corrected fracture failure criterion based on CTOD/CTOA

In engineering design, a difficulty has always existed in those standard laboratory tests that cannot accurately predict the behavior of large structures like pipelines due to the different constraint levels. At present, extensive work has been done to characterize the constraint effects on fracture toughness by introducing a second parameter, while the systematic research on constrained transformation is inadequate. To address this issue, the ductile fracture process of X65 SENB specimen is simulated through the finite-element method coupled with the Gurson–Tvergaard–Needelman model. The parameters crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) are chosen to characterize the fracture behaviors. The effects of specimen thickness on fracture toughness based on CTOD/CTOA and constraints ahead of crack tips in SENB specimen are studied. The results indicate that the critical values of CTOD/CTOA decrease with the increase of specimen thickness, but the constraint parameters are opposite. Furthermore, it finds that there is a near linear relationship between critical values of CTOD/CTOA and the stress constraint ahead of the crack tip. Thus, a constraint-corrected fracture failure criterion based on CTOD/CTOA is proposed, which can be used for the prediction and simulation of stable tearing crack growth in specimens and structures, made of this steel with any thickness value.     

Constraint effect on the ductile crack growth resistance of circumferentially cracked pipes

A systematic study has been carried out by using 2D axisymmetric models to understand the ductile fracture behavior of pipes with internal and external circumferential cracks. Crack growth resistance curves have been computed using the complete Gurson model. Pipes with various diameter-to-thickness ratios, internal pressure, crack depths and material properties are analyzed. The results have been compared with those of corresponding SENT and standard SENB specimens. It clearly indicates that the SENT specimen is a good representation of circumferentially flawed pipes and an alternative to the conventional standard SENB specimen for the fracture mechanics testing in engineering critical assessment of pipes.     

Failure resistance of drilling rig casing pipes with an axial crack

Working conditions of casing pipes in drilling rigs can significantly influence the initiation and development of damage in the material, and therefore also the safe service of the entire system. In this work, an integrity assessment of a pipe with initial defect (machined surface crack) is presented. The position of this defect is on the external surface; unlike transport pipes, where internal surface is often endangered due to the contact with the fluid, casing pipes are also often exposed to damages at the external surface. A pipe segment exposed to internal pressure is examined experimentally and numerically, using the finite element method. Experimental setup included tracking of crack mouth opening displacement (CMOD) values, as well as J integral. Criteria for pipe failure are determined on the finite element (FE) models of the pipe; fracture initiation and plastic collapse are considered as failure mechanisms. Several 3D models with different crack sizes are evaluated. 2D plane strain models are also examined, to determine the applicability limits of this simplified approach. Integrity assessment criteria for the analysed geometries are discussed. Assessment of fracture resistance of the pipeline material is also considered in this work. Besides the standard SENB specimens, Ring specimens cut from the pipe are tested, and the results are compared. Both specimen geometries are modelled using local approach to fracture, by application of the micromechanical Complete Gurson model (CGM), developed by Z.L. Zhang. It is shown that the Ring specimens have similar fracture conditions under bending load as SENB specimens. Since they are much simpler to fabricate from the pipe than standard specimens, it is concluded that they can be used for assessment of fracture of the pipes with axial cracks.     

The effects of constraint on crack tip fields and fracture toughness

The detailed stresses, deformations and porosities in the vicinity of a blunting crack in different fracture specimens, Single Edge Notch (SEN), Three Point Bending (TPB) specimens, and Small Scale Yielding (SSY) model were studied by the larger deformation finite element method. The presence and subsequent growth of smaller scale voids were taken into account by using a modified Gurson's model to describe the constitutive behavior of the material. The dependences of the stresses, deformations and porosities on specimen configurations were associated with the crack tip constraint. The porosity in the tip region, along with the void coalescence criterion, were used to predict the macroscopic fracture toughness as a function of the constraint, and a comparison with experimental data was performed in this paper.     

A framework to correlate a/W ratio effects on elastic-plastic fracture toughness (J c )

Single edge-notched bend (SENB) specimens containing shallow cracks (a/W < 0.2) are commonly employed for fracture testing of ferritic materials in the lower-transition region where extensive plasticity (but no significant ductile crack growth) precedes unstable fracture. Critical J-values J _c ) for shallow crack specimens are significantly larger (factor of 2–3) than the J _c )-values for corresponding deep crack specimens at identical temperatures. The increase of fracture toughness arises from the loss of constraint that occurs when the gross plastic zones of bending impinge on the otherwise autonomous crack-tip plastic zones. Consequently, SENB specimens with small and large a/W ratios loaded to the same J-value have markedly different crack-tip stresses under large-scale plasticity. Detailed, plane-strain finite-element analyses and a local stress-based criterion for cleavage fracture are combined to establish specimen size requirements (deformation limits) for testing in the transition region which assure a single parameter characterization of the crack-tip stress field. Moreover, these analyses provide a framework to correlate J _c )-values with a/W ratio once the deformation limits are exceeded. The correlation procedure is shown to remove the geometry dependence of fracture toughness values for an A36 steel in the transition region across a/W ratios and to reduce the scatter of toughness values for nominally identical specimens.     

On the environmental similitude for fracture in the SENT specimen and a cracked hydrogen gas pipeline

We investigate the use of laboratory fracture specimens to ascertain the resistance to hydrogen embrittlement of a hydrogen pipeline with an axial crack on the inner diameter (ID) surface. In particular, we study the interaction of hydrogen with material elastoplasticity in single edge notch tension (SENT) specimens loaded in hydrogen gas at a pressure of 15 MPa. We find that the transient and steady state hydrogen concentration fields in the neighborhood of the crack tip in the SENT specimen and the real-life pipeline are essentially the same. This environmental similitude warrants the use of the SENT specimen in a gaseous hydrogen environment to examine the compatibility of steel pipelines with hydrogen.     

四种测试陶瓷断裂韧性K_(1c)的方法比较

选择四种测试断裂韧性的基本方法,测定渗入反应碳化硅基材料的断裂韧性,无论从方法本身还是从结果重复性来说均表明直接维氏压痕测试法是一种经济、快速、较理想的方法,特别适合于选材研究和生产工艺过程的控制。     

Measurement and modelling of R-curves for low-constraint specimens

R-curve testings of Grade X65 pipeline steel girth weld for low-constraint specimens were investigated experimentally. Single-edge-notched bending (SENB), single-edge-notched tension (SENT) and central-cracked tension (CCT) specimens were used to measure R-curves using the unloading compliance method. The recently developed single specimen unloading compliance for SENT specimens was validated using the multiple specimen method. Based on the test results, three constraint parameters (T-stress, Q-stress and A₂) were used to derive constraint-dependent R-curves. A comparison of the predicted constraint-based R-curves against the test result was given. It is shown that all three constraint parameters can be effectively used for obtaining R-curves under low-constraint levels. The modelling method can potentially be used for engineering critical assessment (ECA) in various industry sectors.     

A numerical study on the crack tip constraint of pipelines subject to extreme plastic bending

This study investigates the fracture response and crack tip constraint of thick wall pipelines subject to large plastic bending. Such a circumstance frequently occurs during the installation of offshore pipelines (such as the reeling method), and accidental overloading, both inducing inelastic bending. The near-tip stress and strain fields are obtained through the fully nonlinear 3D finite element models constructed to examine the response of a practical range of cracked pipeline geometries and material properties. It is observed that throughout the loading history (up to the large scale yielding of the pipeline), by incorporation of the J–Q two parameter fracture theory, the near crack tip fields do indeed resemble those obtained from a K–T modified boundary layer formulation. This analogy provides sufficient proof for the applicability of the similitude concept inherent and fundamental to any fracture assessment procedure. All the pipelines considered in this study, which had realistic crack sizes, exhibited low constraint behavior (i.e. −1.4 < Q < −0.4). Additionally, Q was observed to decrease as a linear function of the global bending strain. Based on this correlation, simplified design equations are presented by which the constraint of such pipelines could be effectively estimated. The equations would be suitable for incorporation in the constraint-matched integrity assessment procedures that would in turn overcome the overt conservatism produced by the use of single parameter fracture mechanics approaches. Suitability of the low constraint laboratory specimens for fracture toughness measurements is also confirmed.     

Effect of loading rate on dynamic fracture initiation toughness of brittle materials

Numerical simulation is carried out to investigate the effect of loading rate on dynamic fracture initiation toughness including the crack-tip constraint. Finite element analyses are performed for a single edge cracked plate whose crack surface is subjected to uniform pressure with various loading rate. The first three terms in the Williams’ asymptotic series solution is utilized to characterize the crack-tip stress field under dynamic loads. The coefficient of the third term in Williams’ solution, A ₃, was utilized as a crack tip constraint parameter. Numerical results demonstrate that (a) the dynamic crack tip opening stress field is well represented by the three term solution at various loading rate, (b) the loading rate can be reflected by the constraint, and (c) the constraint A ₃ decreases with increasing loading rate. To predict the dynamic fracture initiation toughness, a failure criterion based on the attainment of a critical opening stress at a critical distance ahead of the crack tip is assumed. Using this failure criterion with the constraint parameter, A ₃, fracture initiation toughness is determined and in agreement with available experimental data for Homalite-100 material at various loading rate.     

Finite element simulation of fracture behaviour for aged duplex stainless steels

In this paper, the local approach model developed by Gurson–Tvergaard has been applied to simulate both the crack initiation and the crack growth of aged duplex stainless steel. The parameters of the Gurson–Tvergaard model have been obtained, from axisymmetric notched specimen testing, as a function of the ageing time at 400°C, the ferrite content of the steel and the stress triaxiality. After that, to simulate the fracture of CT specimens, finite element (FE) calculations have been effected in order to obtain the stress triaxiality value at each point on the process zone ahead of the crack tip of these specimens. The adequate damage parameters concerning triaxiality are determined from the ones obtained at the notched specimens, in order to be used in FE simulations of fracture behaviour. With them, the corresponding J−Δa curves have been simulated as representative of both the crack initiation and crack propagation stages, and compared with experimental results in order to validate the methodology proposed.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens. Part II: 3-D effects on constraint

This study describes an extensive set of 3-D analyses conducted on conventional fracture specimens, including pin-loaded and clamped SE(T) specimens, and axially cracked pipes with varying crack configurations. The primary objective is to examine 3-D effects on the correlation of fracture behavior for the analyzed crack configurations using the J-Q methodology. An average measure of constraint over the crack front, as given by an average hydrostatic parameter, denoted Q_avg, is employed to replace the plane-strain measure of constraint, Q. Alternatively, a local measure of constraint evaluated at the mid-thickness region of the specimen, denoted Q_Z0, is also utilized. The analysis matrix considers 3-D numerical solutions for models of SE(T) fracture specimens with varying geometries (i.e., different crack depth to specimen width ratio, a/W, as well as different loading point distance, H) and test conditions (pin-loaded ends vs. clamped ends). The 3-D numerical models for the cracked pipes cover different crack depth to pipe wall thickness ratio, a/t, and a fixed crack depth to crack length ratio, a/c. The extensive 3-D numerical analyses presented here provide a representative set of solutions which provide further support for using constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.     

A NUMERICAL STUDY ON GLOBAL AND LOCAL PARAMETERS CONTROLLING FRACTURE IN THE BRITTLE-DUCTILE TRANSITION TEMPERATURE REGION

Abstract— In this report on fracture studies pertinent to the brittle-ductile transition region the predictive capability of a local fracture parameter, i.e. maximum tensile stress normal to the crack plane (= maximum principal stress), and of a global fracture parameter, i.e. the J -integral, are compared for SENB and CNT specimens fractured at −70°C. The influence of constraint is also investigated, both locally as defined by the ratios of mean (hydrostatic) stress and maximum principal stress to von Mises stress, and globally as defined by the factor m = J /(_γ.CTOD). Results obtained indicate that stress fields in a varying constraint environment (i.e. varying both spatially and with extent of plastic deformation) are not uniquely characterized by J and require additional information on the amount of constraint. Fracture predictions based on maximum principal stress ahead of the crack tip exhibit far less scatter than those based on J , but further investigations are required on the geometry (in)dependence of this local parameter.     

A CTOD equation based on the rigid rotational factor with the consideration of crack tip blunting due to strain hardening for SEN(B)

Crack tip opening displacement (CTOD) from national and international standards was shown to give different values. This paper investigates the feasibility of CTOD determined based on the concept of rigid rotational factor in single‐edge notched bend (SENB) specimens. Based on validated modelling methods, finite element (FE) models were simulated for crack ratios 0.3 ≤ a₀/W ≤ 0.7 and yield‐to‐tensile ratio 0.44 ≤ σ_ys/σ_uts ≤ 0.98. This covers cases of shallow to deeply cracked specimens and a wide range of strain hardening properties. CTOD obtained from the FE models was used as the basis of a newly implemented strain hardening corrected rotational factor, which considers the effects of crack tip blunting due to strain hardening, r_{p sh}. An improved equation considering strain hardening was implemented based on the r_{p sh}. The equation gives accurate estimation of CTOD from the FE models compared with the equation from BS 7448‐1, ASTM E1820, and WES 1180.     

Fracture toughness and hydrogen embrittlement of pipes with notches

A technique for experimental determination of fracture toughness and hydrogen embrittlement of pipes made of API 5L X52 steel is described. The tests were performed using arc-shaped specimens with a notch cut out from pipes under the conditions of a three-point bend. The fracture toughness was determined in terms of the J-integral and the stress intensity factor at the notch tip. The value of K _ρ,c was established using the volumetric method based on the experimentally measured critical load and the results of the FEM calculation of the distribution of elastic-plastic stresses ahead of the notch tip, and J _ρ,c was determined using the method of separable functions. The effect of hydrogen embrittlement was studied using electrolytically prehydrogenated specimens.     

A numerical study of the elastic stress field arising from sharp and blunt V-notches in a SENT-specimen

The elastic stress field arising from a V-notch in a Single Edge Notched Tension (SENT) specimen is studied using the Sherman–Lauricella integral equation. Accurate values of the generalized stress intensity factor, here denoted Q _I, are determined and compared with values from the literature. A Q _I-dominated distance ahead of the notch tip is defined and determined for several notch angles and different notch depth to specimen width ratios. It is found that for depth to width ratios over 0.45 the Q _I-dominated distance is approximately constant while below this value the distance can show a great variation with the notch angle. Additionally, a general formula for the maximum stress in a V-notch with a finite root radius is derived. Its applicability on the SENT-specimen is studied and presented as a family of curves. If used within these curves, the formula can accurately predict stress concentrations, even for very smooth notches.     

Bending modified J–Q theory and crack-tip constraint quantification

It is well known that the J–Q theory can characterize the crack-tip fields and quantify constraint levels for various geometry and loading configurations in elastic–plastic materials, but it fails at bending-dominant large deformation. This drawback seriously restricts its applications to fracture constraint analysis. A modification of J–Q theory is developed as a three-term solution with an additional term to address the global bending stress to offset this restriction. The nonlinear bending stress is approximately linearized in the region of interest under large-scale yielding (LSY), with the linearization factor determined using a two-point matching method at each loading for a specific cracked geometry in bending. To validate the proposed solution, detailed elastic–plastic finite element analysis (FEA) is conducted under plane strain conditions for three conventional bending specimens with different crack lengths for X80 pipeline steel. These include single edge notched bend (SENB), single edge notched tension (SENT) and compact tension (CT) specimens from small-scale yielding (SSY) to LSY. Results show that the bending modified J–Q solution can well match FEA results of crack-tip stress fields for all bending specimens at all deformation levels from SSY to LSY, with the modified Q being a load- and distance-independent constraint parameter under LSY. Therefore, the modified parameter Q can be effectively used to quantify crack-tip constraint for bending geometries. Its application to fracture constraint analysis is demonstrated by determining constraint corrected J–R curves.     

Numerical prediction of creep crack growth in different geometries using simplified multiaxial void growth model

Abstract

This paper considers the prediction of creep crack growth (CCG) in different fracture mechanics geometries using finite element (FE) analysis based on a material independent simplified multiaxial failure strain model at the crack tip. The comparison is first made by modelling C(T) specimen tests under plane stress and plane strain conditions using creep properties of a C–Mn steel at 360°C. In addition, in order to examine CCG due to different geometries, a single edge notch specimen (SENT), centre cracked tension specimen (CCT) and three-point bending (3PB) specimen have been modelled and analysed. In all cases, it is found, depending on the geometry, that for this steel at low creep temperatures the applied load develops a high reference stress/yield stress (σ_ref/σ_y) ratio, which helps reduce constraint at the crack tip. The predictions are analysed under plane stress/plane strain loading conditions identifying the effects of geometry on cracking rates and the implications for predicting long term test or component failure times exceeding where the applied σ_ref/σ_y<<1.     

Fracture behavior of stitched warp-knit fabric composites

Pilot studies are conducted to characterize the macroscopic fracture resistance behavior using linear elastic fracture mechanics and attempt to quantify the fracture parameters in which may govern the fracture and failure patterns of stitched warp-knit fabric composites. Methods based on the J-integral method and Betti's reciprocal theorem in extracting the fracture parameters, critical stress intensity factors, T-stress, and the second term of _y(r,0) near the crack tip prior to fracture initiation are formulated. Two fracture criteria, [_c,r _c] and [_c,r _c] are attempted to characterize the failure initiation for the fiber-dominated failure mode and self-similar crack extension in a given thickness of the laminate. Based on linear elastic fracture mechanics principle, these criteria are transformed into crack-driving forces [K _Q,T] and [K _Q,g ₃₂]. The two-parameter fracture criteria, [K _Q,T] and [K _Q,g ₃₂] provide a good correlation for the CCT and SENT specimens, but not for the high constraint CT specimens. With the limited experimental data, the results tend to show that the large tensile T-stress and large magnitude of negative g ₃₂ may inhibit the crack extension in the same crack plane and promote crack kinking.     

Correlation of fracture behavior in high pressure pipelines with axial flaws using constraint designed test specimens--Part I: Plane-strain analyses

This work presents a numerical investigation of crack-tip constraint for SE(T) specimens and axially surface cracked pipes using plane-strain, nonlinear computations. The primary objective is to gain some understanding of the potential applicability of constraint designed fracture specimens in defect assessments of pressurized pipelines and cylindrical vessels. The present study builds upon the J-Q approach using plane-strain solutions to characterize effects of constraint on cleavage fracture behavior for the analyzed fracture specimens and cracked pipes. Under increased loading, each cracked configuration follows a characteristic J-Q trajectory which enables comparison of the corresponding driving force curve in the present context. A key outcome of this investigation is that toughness data measured using SE(T) specimens appear more applicable for cleavage fracture predictions of pressurized pipelines and cylindrical vessels than standard, deep notch fracture specimens under bend loading. The results provide a strong support for use of constraint-designed SE(T) specimens in fracture assessments of pressurized pipes and cylindrical vessels.